Traditional approaches to a "Theory of Everything" (ToE) propose specific fundamental dynamics and attempt to derive observed physics from them, implicitly assuming physics is objective—a property of fundamental reality that observers merely discover. Scale-Relative Distinguishability Theory (SRDT) challenges this assumption by operating at the meta-theoretic level: rather than proposing specific content, SRDT specifies what any valid ToE must include. The central insight is that physics is not a property of fundamental dynamics (𝓕) alone, but emerges from the quotient 𝓕/𝓞—the equivalence classes of configurations that an observer 𝓞 with finite resolution cannot distinguish. This paper demonstrates SRDT's framework efficacy: its capacity to generate physics-like phenomena from a single mechanism without presupposing physical concepts. Using coupled Hénon maps as dynamics 𝓕 and a finite-resolution observer 𝓞, we show that twelve structural analogs of foundational physics concepts emerge from the quotient operation: space, time, matter, forces, wave-particle duality, entropy, quantization, superposition, locality, apparent randomness, measurement, and uncertainty. All twelve are classified as observer-created or observer-selective under SRDT's diagnostic taxonomy—none are intrinsic to 𝓕. This demonstration constitutes an existence proof: there exists at least one (𝓕, 𝓞) pair for which SRDT produces physics-like structure, validating the framework without claiming correspondence to human physics. The paper establishes that a complete Theory of Everything must specify not only fundamental dynamics but also observer characteristics—and for human physics, this means characterizing what we are as biological, embedded, finite-resolution observers.
Traditional approaches to a "Theory of Everything" (ToE) propose specific fundamental dynamics and attempt to derive observed physics from them, implicitly assuming physics is objective—a property of fundamental reality that observers merely discover. Scale-Relative Distinguishability Theory (SRDT) challenges this assumption by operating at the meta-theoretic level: rather than proposing specific content, SRDT specifies what any valid ToE must include. The central insight is that physics is not a property of fundamental dynamics (𝓕) alone, but emerges from the quotient 𝓕/𝓞—the equivalence classes of configurations that an observer 𝓞 with finite resolution cannot distinguish. This paper demonstrates SRDT's framework efficacy: its capacity to generate physics-like phenomena from a single mechanism without presupposing physical concepts. Using coupled Hénon maps as dynamics 𝓕 and a finite-resolution observer 𝓞, we show that twelve structural analogs of foundational physics concepts emerge from the quotient operation: space, time, matter, forces, wave-particle duality, entropy, quantization, superposition, locality, apparent randomness, measurement, and uncertainty. All twelve are classified as observer-created or observer-selective under SRDT's diagnostic taxonomy—none are intrinsic to 𝓕. This demonstration constitutes an existence proof: there exists at least one (𝓕, 𝓞) pair for which SRDT produces physics-like structure, validating the framework without claiming correspondence to human physics. The paper establishes that a complete Theory of Everything must specify not only fundamental dynamics but also observer characteristics—and for human physics, this means characterizing what we are as biological, embedded, finite-resolution observers.
Scale-Relative Distinguishability Theory (SRDT) is a formal meta-theoretical framework for analyzing what embedded observers can know about fundamental reality. The framework is grounded in a single primitive relation: distinguishability relative to an observer. From this foundation, we develop a rigorous mathematical structure encompassing dynamics (systems that can be observed), observers (specifications of measurement capabilities), the observation operation (constructing models from dynamics via quotient), and a diagnostic methodology for classifying phenomena. The central result: what embedded observers can know is the structure of observation itself—the systematic relationship between observer characteristics and what those observers perceive. This is not a limitation but the most complete answer embedded observers can give. The framework is deliberately agnostic about the nature of finest-grained dynamics 𝓕. Spatial and temporal dimensions are not presupposed—they emerge as observer-constructed interfaces. We establish conditions for deterministic versus probabilistic behavior, prove information-theoretic bounds including a coarsening dominance theorem, and develop a five-category diagnostic methodology for classifying phenomena as intrinsic to 𝓕 versus observer-created. The quotient network—connecting quantum field theory, quantum mechanics, classical mechanics, thermodynamics, and other physical frameworks—is interpreted not as a map of fundamental reality but as a map of human observation: nodes represent characteristic bundles (regions of observer space), and arrows represent transformations from changing observer characteristics. This reframing has profound implications for the Theory of Everything program, requiring that any complete theory specify not only fundamental dynamics but also observer characteristics.
We present a computational demonstration that the apparent wave-particle duality inthe double-slit experiment emerges naturally from the quotient structure connecting two observerbundles: the quantum-coherent bundle OQM (which perceives interference patternsand superposition) and the measurement bundle OMeas (which perceives discrete detectionevents). Through numerical simulations, we show that individual detection eventsappear random and particle-like while statistical accumulation reveals the underlying wavepattern—without invoking wave function collapse. Crucially, this analysis adopts the epistemic structuralism of Scale-Relative DistinguishabilityTheory (SRDT): we make no claims about the intrinsic nature of fundamental dynamicsF. The wave function ψ(x, t) is what OQM perceives; discrete detections are whatOMeas perceives. Both are quotients of F, denoted F/∼O. Asking “is the electron reallya wave or a particle?” is asking about F’s intrinsic nature—a question that lies beyondembedded-observer access. Our simulations validate the quotient structure quantitatively: pattern visibility metricsshow smooth transitions from particle-like to wave-like statistics as detection number Nincreases, with correlation coefficients exceeding 0.99 between simulated and theoreticaldistributions. We derive testable predictions for the critical detection number Ncritical ∝(δx)2 as a function of detector resolution. We further demonstrate that the double-slit experiment instantiates universal SRDTpatterns appearing across multiple physics transforms: wave-particle duality dissolves asobserver-relative descriptions of an F-unity, and the wave-to-particle transition is structurallyisomorphic to the Wave Optics → Geometrical Optics transform. The question“which slit did the photon go through?” is shown to be a category error analogous to askingfor the temperature of a specific microstate.
This work introduces and formalizes Horizon Monism, a foundational relational research program built upon minimal ontology. It postulates a timeless, scale-free, geometry-free totality of relations \mathfrak{R}, together with a collection of irreducible first-person referential anchors. All observable physical phenomena emerge from a single core constraint: finite distinguishability. Each referential anchor carries a non-injective information extraction map, which induces reference-dependent equivalence relations. These partition the underlying relational totality into quotient spaces of effectively distinguishable states. Non-commutative algebraic structures (quantumness), effective time and its arrow, Lorentzian spacetime geometry together with gravity, and gauge interactions all arise homologously as effective descriptions for observers confined within finite referential horizons. We rigorously demonstrate that finite equivalence classes equipped with relation groupoids yield non-commutative C^*-algebras. A four-point classical toy model further illustrates that incompatible extraction operations can naturally produce non-commutativity, serving as a mathematical prototype for the horizon-based origin of quantum structures. We clearly separate three tiers of statements: constructively proven mathematical results, hypothetical emergence mechanisms, and low-energy effective phenomenology. The Standard Model gauge group and particle spectra are treated as low-energy emergent features to be derived in future work, rather than fundamental axioms. This framework avoids circular reasoning by not presupposing time, probability, spacetime geometry or quantum states at the ontological level, offering a falsifiable relational pathway toward quantum gravity.
We propose a reconstruction of physical theory based on the principle of distinguishability, formulated within the framework of Universal Modular Dynamics (UMD). Instead of assuming spacetime, fields, or dynamical laws as fundamental, we begin with a minimal relational structure defined by distinguishable proto-states. We show that consistency requirements on distinguishability lead naturally to a probabilistic structure, whose basis-invariant representation is given by the density operator ρ. The associated modular generator K = −log ρ encodes the intrinsic organization of the system, while its spectral distribution provides a complete description of informational structure. Within this framework, dynamics is reinterpreted as a flow in the space of states, and the renormalization group is identified with spectral evolution of ρ. Phase structure emerges from the behavior of optimal partitions, leading to an operational notion of criticality defined by landscape flatness and switching rates. We demonstrate that geometry, gauge structure, and gravitational behavior arise as emergent phenomena associated with specific dynamical regimes. In particular, gauge symmetry is interpreted as access-relative redundancy, and spacetime structure appears as an effective description of underlying spectral organization. The framework is supported by a computational program that introduces operational diagnostics, including spectral observables, modular commutators, and phase classification criteria. These tools allow for numerical exploration and identification of domains of validity. The results suggest that a unified description of physical reality can be constructed from a minimal informational ontology, in which all structures arise from intrinsic properties of the density operator and its modular dynamics.
The file on this site provides the slides for a lecture given in Hangzhou in May 2018, and the lecture itself is available at the URL beginning 'sms' in the set of links provided in connection with this item. It is commonly assumed that regular physics underpins biology. Here it is proposed, in a synthesis of ideas by various authors, that in reality structures and mechanisms of a biological character underpin the world studied by physicists, in principle supplying detail in the domain that according to regular physics is of an indeterminate character. In regular physics mathematical equations are primary, but this constraint leads to problems with reconciling theory and reality. Biology on the other hand typically does not characterise nature in quantitative terms, instead investigating in detail important complex interrelationships between parts, leading to an understanding of the systems concerned that is in some respects beyond that which prevails in regular physics. It makes contact with quantum physics in various ways, for example in that both involve interactions between observer and observed, an insight that explains what is special about processes involving observation, justifying in the quantum physics context the replacement of the unphysical many-worlds picture by one involving collapse. The link with biology furthermore clarifies Wheeler’s suggestion that a multiplicity of observations can lead to the ‘fabrication of form’, including the insight that this process depends on very specific ‘structures with power’ related to the 'semiotic scaffolding' of the application of sign theory to biology known as biosemiotics. The observer-observed 'circle' of Wheeler and Yardley is a special case of a more general phenomenon, oppositional dynamics, related to the 'intra-action' of Barad's Agential Realism, involving cooperating systems such as mind and matter, abstract and concrete, observer and observed, that preserve their identities while interacting with one another in such a way as to act as a unit. A third system may also be involved, the mediating system of Peirce linking the two together. Such a situation of changing connections and separations may plausibly lead in the future to an understanding of how complex systems are able to evolve to produce 'life, the universe and everything'. (Added 1 July 2018) The general structure proposed here as an alternative to a mathematics-based physics can be usefully characterised by relating it to different disciplines and the specialised concepts utilised therein. In theoretical physics, the test for the correctness of a theory typically involves numerical predictions, corresponding to which theories are expressed in terms of equations, that is to say assertions that two quantities have identical values. Equations have a lesser significance in biology which typically talks in terms of functional mechanisms, dependent for example on details of chemistry and concepts such as genes, natural selection, signals and geometrical or topologically motivated concepts such as the interconnections between systems and the unfolding of DNA. Biosemiotics adds to this the concept of signs and their interpretation, implying novel concepts such as semiotic scaffolding and the semiosphere, code duality, and appreciation of the different types of signs, including symbols and their capacity for abstraction and use in language systems. Circular Theory adds to this picture, as do the ideas of Barad, considerations such as the idea of oppositional dynamics. The proposals in this lecture can be regarded as the idea that concepts such as those deriving from biosemiotics have more general applicability than just conventional biology and may apply, in some circumstances, to nonlinear systems generally, including the domain new to science hypothesised to underlie the phenomena of present-day physics. The task then has to be to restore the mathematical aspect presumed, in this picture, not to be fundamental as it is in conventional theory. Deacon has invoked a complex sequence of evolutionary steps to account for the emergence over time of human language systems, and correspondingly mathematical behaviour can be subsumed under the general evolutionary mechanisms of biosemiotics (cf. also the proposals of Davis and Hersh regarding the nature of mathematics), so that the mathematical behaviour of physical systems is consistent with the proposed scheme. In conclusion, it is suggested that theoretical physicists should cease expecting to find some universal mathematical ‘theory of everything’, and focus instead on understanding in more detail complex systems exhibiting behaviour of a biological character, extending existing understanding. This may in time provide a more fruitful understanding of the natural world than does the regular approach. The essential concepts have an observational basis from both biology and the little-known discipline of cymatics (a discipline concerned with the remarkable patterns that specific waveforms can give rise to), while again computer simulations also offer promise in providing insight into the complex behaviours involved in the above proposals. References Jesper Hoffmeyer, Semiotic Scaffolding of Living Systems. Commens, a Digital Companion to C. S. Peirce (on Commens web site). Terrence Deacon, The Symbolic Species, W.W. Norton & Co. Karen Barad, Meeting the Universe Halfway: Quantum Physics and the Entanglement of Matter and Meaning, Duke University Press. Philip Davis and Reuben Hersh, The Mathematical Experience, Penguin. