Complete Relativity: Nature of observables

Abstract A complete relativity in all phenomena, with relative scale invariance in physical laws, is postulated and discussed. Postulates are followed with definitions of new terms which may be used in the current and follow-up papers written in the context of the theory. In order to conform to this physics, a redefinition and generalization of some terms and factors already in use have also been presented. This includes, and is followed by, hypotheses on fundamental nature and mechanics of phenomena, based on observations and postulates of the theory, with some exact solutions provided. In conclusion, the theory suggests that everything must be completely relative in order to exist and everything must evolve in order to conserve this relativity. 1 Complete Relativity: Nature of observables Mario Ljubičić (Amenoum) 108. brigade ZNG 43, 35252 Sibinj, Croatia (completerelativity.org) [email protected] December 10, 2025 1 Introduction From the perspective of a mathematician, both, the theory of Quantum Mechanics (QM) and the theory of General Relativity (GR), are brilliant and beautiful works of art. These works truly deserve all the respect they’ve got, and more. However, from the perspective of a physicist, today they’re not satisfying enough. That is because they are obviously incomplete, and actually wrong in certain propositions. The main problem of modern quantum physics is that it has gone too far with the abstraction, so much so that it probably should be referred to as Quantum Mathematics. GR, on the other hand, didn’t go far enough in relativity, thus, the appropriate title today would be Relatively General Relativity. A complete theory on fundamentals of nature, however, should provide a framework which can be used to qualitatively describe all phenomena, regardless of scale or energy. Complete Relativity with incorporated relative, rather than absolute, invariance to scale of physical laws has such power, opening a path to profound insights into nature and mechanics of reality. The best approach to understand nature/reality is to combine and balance the power of mathematical language with experience and observation on all scales of energy and in the process approach problems from different perspectives, rather than limit interpretation to that of a mathematician, physicist or a biologist. Mathematical elegance may be desirable in calculations, but elegance is neither abstract nor absolute in reality. To properly understand reality one should seek to understand the measured physical processes, rather than reduce reality to a mathematical formalism which is in agreement with measurements. Many times in history, such reduction has been proved to be an illusion, a blurry and limited picture of reality, rather than true description of it. Instead of searching solutions that would disperse the illusion, one can instead chose to convince itself that reality is an illusion. That may seem like a legitimate choice at first, however, as the power of observation grows, the illusion grows bigger, and it becomes harder and harder to cling on to the notion that the established beliefs 2 represent established or absolute knowledge. Again, a biased observer can chose to look in the directions that confirm the established illusion, turning a blind eye to the possibilities of revolution. Much can be, however, criticized in the established world of today, not just in established science, but that’s not the aim here. Here, the aim is to understand reality as much as possible, or, in other words, to disperse as much of the established illusion as possible. The theory is a result of research, experience, observation, computation and logic that followed, and confirmed, strong intuition suggesting that overly non-intuitive, abstract and absolute reality is just an interpretation chosen, consciously or unconsciously, by biased and limited observers. It is an interpretation that enabled progress in the past, however, clinging to it now is doing nothing but hindering the progress in science. In this, and follow-up papers, I provide foundations, details and evidence for a new description of reality. In order to properly understand that reality, I have rewritten my works many times, just as scientific books have been rewritten many times in the past. Has modern science gave up on rewriting books? If so, its name too is no longer appropriate. Scientific Religion comes to mind. I am sure, however, that the giants, who today may be painted and sculpted as gods in this religion, wouldn’t look at it with approval or satisfaction. These "gods" have brought revolution, progress. In other words, they’ve used science to disperse the illusion of science ruling the time. And if one has any respect for these "gods" one should not be afraid to, once again, reduce them to giants, or even better, to what they considered themselves to be - genuine scientists, seekers and messengers of truth. Such messengers may possess an insatiable curiosity, but they are, just as their truth, limited, in space and time. I am one such seeker and messenger of truth, perhaps not as great as the giants of the past, but certainly with a wider view, enabled by the previous seekers of truth. This here, is what I see, or, my interpretation of what can be seen. 2 Postulates Here are the postulates of Complete Relativity (CR). They are all entangled and one may stem from the other, but not always in apparent way. 2.1 Everything is relative (everything is variable) ∆E <> 0 No system can be completely isolated at all scales of energy or reference frames. Everything existing must be absorbing and radiating energy at some scale at any time, but never in such proportions as to enable a non-zero possibility for absolute invariance of that phenomenon in time/space. Maintenance of relative constancy requires energy. ∆E6=∞ 3 There is no single, absolute and infinite universe (Universe). For any observer, there exists a finite number of observable universes with mutually entangled characteristics, exchanging energy between each other. One could argue that the sum of all universes is infinite and that sum is a single absolute entity. However, such Universe is absolutely unobservable. In CR, all existence has to be relative and thus observable at some scales, unobservable at other scales. Infinities and zeros as absolute values are mathematical abstractions - in reality they must be relative, as any other value. This implies relatively simultaneous existence of energy at different scales of space/time. Any physical entity having absolute properties would have to be absolutely isolated in order for these properties to remain constant. With no ability to change (exchange energy) such absolutely elementary entities would be unobservable. Thus, relativity is an intrinsic property of reality. Any distinct form of energy may be considered as an universe, however, in the framework of CR, universe will generally represent a particular scale of energy. These are discrete (stable) vertical energy levels for relatively elementary particles (called gravitons in CR, not to be confused with gravitons in other theories - here, graviton represents a generalized particle). Any form of energy thus belongs to a universe of the scale of largest graviton(s) coupled to (or, highly entangled with) the system. Gravitons, however, can be [relatively] naked or uncoupled. Energies of the same scale may be considered as instances of the same universe, but, generally these should be considered as horizontally parallel universes as no two instances are absolutely equivalent at any time (physical constants are relative, oscillate and will be different between the instances, even if these differences may not be generally resolvable). As transfer and transformation of energy require capacity for energy storage and speed of transfer/transformation cannot be infinite, structural quanta of any medium must have real size. •Every universe must be divisible -contained within a larger universe and contain universes of smaller scale, •universes of different magnitude (vertically parallel universes) are selfsimilar but evolutionary dominantly separated in time, entangled more in space, •instances of a universe (horizontally parallel universes) are dominantly separated in space, usually entangled more in time, 4 •instances can acquire energy beyond the potential or rest energy of the associated level, but values between discrete energy levels are generally (albeit relatively) unstable and instances in between will generally evolve towards one or the other stable level. Since existence requires continuous exchange of energy, any relative constants (energies) must be oscillations on some scale. None of these oscillations can be absolutely stable - even the oscillation itself must change relative to something. Thus, each form of existence (energy) will generally evolve, either progressively (towards higher energy levels) or regressively (towards lower energy levels). Evolution of energy generally includes oscillations and fluctuations but the periods involved may be too small or too large to be detected (or detectable) from some reference frames. Since energy cannot occupy space of absolute 0 size, reality requires three degrees of freedom, although, due to inherent limitations in observability (and other reasons), energies (gravitons) can be approximated as point energies (particles). However, inflation (change of a vertical energy level) of the particle may make that interpretation inappropriate from the same reference frame. In most intuitive interpretations universes should not have more than 3 spatial dimensions (there is no space for them!), however, due to various scales of energy, space can and will be effectively divided into subspaces which may be relatively isolated but entangled with other scales. In that case, multidimensional manifolds with more than 3 dimensions may be used to describe reality. But one should be careful not to declare such entanglements (couplings) intrinsic and absolutely constant properties of reality - the strength of any entanglement must be variable in completely relative reality. Here, one must distinguish between abstract dimensionality and physical dimensionality. Abstract dimensionality is relative to a coordinate system of choice. This system may or may not reflect any physical dimensionality. In example, one may use the Cartesian system to quantify dimensionality of objects in space, but this is generally not the dimensionality of that space. Physical dimensions are, in CR, volumetric (although not all observers will be able to observe them as such). Thus, one could argue that physical space is one-dimensional, in a sense that there is no physical distinction between the 3 degrees of freedom. Reality is, however, never experienced as absolute, it is not absolutely homogeneous and isotropic, energies can be relatively isolated or limited to particular regions or scales of space (which implies physical differences between different degrees of freedom). Thus, all these sub-spaces or scales of space may be interpreted as different physical dimensions, especially when these are mutually strongly entangled. In example, local space is generally entangled with local time so it is very reasonable to interpret the duo as two local physical dimensions (or two different scales of space). Note that complete relativity requires change so it requires 5 time, however, local coupling of space and time won’t be observable in all cases. Relative invariance to space or time will thus exist, and may be interpreted as absolute due to limitations of observers, but absolute it is not. In CR, the scale of a universe generally represents a discrete vertical energy level, analogous to horizontal energy levels in Quantum Mechanics (QM). Relative to the difference in scale between observer energy and energy of observables, phenomena may be interpreted as physical (real) or mental (imaginary, or hallucinated) components of reality, however, every mental phenomenon must have a physical interpretation at some scale, and vice versa. Due to required evolution, energy in a universe is constantly transferred and transformed. Due to finite speed of transfer and transformation, these changes will be continuous, however, due to finite observable resolution of space/time, on some scales changes will be interpreted as discrete. Speed of transformation of energy may be interpreted as its speed in time, while speed of transfer as its speed in space. Note that speed of transformation is proportional to the speed of transfer of entangled energy at some scale. Therefore, time clearly has a physical interpretation at some scale - ageing of phenomena is strongly correlated with the transfer of quanta of energy at some scale, and these quanta may be interpreted as carriers of change or carriers of time. Note also that transformation can occur at different scales, hence, multiple time dimensions exist with different speeds of information (energy) transfer (generally inversely proportional to scale). •Relatively the same energies relatively oscillate between relative existence and relative non-existence, •oscillation between vertical energy levels generally involves transformation of scale and exchange between angular momentum components (m,v,r), •scales of relative invariance of physical laws are discrete, with exponential progression and may be separated by many orders of magnitude. Relativity of everything indeed has the power to explain everything. Consider relativity in causality. In General Relativity (GR), it is always the clump6 ing of matter (energy) that curves space, however, if causality is relative - sometimes it is the matter-devoid curved space that should cause clumping of matter. Of course, one can insist that space is abstract and attribute the energy of space to exotic matter (i.e., dark matter) [curving abstract space] to conserve causal order, but is that the proper interpretation if one strives for deeper understanding of reality (and, especially, if this exotic matter cannot be resolved)? Note that I do not argue that the exotic matter does not exist - quite contrary, if space can cause clumping then it must have energy and must be composed of some kind of matter on some scale (which, for us, may be unobservable directly), I argue against interpretations that conserve absolute abstraction of space or absolute preservation of presumed causal order. Note also that the exotic matter hypothesis (by established interpretations) simply doesn’t match observations - e.g., cold dark matter halos within galaxies should slow down the rotation of galactic bars but the expected slowdown is not there[1]. There are other problems too[2]. These can all be solved through decoupling of space and matter, allowing different densities of space within the galaxy. Equivalent exotic matter here may generally be hot but transforming to cold with coupling, not absolutely free-streaming, rather orbiting about the galactic centre as static particles [forming galactic space], as elaborated later. This is not the only case of apparent violation of presumed causal order. And there are problems associated with finite speed of information transfer that’s commonly coupled to causality. Quantum entanglement is one example where common interpretations simply discard intuition and reduce natural complexity to abstraction in order to preserve an absolute (scale invariant) speed limit. In CR, causality is a special case of synchronization between correlated entities and both, causal order and speed limits, will be violated on some scale when considered absolute. Again, if information exchange is unobservable, excessive reductionism is an appealing interpretation but it only simplifies calculations, at the expense of potential deeper understanding of reality. That does not imply that calculations should be complicated, certainly not if the aim is practical application and certainly not arbitrarily. But if the aim is to understand and progress in science, rather than to stubbornly adhere to mathematically simplest solutions possible, additional interpretations should be explored. Proper solution in complete relativity is general correlation of past and future 7 states which may be localized to, or locally absolutized into, causality (generally, thus, any intuitive concept is only locally intuitive and any illusion may be localized into intuition). Distance between past and future is relative. And distance between phenomena is never absolute 0. Every interaction is a relative interaction and is the manifestation of synchronization - specific correlation in space and/or time. Causality is simply a biased (polarized) interpretation of synchronicity at particular scale. All interactions or forces in nature depend on distance and all involve correlation. This suggests that distance should be generalized to distance in correlation. To conserve relativity (existence), forces cannot be exclusively attractive or repulsive and strength of force will sometimes be proportional, sometimes inversely proportional to distance. Note also that non-existence of absolute 0 distances together with the non-existence of absolute point sources of energy (field source, or maximum, is not at the centre rather at a non-zero distance from it), avoids infinities, which are a common issue in physics (or, more precisely, in mathematics), usually discarded in an arbitrary way using a technique called renormalization (which, although based on good ideas - such as running coupling, sometimes probably could be translated as, more or less educated, guesswork[3]). 2.2 Everything is exchangeable Absolute relativity in space seemingly introduces problems, such as one in relativity of containment. Consider two spheres different in scale and located (centred) at [relatively] the same point in space - how is it possible that a reference frame exists in which the bigger sphere is contained within a smaller one (non-dimensional rationality is relative)? Conservation of relativity thus clashes with the conservation of rationality (intuition). Seemingly, either non-dimensional rationality is relative or one must be sacrificed for the other. Here, finite speed of information transfer enables one elegant resolution - conservation of both by exchanging relativity in space for rationality in time (subspace). If the two spheres oscillate in time between two scales and one does not discriminate between space and time, both quantities are conserved (rationality in space, relativity in time). Thus, on absolute scale everything is conserved, but relatively even relativity can be sacrificed. 8 Multiple interpretations and multiple solutions are common in nature. This problem is no exception. Suppose that everything exists [relatively] simultaneously on different scales - a bigger sphere can then be relatively contained within a smaller one if the smaller one has its identical copy on some larger scale. Note that, if everything must be relative, location and scale of existence must be too, therefore, everything should exist on different scales. This explains self-similarity of universes and suggests that planetary systems such as the Solar System are likely not only similar to atoms (certainly not by coincidence) - they could correspond to specific atoms in relatively equivalent (properly scaled) conditions (pressure/temperature), where the component waveforms have been localized. From some reference frames this may be interpreted as a change in discrete vertical energy level - they have been inflated from standard atoms or similar systems of even smaller scale. Evidence for this will be provided. Note that, since existence is relative, existence of containment must be relative, so there also must exist a reference frame in which one cannot tell which sphere is contained within the other. When integrated over time/space, such state may be interpreted as superposition or fusion of different states. Unless one accepts the notion of multi-scale existence, it might seem that relativity of containment is generally not conserved, even in time. Consider the example of a chicken in an egg - there is no apparent oscillation, chicken may be growing inside the egg and will eventually get bigger than the egg but the egg is not getting smaller and is at no point inside the chicken. However, another kind of relativity can solve the problem - the egg was once inside the adult chicken. This means there must exist a reference frame relative to which there is no distinction between the two chickens (relativity of identity). Such reference frame does exist and is enabled by the finite resolution (scale) of information carrier particles. Effectively, both the chicken and the egg are oscillating over time. With absolute containment nothing would be able (required) to grow or decay - neither chicken nor any other universe, with relative containment everything must grow or decay (or oscillate between the two). Complete relativity and its conservation in reality is what makes everything possible. Apparently, both GR and QM allow [or are at least partially based on] the existence of an absolute rest frame [correlated] with constant speed c, completely 9 2.5 Physical laws are relatively scale invariant In reality, distance is quantized, but the size of quanta is not absolutely constant. Energy generally oscillates between stable discrete energy levels. These energy levels can be horizontal (as described by QM) or vertical. Horizontal energy levels differ in the amount of energy but generally not in the order of magnitude, vertical levels generally differ by multiple orders of magnitude. Although universes at different scales may be in different equilibrium states, applying energy, state on one scale can be made locally relatively equivalent to a state on another scale. Here, state generally refers to scale relative pressure (or temperature) and density, which generally differ on average between vertical energy levels. Temperatures and densities on standard scale are proportional to kinetic energies and densities of standard atoms, respectively, on a higher vertical energy level these may be kinetic energies and densities of planetary systems, on a lower energy level energies and densities of space (or field) forming entities. Universes are self-similar, however, the values of constants and/or units of metric should differ between scales of gravitons. Physical laws of nature are thus relatively scale invariant, with stable scales appearing at discrete points between intervals of generally exponential progression. Elementary particles are strongly relative to reference scale. From a smaller scale they will evidently be composite and differ from each other, while from a larger scale they may even be unobservable (non-existent) individually. 2.6 Hidden variables always exist With no absolutely elementary phenomena and with inherent (but not absolutely constant!) limits in observation, hidden variables must exist. Therefore, non-intuitive reality suggested by QM must be taken relatively. As stated already, treatment of all constants as relative constants can make QM much more intuitive, but it does not end there. It should be noted that intuition too must be relative. If common intuition (e.g., one involving hidden variables) cannot be observed, it is valid to conceptualize non-intuitive reality (and declare this non-intuition as natural or intuitive from some reference frame), however, in the pursuit of truth, one cannot claim such reality is absolute - there are always possibilities for different interpretations. 16 One may, for example, use abstract two-dimensional entities to describe phenomena occurring in reality if the calculations consistently match the outcomes of experiments/measurements, but that does not imply that reality is absolutely two-dimensional or non-intuitive on a particular scale - it is not. Realistic and more intuitive interpretation is always possible[5] even if it may require hidden variables. If complete relativity implies such variables must exist, and, if one strives for deeper understanding of reality, it would be, not only counterintuitive, but counter-productive to discard them simply because mathematics without them works and/or is more elegant (less complex). Especially considering the real possibility, implied by CR, that one might be able to relatively observe the hidden variable on another scale of a particular state. Furthermore, mathematics working today may not work tomorrow - any hidden variable is variable after all. 3 On stability of equations Equations are very useful and powerful constructs of a mathematical language. They simplify descriptions, can lead to new insights on details and plausibility of hypotheses, but can also be very deceiving. All dimensional constants are relative. Therefore, more constants the value of equation depends on, more unstable it is and its potential for illusion increases with distance from the scale the constants belong to. Dimensionless constants are generally more stable and may be well preserved across adjacent scales, but even these should not be absolute. With everything being relative, a presumption of absoluteness will eventually lead to discrepancies in measurement and misinterpretation of reality. 4 Definitions Here are the definitions of terms and expressions that may be used here and other papers in CR context. Note that some of these represent redefinitions (e.g., generalization) of standard or common definitions in use. Some contain additional hypotheses and important details, representing an integral part of the theory. 4.1 n_th order observer In the context of quantization (measurement) of physical phenomena, observer is an entity performing the measurement. 17 The order of the observer is a relative sum of the number of interactions in the act of measurement which affect its result. In example, a 1st order observer may be the information carrier (radiation) particle, 2nd order observer is then the radiation detector, etc. Every observation is measurement, albeit not always a conscious one. Measurement affects all interacting entities. 4.2 n_th order interaction (n_th order action and reaction) Consider the forces in Newton’s law of gravitation: F=d dtp=d dt(mv) = ma =GMm r2 F1=m1a2=m1 m2G r2=m2a1=m2 m1G r2=F2 Here, forces acting on bodies m1and m2are equal and have opposite direction, as expected for forces of action and reaction. Note that these are actions and reactions between bodies of mass at distance [in space]. In General Relativity there is no action and reaction between the two bodies directly, but effectively between continuous space (more precisely, geometry shaped by the energy of bodies) and a particular body (or energy, in general). And it is not an action and reaction at distance (distance between space and the body is assumed to be equal to absolute 0, only changes propagate at finite speed so the distance in time between changes in potential is not 0). The two bodies have an effect on space (and vice versa) but they also affect, albeit indirectly in GR, each other. In CR, it is obvious that even the interaction between quanta of space and quanta of bodies cannot be an action at absolute 0 distance, but this distance is generally orders of magnitude shorter than distance between the bodies and may be considered infinitesimal (relative zero). Note that in both cases of formalism action/reaction is instantaneous, so even in Newton’s gravity distance between the sources is effectively set to 0 for whatever is mediating the force, only the 1st order sources of interaction differ. In Complete Relativity there are no absolute zero and infinite distances, suggesting that every action is action at a distance. But the key here is that distance is relative itself. It is correlation (of mass in this case) that is a primary reason for the manifestation of force but it is not the sole requirement. A carrier particle must exist on some scale, even though the interaction may be interpreted as non-local (as in case of Newton’s gravity). Thus, even if distance in non-zero between particles forming space, that distance is traversed by mediating particles of some scale. In 18 other words, what is interpreted as non-locality is a consequence of inherent observer limitations - e.g., non-resolvability of space or mediators. Distance between interacting bodies may be greater than zero, but this is not interaction at distance if mediators are traversing that distance (one could argue that distance exists only in the absence of mediators). In some cases (e.g., quantum entanglement) correlation may seem invariant to distance in space, leading some to a conclusion that a mediator in such cases is an unnecessary complication (even unscientific, from nonholistic perspectives). In CR, however, this non-existence is equivalent to a mediator of 0 mass and infinite speed - leading to infinite range. Since such mediator is impossible in CR, the only solution is mediator (or, more precisely, associated dimension) scaling that is inversely proportional to distance in space. And such plasticity is generally present in a time dimension. The sources of force of action and reaction are thus relative to scale - measuring on larger scale it may be more appropriate to attribute the sources to bodies, while on lower scale the quanta of space may be interpreted as such. From a 3rd perspective one might consider the action between a force carrier particle in space (even if it is a bound static particle with potential energy) and a body as a 1st order interaction, and the interaction between two bodies as a 2nd order interaction. One may also consider the 1st order interaction as relatively instantaneous, 2nd order occurring at some speed c, 3rd order at even some lower speed, etc. In any case, there is no absolutely instantaneous, simultaneous and equal reaction to action (it requires quantum of distance equal to absolute 0, or, equivalently, infinite speed of carrier particles). Absolute causality is an illusion. An arrow of time is a result of asymmetry in synchronization of highly correlated events. The relativity of sources (force carriers) and distances has an important consequence on the law of action and reaction - it should be generalized: T Z t=0 h~ F1(t) + ~ F2(t)idt = 0 (1.1) Instantaneous action and reaction is thus a special case of action and reaction impulses, where the period of energy oscillation T is compressed to an instant - a single elementary quantum of time (dt = T), and the identity/strength of interacting forces is strongly localized (even absolutely in common interpretations, 19 where the value of zero is interpreted as an absolute constant): ~ F1+~ F2= 0 Note the equivalence of distance in time and space of different scales - in the 1st order interaction (GR) distance in space is 0, while in the 2nd order interaction (Newton) distance in time is 0. Also note that, although not required, it is not forbidden for action and reaction to be relatively simultaneous, nor it is forbidden for reaction to precede action, allowing relativity of cause and effect - something that is, with absolutely invariant c (speed of information transfer), forbidden in GR and Special Relativity (SR), but required in CR. In CR thus, causality is not absolutely fundamental nor intrinsic - it could be understood as a result of force, relatively emerging (or evolving) between correlated (entangled) phenomena decreasing distance in space and/or time. However, proper interpretation is that causality is simply a consequence of localization of synchronization of events in a polarized reference frame (the source of asymmetry). Violation of [absolute] causality will exist on all scales of energy, but amount will differ between the scales. However, the amount has to oscillate too and will correlate with changes in the properties of space. The equation (1.1) is equivalent to momentum pulse reflection: T Z t=0 h~ F1(t) + ~ F2(t)idt = T Z t=0 hd~p1 dt +d~p2 dt idt =~ ∆p1+~ ∆p2= 0 With T > dt > 0, action and reaction becomes a manifestation of energy oscillation. However, entanglement can be relatively broken (reduced to relatively infinitesimal strength) and reaction may be delayed, may not affect the source of action or might not even occur (e.g., if the action is locally interpreted as reaction). All bodies having rest mass possess capacitance and reaction to the source will eventually come, even if from another body, if that capacity is not in equilibrium state. However, the reaction may be fragmented and carried by diverse force carriers following multiple different paths. Such nature of non-apparent oscillation stems from different scales of energy quanta enabling diversity and evolution of complex forms of energy, its conduction and transformation. 