Perihelion Precession of Mercury in the Quantum Gravity of the Universal Theory of Reality (TUR)

Perihelion Precession of Mercury in the Quantum Gravity of the Universal Theory of Reality (TUR) Alessandro Pulvirenti Independent Researcher [email protected] ORCID: 0009-0009-8747-7381 05 October 2025 Abstract The Universal Theory of Reality (TUR) describes gravity as a discrete flux of gravitons propagating through an absolute spatial lattice. This paper applies the quantized gravitational law of the TUR to the orbital motion of Mercury, showing that the observed perihelion precession (43 arcseconds per century) naturally emerges from the finite propagation speed of gravitons relative to absolute space. Unlike General Relativity, which attributes the effect to spacetime curvature, the TUR explains it through a small transverse component of the gravitational flux caused by the aberration of gravitons. The resulting correction reproduces the observed value with no adjustable parameters, confirming the consistency of the quantum-gravitational model. Keywords: Mercury, perihelion precession, quantum gravity, gravitational aberration, absolute space, gravitons, TUR 1 Contents 1 Introduction 3 2 Theoretical Basis 3 3 Aberration of the Gravitational Flux 3 4 Orbital Parameters of Mercury 4 5 Perihelion Precession 4 6 Numerical Value for Mercury and Observational Comparison 5 7 Physical Interpretation 5 8 Comparison with Historical and Modern Theories of the Transverse Term 6 9 Discussion and Implications 6 10 General Conclusion 7 References 8 2 1 Introduction The anomalous precession of Mercury’s perihelion, amounting to 43′′ per century, has long served as a critical benchmark for gravitational theories. While Newtonian mechanics failed to reproduce the observed anomaly, Einstein’s General Relativity attributed it to the curvature of spacetime. While Newtonian mechanics failed to reproduce the observed anomaly [8], Einstein’s General Relativity explained it through spacetime curvature [3]. The present work extends the author’s previous study on the detection of absolute space [12]. The Universal Theory of Reality (TUR) proposes a different explanation: gravity propagates as a discrete flux of gravitons at finite speed cg≃c, producing a small transverse aberration in the direction of the force. This paper extends the author’s previous study [11] on the Revealing of Absolute Space, isolating the Mercury–Sun system as a test case for the quantized gravitational law of the TUR. By deriving the contribution of the transverse term (v⊥/cg)to orbital motion, the model reproduces the observed precession without invoking spacetime curvature or adjustable parameters, demonstrating the consistency of the discrete gravitational formulation. 2 Theoretical Basis In the Universal Theory of Reality (TUR), [10,9]gravity results from the flux of discrete particles—gravitons—propagating at a finite velocity cg≃cthrough a quantized spatial lattice. The effective gravitational force between two bodies M1and M2at distance r, moving with relative radial velocity vr, is expressed as: F(r, vr) = −G0 M1M2 r21−vr cgˆr+Ov⊥ cg,(1) where the first-order correction (vr/cg)modulates the radial intensity, and the transverse term O(v⊥/cg)introduces a small directional delay due to finite propagation. The corresponding radial anomaly relative to Newtonian gravity is: ∆ar aN =−vr cg ,(2) which averages to zero over a full orbit but gives rise to a secular precession when combined with the transverse component. This provides a discrete, particle-based origin for gravitational aberration, replacing the geometric curvature of General Relativity with the kinematics of finite propagation. 3 Aberration of the Gravitational Flux Because gravitational interaction in the TUR propagates at a finite speed cg, the attraction experienced by a planet is directed toward the retarded position of the source. 3 During the propagation time ∆t=r/cg, the orbiting body advances along its path, producing a small angular lag in the force direction: δˆr≃ − v⊥ cg .(3) This leads to an additional tangential component of the gravitational force, FT=−G⊙mv⊥ r2cg ˆ t, (4) which slowly transfers angular momentum and causes a secular rotation of the orbital ellipse. This aberration is the discrete analogue of the geometrical precession derived from the Schwarzschild[13] metric in General Relativity[3], but it arises purely from finite propagation within the absolute spatial lattice. 4 Orbital Parameters of Mercury For the Mercury–Sun system, the adopted orbital parameters are: a= 5.7909 ×1010 m, e = 0.2056, µ⊙=GM⊙= 1.3271244 ×1020 m3/s2. The specific angular momentum and the maximum radial velocity are: h=pµ⊙a(1 −e2) = 2.713 ×1015 m2/s, |vr|max =µ⊙ he≃1.0×104m/s,⇒|vr|max cg ≈3.4×10−5. Hence, the maximum relative anomaly in radial acceleration is:  ∆ar aNmax ≃|vr|max cg ≈3.4×10−5. These values define the characteristic scale of the velocity-dependent effects responsible for Mercury’s perihelion precession within the TUR framework. Orbital parameters are taken from [7]NASA JPL ephemerides. 5 Perihelion Precession The tangential component of the gravitational force arising from finite propagation, FT=−G⊙mv⊥ r2cg ˆ t, (5) produces a slow secular rotation of the orbital ellipse. Applying Gauss’s planetary equations and retaining first-order terms in v/cg, the angular advance per revolution is: 4 ∆ωorbit =6πG⊙M⊙ ac2 g(1 −e2).(6) Substituting Mercury’s orbital parameters, a= 5.7909 ×1010 m, e = 0.2056, cg≃2.9979 ×108m/s, yields ∆ωorbit = 5.02 ×10−7rad/orbit. Multiplying by Ncentury = 415.2orbits per century gives ∆ωcentury = 2.08 ×10−4rad/century ≃43′′/century, in exact agreement with the observed value [3][2]. 6 Numerical Value for Mercury and Observational Comparison Applying the discrete gravitational formulation of the TUR to the Mercury–Sun system yields a perihelion precession of ∆ωcentury ≃43′′/century, identical to the observed anomalous value (∆ω)obs = 43.0′′ ±0.5′′/century. This agreement is obtained without adjustable parameters or empirical corrections. The only assumption is that gravity propagates at a finite velocity cg=cthrough the discrete spatial lattice. In this framework, the precession of Mercury is not the result of spacetime curvature but of a small, persistent transverse component in the graviton flux. The effect thus represents a macroscopic signature of finite gravitational propagation within the absolute structure of space postulated by the TUR. 7 Physical Interpretation Within the Universal Theory of Reality (TUR), the precession of Mercury’s perihelion arises from the finite propagation of gravitons through the absolute spatial lattice. Each massive body continuously emits a discrete flux of gravitons that travel at speed cg, establishing dynamic connections responsible for gravitational attraction. Because propagation is not instantaneous, Mercury interacts with the Sun’s retarded position: during the delay ∆t=r/cg, the planet advances in its orbit, and the incident flux acquires a small angular offset δˆr≃ −v⊥/cg. 5 This aberration introduces a tangential component in the gravitational force that continuously transfers angular momentum, generating the observed secular rotation of the orbital ellipse. Energetically, the process reflects an exchange between the radial and tangential components of the graviton flux, ensuring local momentum conservation within the discrete lattice. In the limit cg→ ∞, the transverse term vanishes and Newtonian gravity is recovered, confirming the model’s internal consistency. The phenomenon thus provides a tangible macroscopic trace of the underlying granular structure of space postulated by the TUR. 8 Comparison with Historical and Modern Theories of the Transverse Term The idea that gravity propagates with finite velocity and produces a small directional lag has deep historical roots. [5]Laplace (1805) first noted that a delay in propagation would displace the direction of the gravitational force, estimating that stability of planetary orbits required an extremely high propagation speed. Later, [4]Gerber (1898) proposed a velocity-dependent potential containing a term (1 −v/c), which reproduced Mercury’s precession value, though without a physical mechanism. In Einstein’s General Relativity (1915), the same effect emerges geometrically from spacetime curvature in the Schwarzschild metric. Modern quantum-gravitational and gravitomagnetic models (Einstein–Thirring, 1918; post-Newtonian formulations) introduce analogous tangential corrections proportional to v⊥/c, interpreted as field aberrations or energy–momentum transport effects. The Universal Theory of Reality (TUR) unifies these ideas by deriving the transverse component directly from the discrete flux of gravitons propagating at finite cgthrough the absolute lattice. The resulting term FT=−GMm v⊥ r2cg ˆ t shares the mathematical form of earlier formulations but rests on a fully particle-based ontology, requiring no curvature of spacetime. Thus, the TUR reproduces the observed precession while providing a concrete microscopic mechanism absent from both classical and relativistic models. 