Information as Reality: The τ-Delay Field as a Physical Mechanism for the Law of Increasing Functional Information

Information as Reality: The τ-Delay Field as a Physical Mechanism for the Law of Increasing Functional Information Bahman Masarrat Independent Researcher ORCID: 0009-0005-7834-0683 October 23, 2025 Abstract In their seminal work, Hazen and Wong propose a “law of increasing functional information,” positing that complexity in evolving systems arises from the selective accumulation of functional configurations over time. This principle extends beyond biology to encompass mineral, planetary, and technological evolutions. Complementing this, Masarrat’s fivedimensional τ-delay field (TDF) model provides a mathematical scaffold, where a dynamical delay scalar τin a compact fifth dimension encodes causal memory and informational flow. By unifying gravity, quantum mechanics, and fundamental forces through retarded projections, the TDF framework offers a physical mechanism for the growth of functional information, transforming abstract selection into spacetime geometry and temporal asymmetry. This synthesis suggests that information is not merely descriptive but foundational, with τas its dynamical grammar. 1 Introduction: The Universe as Information The cosmos, in its vast expanse, whispers a secret: information may be as primordial as matter or energy. Traditional physics treats information as a secondary construct—a measure of entropy in thermodynamics or bits in quantum computations. Yet, recent paradigms challenge this view, elevating information to a fundamental ontology. In their 2023 PNAS article, Robert M. Hazen and Michael L. Wong introduce the “law of increasing functional information,” arguing that evolving systems tend to accrue configurations that perform useful functions, driven by selection pressures akin to Darwinian evolution but applicable universally. Functional information, as defined by Hazen and Wong, quantifies the efficacy of a system’s states in achieving persistence or adaptation. For instance, 1 Earth’s mineral diversity exploded from a handful of primordial types to thousands through geochemical processes favoring stable, catalytic forms. This law complements the second law of thermodynamics: while entropy disperses energy, functional information carves order from chaos, ratcheting complexity in pockets of the universe. Philosophically, it evokes a teleological undercurrent— not divine design, but an emergent directionality where the cosmos bootstraps its own sophistication. Yet, this proposal begs a mechanism: How does functional information accumulate without violating physical laws? Enter Bahman Masarrat’s fivedimensional τ-delay field (TDF) model, a theoretical framework that posits information as encoded in temporal lags within a higher-dimensional reality. By integrating delay dynamics with general relativity and the Standard Model, TDF suggests that the universe’s informational evolution is not abstract but geometrically inscribed in spacetime. If Hazen and Wong chart the “what” of complexity’s march, Masarrat provides the “how”—a poetic fusion where delays become the scribes of existence. 2 The τ-Delay Field Framework At the core of Masarrat’s TDF model lies the delay scalar field τ(x, t), a dynamical entity parameterizing retardation in causal propagation. Unlike conventional four-dimensional theories, TDF extends spacetime to a five-dimensional manifold M5=M4×Rχ, where χis a compact extra dimension representing delay. The metric takes the form ds2=gµν(x, χ)dxµdxν+ϵΦ2(x, χ)dχ2, with ϵ=±1 and Φ governing the dimensional scale. Observers in 4D perceive projections of 5D dynamics, where τencodes local memory—the lag between cause and effect. The model’s action is ghost-free, drawing from Horndeski scalars: S=Zd4x√−gM2 Pl 2R+K(τ, X)−G3(X)□τ+Sm[g, ψ], where X=−1 2gµν∇µτ∇ντ,K(τ, X) = X+β Λ4X2−V(τ), and G3(X) = c3 Λ3X. This ensures stability, with Vainshtein screening evading Solar System constraints while allowing cosmological modifications. Philosophically, τtransforms spacetime into a mnemonic medium. Each point harbors an intrinsic delay, storing causal histories like echoes in a canyon. This “local memory” couples information flow to geometry: gradients in τinduce effective curvature, mimicking dark energy and resolving Hubble tension without exotic components. In black holes, delays smear singularities, replacing infinities with finite de Sitter cores—a regularization born of informational diffusion. Thus, TDF reframes physics as informational: Matter sources delays, which in turn sculpt spacetime, fostering the conditions for complexity’s emergence. 2 3 Linking Functional Information to τ-Dynamics Hazen and Wong’s law posits that functional information Ifincreases as systems explore configuration spaces, with selection favoring viable states. Mathematically, If≈ −log2(p), where pis the probability of a functional configuration. But what drives this probabilistic bias physically? In TDF, the answer lies in τ-dynamics, analogous to Ricci flow in the delay dimension. Ricci flow, famously used by Perelman to prove the Poincar´e conjecture, smooths manifolds by evolving metrics under ∂gµν ∂t =−2Ricµν . Similarly, τ’s evolution along χ“flows” informational structures: Delays retard inefficient paths, amplifying functional ones through nonlinear terms like the cubic Galileon. Consider galactic rotation curves, fitted in TDF via Yukawa potentials V(r) = −GM r[1 + αe−r/λ], where λ∼m−1 τ. This emerges from τ-induced fifth forces, clustering matter in ways that enhance stability—a direct boost to functional information, as stable galaxies host star formation and chemical evolution. Cosmologically, τ’s background equations yield effective densities ρτ= 2XKX− K+ 6HX ˙τG3X, driving acceleration while resolving dark-sector mismatches. Here, the increase in Ifcorresponds to Ricci-like smoothing in τ-space: Inefficient configurations dissipate via delays, while functional ones persist, etched into geometry. This physicalizes selection—not as external pressure, but as intrinsic temporal filtering, where the universe’s memory biases toward order. 4 Time, Gravity, and Learning Time’s arrow and gravity’s pull, cornerstones of physics, find new meaning in this synthesis. The second law decrees entropy’s rise, yet Hazen and Wong’s principle counters with informational growth. TDF reconciles them: Delays enforce asymmetry, as retardation is forward-directed, imprinting past on future without reciprocity. Gravity, in TDF, arises from τ-gradients, disformally coupling matter and photons: ˜gµν =C(τ)gµν +D(τ)∇µτ∇ντ. This turns gravitation into informational flow—curvature as the fossil of accumulated functions, pulling systems toward complexity maxima. Analogies with learning systems abound. In neural networks, backpropagation minimizes loss by adjusting weights; in TDF, τ’s feedback loops (via G3) screen inefficiencies, akin to entropy minimization in AI. The cosmos, then, “learns” by encoding functional information in delays, evolving laws as attractors rather than fixtures. Quantum mechanics emerges similarly: Superpositions as unresolved τ-projections, entanglement as shared delays in χ. Poetically, gravity binds not just mass, but memories—the universe’s way of remembering what works, minimizing global entropy while maximizing local function. 3 5 Philosophical Implications If information underpins reality, TDF posits τas its grammar—a syntax of delays structuring existence. This shifts ontology: No longer a clockwork machine, the universe is a narrative engine, where τweaves chaos into coherence. Philosophically, it echoes Bergson’s dur´ee—time as creative duration, not mechanical ticks. Selection becomes cosmic creativity, with τas the medium of becoming. Ethically, if the universe “remembers and learns,” humanity’s role amplifies: Our technologies accelerate functional information, stewards of an evolving cosmos. Yet, caution lingers: Is this anthropic illusion, or profound truth? TDF’s testable predictions—modified gravity on scales, singularity resolutions—offer empirical arbitration. 6 Conclusion In harmonizing Hazen and Wong’s law with Masarrat’s TDF, we glimpse a unified vista: Information as the bedrock of being, propelled by delays that encode, select, and evolve. If information truly forms the foundation of existence, then the τ-field is its grammar—the way the universe remembers, learns, and becomes. References [1] Hazen, R. M., & Wong, M. L. (2023). On the roles of function and selection in evolving systems. Proceedings of the National Academy of Sciences, 120(43), e2310223120. [2] Masarrat Bakhsh, B. (2025). A Theory of Everything via the FiveDimensional Delay Field Model: Unifying Gravity, Quantum Mechanics, and Fundamental Forces. ResearchGate preprint. 4