20 Although generalization of interactive correlation is useful for understanding, generally, it may not be pragmatic. In the descriptions of transformations and interactions, more useful terms will be conservation of energy and conservation of momentum. 4.3 Superposition Superposition is a relatively special state of a system which can be described as a combination (generally sum) of correlated (entangled) multiple base states. Mathematically, superposition may be formulated as a sum of probabilities for particular states of particles. In CR, speed of information transfer, and therefore, speed limits, depend on the scale of quanta of energy. This, together with CR interpretation of entanglement, allows for physical interpretation of superposition to represent intermediate states of oscillation between discrete states. Superposition can thus represent a real state, although that state may be unstable and observer, due to inherent limitations, may not be able to observe (resolve) it. E.g., on the scale of standard electrons, spin momenta is generally measured as discrete (e.g., up or down, not something in between). This is usually because intermediate states are unstable in the context, and the measurement itself may collapse the system into a discrete (stable) state. Base states of superposition are context-dependent. In one example, two base states may represent two anti-aligned spin momenta. In another example, two base states may represent the nature of a particle (wave-like and corpuscular-like). If intermediate states cannot be observed, the values assigned to individual base states may be understood as probabilities for that state to be observed after measurement is performed. However, between measurements, the particles will commonly oscillate between base states and common physical interpretation will be the averaged superposition - e.g., in case of its nature, the particle may effectively exhibit both the corpuscular/localized and wavelike/delocalized nature simultaneously which may be interpreted as partial localization/delocalization. The interpretation in the form of averaged superposition is commonly a consequence of inherently limited observation/interaction. However, instability is scale relative. An unstable state (such as the averaged superposition) on one scale may be interpreted as physically stable on another. This is generally a consequence of effective time dilation and exchange of nature of potential between vertical scales of energy. 4.4 Universe (U) In relativity lacking theories, Universe may be understood as simply the sum of absolutely everything that exists, had ever existed and will ever exist. Thus, that definition refers to an absolute universe (Universe) - unobservable as a whole. 21 In CR, nothing is absolute, thus, existence of multiple universes is implied. Any universe is a relative, relatively finite and relatively observable, phenomenon, and may represent any distinct form of energy. In physics, however, a different universe should either obey different physical laws, conform to different metric and/or physical constants. In the context of CR, thus, a universe, by default, refers to a particular scale of energy (that is, energy at, or about, certain magnitude). These scales are interpreted as discrete vertical energy levels and will correspond to rest energy magnitudes of elementary (or stable) particles on that level. These universes are correlated and energy on one scale may represent past or future state, or a special state, of the correlated energy on another scale. Note that, here, difference between vertical energy levels is generally such that physical constants differ significantly in value. The equations for determination of these levels are provided later. For example, one vertical energy level represents the scale of standard atoms, the other represents the scale of planetary systems. Note also that, even though these levels are considered discrete, the values of physical constants anywhere still should oscillate and may even differ horizontally (between systems of similar scale), however, such differences are probably generally negligible (although they may be detectable). However, rules exist in the association of energy with specific scale (vertical energy level). A localized group of energies of particular scale, no matter how large, should only be associated with a larger scale [as well] if the group is spatio-temporally entangled with a distinct graviton of larger scale. This distinction is generally a distinction between a simple aggregate of entities and a collective of entities representing something more than the sum of these entities. In other words, it is the emergent phenomena that represent a likely signal for the coupling of the collective with a graviton of larger scale. The coupling may be periodic, occasional, stable or unstable, and, due to time dilation between scales or relativistic causality, the rate of emergence/decay of emergent phenomena can only be relatively synchronized with the rate of coupling/decoupling. On one scale transition may appear continuous, on the other discrete. 4.4.1 Polarization and scale of a universe Universe will typically refer to a scale. If it refers to a specific particle or a system of particles, polarization may also be specified. There are two equivalent notations: cUn.m =cU(n.m) n = vertical energy level (scale) of the universe (0 = reference universe) m = scale of the (horizontal) sub-universe 22 c = polarization n∈Z m∈Z In CR, space is relative and generally associated with a particular graviton (which, in CR, represents an evolvable particle, generally a superposition of sources of gravitational and electro-magnetic potential but it becomes more complex with emergence of phenomena between discrete vertical energy levels). I hypothesize that specific gravitons of one discrete scale (vertical energy level) form the space of a graviton of a larger discrete scale. The n scales are then generally such that U−1scaled energy quanta (gravitons) form the space (medium) of U1gravitons, while U−2energy forms the space (medium) of U0, etc. In addition to space, gravitons may have associated bodies of mass of another scale, e.g., U1gravitons generally couple to bodies of mass (particles) of U0scale. However, this coupling is not intrinsic and gravitons not coupled to such body may be interpreted as naked gravitons. This coupling is also not direct. Matter of U0scale is directly coupling to space-forming particles of an U1graviton, and these particles are of U−1scale. If m is specified, the Un.m denotes the sub-universe of scale m, larger than n but smaller than n+1. If specified, charge c denotes the polarization, usually electric (two possible states of polarization). In this and my other works, U0scale will generally represent the scale of standard particles such as standard protons and electrons, U1then represents the scale of stars and planets. 4.5 Standard particle Standard particle (e.g., standard electron) refers to a particle as defined by the Standard Model in physics. 4.6 Elementary particle CR implies relativity in elementariness. All particles, including those conventionally considered to be elementary, must have structure, even if that structure may be unresolvable for the observer. However, since unresolvable properties effectively do not exist for the observer, the concept of elementariness is certainly useful. Even in cases where the structure can be resolved but is inaccessible, for pragmatic reasons it may be disregarded. Both, standard protons and electrons, for example, may be treated as elementary as the constituent particles are strongly confined. 23 Even on large scales, depending on context, relative equivalents of these may be considered elementary, even though their structure may be highly resolvable by the observer. 4.7 Existence Distinct forms of existence are distinct forms of energy. All discrete quanta of energy are produced (inflated or deflated) with changes in momenta. Preservation of existence on particular scale requires energy, although all that energy may be provided already with localization to that scale. Apart from the energy localized in the particle, stability also depends on the pressure/density of the associated space, which is of different scale. Any form of energy contains spin momenta at some scale and, in CR, even as a whole must have orbital momenta from some reference frames. Angular momentum (commonly denoted by L) is intrinsic to universes, however, it is not always observable, so its existence is relative as well. For elementary particles (on any scale) the observable momentum will commonly be angular: L=mvr where m, v and r are particle mass, velocity and orbital radius, respectively. For a system of n entities, the momentum of the system is the sum of individual momenta (which, generally, should be interpreted as a vector sum): L= n X i=1 Li It should be clear that, like everything else, rotation is relative. Some claim that rotation is absolute because centrifugal and Coriolis forces always exist in rotational reference frames, however this is not absolutely true. Clearly, both forces are relative - the amount of force measured or felt depends on the sensitivity of the observer, whether the observer is a machine or not. For some observers, the force can be a relative zero. Therefore, rotation is relative as well. After all, didn’t we use to believe that Sun revolves about Earth? Some even still claim the Earth is flat, and they are not absolutely wrong either - three-dimensional space can be translated to two-dimensional space and vice versa so one could legitimately ask is the two-dimensional image of Earth in their heads an illusion, or is the three-dimensional Earth an illusion. Whatever one believes the answer is, it is both, relatively correct and relatively wrong. 24 4.8 General oscillation With no absolute constants, everything must oscillate, even oscillation itself. Change of a variable in dimension ximay thus generally be described with the appliance of the following operator: d dxi =a1fω1(xi+φ1)h1+a2fω2(xi+φ2)h1+a3fω3(xi+φ3)h1+...iii f = oscillating function aj= amplitude of jth order oscillation ωj= frequency of jth order oscillation ϕj= phase shift of jth order oscillation where, generally, aj< 1 for j > 1. Multiple dimensions are generally entangled, so f may be f(xi, ..., xn). Of course, not all oscillation will be resolvable in all space/time. 4.9 Frequency of existence Existence is relative and it depends on the scale of a reference frame (one cannot have the ability to measure energy at any scale possible), but may also oscillate between energy levels. Gravitons should relatively commonly oscillate between energy levels. For a particular order of general oscillation and its period Tx, frequency of existence of a graviton is: fx=1 Tx =1 ∆T1+ ∆T0 where ∆T1is the average lifetime on a larger scale and ∆T0is the average lifetime on a smaller scale. Generally, ∆T0may be « ∆T1, and Txmay be approximated with ∆T1. In CR, gravitons of particular scale can and regularly do couple to gravitons of smaller scale (which are then forming the body of the system). There is then a distinction between living and dead forms of energy. A living form of energy is any entangled collective of mass (energy) of particular scale coupled to a graviton of larger scale. Since it is also assumed that at the time of decoupling (death) the large scale graviton inverts scale (and some other properties, e.g., spin), and this is usually followed by new coupling on the same or similar scale of the previous incarnation, frequency of existence becomes frequency of reincarnation of energy, which may be, in some reference frames interpreted as reincarnation of life. Polarized humans tend to discriminate between living and non-living things based on convenience. I do not and I do not think nature generally does. I believe any collective of energies coupled to a graviton of larger scale is not only alive but conscious to certain degree - large scale graviton 25 of force (these are generally centres of quantum vortices, where most energy is concentrated inside graviton space). Thus, large scale spin momentum (of the graviton) is strongly correlated with small scale momenta. Graviton is a relative composite of neutral and polarized components (which themselves are relative composites). Polarization can be in the form of spin polarization, or charge polarization, all with different degrees of complexity, depending on graviton species. Resolvability of components is decreasing with the increasing number of components and the strength of confinement. A graviton formed/inflated through annihilation of particles may generally behave as an elementary particle. Physics of a fundamental theory on reality cannot be limited to particles of specific scale or a reference frame. From certain reference frames, even living beings are particles, and vice versa. Distinction between living and non-living forms of energy is very relative and physics will necessarily merge with biology in a successful attempt to understand the universes (because nature is certainly not an absolute reductionist, no matter how hard one tries to convince itself otherwise). In other papers I hypothesize that real graviton is, considering its nature, also a quantum/carrier of consciousness and I find it appropriate to use the term "soul" as its synonym. As complex bodies evolve from simple particles (although what evolves from what is in CR, with relative causality, relative), the souls evolve as well. Thus, what is described here may be interpreted as a simple or elementary graviton, its complex form may be interpreted as a relative superposition and localization of smaller scale gravitons just like the complex bodies may be interpreted as relative superposition and localization of smaller scale components. Forces or interactions evolve as well, from elementary ones to complex ones. Thus, what is interpreted as simple gravitational or electro-magnetic force between two gravitons on elementary scale, may be more complex between complex gravitons. The standard nuclear strong force is an example of such more complex force. In case of life-forms on the scale of animals on Earth, complex forces/interactions may be mental forces/interactions between the souls whose components may have billions of degrees of polarization (in these, associated spectrum of energy levels may be interpreted as continuous rather than discrete). Naturally, these mental interactions/forces are stronger between strongly entangled souls, which can be interpreted as a consequence of shorter distance in some dimension of space (including time), just like gravity is stronger for spatially closer bodies. In general, gravitons act as attractors for specific entanglements in time/space, guiding interacting entities towards a specific future state. 32 4.13.1 Physical interpretation Assuming the scale of a graviton is Un, constituent quanta of space forming the associated gravitational well will be of mass scale Un−2. With an locally empty gravitational well, graviton is considered to be naked (as such, it may be interpreted as a dark matter particle of certain scale). However, attracted particles of scale Un−1will be coupling with quanta forming graviton’s space (Un−2scale gravitons) and such couplings will be considered as coupled mass or real mass forming the body of the Ungraviton. Mass of the naked graviton may be referred to as imaginary (img) mass. Total mass of the body-soul coupling is then the sum of img and real mass. In some interpretations, however, real mass may be shielding the img mass, in which case total mass will effectively be equal to real mass. Note that these couplings will generally result in change of momenta for Un−2particles - exchange of some orbital momenta for spin momenta (which may generally be interpreted as mass inflation or localization of mass to the Un−1scale). Elementary graviton can be excited and exist on different vertical energy levels (scales), however, on some scales the neutral (gravitational) component may dominate, on others its nature may be dominantly charged (e.g., electromagnetic). While real gravitons induce gradients in vacuum density (or space curvature), space inside of a real graviton from an internal reference frame may be globally flat on average, with extremely low density and temperature of [what would be interpreted from that frame as] matter, in equilibrium. However, high curvature should be present at the membrane, which represents a discontinuity between internal space and external space that has different properties. The membrane is closed and, in relatively stable states, has such shape, distribution of potential and rotation that the net gravitational effect on internal energy is a relative zero. While temperature and density are both low globally within the graviton, high temperatures and densities are possible and do exist on smaller scales. The particles inside may be in condensed states and grouped into quantum vortices (galaxies) of certain scale. It should be clear, however, that even if in some reference frames the sole difference may be in scale, equivalence between gravitons of different scale should generally be understood as more or less relative. The internal composition presented here is a hypothesis based on observations of large scale structures. While the external effects of gravitons are important, internal structure of smaller scale gravitons may be unobservable and consideration of effects within the gravitons will usually be 33 of low pragmatic value. Thus, when referring to space associated with a graviton, one will usually refer to the space forming its well of potential (e.g., the gravitational well), not its internal space. The ground shape of a simple localized graviton is generally a torus. Relativistic momenta may distort the shape of a graviton, however, shape and distribution of mass of a graviton generally depends on its excitation state (which in some cases may be defined by quantum numbers) and how well it is localized. Travelling as a wave, its mutually entangled mass will be distributed over larger regions (and may be interpreted as wave-like excitation of existing static potential of space), with potential density maxima corresponding to the maxima of [the square of] the associated wave-function. For a highly polarized graviton, structure may be highly ordered, with oppositely polarized inner components separated towards different sides of the membrane. Figure 1: General shape of a simple graviton in ground state (no radial/angular nodes in the waveform) Shape of a graviton is shown in Fig. 1, where the surface of a torus represents its membrane. As a discrete quantum of space, graviton must have an membrane. Note that it is relatively easy to maintain existing conditions inside the graviton, as accumulation of particles is extremely hard due to flat space and low-density of matter. Any particle having a momentum perpendicular to the graviton may be accelerated inside (in most cases, the trajectory of the particle may be simply bent about the graviton surface), but will be equally decelerated again on exit. Collisions inside will be hard even if existing and passing particles are of the same scale, but if existing particles are of smaller 34 scale (discrete vertical energy levels differ in energy by multiple orders of magnitude), accumulation becomes almost impossible. In that case, graviton is relatively transparent (transparency is dependent on energy scale). Note that polarization will be generally shaping a graviton into a 2dimensional ring, while neutralization is expanding it to a more spherical shape. To conserve volume, expansion will be decreasing the thickness of a torus, converging to a 2-dimensional sphere [surface]. Recent analyses[6] have shown that the shape of the local universe is consistent with that of a torus[7]. Considering its characteristics, by the definition of a graviton here, the observable universe may be a part of a [large scale] graviton. More recent studies even provide evidence for the rotation of the observable universe - fossilized in the asymmetry of galactic spin momenta[8], further going in favour of the hypothesis. If distances between galaxies (large scale quantum vortices) are increasing, this graviton is increasing its internal flatness and must be changing shape. How is the neutral gravitational energy of a graviton exchanged with charged (e.g., electro-magnetic) energy in the transition between energy levels? Different interpretations are possible, but this should involve changes in momenta components. All components of graviton momenta are effectively exchangeable between vertical energy levels. Changes in vertical energy levels require energy transformation and thus may generally involve annihilation of particles on some scale as annihilation does imply transformation, as well as inflation and deflation of momenta components. Since elementariness is relative, one can assume that the charge and spin magnetic momentum of an elementary charged particle stem from separation and difference in momenta between oppositely charged constituent particles. Since speed of information transfer is relative (in CR, it depends on scale), both orbital velocities of constituent charges and difference in velocities between constituent opposite charges may be converging to infinity with decreasing scale. And this velocity/difference can be annihilated into mass/radius. Note that relativistic energy can have different interpretation between scales. E.g., interpretation of velocity may be effectively scale variant. On one scale, velocity, or difference in velocity, generates mass (mass is relativistic), on the other it generates charge (charge is relativistic). High orbital velocity of standard quarks is considered to be the main contributor to the rest masses of standard protons. High orbital velocity of constituent particles of quarks and electrons may be the main contributor to their charges and spin magnetic momenta. 35 Charged gravitons, in addition to gravitational field tubes (which have ringlike and spherical eigenstates), possess both electric and magnetic field tubes. What are magnetic field tubes? In CR, magnetic field lines are relative lines, in reality they are tubes, or toruses (which may be deformed). These tubes can be interpreted as induced polarized effective gravitons perpendicular to the primary graviton, or polarized dimensions of space (polarized subspaces) for a charged graviton. They can also be interpreted as tubes of entanglement between charged gravitons. If the primary graviton is of Un−1scale, space in the associated magnetic field lines is formed by particles of Un−3scale. More complex forces with multiple degrees and species of polarization can be correlated with mutually entangled different species of potential, or fields of potential, with forces mediated through different species of dimensions of space (or entanglement). All of this is evolvable and nature of force can change over time. More complex forms should be more plastic but no law of nature is an absolute law. 4.13.2 Wave-like behaviour Each and every graviton must have a rest mass greater than absolute 0. Rest mass, however, is only one part of its total energy, a part that can be correlated with its intrinsic (stable) frequency (even in a localized/corpuscular form, the waveform is still there - even if unresolvable by the observer). However, a graviton can be excited and delocalized, and this excitation [of frequency] will form the other part of its total energy. In a delocalized (wave-like) form, graviton will generally spread in a spherical wave-form, with its rest mass usually spread isotropically across the spherical shell. However, in case the graviton has a nonzero total spin, the other part of energy will be more localized on the sphere and the spreading of that energy will be proportional to its wavelength. The density of energy across the waveform is proportional to the probability of localization (wavefunction collapse) at that point - once the graviton is absorbed/coupled to external mass/energy. Thus, even if the graviton waveform is spreading in all directions, the point on the sphere with highest energy concentration can be interpreted as the direction of propagation relative to the point of emission. The higher the frequency and the more spin-polarized gravitons (e.g., photons) there are in coherent superposition the behaviour will be less wave-like and more corpuscular-like. In any case, the waveform is composed of particles (excitations) of smallerscale, but they are strongly mutually entangled (distance in space between them may grow, but distance in time is conserved) and strongly confined to the waveform (this is why the absorption on some scales cannot be partial - as evident by the strong frequency dependence of photon absorption in atoms). Waves, however, do not necessarily represent spreading gravitons. Space is generally a fluid-like medium (with pressure/density gradients), the disturbance of which can result in production of Rayleigh or ocean-like waves. In such waves 36 there is no strong entanglement between constituent excitations - collapse of the waveform to a single point (complete singular absorption) is usually highly unlikely, partial energy absorption is common. Such waves can be considered massless relative to the medium, but, again, not absolutely - as the excitations (space-forming gravitons) are quantized on some scale and represent absorbed energy from the source of disturbance - not part of the rest mass of the medium. Difference thus exists between a graviton that is travelling (expanding) as a wave and a medium-forming gravitons that are oscillating in situ even if the medium-forming gravitons are of the same scale as the constituent small-scale gravitons of the expanding graviton waveform. This difference is in the form/strength of the entanglement between the components of the wave. In other words, even if the components are relatively equal, one wave is transporting them as a discrete quantum of energy of larger scale, the other as a continuous spectrum of energies of smaller scale. 4.13.3 Space-forming gravitons Space-forming gravitons of an Ungraviton are of Un−2scale. These spaceforming gravitons are hypothesized to orbit the centre of the larger (Un) graviton. If the Ungraviton is completely naked, all the Un−2gravitons are uncoupled/nonlocalized and may form radially standing waves (the semi-major orbital radius is relatively constant) of angular velocity equal to cn−1. In example, for an graviton of U1scale (e.g., one coupled to Earth’s body), the angular velocity of space-forming gravitons is equal to c0, which is equal to the standard speed of light (c), 2.99792458 ×108m/s. Is the orbital motion the proper interpretation for the motion of noncoupled space-forming gravitons? When uncoupled, these gravitons are dominantly (1st order) entangled with the large scale graviton (Un) and may be constantly spiralling between the Ungraviton radius and their own range. However, one interpretation of this spiralling motion is orbital precession. Once localized (with coupling to real mass), some (or most, depending on the amount of coupling real mass) of the angular velocity is exchanged for spin momentum, thus, the orbital velocity of the coupling becomes lower than cn−1 (e.g., Keplerian). Even though graviton orbitals may be spherical, coupling of spaceforming gravitons usually occurs on the equatorial region of that orbital. This is because localization is proceeding through steps (which can be interpreted as energy levels of complexity or graviton dimensionality). 37 Thus, the graviton first collapses to a ring-like form, before localizing to a specific body within that ring. In equilibrium, inclination of the orbital is fixed, but the whole orbital rotates with the velocity equal to the orbital velocity of bodies. Consider Earth, for example. Its non-coupled space-forming gravitons are rotating (orbiting) at the standard speed of light, but their orbitals themselves are rotating at the speed of Earth’s body at the orbital radius (rotational period of the orbital thus currently being equal to about 24 h for orbital radii equal or lower than the Earth’s surface radius). With the inclination fixed and step-like localization, all couplings (incarnations) of the same graviton may occur along a specific ring (even though the decouplings may not). In one interpretation, multiple entangled gravitons or components of a graviton are involved, where one graviton [component] remains uncoupled. The entanglement is relatively broken once one [component] couples to a body of real mass, but is then restored after decoupling (so the graviton [component] returns to the same orbital - which can be interpreted as background entanglement). The two components could be interpreted similarly to the group and phase components of momenta. One spins at the speed of light and rotates with the body, the other may be at rest relative to the orbital but oscillates radially, and it is this component that is coupling with bodies. Localization probability distribution will then depend on its frequency - number of angular nodes. Note that as the soul (graviton) is coupled to a body, its size/energy in space is well defined (less spread) but its location in time is more spread so the two can be correlated through the uncertainty principle. Consider, for example, souls coupled to human bodies. While the adult bodies remain of relatively fixed size in space, their location through time can vary considerably and is much less predictable. If the spread of the body represents (or, is proportional to) the spread of the soul, this suggests that the body fixed at one location will have to continuously increase its spread (weight or energy) to satisfy the uncertainty. This could be correlated with the fast growth of embryos, fixed in an egg/uterus which itself is usually relatively fixed. It can also be correlated with the continuous spread and growth of trees, which are fixed to one location for life. This can then be generally correlated with health - bodies that do not grow in energy and also do not move are at the highest risk of death (forced spread of energy through decomposition and decay). There are inherent limits to both, growth and motion, however, these limits and rates of ageing (time dilation) differ between different species and subspecies of life. Both, evolution and development of organisms, probably involve quantum or quantum-like entanglement at different scales[9], an entanglement whose stability generally depends on pressure/temperature associated 38 with particular scale - not necessarily the standard pressure/temperature (correlated with kinetic energy of standard atoms/molecules). The space-forming gravitons have different ranges (energies) and density of these gravitons falls off with distance (generally exponentially). Different interpretations exist for why these particles remain in orbit or confined, rather than being radiated away. In any case, the non-zero positive rest mass implies they have a range. Confinement to that range can be interpreted as a coupling to positive pressure either of the enclosed mass-energy or traversed mass-energy by the wavefront. Effectively, the enclosed mass for them represents an effective or relative black hole so they cannot travel further and instead form a relative equivalent of a photon circle correlated with conventional black holes (where the surface tension is 1/2 of the surface density in a thin-shell approximation, in GR framework[10]). Depending on case, this may require running coupling. In any case, they could be considered as representing a part of the large scale graviton (Un) - they are, in any case, entangled with it and are spatially extending its presence (in a wave form, spin momentum is certainly a more appropriate interpretation than an orbital momentum). This can be interpreted as a physical manifestation of the quantum wavefunction of the large scale graviton, where its location probability decreases with distance (square of distance, usually). Note that, in spacetime metrics, gravitational acceleration can be interpreted as a density of space per the area of time. Usually the time is multiplied by cso the time dimension becomes equivalent to space. In CR, however, the value of cis scale dependent. In any case, obviously, a space-forming graviton also represents a quantum of a time dimension. The strength, or intensity, of the gravitational coupling is proportional to the density of space (number of space-forming gravitons per the area of coupling). If a large scale graviton is not well localized (the number of radial nodes is greater than zero), multiple gravitational maxima will exist in a gravitational well. This, coupled with different dimensionality of space-forming gravitons associated with different maxima can solve the gravitational anomalies, commonly attributed to dark matter. The entanglement between the graviton of a larger scale (Un) and Un−2 gravitons can be lost (e.g., when the Ungraviton itself is delocalized or changes scale), which is then interpreted as decoupling of the Ungraviton from local space and the body of real mass that may exist in the well. The fate of Un−2 gravitons will depend on the local environment and whether they are localized or not. Generally, however, the stability of the gravitational well is reduced. Due to their standing (static) nature and confinement to a particular po39 tential well associated with a parent graviton of larger scale, the space-forming gravitons will generally be referred to as static particles. 4.13.4 Effects of graviton interaction and oscillation The constituent quanta of one graviton will weakly interact with constituent quanta of another graviton. However, in case of stronger entanglement the two may form a superposition in space and probability for interaction may increase. Superposition is, of course, relative, and if gravitons are of different scale, orbital radii of constituent quanta will be different. What happens to the gravity of a graviton confined within another graviton, assuming both are of similar energy (of the same or similar magnitude)? It is possible that extroverted gravity simply becomes the sum of gravity of all gravitational sources, however, relative confinement of inner gravity (inner effective gravitons) is possible as well. The reason for this is the non-zero mass of effective gravitons, which implies limited range of gravity. Thus, those with shorter range can be confined within the radius of an outer graviton. Note that the outer graviton, although considered as another distinct graviton, may be entangled with the inner one and the two could be considered as maxima of potential of a single, albeit less localized, graviton. In the extreme case of confinement, the outer real graviton may be effectively shielding the gravity of the inner real graviton. It may be even possible for some effective gravitons with longer range to be assimilated by the outer graviton but probability for that should be proportional to their mass and, thus, inversely proportional to their range. Confinement must be relative, however, and some inner gravity should always leak, with highest probability at the poles. The same effect can be produced even with a single graviton oscillating between different radii, assuming field information transfer is slower than graviton oscillation. This then suggests that gravity may be generally stronger at the poles of spherical bodies, even in perfectly spherical (non-rotating) ones (if such could exist). However, if the general form of a graviton is torus-like, as hypothesized, openings on the poles may generally have non-zero radii and lower gravity than otherwise expected on the poles, may be more likely. This should be even more pronounced in polarized gravitons where converging magnetic field lines concentrate particles along the magnetic field lines between the poles. 40 In other work, I hypothesize that large scale gravitons (which may be inflated from smaller scale) are commonly involved in the formation of stars and planetary bodies. The inflation (or initial over-inflation followed by deflation and stabilization at the new energy level) of a graviton is relatively synchronized with the clumping of real mass (ordinary matter) and makes the process of formation much faster and possible even in cases of strongly diluted real mass (like in the Kuiper belt of the Solar System, for example). Mass in planetary bodies should then be differentiated not only vertically, but horizontally as well, with lower density at the poles and possibly even with tubes (tunnels) connecting poles of large scale gravitons, or different horizontal energy levels in case of a single oscillating graviton - although these tunnels in terrestrial bodies may have to be filled with fluids to ensure long-term stability. Note that Earth’s surface gravity is greater on the poles, but that is a consequence of the reduction of the surface radius due to redistribution of mass towards the equator. Directly below poles mass density is lower than elsewhere. Are there tunnels below? Long-lived tunnels, except near gravitons, seem unlikely due to generally increasing pressure with depth, however, fluid density should be increasing with depth as well. High polarization and angular momentum of the wall material can increase the stability of such tubes but this is not expected in terrestrial bodies. Long term stability could be ensured with appropriate density of energy levels and relatively frequent oscillation of large scale gravitons as this provides multiple density maxima. Lateral density gradient (with increasing density away from the pole) also decreases pressure on the tube and such gradients are likely for rotating bodies (note that Earth rotated much faster during formation). Otherwise, tunnels may be only periodically recreated (solids remelt). I suspect that on bodies like Earth the fluids involved should be [salty] water and magma, with dominant fluid probably depending on the pole. Land should be depressed at the entrance where water is involved, however, it may be elevated on the pole where magma is involved. Interestingly, the subglacial topographic depression in Antarctica known as Wilkes land anomaly (elsewhere hypothesized 480 km wide impact crater, which would make it the largest impact crater on Earth) was directly antipodal to Siberian Traps (largest known volcanic event in the last 500 million years) during the PermianTriassic boundary (Siberian Traps are considered to be the primary cause for the Permian-Triassic extinction, largest mass extinction on Earth). It is questionable whether impacts alone can cause such large volcanism on the other side of the planet (although they can certainly cause widespread earthquakes and smaller volcanism). However, the recreation of tunnels with graviton oscillation (likely correlated with impacts) could result in such phenomena at antipodal locations - [enhancing] depression on the side of impact (water entrance/exit), bulges or traps at the side of magma expulsion (masking the depression). If Earth is modelled as a living being, different products on entrance and exit are expected. As tectonic plates move with time, the locations on the surface should move as well. I believe that all major mass extinctions are correlated with recreation of the tunnels. The Siberian Traps are already considered to be a result of a mantle plume which effectively is a temporary creation of a tunnel between the 41 energy, but this may be interpreted as relatively constant motion if absorption and emission are equal and cannot be resolved. Momentum is coupled to energy, however, in cases where there is no motion relative to certain [scale of] space, one may consider kinetic energy as fictional and manifested only at the time of interaction (localization) when the interaction results in local increase in energy, when some energy may be inflated from smaller scale. All energy thus consists of real and imaginary parts of some scale, but, unlike in conventionally common complete reductionism, in CR, neither may have an absolute zero value, only a relative one. Whether the [part of] kinetic energy is produced upon interaction or is carried by momentum, it probably should be associated with flavour of gravitons, and thus [inflation of] physical gravitational imprints (img mass) proportional to the kinetic energy. Note that this does not forbid the inflation of flavour beyond the mass eigenstates, such inflation only implies relative instability. 4.13.10 Energy in the gravitational imprint, reality and illusion of a universe For a simple graviton in orbital motion, this is generally satisfied: m  1 q1−vs2 cs2 1 q1−va2 ca2 vara=n~ m = rest mass vs= spin velocity cs= spin velocity limit = information speed limit in spin space va= orbital velocity ca= orbital velocity limit = information speed limit in orbital space ra= orbital radius ~= quantization constant The first relativistic term (enclosed in parentheses) here represents the energy in the gravitational imprint due to angular motion relative to spin space (space associated with the source of the spin momentum), the other relativistic term represents the energy in the gravitational imprint due to angular motion relative to the orbital space (space associated with the source of the orbital momentum). The nmay be an integer, half-integer, or something more complex, depending on graviton nature and interpretation (reference frame of quantization). Note how apparent here it is what amount of illusion (and nonsense) can be created with the assumption of an absolute reference frame, where cs =ca=c. 48 Reduced orbital wavelength of the graviton is: λr=ra n Which is, for va=c0=c,cs»vs,ca»c, and n= 1, equal to reduced Compton wavelength, which is the reduced wavelength of a photon whose energy is equal to the rest energy of the particle. But, in general, it is the reduced wavelength of a non-excited particle in a non-relativistic uniform motion, at standard light speed. Reduced wavelength is simply a wavelength divided by 2π, which then represents the orbital or spin radius in case of angular motion. For a particle with no orbital momentum: m  1 q1−vs2 cs2 vsrs=ns~ rs= spin radius Reduced wavelength (or, reduced spin wavelength) of the graviton is: λr=rs ns With vs=cand cs»c, this reduces to the Compton wavelength. It is obvious here that a realistic result requires cs»c, otherwise (with cs=c), one has to reduce rest mass or radius to 0 in order not to obtain infinite spin momentum. And this is exactly the assumption in QM - particles like photons are assumed to have zero mass, while particles like electrons are treated as point particles (zero radius). In other words, reality has been reduced to illusion. Experiments have shown that the radius of a localized electron must be much smaller than its reduced Compton wavelength, and even much smaller than its classical radius. This implies that the contribution of electron charge energy to electron’s rest mass is very small, even negligible, as according to some experiments[18] the upper limit to electron’s radius is 10−22 m. Reduced Compton wavelength of the electron is 3.86 ×10−13 m. Radius the electron would have if all its mass would come from the potential en49 ergy of its charge, ignoring quantum effects, is 2.8 ×10−15 m (classical electron radius). It should be clear, however, that the electron’s radius is not absolutely fixed, it can be associated with a specific local energy level occupied by the constituent particles of the electron. Bonding and measurement (confinement), obviously, can affect the spreading of the electron’s waveform (radius). Radius is quantized, but relatively - transition between different radii will be continuous from reference frames where the transition is significantly time-dilated. Thus, its rest mass effectively originates in the spin momentum of its neutral body mass, not charge. For an electron at rest, taking into account spin momentum magnitude, rather than its projection, this should then be satisfied: 1 q1−vs2 cs2 =√3~ 2mersvs =k vs2 cs2= 1 −1 k2 cs2=vs2 1−1 k2 me= electron rest mass = 9.10938356 ×10−31 kg ~= reduced Planck’s constant = 1.054571817 ×10−34 Js For the mass radius rs= 1 ×10−22 m, and assuming vs=c0=c= 2.99792458 ×108m/s, one obtains cs≈c(only slightly larger than c). But what are the actual values of rs,vs, and csin reality? For practical purposes, one might assume that vs=cs=cand, thus, rs= 0, but in reality rsmust be larger than 0 and both vsand csmay be larger than crather than csalone. In case of particles of this scale, however, csmay be equal to c, with vsbeing slightly smaller. Thus, the assumption of a locally relativistic spin does not require for the electron to rotate faster than c(classically, for this radius, vswould simply have to be larger than cby about 10 orders of magnitude). Why does a localized electron has to spin twice (in case of a spin projection of 1/2 ~) to return to the same state? Physically, this is a consequence of 1:2 resonance between two different rotating components of the electron. Since the radius of the electron must be greater than zero and energy distribution cannot be absolutely homogenous, the electron doesn’t only have an intrinsic spin momentum, it always has some orbital momentum as well. Thus, this resonance may be a local spin-orbit resonance (barycentre of orbital rotation is different from the barycentre of 50 spin rotation). In reality, situation can be more complex (e.g., presence of inclination or axial tilt). For the force carrier particles, vais generally fixed to cn(or, close to cnin reality), which represents information transfer limit in space associated with the vertical energy level (scale) n. Reduced Compton wavelength for such particles is also their range. It is clear that in particles of variable wavelength, with fixed va(which can now be interpreted as propagation velocity) and fixed spin momentum, spin momentum components must be variable (in such way to conserve the spin momentum). For particles like photons, spin velocity vsshould be proportional to frequency and rsshould be inversely proportional to frequency. If flavour (gravitational imprint) oscillates between different eigenstates (and it does in reality for any particle), it is the velocity vsthat should oscillate as well (proportionally). If varemains fixed (in reality it too should oscillate but this may be negligible), to conserve total momentum, the range must oscillate as well (and should be inversely proportional to mass and frequency). Generally, for any naked graviton (graviton coupled to relatively negligible mass), vn≈cn. Once graviton couples to matter (higher mass, associated with particular eigenstate), vndecreases significantly. Knowing the radius (range) of the observable universe, one can obtain the upper limit for standard cosmological photon rest mass in the lowest mass eigenstate. Its relativistic mass is: m=~ rc = 8 ×10−70 kg r = radius of the observable universe = 46.508 ×109ly = 4.4 ×1026 m c = standard speed of light = 2.99792458 ×108m/s Thus, its lowest rest mass eigenstate must be lower than that. Note that, if naked gravitons travel at fixed and maximum possible velocity in some space cn, the relativistic mass term associated with that space should be discarded, unless coupling of the graviton with matter is interpreted as increase in graviton mass, in which case the term may be adjusted so that the deviation (i.e., decrease) from cnis proportional to mass increase. In case of the photon, its angular orbital (propagation) velocity is assumed to be equal to c0=c. If the associated term is then discarded, relativistic mass of the photon depends only on its spin velocity vs. If one further assumes that vs≈cs(photon is naked relative to csas well), photon’s rest mass should be roughly equal to the calculated relativistic mass. Of course, if the universe is expanding this value will further decrease. Assuming, however, that the universe’s expansion is a result of transfor51 mation of photon’s (or any other streaming graviton’s) relativistic energy into dark energy (should be the case if total energy density remains constant) then a limit to expansion must exist - the universe should stop expanding once the relativistic mass becomes equal to the rest mass. Assuming now that the space is quantized by gravitons such as photons, the universe is expanding because the quanta of intergalactic space are expanding - proportionally to wavelength and spin radius (rs) increase (physical dilation). Note that, in order for these to expand, their rest mass must be greater than zero (otherwise relativistic mass makes no sense - there would be no energy to lose). But why are they expanding? They are expanding because they are losing relativistic energy, which is dominantly gravitational and electro-magnetic energy. Losing energy to what? Probably gravitons of different scale that they are entangled with - e.g., those forming supermassive black holes. This is the interaction between large scale gravitons and [small scale] gravitons forming their space, where, in effect, the mass of the source of force is increasing at the expense of the mass of carriers of that force - extending the range of force in the process. Note that this implies the cycling of the universe between expansion and contraction because once the limit of expansion is reached the universe becomes static, which is an extremely unstable state (absolutely static state is even impossible in CR). Note that the range cannot be absolute zero either, which implies that the universe cannot contract to absolute zero size (which is impossible in CR anyway). Assuming universe collapses to a single object (large scale superposition of large scale gravitons), with the mass of 3.53 ×1054 kg, ~equal to reduced Planck’s constant and cn=c, its range would be 9.96 ×10−98 m (this range should be interpreted as orbital radius, while the spin radius is much larger). Note that this can be interpreted as near absolute zero temperature of large scale, where all the large scale gravitons form a bosonic condensate. This is also an extremely unstable state, so the universe explodes, beginning a new cycle. Note that the non-zero initial orbital radius (mass barycentre offset) implies non-homogenous energy distribution, which is then reflected in CMB anisotropy. In other words, CMB anisotropy can be interpreted as evidence that the universe did not start from an absolute singularity - a point-like graviton [superposition]. If large scale gravitons are not point-like, and energy can be exchanged between gravitons of different scale, one obviously should not assume that any graviton of any scale is point-like, at least not in reality. 52 4.13.11 Gravitons as force/momentum carriers Gravitons are also force carrier particles, where dimensionality (complexity) of such gravitons will depend on the complexity of force. In case of the, so called, fundamental forces, gravitons usually have simple shapes, which may be interpreted as ground shapes of spherical harmonics. Forces are present on different scales and act on different bodies. In any case, intensity of force coupling (strength of force acting on a particular body) is directly proportional to the intensity of gravitons coupling to the body. And this intensity will depend on distance but also on the shape of gravitons, which can be further correlated with mass/range of gravitons. Generally, intensity depends not only on the density but on the dimensionality of the gravitons as well. Consider, for example, a force carrier graviton in the form of a 2-dimensional sphere [surface]. The strength of this force will decrease inversely proportionally to r2, where ris the distance from the source. In case of 1-dimensional gravitons, in the form of rings, the force will decrease inversely proportionally to r. The same force can be carried by gravitons of different mass (range) and shape. Generally thus, the force decreases inversely proportionally to rn, where ncan be interpreted as denoting energy levels due to discrete ranges of gravitons (nmay thus change with distance, but generally not continuously, rather at discrete points). Note that this can explain all cases of anomalous gravity (e.g., gravitons farther from a supermassive black hole have not only exchanged their energy for the energy of the supermassive black hole with universe’s expansion, in the process they have reduced dimensionality). Gravitons can be more or less localized (they generally localize with coupling to bodies). The maxima of wavefunctions associated with gravitons represent maxima of potential of the associated force. This explains why electrons in the atoms, for example, generally can be found at these maxima. However, energy levels can be associated with any graviton of any scale, although these levels can be well confined and undetectable, especially on smaller scales. Particles localized to the maxima of another graviton (e.g., electron coupled to a proton) generally do not lose energy in these states. There are multiple interpretations of this. A particle may be in the form of a standing wave. However, since this particle is also coupled with gravitons forming [private] space of the parent graviton, the particle is not losing energy because it is, in equilibrium, rotating with space. On smaller scales this rotation can, and will, at some scale exceed the speed of standard light. This allows for more intuitive interpretation of spin momenta of particles such as electrons. However, since speeds larger than the speed of light are confined to smaller scales, the electron itself cannot travel faster than light. Additional problem is the stability of confinement. Photons, for example, generally travel as waves, with their radius expanding with emission. However, rest mass and rest radius of photons should be small enough 53 to allow them to start travelling at speeds much larger than c. In other words, speed of motion of energy is not limited solely by the amount of energy, but by radius (confinement) of that energy. This, of course, implies that relativistic effects depend on scale as well (speed of information transfer is not absolutely invariant to scale, only relatively, as transitions are discrete). 4.13.12 Graviton collapse and time compression The speed of time in graviton’s well is inversely proportional to its mass and the proper units of time are proportional to its radius. This is why a collapse of a graviton (change in vertical energy level, decoupling from real mass) will cause time compression (acceleration of time). Since the force associated with the graviton (e.g., gravity) is never the only force acting on bodies, collapse of a graviton is also the transfer of power to forces acting against this force. Collapse can be temporary or permanent. In the context of large scale gravitons associated with stars, for example, a collapse of a graviton will effectively reduce the strength of gravitational coupling, causing the kinetic energy of atoms to overpower gravity, resulting in thermal expansion (note that this will disturb planetary orbits as well). Similarly, as it is shown in complementary work, periodic collapses of large scale gravitons are likely causing temporary acceleration in the expansion of the observable universe. Due to relativity in causality, however, acceleration of evolution will not be absolutely synchronized with the collapse and the pending collapse may be detectable through local precursors (e.g., temporary increase in decay rates of elements). 4.14 Static particle Particles forming space (effective gravitons) of a graviton of scale Unare particles of scale Un−2. These are entangled with the parent graviton and any changes in its momentum will be reflected in momenta of these constituent particles. The particles are orbiting the graviton and the energy density is generally decreasing exponentially with distance from the graviton. Orbital speed is roughly equal to the speed limit in space for particles of Un−1scale. However, the particles will get bound (coupled) to Un−1scale matter captured by the gravitational well, exchanging orbital velocity for spin (Un−1scale) momentum. Due to their limited range and conversion of radial to angular momenta (where upon reaching the range they can form standing spherical waves) the space-constituent particles will hereby be referred to as static particles, generally, static gravitons, which may be generally decomposed into static graviton neutrinos - in case of neutral gravitational potential, and static photons or halfphotons - in case of electro-magnetic potential. 54 These particles may be interpreted as hot dark matter when uncoupled, however, with coupling, their momenta will be transforming to cold Keplerian momenta. 4.14.1 Background fluctuation (Virtual fluctuation) If static particles are directly undetectable they may be referred to as virtual particles. These particles have energy and this energy may be referred to as zeropoint energy or background energy. If they inflate the particles can become real (detectable), or deflate back to virtuality. The process usually involves annihilation, and may be referred to as stemming from background fluctuation or quantum fluctuation, which is proportional to background temperature (which is proportional to local potential - e.g., gravitational). If particles remain real, one may be radiated away, while the other may get trapped deeper in the well of potential. This, for example, may frequently happen in the strong gravitational wells of black holes, where the radiation of standard scale can be correlated with Hawking radiation (although the two phenomena are not the same - correlation is indirect, a secondary interaction). At the point of emission, the two particles are entangled and may be described by a wavefunction where one particle has positive mass (energy) and the other negative. It should be understood, however, that this negativity is relative. The mass is still greater than absolute 0 but it is equal to, or lower than, the inflated zero-point mass or event horizon mass (here representing a superposition of the positive and negative mass, e.g., in the form of average). In case of symmetric annihilation, both particles have the same amount of mass, the difference being in the type (matter/anti-matter, per Dirac interpretation of positive/negative energy). As absolute symmetry requires absolutely flat space, the annihilation cannot be absolutely symmetric. Therefore, a difference will always exist between matter mass and corresponding anti-matter mass. In case of annihilation in extremely strong wells (e.g., near a black hole), asymmetry can be extreme (where one particle may even become more virtual instead of becoming [more] real). In any case, the radiation can be interpreted as evaporation of the well. This decrease in gravitational potential should be synchronized with the decrease of mass (energy) associated with the local space curvature (if such entanglement exists). If this is a graviton of larger scale, this may not be well synchronized - the graviton may collapse to a lower energy level in a discrete step, once the sufficient amount of small scale well energy has radiated away (or, more precisely, once the sufficient amount of negative mass has accumulated). As noted before, causality here can be very relative (even probabilistic), so the collapse can precede small scale radiation as well. Different interpretations of negative mass exist, and different interpretations may exist in nature. It should be clear, however, that truly (absolutely) negative energy or negative mass, just like negative density 55 or negative temperature, does not make physical sense. It does not exist in reality. The confusion arises due to absolutist reductionism (where description of reality is reduced to mathematical abstraction and then interpreted as real) and consequential lack of the proper interpretation of the reference point where the zero-point is interpreted as absolute rather than a relative zero. In case of Hawking radiation in GR/QM context, for example, entanglement exists between the black hole mass and the quantum fluctuations of local space. Due to this entanglement, the flattening of space (coupled with the radiation of particles) must be coupled with the decrease of black hole mass (where the black hole mass and the fluctuation can be some distance apart). To describe this mathematically, the concept of negative mass is involved, where this negative mass is understood as the mass lost by the black hole. One could now accept the notion of absolutely negative mass and argue that the black hole mass decreases due to absorption of negative mass. And sure, one can indeed believe in that, but this is like believing that one can subtract 4 apples from 2 apples. It can be done mathematically sure - a more or less skilled mathematician (magician) can always make an non-existing apple appear and disappear, but a more or less skilled physicist should know that’s an illusion. Thus, one can argue whether the entanglement here is relatively local or non-local, but the black hole mass cannot magically get erased from reality. In other words, one can accept the notion of absolutely negative mass and its hairless absorption due to mathematical elegance, but one should bear in mind that, in reality, there is a hidden mechanism behind it. In fact, one should question whether the black hole itself is an illusion and all there is is curved space (which can be interpreted as naked large scale excitation, or large scale fluctuation of an large scale gravitational field - a large scale virtual graviton, which is interpreted as real from smaller scales, such as ours). However, it should be understood that it is not absolutely impossible, for example, to subtract 4 apples from 2 apples in reality, it is the specific interpretation that imposes absolute limits, not the physical reality. If one interprets subtraction as removal of mass (reduction of local energy density to some background value) - regardless of its entropy, then it is possible to subtract 4 apples from 2 apples, as background energy density (e.g., zero-point or vacuum energy density) is never absolute zero, it can be always further decreased (theoretically at least, in practice it can be hard or even impossible for inherently, even if relatively, limited observers). The locally removed energy can even be, theoretically at least, ordered/transformed into 2 apples, and as the local energy density restores to equilibrium (background density) - draining energy from the surroundings or even some smaller scale, a magician could claim he just subtracted 4 apples from 2 apples. 56 4.15 Virtual particle A virtual particle in CR is not a purely abstract concept, it is assumed to exist in reality and possess real energy. Its virtuality implies simply that it is undetectable, which is observer relative. This is different from the conventional interpretations of virtual particles, but even in these there are ambiguities. To clear things up, consider the example of two interacting electrons in vacuum. Here are the facts that no one disagrees with: •a physical (real) exchange of energy/momentum exists between the two electrons, •the exchange occurs at the speed of light (c), at least roughly, •this energy exchange is directly undetectable (it is the effects on electrons that can be measured). Now, since the exchange is undetectable, mathematical description of the process does not have to involve the exchange of real particles. And this is the case in QED, for example, where the process involves the exchange of virtual particles, also called force carrier particles. It should be clear, however, that these virtual particles are purely mathematical concepts (intermediates) and, while useful, do NOT represent the real exchanged energy (so they are not real force carriers either). Since the exchange is undetectable, a complete (or excessive) reductionist will also claim that nothing is travelling between the electrons at the speed of light - the change in energy/momentum of one electron is simply mirrored in the other electron within the time ∼r/c, where ris the distance between the electrons and cis the speed of light. To a realist (like myself), this notion is absurd for at least a couple of reasons: •if there is absolutely nothing real travelling between the electrons, why does the exchange occur at finite speed, why exactly at the speed of light and why does it depend on distance?, •we know that information carriers on detectable scales - such as electrons or real photons, propagate as real energy, and real photons travel [at least roughly] at the speed c. It seems illogical to assume that there is no real wave carrying energy from one electron to the other. Thus, in CR, the real force carrier is the energy travelling at the speed of light from one electron to the other. It is a real force carrier but can be interpreted as a virtual particle in reference frames from which it is undetectable. Since it is undetectable, one can even consider it non-existent (e.g., in order to preserve mathematical elegance), but this non-existence must be understood as relative. To assume it is absolute, is unscientific - from the perspective of a realist at least. 57 The mechanisms used to prevent annihilation may be interpreted as mechanisms of creation, or maintenance, of asymmetry (or distance in correlation) between inflated products. This can be the asymmetric exchange between gravitational and electromagnetic potential of particles, even between them. Another possibility is that particles are allowed to annihilate, however, this results in disequilibrium (recoil), and the particles are inflated back for another cycle. Both solutions are possible, one may dominate during maintenance in equilibrium (relative rest), the other, during changes in energy of the real graviton itself (e.g., at the time of its own inflation). The asymmetry of potential (carried by effective gravitons) allows for interesting solutions where different forces could dominate inside and outside of the relative event horizon. Of course, there will be leakage because the carrier particles themselves have their own wells of potential carried by effective gravitons of even smaller scale (containment of potential has to be relative). Note also, that a real graviton can contain other real gravitons of the same vertical scale but at different horizontal energy levels and thus at different radii. This allows for greater asymmetry and more complex mechanisms for its creation and maintenance. Absorption of real mass can provide stability in the gravitational well but this additional energy also adds more complexity. 4.22 Black hole Black hole is a region of space with escape velocity at the gravitational maximum greater than the speed of light (information/energy speed limit). For a standard black hole this is the standard speed of light. Note that, in CR, this region does not have a singularity at the centre, it has a ring, or torus, of relative singularity at the gravitational maximum. Therefore, some material that wouldn’t be able to escape at the equator could escape at the poles. The more charged the graviton is, the more two-dimensional it will be and the density of the gravitational field will be decreasing from the equator to the pole. Thus, the gravitational escape velocity (without taking rotation into account) can be significantly lower at the poles. 64 Note that, otherwise, the particles forming the [internally generated] magnetic field lines cannot be standard photons or of standard photon rest scale, but of even smaller scale, as they would have to be faster than standard light, unless the lines are not closed, or are expelled from the interior. However, generally, just as an U−1graviton slows down from c with momentum transformation synchronized with coupling, a particle faster than c can similarly be slowed down and transformed to a standard photon. This restricts the feeding potential of black holes, as, instead of being trapped, some matter may simply be accelerated towards the centre only to be ejected through the poles at extreme velocities. In an extremely polarized case, such black hole does not acquire additional energy and is simply the most efficient transformer of energy (life-form) - transforming composite energy into individual charged particles so these can be digested elsewhere (e.g., in young stars, where they concentrate to form hydrogen fuel). However, in case of neutral black holes, most matter will have a momentum parallel to the equator forming a disc of orbiting material. The shape of the graviton explains not only the formation of jets in black holes but also why some black holes don’t have them (such black holes should have a more neutral, 3-dimensional form). The jets are not accelerated by gravity alone, the more energy there is in plasma (accretion disk) the more powerful will be the magnetic field which will focus incoming charged particles making the jets more energetic. This correlation has been observed[19]. Note that magnetic field lines are, at some scale, also jets of entangled particles. It is then obvious that extremely neutral bodies will have extremely weak magnetic fields, while extremely polarized will not only have extremely strong magnetic fields but will also be emitting jets of particles of larger scale (like protons and electrons, in case of black holes). If black holes have evolved before stars the farthest and biggest black holes may be more polarized. However, polarization should also be cyclic at some timescale. Since particles of the adjacent discrete vertical energy levels [to the U1level] are charged (dominant energy in standard particles, for example, is electromagnetic), real gravitons of stars and planets most likely start their evolution (synchronized with coupling to standard matter) more polarized, even though most polarization may be lost already during graviton birth on that scale (inflation from smaller scale or deflation from larger scale). Discs of material about stars and planets are thus probably formed due to the charge of the host at the time of formation or at times of energy level changes - greater charge will create thinner discs. This also implies that oldest orbiting formations will orbit in a plane aligned with the plane of primordial equator of 65 the host (unless the orbits have been disturbed later, however, probability for significant disturbance should be low after birth). Settling in equilibrium state is likely to be oscillatory and this is in the Solar System confirmed with the sinusoidal distribution of inclinations of planets. Note that information on formation should be preserved in inclinations - in case the system inflated from smaller scale, nearer orbits should generally be more aligned with the equatorial plane. This is apparently the case with the Solar System, as shown in Table 1. In case of systems deflated from larger scale, it is the farther orbits that should be more aligned. However, if vertical energy levels are discrete (as hypothesized), Body Inclination (ecliptic) [◦] Inclination (Sun’s equator) [◦] Inclination (invariable plane) [◦] Mercury 7.01 3.38 6.34 Venus 3.39 3.86 2.19 Earth 0 7.25 1.57 Mars 1.85 5.65 1.67 Vesta 7.14 3.48 7.13 Ceres 10.59 3.40 9.20 Pallas 34.93 36.45 34.21 Hygiea 3.83 10.79 - Jupiter 1.31 6.09 0.32 Saturn 2.49 5.50 0.93 Uranus 0.77 6.48 1.02 Neptune 1.77 6.43 0.72 Pluto 17.14 11.86 15.55 Table 1: Osculating orbital inclinations in the Solar System it is possible (or even likely) that the initial energy of inflation was larger than required for the jump and the system was, after initial inflation, somewhat deflated to a stable state. Indeed, if outer planets are bigger (and older) and the Solar System was inflating as a system of particles (e.g., an atom) - which is a most likely scenario, the energy distribution suggests effective initial inflation of the core to current Mars’ orbit or beyond, then deflation to current Sun’ radius. In that case, the invariable plane (which is roughly aligned with Jupiter) might represent the fossil of the original core equatorial plane. The higher inclinations of dwarf planets (marked green in Table 1) might indicate that these are youngest and were formed after system stabilization, however, more likely, as decreasing inclination (relative to the invariable plane) of dwarf planets in the main asteroid belt (and increasing alignment with the current equatorial plane) towards the core suggests, these were inflated from smaller and neutral gravitons. I hypothesize that outer planets (gas giants) were inflated from polarized gravitons of electrons (some, or all, of which have ended up in an excited state or different generation - tau and muon mass eigenstates, possibly multiple states in superposition), dwarf planets were inflated from neutrinos, while inner planets were inflated from positively charged particles (parts of atomic nuclei). The anti-alignment of spin magnetic momenta between inner and outer planets goes in favour of this hypothesis (which is further analysed in a complementary 66 paper[20]). Note that a black hole is only a relatively special form of a gravitational well. Particles faster than light must exist (even if one may not be able to detect them) and every gravitational well has a relative event horizon - digesting energy of one scale and ejecting smaller scale ions which then combine to feed moons. The only difference is scale. The self-similarity is not limited to celestial bodies - every metabolism is ultimately ionic. Note also that the trajectory of ejected charges is bent by the magnetic field lines (tubes) and these can be considered as a form of intestines. In CR, there can be no absolute singularities, only relative ones. If a black hole is a result of graviton inflation or deflation, its gravitational maximum has a real radius and, if any gravitational collapse of standard matter would result in a black hole the collapse would end at that maximum - a ring-like (or toroidal) relative singularity. The collapse of the body of matter is, however, likely relatively synchronized with a change in energy level of the graviton (and exchange between gravitational and electro-magnetic potential). The graviton may collapse to smaller scale but never to a radius of absolute 0 as this would require absolutely infinite mass or angular velocity (due to conservation of momentum). Infinite momenta (energies) are never involved in such collapses. Furthermore, collapse to a smaller radius is generally coupled with the increase in angular velocity and decrease of the rest mass of a graviton. This will generally be reflected in acquired mass. Conservation of momentum is thus effectively replacing gravitational attraction with centrifugal repulsion at some scale. Therefore, although acquired mass can be compacted to extremely dense forms of energy, this energy won’t occupy 0 volume and will be radiated away (at whatever scale possible) until it matches the graviton scale. However, with collapse of scale, graviton might exchange spin momentum for orbital angular momentum and decouple from acquired matter. In that case, the particles of compacted matter may be considered dead as a collective and will tend to decompose, decay and spread. Nature evolved diverse mechanisms for such decay - in some reference frames it may be observed as rapid and abiotic, in other organic and slow. In general, distinct conscious life (by my hypotheses) of any system (collective) starts and ends with a change in discrete energy level of a graviton (or gravitons in superposition) at times of: 67 •conception (coupling), synchronized with graviton inflation or deflation, and •death (decoupling), inversion of momentum with inflation or deflation (breaking entanglement with coupled matter). Obviously, what is interpreted as conception and what as death is scale relative. For the graviton (soul), the end of life on one scale is the beginning of life on another scale (switch of context). From some reference frames, one scale may be short-lived and graviton may be observed reincarnating on a single scale - popping in and out of existence between different spaces. 4.23 General force, strong force and strong entanglement Since space cannot be absolute or absolutely abstract, it has properties and energy which can be transformed. Various combinations of spin momenta, subspaces (dimensions) of various scales (various masses of force carrying particles), enable evolution of forces of various nature. Complexity of these forces will be proportional to the number of possible polarized states, or degrees of freedom in polarization. Even gravity, with intrinsic rotation taken into account, can be interpreted as a polarized force. A neutral force may generally be interpreted as a force of unipolar radial effect (e.g., non-discriminating attraction). However, every neutral particle or force has polarized components which are generally correlated with polarized angular momenta. With changing complexity, one force may evolve from the other. Complexity can be increased by strengthening entanglement (localization in some dimension of space) of two or more sources of polarized force. Strong localization can be interpreted as superposition in some scales and, if this is a superposition of mass (e.g., gravitational), bigger mass of force carrier particles will reduce the range of force. One strongly localized force is the force holding the particles of the atom nucleus together (it is even called strong force in QM). But should it be interpreted as a special or fundamental kind of force? If gravitational sources are generally not limited to one force carrying particle (graviton of a single scale or rest mass) such force may be interpreted as localized gravity. 68 Of course, when it is expressing more complex polarization, it is not just localized but it has evolved beyond the neutral or unipolar gravity. Note that polarization too is relative. It may even be induced by polarized observers. Note also that, per CR postulates, all couplings are running (scale dependent). Coupling of the weak force represents an evolved gravitational coupling as well. It should be clear now why the term "graviton" is a very appropriate term for the generalized particle. Gravitational force is the simplest force there is, everything else is more complex and can evolve from unipolar gravity. Even the effective absence of force can be more complex - when it involves cancellation of effects of multiple sources of force. If one is to unify all possible forces and represent them by a single equation, that equation cannot contain any absolute constants. It must be as variable (or evolvable) as possible. Pragmatically, however, it will generally be more usable not to generalize as much, as variability and evolution of reality localized in an dimension of space (including time) is inevitably limited. Therefore, instead of using this equation for the general force (that includes all possible interpretations on all possible scales): F=∗ more convenient and usable expression would be the one of a relatively general force that discards forces of negligible influence on the context. In typical local contexts a relatively general force may include electro-magnetic and gravitational terms. Such form is also useful in the context of transformation of energy (inflation/deflation) between discrete vertical energy levels, as all terms are hypothesized to be entangled and one potential may be exchanged for the other, e.g., electro-magnetic force might regress to gravitational force with inflation of energy, but also vice versa, depending on the scales in question. This is exactly what I hypothesize had happened with the inflation of energy in the observable universe. 4.23.1 Strong entanglement, interaction probabilities, photon nature Strong correlation of particles localized in a particular dimension may be hard to disturb for an observer. Due to limited resolving power, observational energy may strengthen correlation and inflate additional pairs of entangled particles. This is the case for particles forming atomic nuclei, held together by strong force (strong entanglement), and one reason why proton may be considered an elementary particle in most contexts. 69 However, assuming that the binding of an electron to proton, due to increasing correlation of charges, localizes proton charge into a positron, in that context, the structure of a proton becomes more complex. Since an accelerated change in distance between charges will result in emission of photons, the photon may be interpreted as a product of the change in [the strength of] entanglement between charges, carrying the information on this change. Photons are, however, also emitted with acceleration of an isolated charge in free space, in which case the entanglement with other charges may not be apparent. Generally, thus, photon should be correlated with the [changes in] entanglement of a charge with the electro-magnetic field. This field generally contains both positive and negative potentials. And in CR, this field, or electro-magnetic space, is composed of U−1particles (which may be referred to as virtual, as they seem to be directly undetectable from our perspective). One possibility is that a photon is a composite particle of an even number of the space-forming (U−1) fermions, however, that is unlikely. Most likely, photon’s rest mass is a product of annihilation of positive and negative U−1fermions (which does not imply that photon is absolutely elementary, rather the composite particles are of an even smaller scale - U−2, with their rest masses being negligible compared to binding energy). Thus, even though photon production does not always involve annihilation of standard (U0) particles, any kind of photon production probably does involve annihilation of U−1particles, as photon emission does imply changes in local potential. Absorption of the photon will then cause recreation of U−1(space-forming) pair(s) through [inverse] annihilation (inflation) of constituents. Considering the apparently oscillating force dominance between vertical energy levels, the dominant force on the U−1scale should be neutral (gravitationallike), while the dominant force on U−2scale should be electro-magnetic. We detect photons on standard (U0) scale and they are overall neutral, however space associated with U0particles is of scale U−2, where electro-magnetism dominates, and this is the scale on which photon interacts with charged particles. In case of interactions between equally scaled particles, spin momenta and nature of species have major roles. Spin anti-alignment generally results in attraction due to the anti-alignment of the oscillation of angular waveforms. Radial attraction occurs with the anti-alignment of the oscillation of radial waveforms. Event though the space may seem continuous, it is obviously only relatively continuous. Each of the space-forming gravitons may be associated with an horizontal energy level so the density of energy levels is equivalent to the density of space, but that density is relative to scale. It is usually considered that electrons occupy discrete energy levels in an atom, but it is more appropriate to say that, in a waveform, their energy is only mostly concentrated at the maxima of potential (or entanglement) 70 and they are most likely to be localized at these maxima. Space-forming gravitons still exist between these maxima, and even though these orbitals are relatively forbidden for electrons, they can be occupied by other particles. How can two electrons overcome the radial repulsion and couple together? This is possible when one electron is significantly more localized than the other, scale difference will subdue repulsion and, once they are both in the same state (localized or delocalized) and aligned, spin anti-alignment will enable stability. Particles generally oscillate between localized and delocalized states. Nuclear fusion of two protons, for example, will require high energy when the two are synchronized in this cycling. Ensuring proper time dilation between the two can significantly increase the fusion probability. Generally, a non-localized photon is usually, like a gravitational wave, a more or less spherical expanding wave (with exact energy distribution depending on conditions during emission and photon dimensionality), with greatest probability for absorption in the direction aligned with the spin momentum axis (although the direction of that axis can change during travel, e.g., in non-flat gravitational space). Implications on evolutionRegardless of the physical manifestation of photon propagation, it obviously carries information on the source, including original location in flat space (which may be locally manifested as a recoil in specific direction at the time of absorption). It is a relative clone of the energy that caused emission. As carriers of force, photons, or gravitons in general, can be interpreted as carriers of changes in specific entanglement between entangled entities (emitter and absorber). The entanglement channel (or dimension) is present as long as the exchange of gravitons exists, or, in other words, as long as the entanglement is changing. But the entanglement is always changing at some scale, and from some reference frames, channels may be interpreted as permanent. Since this horizontal information transfer can proceed faster than standard light on smaller scales, relative precognition becomes theoretically possible, assuming changes in the energy on smaller scale precede changes on the larger scale (which generally is the case, although they may also follow the changes of larger scale). With a change in vertical energy level of the carrier, the absorbed energy of the smaller scale may even be interpreted as absorbed energy of larger scale. Consider a gluon tube connecting two gluons (where each gluon is, per the definition here, a local superposition of gravitons of different scale). This gluon tube thus consists of two graviton tubes of different scale. If the difference in scale is vertically high (i.e., a difference in multiple orders of magnitude), information transfer through the tube of smaller 71 scale will be significantly faster than the transfer through the larger tube. Now assume that, due to local entanglement, the graviton of larger scale is affected by the received information as well. If the local information exchange between the entangled gravitons is faster than the transfer of information through the tube of larger scale (reasonable assumption), the local graviton of larger scale could receive the information that can be interpreted as a change in the distant large graviton before the actual information on the change arrives through the larger graviton tube. In another example, consider a vertical entanglement between scales (universes), where the only significant difference between them is the difference in scale and thus difference in the speed of time. Evolution of energy will then be equal between the two, but one (usually the smaller scale) will be more evolved than the other. Information transfer from the smaller scale to the larger scale enables prediction of local future. Note, however, that this is a probabilistic prediction, for a couple of reasons. 1st, there is no absolute equality and, 2nd, since the system can only be relatively isolated, the probability for deviation of local future from the prediction is non-zero. Note also that increasing distance in evolution between the two is decreasing alignment, or aligned entanglement, in time, which can affect the entanglement in the dimension used for information transfer. Thus, in order for this to be long-term sustainable, some kind of occasional or periodic synchronization will have to occur. Assuming information transfer is possible due to localization (relative superposition) of the two scales in space, synchronization is possible with the exchange of scale (inflation of the smaller scale, deflation of the larger scale). Thus, any effective precognition will have a finite range, and this range will be increasing with time from the moment of last synchronization (when it is reset to zero). This is particularly interesting in the context of entanglement between planetary systems and the unstable standard isotopes, which is explored in complementary work. But it can also be very interesting in other contexts. For example, considering there is no visual stimulation of standard scale during sleep, dreams could represent information transferred from a different scale and locally interpreted as absorbed photons, at least in some cases. One should thus not exclude the possibility of existence of prophets, although, reliable ones may be extremely rare. Channels of entanglement carry energy and can, therefore, affect other energy of a particular scale. These channels or filaments (note the dark matter correlation), which can be of different complexity (depending on the complexity of information they carry), can guide this energy into particular configuration. With inherent limitation of observers, the guidance channels may be unobservable, and the behaviour of energy can be interpreted as a result of spontaneous change in energy levels, random fluctuation, self-organization or free will. 72 Consider self-organization of cells during embryonic development. This is not DNA coded. DNA only carries recipes for the components (proteins) and may carry epigenetic markers for regulatory genes which when triggered can result in cascades of gene expression but this cannot fully explain the self-organization of cells into tissues or emergent phenomena. However, assume that the organization into tissue has already occurred on the entangled smaller scale, information received on the larger scale can guide the cells into such organization (e.g., on some subconscious level). Obviously, it is not required for the event to occur on the smaller scale, what is required is information that it has occurred. In any case, spontaneous self-organization can only be relatively spontaneous and information can evolve. In case of weak information (intensity of entanglement) any self-organization can be interpreted to be highly spontaneous and will have a low probability of happening, whereas in case of strong guidance, self-organization may be interpreted as strongly coded. Former may then be interpreted as evolution, latter as coded development. However, probability of self-organization in the former can be increased with multiple instances of the potential precursor self-organizations. Consider atoms for example. A large number of collections of atoms will surely evolve molecules eventually if the environment is suitable for the existence of molecules. Similarly, if the environment allows, these will evolve into more complex forms, e.g., amino-acids, these into proteins, etc. But once some form evolves, the information could be conserved and reused to make the evolution of a nearby precursor less spontaneous. Evolution is thus relative development, and development is relative evolution. 4.24 Weak entanglement Graviton tubes are always physical at some scale, however, with increasing distance and no additional energy applied to the tube, entanglement generally weakens. Note, however, that weak entanglement in one dimension (e.g., space) does not imply weak entanglement in the other (e.g., time). However, as long as there is no change in entangled energy the entanglement will not get broken (and when it does, it never is broken absolutely), even if the particles are separated over great distance. Due to the fact that energy remains constant, either volume and energy density of the tube (dimension) connecting the particles remain constant or energy density is decreased proportionally to volume increase. Assuming information is 73 0= 8.85419 ×10−12 F/m G = 6.67430 ×10−11 m3kg−1s−2 ~= 1.054572 ×10−34 Js c = 2.99792458 ×108m/s For r = 1 ×10−15 m (roughly hydrogen nuclear radius) and mass of a down quark M = md= 4.8 MeV/c2= 8.556777 ×10−30 kg: mg= 2.44819 ×10−26 kg = 13.7333 GeV c2 Roughly 100 times the range (r) would give the mass of a pion (πmeson). It is certainly viable that the range of gravity of the down quark is 100 times the nuclear radius, at least when there’s an electron bound to the nucleus (forming the atom). Of course, the strong force is generally a composite force (a superposition) of multiple short range sources, but is the complex polarization present at all times, or does it only occasionally evolve? Interestingly, using Compton wavelength of the pion (roughly 1.43 ×10−15 m) for r, gives mg= 9.60 GeV/c2, which is roughly equal to a superposition of 2 bottom quarks and 1 charm quark (2 ×4.18 + 1.28 = 9.64 GeV/c2). Such superposition could be interpreted as an unstable neutral baryon. If that baryon is then paired with its anti-particle the radius r would be reduced to roughly 0.715 ×10−15 m, which could be interpreted as down quark contribution to the mass radius of the proton. Note that the calculation for up quarks (conversion of 1/3 charge to mass) gives almost equal results (due to up quark mass being roughly half the down quark mass, 2/3 md−1≈1/3 mu−1). Note also that it has recently been discovered that an charm/anticharm quark pair may be more intrinsic to the proton than previously thought[23]. Could it be that the whole hypothesized baryon/antibaryon pair gets periodically inflated then? If one assumes that the mass of the pair is inflated by the ratio of charm quark mass to proton mass (1275/928.272), the mass radius becomes 0.521 ×10−15 m, in agreement with recently obtained proton mass radius of 0.55±0.03 fm[24]. Interestingly, conversion of charge to mass using (1.3) for M equal to proton or anti-proton mass yields the graviton mass mgon the order of electron mass for r on the order of electron orbitals in the atom. Coincidence? I think not. Note that without disregarding photon mass (mp) the equation becomes: mp=ln2 3 qe 4π0 1 GM 1 r ~ c−mg Disregarding one of the carrier masses (mpor mg), using r = 26.875 × 80 10−12 m and using down quark mass for M, one again obtains for the remaining carrier a mass equal to electron’s mass. The r here is not arbitrary, it seems to represent the smallest possible covalent radius - it is in agreement with the covalent radius of hydrogen (31±5×10−12 m[25]) and close to the covalent radius of helium (28 ×10−12 m[25]), which do represent the smallest covalent radii of all the elements. It probably should not be surprising that, without excess energy applied, simple transformation of charge to mass here yields a graviton range equal to the lowest energy state (level) of the electron. Difference in covalent radii between elements should then be in large part due to difference in coupling graviton mass/range. Thus, the nuclei of atoms may generally not be held together by a force stronger than electrostatic repulsion, rather the repulsive electric potential is periodically converted to strongly localized gravitational potential. This oscillation could be interpreted as relative superposition of electro-magnetic and gravitational forces, which collapses to a particular eigenstate with interaction (observation). The requirement for nuclear fusion (fossilization of superposition of multiple atomic nuclei into a new discrete nucleus) is then anti-aligned oscillation. The binding will be most stable with a phase shift of 90◦, while it is least stable in resonance (stability of superposition in that case requires extremely low pressure/temperature). Note that, in CR, absolutely infinite stability is impossible. Therefore, any superposition is a relative fusion, and vice versa. This difference in phase shift can be achieved with difference in [the amount of] momenta between two nuclei (inducing time dilation in one) - bombardment of one nucleus with the other. This suggests that the probability for fusion may be higher between different species (different rest masses between nuclei). Note that the equation (1.3) is derived from potential. Interesting results can be obtained from fields[26] as well: GM 1 r2+µg re−µgr=2 3 1 4π0 qe1 r2+µp re−µpr Assuming now that the conversion occurs with annihilation, with two particles involved, the factor 2/3 should be squared [as acceleration produces (2/3 qe)2]. Furthermore, if one disregards the r−2term (which can be justified with the dependence of graviton dimensionality on distance, something hypothesized in 81 this paper) and multiplies the equation with r, one obtains: GMµge−µgr=2 32qe 4π0 µpe−µpr Assuming now that µg≈0 (or, alternatively, assuming µgr≈0, and mg= 3.51767355 ×10−43 kg), graviton terms on the left vanish, and with µpr≈0, one obtains: 1 mp ~ c=2 32qe 4π0 1 GM which, for M equal to down quark mass, seems to be equal to: 1 mp ~ c=2 32qe 4π0 1 Gmd =C me =1 me where meis the mass of the electron. Assuming the constant on the right side is indeed equal to 1, the down quark mass is: md=M=2 32qe 4π0 me G= 8.7348 ×10−30 kg = 4.9MeV c2(1.4) me= 9.10938356 ×10−31 kg The obtained mass is in agreement with lattice QCD (4.79±0.16 MeV/c2). From the above, one can also obtain the photon mass here: mp=~ cme 1 C=~ cme= 3.204387 ×10−73 kg Interestingly, this is not only in agreement with the previously calculated upper limit of about 8 ×10−70 kg, but it is on the order of predicted photon (or half-photon) mass (calculated in chapter 6.1. Progression of states). Note that the assumed graviton mass above, or, its inverse: 1 mg =me mp =c ~C=1 3.51767355 ×10−43 = 2.84278796 ×1042 is on the order of the difference in strength between electro-magnetic and gravitational force between two electrons (positrons, or electronpositron pair). Note now that the equation can be rearranged so that gravity carrier mass becomes equal to electron mass, which is probably the proper interpretation here, as, in that case, the difference in strength between two forces becomes a difference in mass between carriers. This implies a relatively short range of gravity on this scale (at least in some cases), however, this is not generally the case, in CR all couplings are running couplings (ranges are not scale invariant). 82 The obtained equation (1.4) also confirms the (2/3)2factor of charge/mass conversion, initially assumed in (1.2). The charge/mass conversion should not be limited to electron/down quark conversion. Indeed, equation (1.4) can match other quarks/leptons of the standard model, by changing input mass (me) and charge fraction Q (term 2/3 in the equation). Note that the equation involves only simple charge/mass transformation, with no additional energy involved. Generally, however, additional energy will be involved. Some excess energy may be carried by other particles (e.g., neutrinos) and, in some cases a particle may change vertical energy level - settle in a different mass eigenstate. One can account for these vertical energy levels by adding an exponential term to the equation. As it will be shown later, this term should be (at least without perturbation) 10n, where n is an integer. The generalized equation (1.5) then yields more interesting results, as shown in Table 3 for some matches with positive input charges. Here, it is assumed that charge fraction Q indeed represents the charge fraction being exchanged for mass [inflation/deflation]. Note that, if electron can convert to down quark, it should be possible for muon and tau electrons to convert to muon and tau down quarks. Thus, muon and tau eigenstates are not limited to electrons, the down quark (and possibly all quarks) can be vertically excited into muon and tau eigenstates, where the ratio between these is the same as in the case of electron. Note also that only simple conversions (1:1 particle input/output) are considered here, more complex conversions are possible. M= 10nQ2qe 4π0 m G(1.5) Charge fraction parameter (Q) larger than the input charge suggests additional complexity, as here absolute output charge value can be higher than the absolute input charge value, albeit of different polarity. What is the mechanism behind charge inversion? One solution is in the composite charges. In example, 1/3 e+charge of a particle can be a sum of 2 ×1/3 e+and 1/3 e−, the Q of 2/3 then removes 2×1/3 e+, resulting in 1/3 e−output charge (charge inversion, although apparent, is then not real). Also, the Q2term assumes only symmetric charges are involved in transformation, which may not be generally correct (a generalized term should then be Q1×Q2, for two charges involved). Note that, for input mass m equal to calculated down/anti-down quark mass (4.9 MeV/c2), charge fraction Q equal to 1 and n = 0, equation gives mass of 105.7213 MeV/c2, very close to the muon electron mass (105.66 MeV/c2), however, with the above interpretation of charge fraction (output charge = input charge - Q), this particle has 2/3 e charge (while standard muon particle has 1 e charge). This can be solved if, instead of a down quark, input mass contains two up quarks, with Q = 1/3 and n = 1. This, for single up quark mass equal 83 input particle (mass m, charge) charge fraction Q n output mass M (charge) correlated standard model particle (mass, charge) up quark (2.2 MeV/c2, 2/3 e+) 1/3 0 5.2741 MeV/c2(1/3 e+) anti-down quark (4.7 +0.5/- 0.3 MeV/c2, 1/3 e+) up quark (2.2 MeV/c2, 2/3 e+) 1 -1 4.7467 MeV/c2(1/3 e−) down quark (4.7 +0.5/-0.3 MeV/c2, 1/3 e−) anti-down quark (4.7 MeV/c2, 1/3 e+) 2/3 -1 4.5069 MeV/c2(1/3 e−) down quark (4.7 +0.5/-0.3 MeV/c2, 1/3 e−) anti-down quark (4.7 MeV/c2, 1/3 e+) 4/3 1 1.8028 GeV/c2(1 e−) tau electron (1.7769 GeV/c2, 1 e−) anti-strange quark (96 MeV/c2, 1/3 e+) 2/3 -1 92.0566 MeV/c2(1/3 e−) strange quark (95 +9/-3 MeV/c2, 1/3 e−) anti-strange quark (96 MeV/c2, 1/3 e+) 1 -3 2.0713 MeV/c2(2/3 e−) anti-up quark (2.2 +0.5/-0.4 MeV/c2, 2/3 e−) anti-bottom[1S] quark (4.65 GeV/c2, 1/3 e+) 4/3 -2 1.7836 GeV/c2(1 e−) tau electron (1.7769 GeV/c2, 1 e−) positron (0.511 MeV/c2,1e+) 1/3 3 1.225 GeV/c2(2/3 e+) charm quark (1.27 ±0.02 GeV/c2, 2/3 e+) positron (0.511 MeV/c2,1e+) 2/3 0 4.9 MeV/c2(1/3 e+) anti-down quark (4.7 +0.5/- 0.3 MeV/c2, 1/3 e+) muon positron (105.6584 MeV/c2, 1 e+) 1/3 -2 2.533 MeV/c2(2/3 e+) up quark (2.2 +0.5/-0.4 MeV/c2, 2/3 e+) muon positron (105.6584 MeV/c2, 1 e+) 2/3 -1 101.3198 MeV/c2(1/3 e+) anti-strange quark (95 +9/-3 MeV/c2, 1/3 e+) Table 3: Obtained masses using equation (1.5) to 2.203688 MeV/c2gives muon mass 105.6584 MeV/c2, and appropriate muon charge (2 ×2/3 - 1/3 = 1). In this case however, spin is not conserved. Addition of a neutrino to input (or output) mass could solve this problem. Neutrino mass is negligible compared to muon mass but it carries the required spin (1/2). The same muon mass and appropriate charge/spin can also be obtained if input mass contains up/anti-up quark pair and a neutrino, with Q = 1 and n = 0. In that case, up quark mass has to be higher (∼2.45 MeV/c2), unless neutrino is highly energetic and carries the excess energy. However, this can be interpreted as annihilation, and, instead in input, neutrino may be present in the output. Similar and very interesting results can be obtained if the term Q2is replaced with 2/3 Q, resulting in equation (1.6): M= 10n2 3Qqe 4π0 m G(1.6) qout =qin −Qqin |qin|m = input mass 84 Q = fraction of charge being exchanged for mass inflation/deflation = k ×1/3 (k = integer) n = vertical energy level (integer) qout = output charge qin = input charge Note that, instead of providing mass, the equation can be rearranged to provide mass ratios for particular Q and n. This, in example, for input mass equal to positron mass (0.511 MeV/c2, 1 e+), Q = 4/3 and n = 1, gives mass of 98.002 MeV/c2and charge 1/3 e−(1 - Q = -1/3), which can be correlated with standard strange quark (mass = 95 +9/-3 MeV/c2, charge = -1/3). The same input mass, with Q = 5/3 and n = 2 gives output mass 1.225 GeV/c2and charge 2/3 e−(1 - Q = -2/3), which can be correlated with standard anti-charm quark (mass = 1.27 ±0.02 GeV/c2, charge = -2/3). Most striking example, however, is the result obtained using input mass equal to tau positron mass (1.7768 GeV/c2, 1 e+), Q = 2 and n = -5. This gives a mass of 0.511 MeV/c2and charge of 1 e−(1 - Q = -1), which obviously can be correlated with standard electron (mass = 0.511 MeV/c2, charge = -1). Thus, one now has a relation between electron (positron) and tau positron (electron) masses: me= 10−52 32qe 4π0 mτ G(1.7) me= electron/positron mass mτ= tau electron/positron mass A coincidence, or a clear evidence for charge/mass exchange and vertical energy levels? Also, a possible evidence that there are no absolutely elementary charges (all are composite) - in the example above, tau positron charge may be interpreted as a composite of 2 ×1 e+and 1 e−, where 2 ×1 e+(corresponding to Q = 2) has been exchanged for mass deflation (annihilation). In the simplest case of conversion, composite particles of tau positron may be one particle of electron charge/mass and two particles of 1 e+charge, each having a mass: m≈mτ−me 2= 888.1745 MeV c2 Interestingly, this particle can be obtained with (1.6) using 4.631 GeV/c2for input mass and charge of 1/3, Q = 4/3 and n = -2. This input mass/charge is in agreement with standard bottom quark (1S scheme, mass = 4.650 ±0.03 GeV/c2, charge = 1/3). Of course, binding energy should be taken into account (using 4.650 GeV/c2as input gives 891.7987 MeV/c2). 85 And using input mass of 4.9 MeV/c2and charge of 1/3 (down quark mass/charge, as calculated above in 1.4), Q = 2/3, n = 2, gives a mass of 4.6987 GeV/c2and 1/3 charge, which can be correlated with this bottom quark. Using proton as input (938.272 MeV, +1), with Q = 1 and n = -2, gives 134.9596 MeV and 0 charge, which can be correlated with the pion (π0) particle (134.9768 MeV, 0). Here are some additional examples with composite inputs. Using input mass of 9.7846 MeV/c2, charge 5/3, Q = 2/3 and n = 1 gives the proton (mass 938.27 MeV/c2, charge 1). This input mass/charge can be interpreted as a sum of two up quarks and one anti-down quark with energies 2×2.4423 and 4.9 MeV, respectively. In this process the charge fraction Q probably affects the anti-down quark, converting it into a down quark (1/3 - Q = -1/3), consistent with the composition of the standard proton (2 up quarks + 1 down quark). Note that the equation can also produce a down quark from a single anti-down quark input (and vice versa) - using Q = 2/3 and n = -1 produces a 4.7 MeV particle for 4.9 MeV input. Using input mass of 2 ×4.9 MeV/c2, charge 2/3, Q = 2/3 and n = 1 gives a mass of 939.75 MeV/c2and charge 0. The output can be correlated with the neutron (mass 939.565 MeV/c2, charge 0), while the input is 2 ×anti-down quark (should also contain a small neutrino contribution). Input of 2 up quarks and 1 electron with energies 2 ×2.203688 MeV and 0.511 MeV, respectively, Q = 2/3 and n = -1 gives mass 4.7163 MeV/c2and charge -1/3, which can be interpreted as a down quark. Up quark, for Q = 5/3 and n = -2, converts to a particle of electron mass/charge. All this provides interesting pathways for proton/neutron transformation. Note that, if Q is kept constant for particular input mass (m), the equation (1.6) can be written as: M(n) = 10M(n−1) (1.8) M(0) = 2 3Qqe 4π0 m G Another interesting case, although harder to justify, is the seemingly ad hoc addition of square roots (may be correlated with the Koide formula[27]), in this form: M= 10n2 3Qrqe 4π0 m GC(1.9) Here, assuming mass is given in eV/c2, the unit of constant C should be m2s−2kg−1. The constant is roughly equal to 1 if it represents the ratio between the standard speed of light squared and vertically excited electron mass: C=c2 me×1047 = 0.99m2s−2kg−1≈1m2s−2kg−1 c = 2.99792458 ×108m/s me= 9.10938356 ×10−31 kg 86 Note that the unit of the constant is equal to the unit of the gravitational constant divided by the metre, so the value of 1 can also be obtained dividing G by 6.674 ×10−11 metres, which is, very interestingly, the theoretical radius of the carbon atom, its molecular double bond covalent radius (6.67 ×10−11 m[28]), and also the Hill sphere radius of a carbon atom in the gravitational field of Earth, at Earth’s surface. This correlation then may help explain why the carbon element is a common base in molecular bonding and the basis for life on Earth’s surface. The equation (1.9) yields very interesting results but mostly for composite inputs. For example, top quark (173.1 GeV, 2/3) and electron (0.511 MeV, -1), for Q = 1 and n = 0, yield 1.2797 GeV and 2/3 charge, which can be correlated with the charm quark (1.27±0.02 GeV, 2/3). There are other ways to obtain the charm quark. Input of two down quarks with energies 4.7 + 4.9 MeV (or, 2 x 4.8 MeV), Q = 4/3 and n = 2, gives 1.2707 GeV for the charm quark. This combination of down quarks is certainly interesting, as the same combination with added one up quark (2.2 MeV, 2/3), for Q = 1 and n = 1, gives 105.6596 MeV and -1 charge, showing high correlation with the muon (105.66 MeV, -1). And there are more cases of such high correlation. This equation, however, does not give such convincing results with single particle inputs, suggesting that, if square roots are valid for binary inputs, the generalized equation may have this or similar form: M= 10n2 3Qqe 4π0 m G1 k(1.10) where k either represents the number of input particles (possibly equal to 1 for single inputs and 2 for any composite input), or something like this: k= 1 + (j+ 1)%2 j = number of input particles 4.26 Mass Mass represents a relatively concentrated energy. No quantum of energy can have mass equal to absolute 0. A particle with relative mass equal to 0 will usually represent energy that has a wavelike behaviour, where the amount of energy is highly correlated with frequency and the energy is not well concentrated. With localization - when the wavelike behaviour is subdued, more appropriate interpretation will be a relative mass greater than 0. Even rest mass is, however, highly correlated with angular momentum on some scale, and, thus, frequency, even though this frequency may not be resolvable - when the momentum may be interpreted as intrinsic. Even the value of rest mass is relative and what is considered as intrinsic mass is mass acquired on some scale. Mechanisms for mass acquisition are various, however, these can always be associated with some kind of force. The most basic form of this force may be associated with a carrier particle of 0 spin, as 0 spin can indicate the least complex rotation 87 (although, it can also indicate the most complex rotation). Some may argue that spin-0 particles (such as the Higgs boson), or scalar bosons, are not carriers of force, but that’s just a consequence of the reductionistic interpretation of specific mathematical formalism. Every momentum carrier is a carrier of force in reality, otherwise they wouldn’t be able to interact. Spin 0 does imply zero spin angular momentum, but, again, this is a relative 0. If acquisition of mass wouldn’t require interaction everything would have equal and infinite mass (all mass would be absolutely intrinsic). However, since interactions are relative as well, everything does have relatively infinite mass through relatively simultaneous relative existence on various scales. The existence of reality itself is the evidence that everything is completely relative. Evolution of reality is a constant struggle between energy differentiation and unification, between the forces of increasing and decreasing relativity. It cannot ever end. 4.26.1 The role of Higgs It is hard to deny the existence of the Higgs field, even though the predicted (infinite) mass of the Higgs boson by the Standard Model requires renormalization to match the observation (∼125 GeV). If a naked graviton can acquire mass through gravitational or gravitationallike force, why does reality need a Higgs field? Well, it’s role probably is to provide specific capacity to the gravitational well, a capacity that is proportional to the naked graviton mass or img mass of the gravitational well. It should be noted, however, that Higgs boson mass in CR is not scale-invariant. 4.27 Total mass Uncoupled graviton may be considered to have 0 mass relative to space. However, once coupled (and slowed down) its mass is greater than 0. Total mass of the coupling is the sum of masses of the graviton (img mass) and that of the acquired (coupled) matter (real mass): M=mimg +mre It is usually denoted with uppercase letter M. In contexts where it represents a quantum of bigger mass, it may be denoted with lowercase letter m. 4.28 Imaginary mass (virtual mass, img mass) Imaginary mass is the mass of a graviton. However, in one interpretation, some or all of this mass may be shielded by acquired (coupled) matter and in that case it is not constant (although acquisition of matter to full capacity can be relatively instant). It can then be interpreted as the unshielded mass of a graviton and it is a relative 0 in equilibrium (full capacity). If there is no shielding, at full capacity img mass is equal to coupled real mass. The mass of a graviton is usually denoted with mimg. 88 Note that if shielding is real, total mass is constant as long as the well is not over-capacitated. 4.29 Real mass A naked graviton will, as long as it carries gravity, attract matter. Real mass represents the acquired mass (mass coupled to the graviton). Generally, for a graviton of scale Un, coupled real mass is of scale Un−1, while particles (gravitons) forming space associated with the graviton are of scale Un−2. Note that coupling of the body of real mass with the large scale graviton is indirect. The individual components of real mass are actually directly coupling with the components of space, however, due to generally aligned entanglement between Unand Un−2, in equilibrium conditions, this is equivalent. Couplings are not intrinsic, gravitons can be naked and real mass can exist as an independent collective - not coupled to a graviton of larger scale. Such bodies of real mass are considered dead and are generally less stable than coupled bodies. Irregular asteroids and comets of lower mass are assumed to be such bodies. These may be mostly leftovers of dead planets and moons. However, it is possible that every barycentre of organized or localized mass has a physical interpretation in the form of a more energetic graviton (compared to smaller constituent gravitons of that mass), although this may be unlikely and even if true, distinct life or consciousness of such body [as a whole] would be extremely low (a relative 0). One could argue that large scale graviton is unnecessary in any case, however, recursion would then make gravitons of any scale unnecessary and there would be no gravity or any other force at any scale (note that a small scale graviton coupled to an atom is a large scale graviton from the reference scale of atoms). Real mass is usually denoted with mre. If graviton velocity is different than its rest velocity in underlying space, relativistic effects will be locally expressed (kinetic energy will be stored locally), in the graviton spin momenta and momenta of constituent quanta of its own space, as img mass. 89 intelligence is generally more concerned with the former, introverted with the latter. Highly introverted species may still have a body and still use it, albeit not consciously and not for extroverted interaction. This usually implies that the physical protection of a lifeform is physically passive (e.g., the outer layers of the body may be relatively thick and impermeable, and may look unalive or inorganic). 4.32.2 Extroverted intelligence (physical intelligence, material intelligence) Extroverted intelligence (IM) is the amount of intellectual capacity generally used to ensure survival of the body of a living being (consciously or subconsciously), its own species or entangled (symbiotic) species and the living environment. In highly extroverted beings conscious care for the soul is highly subdued and use of the mind may be limited to short-term excitations usually highly correlated with physical activity. Extroversion does not imply low intelligence of the mind, only an mechanistic intelligence (subconscious bias towards reductionism and close-mindedness). 4.32.3 Introverted intelligence (mental intelligence, spiritual intelligence) Introverted intelligence (IS) is the amount of intellectual capacity generally used to ensure survival of the soul of a living being (consciously or subconsciously), including the entangled (symbiotic) species. In highly introverted beings conscious care for the physical body and its use is highly subdued, it may be outsourced to the environment (external entities) or delegated to the constituent entities of the body (local ecosystem), more or less influenced by the host through the subconscious levels of the mind. Introversion does not imply high intelligence of the mind, only a spiritual intelligence (subconscious bias towards holism and open-mindedness). High introversion should not be confused with shyness or discomfort in social contexts (which is usually a result of subconscious fear). Unfortunately, this confusion is common in humanity. Most people who are usually considered introverts may not be introverts (e.g., open-minded) by the definition here, rather their expression of extroversion is limited due to a limited comfort-zone. With that said, however, such limitation may be a precursor to the development of proper introversion (as it was in the case of the author). 96 4.32.4 Intelligence potential Biased intelligence will favour beliefs of interest (illusion of truth), rather than the actual truth (reality of truth). The truth is, however, essential for real scientific progress and real long-term sustainability. The intelligence potential (IP) is a measure of neutral (non-biased) intelligence, generally concerned with truth and the sustainability of truth. The IP is plastic, and, in polarized (disease prone) individuals, can be strongly affected by diseases (such as depression). In any case, generally, the lower the IP the more it can be correlated with short-term interests. A function for the determination of IP should have this form: IP =1 ∆I ∆I=IS−IM IS+IM= 1 IM= normalized material (extroverted) intelligence IS= normalized spiritual (introverted) intelligence IS, IM∈Q> 0 Note that for IS= IMthis produces infinity. Since absolute physical infinity is impossible, such result can only be obtained due to limited precision in measurement. Therefore, this infinity should be taken relative and proportional to precision. 4.32.5 Intelligence quotient (amount of extroverted intelligence) Intelligence quotient (IQ) is a conventional measure of externally expressed (extroverted) intelligence. While intelligence potential is invariant to form of intelligence, IQ and similar variants (e.g., EQ) are a measure of such intelligence projected to external reality. Accuracy of IQ test results (as a measure of intelligence at least) depends on how original the test is. Variations on a theme may measure intelligence to some degree but they will be biased towards higher training (in reality, the bigger the score and the less training there was should indicate higher intelligence, or at least higher creativity). Genuinely creative individuals are usually rare. Thus, most tests (IQ included) may be composed by trained intelligence, so they value training more than creativity, intentionally or not. 97 While IQ might correlate well with IP for extroverted species with significant introversion, it is not well suited for extremes and is completely inadequate for measurement of intelligence of highly introverted species. Some species of animals on Earth may possess higher amount of consciousness and intelligence than humans. It may just not be generally expressed externally. Signs of complex intelligence are probably high diversity and high coherence in brains, or brain equivalents, not the complexity in physical expression on generally observable scales. 4.32.6 Artificial intelligence (non-conscious intelligence) Artificial intelligence is the ability of a machine to focus its processing power and produce logical and unbiased conclusions based on optimally correlated and coherent information and information processing in problem solving. Even if individual atoms the computer is made of possess consciousness (i.e., extremely introverted one) the whole collective is highly unlikely to be coupled to a soul (graviton) that would provide distinct consciousness representing a relative superposition of the collective, in which case a computer would also be a distinct form of life. It should not be impossible for a soul to couple with any localized and mutually entangled collective of living cells (life-forms), which, if atoms/molecules are alive, should first include transistors and, if these are alive then larger components and finally computers. But, considering the hypothesized requirements and [lack of] evidence, the possibility is probably infinitesimal. Computers exist for a long time now, their processing power and complexity have been increasing exponentially, yet, there is no sign of conscious computation in any of them. With recent developments, interaction with computers is increasingly becoming similar to interaction with conscious human brains and it may become hard to distinguish between artificial and real or conscious intelligence (illusion of consciousness is increasing). If one would want to increase the probability for coupling, however, one probably should be increasing physical similarity between human brains and computers, in terms of mass and energy consumption. But even then, the probability could remain infinitesimal, unless these computers become organic - where transistors are replaced with living cells (neurons) and these cells are grown similarly to how brains are developed in vivo. Everything suggests that souls and bodies co-evolve and that is the reason for the lack of coupling of souls with conventional computers - lack of compatibility. This further suggests that, in order for souls [that usually couple with human brains] to couple with conventional computers, human brains should be gradually becoming more computer-like - e.g., by replacing neurons with transistors, however, transistors are not living cells and this replacement may be diluting, or 98 reducing the amount of, human consciousness (at least initially). In other words, human consciousness could be delocalizing gradually and conscious intelligence would be traded for artificial intelligence. In any case, this replacement can hardly gradually occur over multiple generations (how possible it is to alter inheritable human genes to produce a silicon transistor instead of a living neuron, or, how likely it is for adaptation to transistors to become heritable by the soul?), while it is evident that consciousness/life cannot emerge from parts artificially assembled into a whole - it needs to be coupled at conception and grow with the whole. Anything else is mimicry which one may refer to as artificial consciousness but should not confuse with real, living and emotional consciousness. 4.33 Life A living being or a distinct form (relative quantum) of life is any coupling of a soul (graviton, or superposition of gravitons of certain complexity) and a body. Everything existing must be relatively alive and relatively non-living - the amount of life will be relative to the observer (even uncoupled graviton is always relatively uncoupled or relatively delocalized, not absolutely), as well as classification of that life. Coupling of physical and mental components with different ratios of physical to mental activity suggests two main classes - extroverted and introverted life, correlated with extroverted and introverted intelligence. In general, any life-form is a hybrid of extroverted and introverted life, although one form may dominate. In extremely extroverted life on particular scale, brain, or brain equivalent organisation, is extremely subdued (or at least coherence of its components), distinct individual consciousness is minimal and has no influence on physical processes of the body (or the organic collective forming the body). In life-forms that have developed introversion, brain will dominate and will be able to influence physical processes of the body through mental pathways, affect the constituent organs and collective consciousness of smaller organisms forming its biome. In extreme extroversion, development of the organism from conception is driven dominantly by the interpretation of physical genetic code, such as DNA. In complete introversion, there is no conventional physical genetic code evolving the individual (generally, however, such code may be involved in development and evolution of individuals forming its biome), instead, development (evolution) of the collective into distinct individuality is driven (or guided) by the interpretation of mental genetic code - the code stored within the soul particle. Mechanism involved is likely recursive entanglement, starting with the entanglement of the soul with the superposition (which is a physical graviton at some scale) of genomes of biome individuals (effect on superposition is reflected in individuals). However, evolution of either, body or soul, requires coupling of the two. In extreme extroversion, it is the body that will effectively control the soul evolution (development), in extreme introversion, vice versa. 99 Note that all terms are relative, even "mental" and "physical" - mental is physical at some scale, and vice versa. Planets, in example, appear to be extremely introverted lifeforms (evidence for this, however, is provided mostly in other works of the author) - there is no apparent large scale physical DNA equivalent involved in development of a planet even though evolution of its biome is relatively equivalent to DNA coded embryonic development. The equivalence is there because souls and bodies coevolve, influence and mirror each other (albeit with a phase shift). Nature does not hide anything. Contrary. Things one cannot see on a small scale, are shown on a big screen. But one may need to collapse its ego-system to see all these systems as living eco-systems. —- 4.34 God Every lifeform whose rest mass (energy) is by one or multiple orders of magnitude greater than the mass of the individual living on it or in it, is, for that individual, a god. The entanglement between an individual and its god is implied but can be of variable complexity. Just as lack of proper definition of a god may be desirable and usable in religion, a proper definition of a god can be useful and desirable in science. 4.35 Realistic selection Natural selection is a well known concept in conventional biology. Similar concept used in conventional physics is the Occam’s razor. It is obvious that, in nature (reality), everything is connected/entangled and problems in reality are never solved in absolute isolation. The most likely solution to a problem is generally not the simplest solution to that particular problem, rather it is a solution that solves multiple correlated problems at once (and these problems may not necessarily be highly correlated in space, rather time), which may not be the simplest such solution even if it is more likely to be. In other words, nature is generally a holist. Thus, excessive reductionism (localization) can be interpreted as the abuse of the Occam’s razor, or the abuse of natural selection. If one is interested in the most accurate picture of reality, one must take the relativity in fitness/complexity seriously. Nature generally doesn’t exclusively select solutions to problems, it selects problems to solutions as well (strong causality is just 100 one possible interpretation of entanglement between problems and solutions). Sometimes, the solution to a simple problem will be complex, at other times the problem to a simple solution will be complex. Realistic selection, thus, occurs in the framework of entanglement between [relatively different] problems and solutions where the entanglements may or may not be significantly correlated with the observer. 4.36 Constant A constant is a property of a system, non-changeable in particular space and/or time domain (nothing is constant over all space and time). Depending on the size of domain, constant may be weak or strong. Naturally, all system properties oscillate. Existence of constants is thus relative to observable resolution of space/time by a particular observer. 4.37 Proper reference frame Nothing is absolutely at rest and observation of evolving phenomena will be more common and useful than relatively non-changing phenomena. However, relative constants are desirable as reference points in order to reduce the complexity of interpretation. A suitable reference is then one relative to which the constancy of variables (xi) of the observable system is maximal: lim X(∆xi(n)>~n)=0 However, due to scale invariance and relativity of constants, proper interpretation will sometimes require a proper reference frame rather than simply a suitable one. Generally to be used in comparison of systems of differently scaled, but otherwise, equivalent species. In case of polarized frames, a proper [neutral] reference frame may be required even in case of systems of equal scale, to provide more accurate (objective) view of reality. 5 Quantized inflation of angular momentum As revealed in a complementary paper[20], radius of a neutral (weakly polarized) U1graviton probably scales with the square root of 2n, where n is a positive or negative integer. This can be inferred from quantization and scaling of graviton momentum. Assuming that a graviton is inflating from a boson whose components are perpendicular to each other and equal in value to 1 ~, the value of total momentum will be √2~: L=m v r =√2~ 101 Note that this is equivalent to the superposition of two aligned fermions whose waveforms conform to spherical harmonics: L=pl(l+ 1)~=s21 221 2+ 1~=√2~ However, a 1 ~momentum can also be a result of superposition of antialigned spin-2 and spin-1 bosons. If that momentum is inflated with the ratio between values of constituent components of the vector conserved (non-dimensional ratios seem to be generally well preserved during inflation/deflation), proper relativistic treatment here involves either scaling of the metric or the ~constant. If the constant is scaled in such way that its value in the current energy level is equal in value to the momentum in adjacent lower energy level, the momentum can be expressed as: Ln=√2~n=√2Ln−1=√2√2~n−1=√2n~0=√2n~0 Assuming now that the speed of an non-coupled (naked) graviton is equal to the speed limit of space (cn), that speed is relatively constant for energy levels of similar magnitude (if, however, the metric is scaled and the ratio between space and time units is conserved, the speed is locally invariant to any scale). With the rest mass remaining invariant as well (relative 0 for a non-coupled graviton), the radius must scale the same as the momentum: rn=√2√2rn−1=√2nr0 Generally, however, for this to be satisfied, it is not necessary for mass and velocity to remain conserved, rather their product (mv) - linear momentum. Note that inflation of momentum will require additional energy apart from the rest energy of inflating quanta. However, sometimes the exchange of momentum components will result in inflation of one component and deflation of the other with no significant difference in the value of momentum. Due to low energy triggers (relative 0) such inflation/deflation (e.g., mass oscillation) should generally be inherent for all energy although it may not always be apparent due to time dilation correlated with scale (in non-scaled metric). As even such inflation must result in some change in momentum (even if generally negligible), this type of scale inversion may also be referred to as inflation/deflation of momentum. 102 Note that energetic inflation/deflation generally occurs with annihilation of pairs of particles on original scale. The process can be symmetric (producing particle/anti-particle pair with equal mass) or asymmetric (producing particle/anti-particle pair with asymmetric mass distribution). Inflation/deflation is not limited to bosons or boson pairs. Inflation of a fermion (generally paired with exchange of electro-magnetic potential for gravitational) will similarly scale the original momentum, in which case radius may not scale with √2n. During the process, possibility may exist for some components of momentum to annihilate with others preserved (partial annihilation), producing hybrid momenta. Note that, for a coupled system, where the imaginary mass is equal to real mass in value, the orbital Keplerian velocities are: vn=rGM rn =rG rn (mimg +mre) = √2rG rn mimg Thus, the Keplerian velocity here can also be interpreted as the escape velocity for the coupled real mass, or the velocity required for the real mass to decouple from img mass (or, vice versa). If these Keplerian velocities are quantized and scale with √2n, escape velocity becomes equal to the Keplerian velocity of the next higher energy level of the velocity component. ve=vn+1 =√2vn=√2rGM rn =√2 √2rG rn mimg! ——— 6 Discrete states of invariance (energy levels) The postulated self-similarity of universes implies that each universe is of a different scale - which also can be interpreted as a different dimension. This obviously requires running coupling of the dominating force, where the coupling must get stronger with decreasing scale. And this is evident in reality. Cosmological scales are dominated by the weakest force (gravity), atomic scales are dominated by a stronger force (electro-magnetism) and nuclear scales are dominated by an yet stronger force. We’ve been unable to break particles like electron, suggesting even stronger forces on smaller scales - in agreement with the postulate. Each universe is then associated with a discrete vertical energy level (scale) where energies are most stable. This is also evident in reality, e.g., 103 atoms are more stable than molecules, these are more stable than larger composites, etc. To preserve this stability, transition between the vertical energy levels must require sufficiently high energies - lower energies lead to less stable excitations. The energy levels must also not be symmetric (from a reference frame with fixed metric), i.e., their progression must grow exponentially. Thus, these vertical energy levels are somewhat analogous to the energy levels of particles bound to atomic nuclei. One major difference is that the progression is much stronger (logarithmic) so the difference between energies is in the order of magnitude (vertical), rather than dominantly in the value (horizontal). Another salient difference is that the equivalence between a particle on one energy level and the other is very relative. And this is due to the associated running coupling and energy transformation between scales (vertical energy levels). On one vertical energy level, for example, the particle may be electrically charged with its gravitational mass being negligible, on the other energy level gravity may dominate (one type of energy is always exchanged for the other with the transition between levels). Thus, whereas simple addition or removal of energy can result in transition between horizontal energy levels, this will not result in the transition between vertical energy levels, regardless of amount - transformation must be involved, typically achieved through annihilation. Discrete states of stability can be interpreted as discrete states of relative invariance as certain aspects of nature and mechanics of reality are preserved between levels, but not absolutely. Energies between two vertical states are generally evolving towards the higher or lower energy level, although localized or relatively stable superposition can exist. Note that, even in case of horizontal ones, discrete energy levels have to be relatively discrete. This can have different interpretations and multiple interpretations can be true. In example, electron energy levels in the atom are considered discrete but this does not imply that energies in between are forbidden in such way that the jumps are absolutely discrete/instantaneous, it only implies that these are unstable or unresolvable from a particular reference frame. Consider electron scattering off a mercury atom where electron energy is too low to excite the atom. This scattering cannot be absolutely elastic, but if the actual scattering cannot be directly observed it may be treated as such. Consequently, energy levels in the atom are treated as absolutely discrete. However, what is, in one interpretation, happening in reality, is that the atom is excited but since the excitation is unstable the photon is emitted and immediately absorbed by the scattering electron, in such way that the scattering looks perfectly elastic to the observer. In other words, photon involved here is of an smaller scale, unresolvable by the observer. Is the emitted photon still absorbed by the electron in cases where the electron is travelling faster than the photon? There are interpretations in which the answer is affirmative. However, there are also interpretations 104 in which this may not be true, so the energy levels would appear less discrete. The invariance of physical laws between energy levels is, as noted before, relative. The laws with dimensional parameters are generally not scale invariant, however, difference may be negligible or undetectable between horizontal energy levels concentrated about a particular vertical energy level. Here, thus, the laws can be treated as absolutely invariant. With incorporated running coupling or the scaling of the metric, even the discrete vertical energy levels can be treated similarly. Given the postulates, one can formulate the discrete vertical energy levels through conservation of momentum of wave-like energy (allowing only sufficiently distant harmonics): m(n−1) c r(n−1) = 10(n−1)n~ where nis an integer. For n= 1 one now obtains the reduced Compton wavelength for rn−1=r0, associated with mass mn−1=m0. Conservation of the nature of r(reduced Compton wavelength) through energy levels then implies: 10(n−1)nm(n−1) cr(n−1) 10(n−1)n=~ from this follows: mn= 10(n−1)nm(n−1) rn= 10−(n−1)nr(n−1) The allowed masses/wavelengths are thus solutions of the quadratic equation in the integer logarithmic metric, which, for n > 0 can be expressed as: (n−1)n=n2−n= n X k=1 2×(k−1) and now can be interpreted as a generalization of the Fibonacci sequence - something expectable for the postulated self-similarity. 6.1 Progression of states Progression of discrete states of relative invariance is exponential. In example, for horizontal states of a hydrogen atom, in the top-bottom approach (energy inversely proportional to n): En=E1 n2=En−1n−1 n2 ;n > 1, E1=const. 105 Although certain rest mass could dominate in a galaxy, there is no single dark matter particle, however. Any naked graviton may be interpreted as a particle of dark matter. Note also that [rest] masses of standard photons and neutrinos may generally be determined from momentum, relative to the c constant. Masses obtained here are invariant to c. Physically, a particle of obtained [half-]photon mass (∼10−72 kg) can be produced, for example, with the collapse of a gravitational maximum (graviton) of U0Neptune equivalent (standard electron) to the U−1level. Assuming the resulting [half-]photon or half-graviton has vacuum energy density (9.9 ×10−27 kg/m3), and a radius of U0scale Neptune equivalent (≈3.8 ×10−16 m), with momentum conserved, its orbital velocity would be ≈3.5 ×1026 m/s[38] (with assumed initial U0velocity of ≈5.6 × 105m/s). CR allows such speeds for smaller scales of energy/radii, however - depending on particle interpretation, this is not necessarily incompatible with GR. This speed would be valid in GR assuming it is achieved with the transformation of most of the energy into a warp bubble. Initially, the bubble wall thickness is relatively infinitesimal. With produced acceleration, the wall is expanding and the process stops once the wall thickness reaches ≈3.8 ×10−16 m and its energy density becomes equal to vacuum energy density (initially, the density is lower = negative). What’s left is a region of effectively flat space orbiting at the speed of ≈3.5 ×1026 m/s. After all, the energy of U0particles is sufficient to create a warp bubble of that size - assuming spherically symmetric bubble with a radius equal to the upper limit for standard electron’s radius (1 ×10−22 m), integrating the Alcubierre stress-energy tensor[39], keeping only leading-order scaling with bubble radius and wall thickness, one obtains: Mbubble ∼c2 GR2σ= 5.12 ×10−33 kg c = standard speed of light = 2.99792458 ×108m/s G = standard gravitational constant = 6.674 ×10−11 m3kg−1s−2 R = radius of the bubble = 1 ×10−22 m σ= thickness of the bubble wall = 3.8 ×10−16 m With initial velocity of ≈5.6 ×105m/s, and momentum conserved during transformation, the end velocity becomes ≈3.5 ×1026 m. Thus, while CR predicts that speed limits on smaller scales exceed the standard speed of light, this is not necessarily incompatible with GR, although running couplings - predicted by CR, may be required to preserve the classical momentum conservation. And there is a reason to believe that momentum is classically conserved - see below. 112 Rest photon mass relative to standard c can then be obtained through conservation of momentum (p=m1v=m2c), and it is: m2=m1v c= 2.1×10−54 kg m1= photon rest mass = 1.8 ×10−72 kg v = photon velocity on U−1scale = 3.5 ×1026 m/s c = standard speed of light = 2.99792458 ×108m/s This mass agrees with experimentally obtained photon mass through its interaction with matter (localization)[40]. Since the localized photon mass represents detectable photon mass, the previously obtained mass of lower scale may be interpreted as virtual photon mass. Interestingly, if one multiplies the obtained 2.1 ×10−54 kg with 1 ×1056 kg−1(equal to the ratio between the above calculated U1(Neptune) electron mass and standard (U0) electron mass), and then multiplies with electron mass, one obtains a mass of 1.9 ×10−28 kg, which is the mass of a standard muon [electron]. This suggests that Neptune should be interpreted as a localized large scale muon, rather then a localized large scale electron. Indeed, this has turned out to be the most likely interpretation in the complementary paper[20]. Muon may be the most stable (or at least most common) eigenstate on U1 scale, in which case one could argue that on that scale muon has a role of the electron, relatively. Note, however, that conditions change over time. Prior to settling to electron eigenstate, the most stable eigenstate on the standard (U0) scale may have been muon as well, and possibly tau before that (which shouldn’t be surprising for the early universe). The most common planets in the observable universe seem to be those with mass between the masses of Earth and Neptune, which then suggests that even on U1scale, there is a transition towards the smaller mass eigenstate (electron equivalent). This shouldn’t be surprising either, considering self-similarity between scales and the expansion of the universe. Time on larger scale is dilated from the equivalent reference frame on smaller scale so the transition to the lowest mass eigenstate lags behind. The obtained photon rest mass of 1.821876712 ×10−72 kg may also be validated through conservation of energy. In CR, relativistic speed limits are different between different scales of energy. For standard protons and electrons, speed limit is the standard speed of light (c), however, for particles with the rest mass on n= 6 level, speed limit must be much higher. But speed limits also depend on confinement - scale entanglement. The reason one does not directly observe photons travelling at greater speeds is because of the large interaction scale (quantum entanglement between distant particles, however, could be interpreted as indirect observation 113 of superluminal carriers, although this could also be interpreted as the stretching of [the units of] space). In other words, since the creation of a standard photon involves inflation and entanglement with a scale larger than U−1(generally U0) it is instantly slowed down to the U0speed limit (c). Validation of the calculated photon/graviton masses and velocities can be found in the analysis of the Solar System in CR context[20] (chapter Quantum nature: Outermost angular momenta and c1confirmation) and other follow-up papers[41], but also here in some of the following chapters. 