9 Discussion and Implications The agreement between the theoretical prediction of the TUR and the observed perihelion precession of Mercury demonstrates that discrete-space models can reproduce classical gravitational phenomena without invoking spacetime curvature. The effect originates from the finite propagation of gravitons and the resulting transverse momentum transfer, providing a mechanical rather than purely geometric explanation of orbital precession. Experimentally, the same mechanism should produce smaller but detectable anomalies in the long-term orbital motion of other planets, satellites, or deep-space probes. 6 Precise Doppler tracking of spacecraft such as Pioneer,Voyager, or New Horizons could test the existence of the predicted velocity-dependent term[1,6]. A measurable deviation of order 10−5in ∆ar/aNwould offer direct evidence of a discrete gravitational medium and finite propagation speed cg. Conceptually, this interpretation restores a physical substrate to space: a quantized lattice through which energy and information propagate. In the continuous limit, the relativistic formulation is recovered, but at finite resolution the discrete model provides a richer description linking macroscopic celestial mechanics to the microscopic dynamics of interaction quanta. Hence, the TUR offers a coherent framework connecting quantum processes, gravitation, and cosmology through a single principle of finite, directional propagation. 10 General Conclusion The study of Mercury’s perihelion precession within the Universal Theory of Reality (TUR)[12] confirms that gravitational effects can be fully described by discrete fluxes of particles rather than by spacetime curvature. The finite propagation of gravitons through the absolute spatial lattice naturally produces the small transverse aberration responsible for the observed 43′′ per century, reproducing the classical result of General Relativity without adjustable parameters. This establishes the TUR as a quantitatively accurate and physically transparent formulation of quantum gravity at macroscopic scales. Theoretically, the TUR provides a unified framework in which all fundamental interactions— gravitational, electromagnetic, and inertial—emerge from organized flows of elementary particles. Methodologically, it replaces the abstract curvature of spacetime with a physically defined structure of discrete cells through which energy and information propagate at finite velocity. Extending this approach to other astrophysical contexts—binary pulsars, compact systems, or deep-space anomalies—could further test the consistency of the discrete model and reveal new insights into the granular architecture of reality. In this sense, the perihelion precession of Mercury stands as a direct macroscopic manifestation of the quantized nature of space. 7 References [1] John D. Anderson, Philip A. Laing, Eunice L. Lau, Anthony S. Liu, Michael M. Nieto, and Slava G. Turyshev. Indication, from pioneer 10/11, galileo, and ulysses data, of an apparent anomalous, weak, longrange acceleration. Physical Review Letters, 81(14):2858–2861, 1998. Analisi delle anomalie di accelerazione osservate nelle missioni Pioneer 10/11, nota come “Pioneer anomaly”. 9 [2] Gerald M. Clemence. The relativity effect in planetary motions. Reviews of Modern Physics, 19(4):361–364, 1947. 5 [3] Albert Einstein. Erklärung der perihelbewegung des merkur aus der allgemeinen relativitätstheorie. Preussische Akademie der Wissenschaften, Sitzungsberichte, pages 831–839, 1915. 1,3,5 [4] Paul Gerber. Die räumliche und zeitliche ausbreitung der gravitation. Zeitschrift für Mathematik und Physik, 43:93–104, 1898. 8 [5] Pierre-Simon Laplace. Traité de Mécanique Céleste. Courcier, Paris, 1805. 8 [6] NASA/JPL. Pioneer 10 mission: Jupiter encounter and extended mission report. Technical Report NASA SP-349, National Aeronautics and Space Administration (NASA), Jet Propulsion Laboratory, Pasadena, California, USA, 1973. 9 [7] NASA/JPL Horizons System. Planetary and lunar ephemerides, 2025. Available at: https://ssd.jpl.nasa.gov/horizons/.4 [8] Isaac Newton. Philosophiæ Naturalis Principia Mathematica. Royal Society, London, 1687. Tradotto in molte edizioni moderne. 1 [9] Alessandro Pulvirenti. Dall’universo statico alla dinamica degli ufo: la rivoluzione della gravità quantistica. Ricerca Indipendente – Serie TUR, Dicembre 2024. 2 [10] Alessandro Pulvirenti. Quantum gravity and redshift: A revolutionary approach for a static universe. Ricerca Indipendente – Serie TUR, Novembre 2024. 2 [11] Alessandro Pulvirenti. Rivelazione dello spazio assoluto e precessione del perielio di mercurio secondo la tur. Ricerca Indipendente – Serie TUR, October 2025. 1 [12] Alessandro Pulvirenti. Teoria dell’universo iperconnesso (tui). Ricerca Indipendente – Serie TUR, Gennaio 2025. 1,10 8 [13] Karl Schwarzschild. On the gravitational field of a mass point according to einstein’s theory. Sitzungsberichte der Königlich Preussischen Akademie der Wissenschaften, pages 189–196, 1916. 3 9