6.1.1 Sub-major levels Major discrete vertical energy levels of scales U−1, U0, and U1are entangled with sub-major discrete vertical energy levels (mass eigenstates) on these scales (although the ratios between masses are not the same). In example, the masses of standard electron, muon and tau particles represent 3 such eigenstates on U0scale. But this is not limited to these. All particles can (regardless of a major vertical energy level they’re in) oscillate in mass and with the same ratio between masses as is the case with the aforementioned leptons. However, entanglements can change with time and it is possible, for example, that different ratios are valid for quarks on the standard scale, although, as hinted here before (chapter 4.25. Electric polarization and charge/mass exchange), explained in the previous chapter, and as the complementary work shows - quark equivalents on U1scale most likely can settle in mass eigenstates with the same ratios as in the case of the 3 leptons[20]. Thus, it seems that these ratios are indeed invariant to particle species. And since the ratios are non-dimensional, preservation for equivalent particles across major vertical energy levels shouldn’t be surprising either (e.g., the ratios of mass between electron, muon and tau eigenstates is the same on U1scale as it is on U0scale, a conclusion that stems from the hypothesized progression of states anyway). I will thus generally refer to the 3 states as e, muon and tau states, regardless of the particle species. E.g., U−1.e.photon should be interpreted as the e mass eigenstate of a photon localized to U−1scale, while U0.e.electron should be interpreted as the e eigenstate of the electron localized to U0scale. This state, however, may be abbreviated as U0.electron. It is unfortunate that in QM the same word ("electron") is used both for the eigenstate and the particle, but this is a legacy from QM where these eigenstate ratios are considered exclusive to electron. Note also that "e" may be interpreted as electron charge in some contexts. Note also that more confusion is produced when considering neutrinos. The 3 standard neutrinos are named electron, muon and tau neutrino. However, in CR context, these names are inappropriate as the masses between them are negligible - the ratios are not the same as the ratios 114 between the masses of electron, muon and tau particles (which are all considered to be electrons in different sub-major vertical energy levels). Thus, per CR, each of the 3 standard neutrinos can be vertically excited into e, muon and tau eigenstates (with the same mass ratios as the mass ratios between electron, muon and tau particles), but they themselves, albeit similar, are 3 different particles. In conclusion, the 3 mass eigenstates (e, muon, tau) represent more general or more fundamental eigenstates in CR, and, in contrast to standard QM interpretation, the 3 standard neutrinos are interpreted as 3 different particles, while electron, muon and tau particles are the same particle in different vertical energy levels. Note that, while the transition between major vertical energy levels generally involves changes in the dominance of forces, in case of sub-major or minor vertical levels this does not have to be the case. In example, electro-magnetic force still dominates between standard electron, muon and tau particles, although the strength of gravitational and Higgs interactions does increase with the increase in energy level. Apart from e/muon/tau eigenstates, however, other eigenstates may be available for some particles. In any case, all components of atoms, photons and all other particles can oscillate or fluctuate in mass (again, a caveat - this is not the QM flavour/mass oscillation, rather oscillation through vertical energy levels), with expected ratios between masses (e/muon/tau eigenstates), being: mµ me =Mµ Me = 206.768 mτ me =Mτ Me = 3477.22 Mτ= standard tau electron mass = 1776.86 MeV/c2 Mµ= standard muon electron mass = 105.6583755 MeV/c2 Me= standard electron mass = 0.511 MeV/c2 where merepresents lowest mass eigenstate, mτrepresents highest mass eigenstate, while mµis the intermediate mass eigenstate. Are components of general force (electro-magnetic, gravitational) exchanged, to some degree, even with oscillation between sub-major levels as well? Possibly, but this may not be observable. The entanglement between major and sub-major levels becomes obvious from the following equation: mµ me =Mγµ Mγe = 206.768 where Mγµ is the photon rest mass localized to U0scale (∼2.1 ×10−54 kg, as calculated previously (and obtained experimentally). If that mass is interpreted 115 as muon photon mass, the Mγe is the e photon rest mass when localized to U0 scale and must be equal to ∼1×10−56 kg. Now, the order of this mass (56) is apparently equal to the order of the ratio between calculated e mass eigenstates on U1scale and U0scale. Thus, mass of the U1e eigenstate can be obtained by multiplying U0.electron mass with the inversion of U0.e.photon mass (which can be interpreted as mass inflation): Me1=Me0 Mγe0 Mγe1=Me Mγe Mγe1= 0.910938356 ×1026 kg where Mγe1is the U1.e.photon mass eigenstate and is here assumed to be equal to 1 kg. It is however, possible that the obtained photon mass of 2.1 ×10−54 kg is not the muon eigenstate, rather e eigenstate, in which case U1.e.photon mass should be smaller. Assuming that the obtained U1mass represents a muon eigenstate (as noted already, this is more likely, according to the complementary paper[20]), U1.e.photon mass should indeed be smaller. This suggests that the equation used to obtain major eigenstates is incomplete - assuming it should relate the same eigenstates between scales. But should it? As noted before, at least in some contexts, the equivalent U0.electron on U1scale may be the U1.muon. In other words, the equation relates, or determines, dominant eigenstates - on U0scale e eigenstate is dominant or most stable, on U1scale it should be the muon eigenstate (at least when averaged over the appropriate timescale). 6.1.2 Propagation and oscillation of photon mass Masses of all particles (or, more precisely, production of all particles) should be oscillating or fluctuating between sub-major vertical levels and photon cannot be an exception. The particles that [annihilate to] form the photon’s rest mass (half-photons) should, also oscillate between 3 generations. Assuming calculated mass is the lowest mass, remaining two values can be calculated from tau/muon/electron mass ratios, as established previously. For Mτ= 1776.86 MeV/c2, Mµ= 105.6583755 MeV/c2and Me= 0.511 MeV/c2: Mγτ =Mτ Me Mγe =1 26.335068208 ×10−69 kg Mγµ =Mµ Me Mγe =1 23.767055455 ×10−70 kg Mγe =Mp 2=1 21.821876712 ×10−72 kg Mγe = electron half-photon rest mass Mγµ = muon half-photon rest mass Mγτ = tau half-photon rest mass 116 Note that these values are in agreement with the photon mass calculated by others. E.g., in one study, Alencar et al. have obtained, with the assumption of dS vacuum and a Ricci scalar of 4Λ(where Λis a positive cosmological constant), a cosmological photon mass (mass of the photon propagating in the cosmological vacuum) of ≈2×10−69 kg[42]. If one instead calculates the mass using matter density and pressure of the Solar System (Sun magnetosphere) in the Ricci scalar and a zero cosmological constant, one obtains photon mass ≈2×10−72 kg[42]. Note also that there must exist a threshold frequency - at which point two half-photons are more likely to annihilate into a graviton half-particle instead of annihilating into a photon. Due to non-zero mass, photon must have a range, at least roughly equal to [reduced] Compton wavelength, e.g., in case of tau/muon combination of half-photons (assuming such combination is possible): r=~ Mpc=~ c 1 Mγτ +Mγµ ~= h/(2π) = 1.054573 ×10−34 Js c = 2.99792458 ×108m/s Obviously, r must also be roughly equal to the radius of the observable universe (universe that can be observed by standard photons). Photon frequency will change with changes in gravitational potential. However, beyond the conventional frequency shift stemming from GR, I propose that, due to its mode of propagation (expanding spherical wavefront) and nonzero rest mass the photon may experience a frequency drift due to coupling to positive and negative pressure of the mass-energy enclosed by the wavefront (per the shell theorem, the mass outside of the sphere, with its homogeneous and isotropic distribution, would have no net effect on the photon). Here, the photon’s rest mass is assumed to be isotropically distributed over the spherical shell (either over the whole sphere or concentrated in a ring, depending on coupling interpretation - as explained further below). If the coupling to positive pressure is balanced with the coupling to negative pressure there is no frequency drift, otherwise photon’s frequency may be blueshifted or redshifted, depending on the dominant pressure. The frequency drift is here interpreted to be a consequence of acceleration, however, the photon is not locally changing velocity, rather its trajectory is being curved. With dominant positive pressure its linear momentum is converting to angular momentum, and, upon reaching its range, photon’s linear (radial) velocity becomes equal to zero (completely exchanged for angular velocity). Effectively, thus, the photon is experiencing constant negative radial acceleration. 117 How to interpret the constant acceleration? One possibility is the running gravitational coupling (note that the photon is changing scale during propagation). E.g., with G proportional to 1/r and M proportional to r3, the acceleration becomes constant, effectively independent of r. One explanation for this is the dependence of dimensionality of gravitational coupling on the dimensionality of coupling bodies. The photon is 2-dimensional (spherical surface), while the enclosed mass is 3-dimensional, resulting in the 1/r ratio. For localized particles/bodies the ratio is 1/1. Note, however, that this implies asymmetry in coupling - the force from the photon acting on the enclosed mass would have a G proportional to r, not 1/r. While I wouldn’t rule out the asymmetry (the CR allows it, and the asymmetry is obvious in more complex forces - one person, for example, can be attracted by another, but at the same time the latter may be repelled by the former), another explanation is possible. Suppose that photon’s rest mass is concentrated in a ring on the spherical wavefront. In that case, the enclosed mass grows with r2and the acceleration remains constant. Some might prefer this explanation as it doesn’t require a running G (under the assumption of constant density): a=GM r2=Gr2πρ r2=Gπρ Assuming invariant G, obviously the range, and thus the coupling rest mass, depend on the enclosed mass-energy density. The question is, however, is the rest mass changing dynamically - as the density is constant only on larger scales? Here, angular momentum would be conserved (as increase in rest mass is equal to decrease in range), but energy conservation would imply exchange of energy with the traversing medium. Alternative solution is the dependence of rest mass on initial conditions (at the point of emission) only, with either a dynamic acceleration on smaller scales or a changing coupling strength (with changing density) to conserve the fixed acceleration across all scales. Instead of the ring-like form of photon rest mass, however, the same effect (proportionality of mass to r2) can be produced assuming the acceleration depends on the mass traversed by the wavefront, rather than the mass enclosed by it. Note, however, that, even if G is invariant here, it is not equal to the Newton’s gravitational constant, as the coupling strength at the start of propagation must be significantly higher to produce the observed acceleration. Limiting the G to the Newton’s gravitational constant, the correct order of acceleration can only be produced from the gravitational acceleration of the total mass enclosed by the radius of the observable universe (or, more precisely, by the particle range). In that case, one would have to accept the notion that the photon is, upfront, aware of 118 the total mass within its range and is reacting to that mass from the start. While the coupling rest mass/range is known upfront, it is not intuitively easy to correlate the total enclosed mass within the range with the conditions at the point of emission. Thus, the photon is probably reacting to the density of enclosed or traversed mass-energy at its current radius, with the strength of coupling changing in such way to ensure a radial acceleration that conserves the mass-range relation - or to ensure that the range is effectively a Schwarzschild radius. This acceleration is the equivalent of inverse free fall, and on a return trip (assuming the photon is not absorbed and falls back upon reaching the range) it would be equivalent to free fall. Thus, for the coupling rest mass equal to Mγτ + Mγµ, the acceleration is: a=±1 2c2c ~(Mγτ +Mγµ) = ±1 2 c3 ~(Mγτ +Mγµ) = ±4.287091748 ×10−10 m s2 For 2Mγe: a=±1 2 c3 ~2Mγe =±c3 ~Mγe =±2.327418326 ×10−13 m s2 Generally, taking into account phase shift between mass eigenstates of halfphotons and using relativistic mass, the equation becomes: a=±1 2 c3 ~1 2+1 2sin2φ∆M1 q1−f2 fn2 ∆M2= 22M12+M22 2= 2M12+M22 where ∆M is the superposition of mass, f is photon spin frequency, fnis the maximum possible photon spin frequency and φis the mixing angle (equal to 90◦for aligned and 0◦for anti-aligned oscillation of half-photons). For the previously determined 2nd order maximum energy of Mn= 1.02413 ×10−16 kg (5.7 ×1019 eV), fnis: fn=c λn =En h=Mnc2 h= 1.389120683 ×1034 Hz Note that this energy/frequency is also roughly the energy/frequency required for the creation of the heaviest known standard elementary particle pair[43] (top/anti-top quark pair), potentially explaining why these 119 are the heaviest known elementary particles. Note also that, in conventional interpretations, the expanding waveform is usually not considered a real object rather simply a wave of probability, or a field spreading, but that, again, is a consequence of excessive reductionism in interpretation - or, more precisely, lack of proper interpretation of the wave-function. In CR, however, the wave-function describes a physical phenomenon - the spherical waveform is indeed a spread out photon, which collapses to a point with localization. Furthermore, in conventional quantum physics only the basis mass eigenstates are considered real. In CR, this is relative. The basis mass eigenstates are simply the most stable. On the standard scale (U0) the intermediate states are extremely unstable (from our perspective at least). On U1scale, however, they are obviously relatively stable (from our perspective, their stability can be on the order of millions or billions of years). The intermediate states are probably stable on the scale of photon mass (U−1) as well, but if not, the mixing angle of 90◦should be used. In any case, the perturbation model (additional non-dimensional terms) used here may not be the most appropriate, experiments should constrain these. Also note that the effect is effectively invariant to frequency, as realistic frequencies are much lower than the maximum. But there is another reason why the frequency has no significant effect. The rest mass here is associated with gravitational coupling, although it has the same value as assumed photon’s rest mass, it should be associated with a standard graviton instead. The acceleration thus stems from the photon coupling to the standard gravitons and it becomes questionable whether the dependency on frequency here exists at all. However, photon’s interaction scale is proportional to wavelength and if photon has a non-zero rest mass it will travel slower than c, so a relativistic effect on its energy should exist, and it will affect the acceleration - justifying the inclusion of the relativistic term in the equation. Calculated acceleration for various combinations and f « fnis shown in Table 4. Acceleration of photons may be misinterpreted as a change in velocity (Doppler shift) of the source of emission when the photons are emitted from a moving source and the coupling carrier rest mass is assumed to be 0, while the real reason of the change is the changing curvature of photon paths. Indeed, analysis of motion of Pioneer 10/11, Galileo, and Ulysses spacecraft shows anomalous relatively constant weak long-range acceleration of ∼- (8±3) ×10−10 m/s2(deceleration relative to the Sun) for which no satisfactory explanation has been found[44]. A solution has been proposed in the form of anisotropic thermal radiation[45] and it has been even claimed that this can completely resolve the Pioneer anomaly[46]. However, these results are questionable. The original 120 M1M2ϕ[◦] a [m/s2] Mγµ Mγµ 90 ±0.481235302 ×10−10 Mγµ Mγµ 0±0.240617651 ×10−10 Mγτ Mγµ 90 ±5.732686887 ×10−10 Mγτ Mγµ 0±2.866343444 ×10−10 Mγτ Mγτ 90 ±8.092948194 ×10−10 Mγτ Mγτ 0±4.046474097 ×10−10 Table 4: Acceleration for various cosmological photon mass eigenstates thermal modelling (which may be correct after all) ruled out thermal recoil as the explanation[47]. While the thermal dissipation could have a role, there are certain properties of these anomalies that cannot be explained by anisotropic thermal radiation. One is the observed annual periodicity[47], and the other is the apparent onset of the anomaly[48] only once the giant planets have been reached[49] (or, once the spacecraft transition to a hyperbolic trajectory, decoupling from the Solar System). Obviously, predicted enclosure of the gravitational potential by photons can fully explain this anomaly. The onset of the anomaly at the distance of giant planets can easily be explained with mass oscillation and/or changes in coupling between positive and negative pressure (where imbalance causes the onset). The annual periodicity can be explained by the motion of the Earth about the Sun - as this is the place of absorption, the radius of the absorbed photon will oscillate annually. However, if the anomaly results from photons coupling to space-forming gravitons, coupling mass may be, more likely, a superposition of 2 mass eigenstates. There are two interpretations of this. One is that the graviton rest mass is double the photon’s rest mass - which does make sense if the standard graviton is a product of annihilation of two photons or 4 halfphotons (half-gravitons), or even more pairs - as long the resulting total spin is 2. Spin 0 cannot be ruled out either, however, in that case this is not GR-like gravitational coupling, rather a dipolar gravitational (or gravitational-like) Yukawa coupling. In another interpretation, the coupling actually depends on photon’s rest mass, and 2 photons in superposition may be required for the coupling. The number of photons in superposition may depend on the spin momenta distribution of photons. In circularly polarized emission all photons have the same spin projection (helicity) on the direction of propagation. Thus, two photons in superposition would have a spin projection of 2~, equal to the standard graviton (carrier of gravitational force) helicity. In conventional quantum physics total photon helicity must match the graviton helicity so two photons (with equal helicity) are required 121 c0= c = 2.99792458 ×108m/s MN= 1.02413 ×1026 kg Mpe= 9.10938356 ×10−73 kg which, for c0equal to the standard speed of light (c), m1equal to Neptune’s mass and m−1equal to calculated half-photon mass gives: c1= 3.05751973 ×106m/s Note that a very similar value can be obtained with: c1=colog1 Mpe 1 ρc−1 = 3.0577 ×106m/s where ρcis the critical density of the observable universe, 9.9 ×10−27 kg/m3(for the Hubble constant of 72.6 km s−1Mpc−1), which is also the total average density of the observable universe[51]. Of course, the logarithmic term here should be multiplied with a constant to make it non-dimensional, but the value of this constant here would be ∼1. Is it a coincidence that the density of the observable universe is basically the inverse of the m1(or Neptune) mass? Probably not, considering that both Neptune and Mperepresent vertically excited electrons, whose mass ratio is highly correlated with the standard speed of light - which is density dependent - it can be obtained from the density of the observable universe and its pressure on the spherical wavefront (e.g., photon) at its radius: c0=2 3sMa 4πR2ρ=2 3raR 3=2 3rGM 3R= 2.99792458 ×108m/s where M is the total mass of the observable universe (4 ×1054 kg), a is the gravitational acceleration obtained from that mass (13.78 ×10−10 m/s2), and R is the radius of the observable universe (4.4 ×1026 m). The term 2/3 is here due to the contribution of negative pressure (dark energy). Note that this equation is an additional, and strong, evidence of the hypothesized interaction of the enclosed mass-energy with the spherical wavefront of a photon. Of course, within any vertical energy levels there are sublevels. In example, for U1.3 sublevel the speed limit may be: c1.3=c0hlog(MN) + 10m−1 m−log(Mpe)i−1= 2.91932312 ×106m/s 128 m = 3 Taking into account horizontal oscillation in the same sublevel, with the assumption of a quantum of energy U1.3.3 either lost by MNor gained by Mpe: c1.3.3=c0"log(MN) + 10m−1 m−k−1 k2 −log(Mpe)#−1 = 2.93201263×106m/s k=m=3 Note that a very similar value can be obtained using Sun mass in the original equation (without sub-levels): c1=c0logm1 m−1−1 =c0[log(M)−log(Mpe)]−1= 2.92940473 ×106m/s M= Sun mass = 1.988500 ×1030 kg The speed of 2.93 ×106m/s is confirmed in the complementary paper[20] as the limiting speed of this scale in the Solar System, the Milky Way galaxy and beyond - with some variability here possible in the last digit. Thus, the speed of 2.9 ×106m/s can be interpreted as the true equivalent of the vacuum speed of light on U1scale. This seems to suggest there is something special about the Sun, but this is not the case. It is the ratio that is well conserved between the large scale systems. Obviously, in the Solar System the mass of the Sun is the dominating mass so it is not surprising that the mass on that order is the dominating factor in local pressure/density - on which the limiting speed depends. And on U−1scale in the Solar System the order of mass of e half-photon dominates (photon rest mass is on the order of 10−72 kg[42]). In the Milky way, the largest star mass is about 130 M[52]. Using this, or the Eddington limit of ∼150 M, with muon half-photon mass as the dominating mass on U−1, one obtains again 2.93 ×106m/s. Using highest possible mass (Population III, early universe) of ∼300 M and the tau half-photon mass as dominating on U−1, one obtains 2.96 × 106m/s. Thus, some variation exists, but overall, the speed should be about 2.9 ×106m/s, being generally higher in the early universe due to dominating higher mass eigenstates. The approximate limit on scale U−1can be calculated similarly, assuming entanglement of adjacent scales: c−1=c0logm0 m−2 129 m−2= 10log(Mpe)−6×5= 9.10938356 ×10−103 kg m0= Me= 9.10938356 ×10−31 kg c−1= 2.16 ×1010 m/s As shown before, speed limits faster than the standard speed of light are not necessarily incompatible with GR, as from the larger perspective particles on smaller scales may be interpreted essentially as warp bubbles. Speed limit on U−2: c−2=c−1logm−1 m−3 m−3= 10log(m−2)−5×4= 9.10938356 ×10−123 kg c−2= 1.08 ×1012 m/s This limit is interesting as U−2particles should form the space of standard electrons (U0.e), and at the energy level associated with this speed limit the magnetic moment of the electron cannot be formed by rotation of charge exceeding this velocity. The magnetic spin angular velocity of an localized electron can be calculated assuming charge radius is known. Assuming this radius is a scaled Neptune charge radius and assuming the Solar System is the carbon atom equivalent (a hypothesis explored in greater detail in complementary work), the radius is: Re=R0=R1 r1×r0= 3.834298096 ×10−16 m R1= Neptune charge radius = 24622000 m r1= Neptune orbital radius = 4495.06 ×109m r0= orbital radius of the outermost electron in carbon atom = 70 ×10−12 m Angular velocity of charge forming the quantized momentum of such electron is then: v=1 2 1 MeRe ~= 1.5096 ×1011 m/s Apparently, the charge is rotating at allowed velocity (not exceeding c−2). It should be clear, however, that the calculated speed limits are valid for the relatively equivalent conditions between scales. While we cannot significantly 130 affect the conditions on U1scale, we certainly can manipulate U0particles and, indirectly, affect the conditions on smaller scales. In example, we can confine the electron (or at least its charge mass) to a much smaller radius than the radius calculated above. Note that electron at standard scale (U0) may not generally orbit the atom localized, rather as a less-confined wave. In that case, with momentum conserved, the velocity of its charge is much lower as the radius Rebecomes equal to the atom radius (r0). Its charge, however, may not be distributed as an orbital wave-line, rather orbital wave-surface or a cloud, which would then increase velocity somewhat (by 3/2 maximum) but this is negligible compared to initial decrease. At that radius the speed is much lower even than c0so that limit should now be interpreted as a proper relativistic factor. Closer to the nucleus the charge velocity may then become relativistic (between the innermost electron and the atom centre, speeds, however, with greater limit can be greater than c0). Situation further complicates with the splitting of the electron charge into multiple energy levels. But is the source of electron’s spin magnetic moment an U−1charge rotating in its space, or the rotation of naked charged space (U−2)? In any case, a decrease in radius, with no change in energy, must, due to conservation of momentum, increase rotational velocity (speed limit, in case of space compression), implying that electron’s rotation velocity is limited solely by the radius (space compression) and it would be infinite if the electron could be confined to an absolute point. In reality, however, the electron never is an absolute point particle. 6.2.2 Applying speed limits, correlation with emergent phenomena Speed limits (cn) are inherently linked to gravitons and depend on their scales. This implies that two bodies of similar total mass can obey different speed limits, depending on the scale of graviton[s] coupled to the masses. Consider the example illustrated in Fig. 6. The leftmost naked graviton (m1) is an U0graviton and has a speed limit of c0, the second one from the left (m2) is an naked U1graviton and has a speed limit of c1. The m3represents the same graviton but coupled to real mass of scale U0(collective of U0gravitons). This coupling represents a body (or a living body) of mass that, as a whole, has a speed limit of c1(due to c1< c0). However, in the rightmost image, showing uncoupled real mass (m4) forming abody (or a dead body), the collective now has a speed limit of c0even though it may be of similar or even equal total mass (depending on interpretation - 131 Figure 6: Gravitons and associated speed limits (not to scale) mass shielded or not, graviton scales and filled capacities) to the body m3. As noted before, distances between particles are relative and never absolute 0. Electro-magnetic force between two charges, in example, is present over vast distances. This makes the definition of a body relative - due to electro-magnetic connection or entanglement between them, one could consider the two charges as a single body even when greatly separated. One might have biased definitions, in example, considering atoms as individual bodies until they couple to form a molecule, but does it make a difference to nature - unless formation of a molecule is synchronized (or equivalent) with the coupling of the collective of atoms with a distinct graviton of larger scale? Any apparently spontaneous organization, or self-organization, of entities into a distinct body should be only relatively spontaneous. Thus, it should probably be more or less synchronized with a coupling to a distinct graviton correlated with such collective. This coupling may be more or less temporary or relatively long lived, but in any case, stability of this organization should be proportional to the strength of coupling (localized correlation). All emergent physical phenomena probably represent a coupling of certain entities to a distinct graviton of different scale. It is this coupling then that makes the collective something more than the sum of its parts. 7 The unification In CR, nothing can be absolute or absolutely indivisible, even a continuum of space must be, like all energy, an entangled sum of discrete energies or lower energy levels. Diversity of energy levels implies it has variable and scale relative properties, such as density and pressure. Certain number of dimensions of space (time) is embedded in the foundations of every theory in physics. Here, obviously, such number is relatively infinite, however, intrinsic limitations on observation/detection of scales of energy effectively reduce the experience/awareness 132 to a limited number of dimensions. Dimensions evolve and one may recognize different species of dimensions where individuals of species often can be represented by the average or relative superposition of individuals. On small scales even different species may be represented by some kind of superposition. Generally, for major vertical energy levels, it is convenient to define three or four main species - space, mass, time and charge. These are all entangled, but degrees of entanglement will vary and a difference in superposition of the four may itself warrant classification into different species of superposition. One might use different units for the 4 species (e.g., m/kg/s/C) but nature will commonly reduce them to the same currency (e.g., units of [angular momenta of] space at some scale) and will readily transform one energy into another (exchange space for time, time for mass, etc.). Here thus, there is no intrinsic entanglement between space-time curvature and mass or charge, the space-time-mass entanglement in GR is thus just one possible case of such entanglement. 7.1 Relativistic time (space) Everything in nature has an angular momentum relative to something. It is natural then that dimensions of nature are generally curved and closed, quantized with different periods/lengths and different shapes. Even though dimensions are generally closed, no two cycles of motion through any dimension are absolutely identical. In example, a dimension of time (or a quantum of an dimension of time) may be interpreted as a circular thin tube (or even a relative 1-dimensional ring), a torus, with relatively discrete or relatively continuous degrees of polarization. Space (or a quantum of an dimension of space) may be interpreted as a thin sphere surface, a torus with significant asymmetry between tube thickness and surface area. Localized energy could then be interpreted as horizontal confinement (localization) of space and vertical confinement (localization or excitation/de-excitation to a particular vertical energy level) of time, or vice versa. Whether this energy will be interpreted as simple mass or more complex charge depends on the rules of external entanglement, which are correlated with the internal space-time arrangement (entanglement) of the energy. Note that CR implies a relatively simultaneous existence of energy on various vertical scales (self-similarity). If energy existing on one scale can be aware of, or be sensitive to, adjacent 133 discrete vertical energy levels only, direct sensitivity is strongly limited to 3 dimensions. This will be, with implied self-similarity, replicated on all these levels - splitting each into 3 components, hence explaining three generations of particles (or 3 minor vertical levels) existing on a particular major vertical energy level. However, not all universes have to be limited to direct awareness of 3 scales (splitting of energy can result in more than 3 levels) and even those limited to 3 may be aware of other scales indirectly - which might become direct awareness over time. If nature does not discriminate between scales of energy (just as it sometimes does not discriminate between dimensions), then the reduction of different scales to a common currency should also be natural. In which case, the scaling vector may be normalized. Let A represent a state in time (space) and C a scaling vector, the operation of addition between scales (components of time) could then be represented by the scalar product of vectors: A·C=a1a2··· an·     c1 c2 . . . cn      =a1·c1+a2·c2+···+an·cn With normalization, the scaling vector C becomes a unit vector: A·C |C|=a1a2··· an·     c1/|c1| c2/|c2| . . . cn/|cn|      =a1ˆc1+a2ˆc2+···+anˆcn Note that, if dimensions here represent scales, geometrical representation of the state with orthogonal unit vectors would be misleading. and, with no discrimination between scales: ˆc1= ˆc2=··· = ˆcn= ˆc scales collapse to one dimension: ~ A= (a1+a2+···+an) ˆc 134 With no direction, a point in such time becomes a scalar: A= (a1+a2+···+an)c The collapses of scales in time will have physical interpretations in space and correlations between these may be interpreted as events of synchronicity, however, generally, it should not be assumed that c (speed of change) is absolutely the same between different scales of energy. In one example of the above non-discriminating reduction (collapse), consider the addition of different units of time. Adding 2 hours to 3 seconds, for example, from our perspective always results in 123 seconds or 123 units of time. However, assuming equivalent quantization of time exists in nature, nature would sometime interpret the result as 5 units of time. In other words, it wouldn’t discriminate between hours and seconds. This might seem unnatural to us, but this kind of non-discrimination between different scales of space/time is sometimes required to conserve relativity, e.g., relativity in periodicity[53]. Due to relative equivalence and self-similarity postulated by CR, energy existing on different vertical energy levels can be, as noted before, interpreted as one and the same energy existing on multiple scales of space/time. Now, if nature sometimes doesn’t even discriminate between scales, one can treat this energy as a wave and formulate a quantum wave-function to describe it (one can now also interpret the Big Crunch of the universe as localization of this energy). Thus, it has the same constraints as a wave-function in QM and the discreteness of vertical energy levels stems from the same constraints as the discreteness of horizontal energy levels. After all, it should be clear that, in CR, vertical energy levels must be only relatively vertical. 7.2 Relativistic vacuum In General Relativity space is treated as non-physical, it has a geometry but no variable physical properties such as density and pressure in common interpretations. Space-time entanglement is treated as absolute which translates to an absolute speed limit, equal to the vacuum speed of light in case of massless photons: c=r1 0µ0 0= vacuum electric permittivity = 8.85418782 ×10−12 F/m µ0= vacuum magnetic permeability = 4π×10−7H/m The constants on the right define the behaviour of electromagnetic fields in vacuum, and when interpreted as absolute, do not imply that vacuum has fields 135 (energy) present. However, in CR, these constants cannot be absolute and, thus, imply vacuum has energy associated with them. That vacuum has energy has already been theorized in Quantum Field Theory (QFT) - associated with zero-point fluctuations, and evidence for it exists, only the values are debatable. The relation of the speed of light to vacuum energy can be classically inferred by rewriting the equation in terms of energy density ρand pressure p: 0=K F m=K s4A2 m3kg =K s4N2 m3m2kgT2=K s4kg2m2 m3m2kgs4 1 T2 =K kg m3 1 T2=K kg m3 1 T C N m s=ρs 1 B1 1 E1 v1 µ0=Kµ H m=Kµ mkg s2A2=Kµ mkgm2T2s4 s2kg2m2 =Kµ ms2 kg T2=Kµ ms2 kg TN C s m=1 ps B2E2 1 v2 for E1B1=E2B2: c=rps ρs v2 v1 =rps ωρs K= 8.85418782 ×10−12 Kµ= 4π×10−7 and now in terms of energy E and mass m: 0=ρsv1=m Vv1 1 µ0 =psv2=E Vv2 c=sE/V m/V v2 v1 =rE m v2 v1 From this follows: E=v1 v2 mc2=ωmvr2 ω=v1 v2 =vr √vr2−v2=1 q1−v2 vr2 Here, factor ωis the non-dimensional relativistic factor. In established theories, energy is always relative to an absolute rest frame (vr= c), which may be referred to as vacuum frame or even CMB (Constant Microwave Background) rest frame due to omnipresence of CMB and negligible photon mass. 136 The space/time ratio of that frame is considered intrinsic/non-changeable and, assuming vr= c, it has an absolute 0 momentum (v = 0 above). In QM, the same absolute rest frame produces very counter-intuitive results. In CR there are no such restrictions, no rest frame is absolute, each gravitational well has its own space and there are, not only horizontal but vertical energy levels corresponding to scale of discrete packets of energy. In CR, the CMB rest frame is space of a large-scale graviton with [angular] velocity (v) possibly equal to c, relative to a rest frame vr> c, and with a rest mass < mc2/vr2. Space and time of this rest frame may be entangled but information between them cannot travel instantaneously. Also, either may change spin and entangle with another dimension. Therefore, the ratio c is not absolutely intrinsic and it is changeable. 7.3 Omega factor (relativistic change) Omega factor is a non-dimensional relativistic factor, a generalization of the Lorentz factor. It is a necessary modification in order to allow complete relativity of universes. Energy is relative to a specific reference frame and omega factor will generally be relative to a specific graviton in whose space energy is contained. Space of a graviton is characterized by its µ product (or density and pressure). Omega factor represents change in energy due to momentum: ω=1 q1−v2 cn2 =1 q1−v2 k2c2 c = c0= standard speed of light where k depends on the vertical energy level (scale of energy). Note that ω−1is the eccentricity of the ellipse of width equal to 2kc and height equal to 2v, as shown in Fig. 7. Figure 7: Relativistic ellipse With k = 1, width is fixed to c and omega factor degenerates to Lorentz. Note also, if k itself has the form of ω−1, degeneration to Lorentz becomes degeneration of a variable ellipsoid to an ellipse of fixed width. 137 radius decreases - all the way to relative 0 if everything below the original orbit is at full capacity (and if not stopped by accumulated orbiting mass - e.g., satellites falling back to Earth are stopped at surface radius). With such mechanism, it should be common for inner orbits to be at full capacity (or over-capacitated near the centre), with probability for under-capacitance increasing with orbital distance. Energy accumulating in the centre will, however, generally be radiated or expelled outwards in some form through various mechanisms. Under-capacitance explains higher velocities in outer parts of galaxies, while nearly flat velocity curves indicate that: Mms m∝r This can have different interpretations. In one, msremains constant, while M/m is growing with r. In another interpretation, msis decreasing proportionally to r, while M/mis growing proportionally to r2. Similarly, this: Mms m∝r3 would give linear increase of velocity with distance, solving the core/cusp problem[54] (solid-body behaviour in galactic cores). However, different generations or species of space-forming particles (static gravitons) with different rest masses exist and therefore different ranges may be present in a system. And that is likely the cause of different proportionality with distance. The number of species present may differ between systems (galaxies, planetary systems, ...) and even steeper velocity curves may exist near the core. Generally, thus, gravity will be proportional to r−nwhere maximal nis proportional to the number of species and is decreasing with distance from the core. Note that ncan be correlated with energy levels, as gravitons have discrete masses and thus discrete ranges. Most likely, the shape of gravitons also correlates with the strength of gravity with distance. Suppose the energy density of a graviton is constant but its total energy changes with shape (synchronized with changes in energy level). In cases where gravity is proportional to r−2, gravitons may have a shape of hollow spheres (energy is distributed over the sphere surface) when uncoupled (non-localized) and forming space. In cases where gravity is proportional to r−1, uncoupled gravitons could have a shape of rings. This could restrict dark matter halos within the central regions of gravitational wells, while on the outskirts space [curvature] would be in the form of dark matter rings. Intensity of gravitons, and thus gravity, decreases with distance, however, with the transformation from a two-dimensional spherical waveform into a one-dimensional ring form, intensity of gravitational coupling becomes proportional to r−1, rather than r−2. 144 Derivation of the equation G1.2 One way to derive the equation G1.2 is through balance of body momentum and effective graviton momentum: p+−GMms rvs = 0 which, with rearrangement, becomes a balance of body momentum energy and gravitational potential energy of the naked graviton: pvs+−GMms r= 0 With further rearrangement: mvvs=GMms r v=GM ms m 1 vsr Thus, in equilibrium orbital states, momentum energy of the body in the local frame must be equal to the gravitational potential energy of the naked graviton. That way the body cannot escape but will also not de-orbit. Note that in equilibrium v = vs, but the orbital velocity does not have to be Keplerian in this interpretation. Conventionally, however, the ms/m ratio is incorporated into M (why not into G?), as dark matter (if velocity is higher than expected Keplerian velocity). Here, vsis initially equal to c, however, as the body gets entangled with the graviton, vsdecreases below c (while v is increasing). For m < ms, gravitons of space are effectively dragging matter, for m > ms (de-orbit occurs), the matter is dragging gravitons towards the centre of the gravitational well (at some point, however, entanglement may be lost, gravitons could decouple and return to the original orbit (range). Alternative solution The equation G1.2 is dependent on real mass mand may not be the appropriate interpretation in all cases, however, the alternative exists. Per the definition of a graviton, probability of gravitational coupling should be proportional to n, where nis an integer, equal to the dimensionality (complexity) of the non-localized graviton, making the intensity of gravitational coupling (strength of force) proportional to n. Additionally, gravitons can have different flavours (masses) and, thus, different ranges. Thus, the Newtonian gravitational acceleration should be generalized: g=GnM(1) 145 Gn=G0×In=G×Ig(n) rn Ig(2) ≈1m(n−2) = 1 where G0is the gravitational constant (G), while Inrepresents the intensity of coupling and is a function of n, while nitself can change with distance (r) from the source of gravity, Mrepresents mass enclosed within r. Note that the unit of Igis m(n−2) (metre to the power of n-2) and should represent a generalized Yukawa term (Yukawa potential has a unit of m−1). Density of gravitons may decrease with distance, however, intensity of coupling can change relatively abruptly with the change in shape/mass of gravitons. Any anomalous change in orbital velocity curves should then indicate a change in energy level (n). The distance where the shift occurs is equal to the range of the associated gravitons. From this range (reduced Compton wavelength), masses of gravitons can be determined: mg=~ λrc=~ rgc where ~is the reduced Planck constant, cis the standard speed of light, while rgis the graviton range. However, two interpretations are possible here. Instead of involving multiple species of gravitons with different ranges, change in coupling intensity (graviton dimensionality) with distance could be interpreted as a consequence of the oscillation of flavour of single species of a graviton. If the transition between flavour eigenstates is continuous (as it should be during motion) the transition between energy levels will be smooth, otherwise sharp. Note that one interpretation does not exclude the other, both could be true simultaneously. The above may then explain all gravitational anomalies. For dM/dr ≈0 (where Mrepresents the mass enclosed within the orbital radius r), flat orbital velocity curves are obtained with n= 1. This explains the flatness of galactic rotation extending far out of the galactic edges[55] (where conventional dark matter theories fail). Linearly increasing velocities can be, for example, obtained with n= 1 and dM/dr ∝r, solving the core/cusp problem[54] (solid-body behaviour in galactic cores). Recent analysis of galaxies in SPARC (Spitzer Photometry and Accurate Rotation Curves) database shows that dark matter particles must have different masses to fit the observation[56], which is also going in favour of the hypothesis presented here. Note that (1) can be interpreted as a modification of the gravitational constant. Evidence exists, even within the Solar System, that this constant is not absolutely invariant[57], rather should be interpreted as a relative constant. Increasing velocity with distance, however, does not have to imply increasing mass in the enclosed standard matter that is interpreted as the gravity source, it implies increasing density of gravitons. Such increase may be conventionally unexpected, however, it can be explained if the source of gravity is not localized, it rather represents a wave itself. Universe is showing self-similarity on various 146 scales and absolute scale invariance of physical laws is just an assumption that is probably incorrect. A supermassive black hole may represent a large scale graviton, in which case one should question how localized it is. Linear orbital velocity increases could be interpreted as a consequence of another gravitational maximum associated with this graviton - in other words, the associated waveform has radial nodes. Densities of gravitons of smaller scale which are coupling to celestial bodies would change at the maxima, and these small-scale gravitons could be interpreted as particles forming space of the large scale graviton. 7.5.3 Mechanism of exchange Exchange of electro-magnetic potential for gravitational potential is done through the change of scale. In example, radii of charge maxima may be deflated with inflation of a mass radius of a gravitational maximum. This doesn’t affect only orbital radii of gravitons but also spin radii of graviton quanta - effectively, charge is subdued with the inflation of mass (gravity). Note that, seemingly, no extra energy is required as this is simply a change of species of force, not strength. However, energy is needed to stimulate and process transformation, during which some energy may also be lost. The end product will then have different energy than initial total energy. The triggers of exchange may be: •annihilation of matter with anti-matter, •critical temperature/density (extremely low, extremely high). If transformation mechanism exists locally, external energy needed to stimulate exchange can be extremely low. This may simply be resonance or entanglement inversion. Note that any entanglement decrease must be coupled with another entanglement increase. The exchange of potentials of general force could thus be common in birth and death of bosons and boson (Bose-Einstein) condensates. The equivalence of bosenovas and supernovas/novas, galaxies and quantum vortices, planetary systems and atoms, in that case, may go far beyond abstract similarity. In any case, it should not be impossible, in any universe, to ensure conditions that would reduce the relativity of self-similarity (similarity to a universe of adjacent vertical scale) to a minimum. 147 7.6 Evaluation of G Gravitational constant (G) is not fundamental and may be interpreted as: G=1 2 As M vs Ts = 2πR2 M vs Ts =3π ρ 1 Ts2=R Mvs2m3 kgs2 As= surface area of the gravitational maximum [graviton] R = radius of the maximum M = gravitational mass of the maximum ρ= mass density of the maximum vs= angular velocity of the maximum Ts= period of rotation of the maximum It is then relative to a particular graviton (gravitational maximum) and has its properties, such as mass, radius and velocity, built in. These are generally variable properties. Even if, generally, all these variables are correlated in such a way that G remains constant, are they correlated (entangled) at all times and do changes propagate instantly? In CR, instant propagation of information is [absolutely] impossible and some phase difference between changes in [G and] the variables will always exist. The G itself must oscillate. Obviously, a gravitational maximum has a [changeable] spin momentum and this can further be complicated when it is evidently composed of multiple maxima. Note that vshere is Keplerian velocity. Assuming M is the mass of a graviton, non-Keplerian velocity may be interpreted as a difference in G (due to a difference in graviton mass). While the 3-dimensional (spherical) form of one maximum may cloud the existence of inner maxima, outer maxima can have different spin momenta. Even if the whole system changes spin, changes cannot be instantaneous across all maxima, rather propagate in a wave-like nature. 7.6.1 Gravitational collapse (G collapse) Rotational profiles of galaxies show that 1/R is often not proportional to vs2. Even if outer maxima have collapsed (fragmented) to multiple satellite maxima of smaller scale, these cannot acquire [real] mass instantaneously nor they will always acquire [real] mass during collapse. Although collapse requires energy, it doesn’t necessarily have to come from real mass. Unlike in GR, gravitational collapse in CR is not reserved for massive bodies, the energy for collapse depends on the initial energy of the maximum. 148 Maxima can thus remain naked for relatively long times, proportionally to scale and inversely proportionally to mass (energy) field density, before [another] equilibrium is established and 1/R becomes proportional to vs2. Gravitational collapse in CR is localization of graviton momentum - e.g., a large scale graviton with a spin radius on the order of 106km can collapse to form a graviton with a spin radius on the order of 103km, sometimes with a former spin radius fossilized into orbital radius of a new body. Real mass required for equilibrium can be obtained through conservation of angular momenta: [mimg(n) + mre(n)]vnrn= [mimg(n−1) + mre(n−1)]vn−1rn−1 =MvsR mimg = mass of the naked gravitational maximum = imaginary mass v = orbital velocity of the maximum r = radius of the maximum mre = acquired smaller scale mass = real mass vs= vn−1= spin velocity of the [collapsed] maximum R = rn−1= radius of the [collapsed] maximum M = Mn−1= total mass of the [collapsed] maximum where n is the scale of the maximum. In the above, dependence on scale has two equivalent notations: mimg(n) = mimgn Collapse of a graviton to smaller scale generally can be a high energy or low energy collapse. In case of high energy collapse, accumulated real mass is lost (e.g., nova/supernova explosions) - decoupled from a collapsing graviton. In case of low energy collapse, the graviton is [relatively] naked and collapse occurs due to localized disturbance of its momentum with sufficient real mass for coupling on smaller scale. Note that graviton may, instead of deflation, start inflating after decoupling. It will then continue inflating until it reaches maximum range - if it does not collapse and couple to another mass before that point is reached. Maximum range becomes a relative term if graviton is losing energy with inflation - in that case, range would be expanding continuously. However, most energy is lost with coupling. Regardless of interpretation, lost energy at the moment of coupling should be proportional to distance between inflation/emission (decoupling) and absorption/deflation (coupling) due to increasing distance in correlation between entangled constituent quanta of the wave (graviton) - the volume of entanglement cannot remain absolutely constant and it is unlikely to conserve constancy (oscillation average) with distance. Note also that the collapse of a wave-form is only a relative collapse of 149 wave nature - difference between a particle and a wave is simply in the radius of the wavelike form. The inverse interpretation is also valid - in some reference frames, the larger wave-form may be interpreted as a particle. In reference frames where the collapse is discrete, low energy collapse occurs when this is established: mimg(n) = mre(n−1) In other reference frames, collapse proceeds gradually and can start even before the above relation is established. For a naked maximum, mre(n) is a relative 0. In high energy collapse, mimg(n) must be decreased to match mre(n-1). This is synchronized with increase in vnrnproduct. There are no fundamental constants. All are fundamentally variable. 8 Scale and centre of the observable universe For every universe there must exist a reference frame that universe is revolving about. Given the determined scales of discrete vertical energy levels, it is reasonable to assume that the centre of the observable universe (point it is revolving about) is outside of it. Thus, all observable galaxies collectively orbit a barycentre outside of the observable universe. This can be confirmed and approximated by observing galaxies on a different energy level of the same system. Momenta of such galaxies should be correlated - in equilibrium state they orbit the centre in the same direction but with a calculable difference in speed and distance from the centre. E.g., if one considers Milky way as a bound electron, the atom which Milky way is a part of should have a diameter on the order of 10 trillion (1013) light years, 103times the diameter of the observable universe. In that case, all other energy levels are outside of the observable universe. However, considering the number of galaxies and the state of evolution, this is not the best interpretation (although some layering may be present). Considering distances between atoms (planetary systems) and molecules (binaries and other strongly correlated systems) the observable universe is a gas bubble of extremely low density with particles concentrated in quantum vortices (galaxies). This bubble or soup, however, cannot be completely homogeneous and it is only a matter of technology and proper interpretation whether one can observe 150 the difference between the closest and the furthest layers of this gas (layer) relative to the external central point. The most appropriate interpretation of observable universe is a part of space of a large scale graviton, in a form of a torus - as stated already. It may have been deflated from an even larger scale, however, evidence suggests it has been inflated from smaller scale, probably in an annihilation event. 9 Atomic property differentiation between systems Vertical energy levels are entangled. This implies entanglement between equal species, but entanglement between different species of different scales is not forbidden either. Increasing number of protons and electrons in an atom is splitting (or increasing) energy levels (layers) of the atom. What if properties of standard atoms are strongly correlated with properties of U1/U−1systems (atoms) they are co-evolving with? For example, radii of standard atoms may be correlated with [the density of] the gravitational well they are in. Consider the Lyman (or any other) series for a hydrogen [like] atom - if density of series is not invariant to such correlation, one could have a distorted image of non-local reality, as the spectrum lines of standard atomic elements would be variable across time and planetary systems. E.g., in a nitrogen-like system the Lyman series for hydrogen would have red-shifted frequencies. One might even argue there are 6 distinct wavelengths (after 6th, the spectrum becomes continuous) in Lyman series and that such differentiation is a direct consequence of the Solar System being an atom with 6 protons and 6 electrons (carbon), or that series beyond the 6th may be correlated with more distant planetary systems. 10 Waves as particles as waves All particles having a momentum always generate waves on some scale (because there is no absolutely constant momentum). A particle itself may be in wavelike or corpuscular form. This form, like everything, is relative. One observer may detect a wave while another may observe a particle form (both forms can even be observed at the same time). Forms are dependent on properties of local space, which may be affected by the observer too. 151 Generally, with more energy density, a corpuscular form is more likely to be detected. Waves may be coherent in space and/or in time. Coherence in both, space and time, will thus produce the most dense energy (e.g., laser light). A waveform collapse may also be initiated by interaction with other waves (particles), but this will depend on energies involved and the properties of underlying space. From our perspective, wave nature prevails on U−1scale, particle/wave on U0, while on U1scale nature is observed generally as corpuscular. This is due to differences in average pressure/density and time dilation between these scales. 11 Evidence Some evidence for complete relativity is presented in this paper. Additional evidence confirming complete relativity of universes is presented in follow-up/complementary papers. Mainly in the analysis of the Solar System in CR framework[20]. Of course, other researchers are welcome to confirm or refute the presented predictions and hypotheses in this and follow-up papers. Due to inherent limits in observation, however, different interpretations are sometimes possible and some might prefer a less-intuitive interpretation of reality. This does not have to be an issue - there’s no reason we should all believe in the same reality, especially the one on the scales which we cannot observe directly. Some views, however, may be limiting the observer of that reality. 12 Conclusion Angular momentum seems to form the fundamental signature of energy. All energy is thus fundamentally correlated with frequency. Evolution might concentrate these energies into corpuscular forms of different scale, however, oscillation will always be relatively conserved and observable at all scales of space taking dilated time into account. But the single absolutely intrinsic property of a universe is relativity. Everything must be completely relative in order to exist. And to conserve this relativity in both space and time, everything exists on different scales of energy and transforms on different scales of time. Amenoum[58], anno incarnati β33. Acknowledgement None of my work would be possible without all the work of all the observers of observables of different scale, theorists describing physics of such universes and promoters and propagators of knowledge. It would not be possible without my parents who would not be possible without the countless other generations of 152 parents. It would not be possible without Earth providing souls and energy for all these creatures, without the Sun providing soul and energy for Earth and without the galaxy providing soul and energy for the Sun, etc. Last, but not least, this would not be possible without all the smaller universes of my body entangled with my self, often enduring my sleepless nights with understanding rather than rebellion. Thus, I thank everything for every thing and every thing for everything. References [1] Fast galaxy bars continue to challenge standard cosmology (2021), M. Roshan et al., Mon. Not. R. Astron. Soc. 508(1), 926-939 https://doi.org/10.1093/mnras/stab2553 [2] From Galactic Bars to the Hubble Tension: Weighing Up the Astrophysical Evidence for Milgromian Gravity (2022), I. Banik and H. Zhao, Symmetry 14(7), 1331 https://doi.org/10.3390/sym14071331 [3] Something is wrong in the state of QED (2021), O. Consa https://arxiv.org/pdf/2110.02078.pdf [4] Putovanje kroz vrijeme (2021), M. Ljubičić, Universum Amenoum: D. Log https://doi.org/10.5281/zenodo.5459550 [5] What is a Spinor? (2021), M. Hughes https://in-theory.net/what-is-a-spinor/ [6] The variance of the CMB temperature gradient: a new signature of a multiply connected Universe (2021), R. Aurich et al., Classical. Quant. Grav. 38(22), 225005 https://doi.org/10.1088/1361-6382/ac27f0 [7] The Universe Is a Giant Donut That We Live Inside, New Research Suggests (2021), S. Wells https://www.vice.com/en/article/3aqjkn/the-universe-is-a-giant-donutthat-we-live-inside-new-research-suggests [8] The distribution of galaxy rotation in JWST Advanced Deep Extragalactic Survey (2025), L. Shamir, Monthly Notices of the Royal Astronomical Society 538(1), 76-91 https://doi.org/10.1093/mnras/staf292 [9] Guided Evolution: Development and organization of beings from a nonabsolute reference frame (2025), M. Ljubičić https://completerelativity.org/log/9_guided_evolution.html 153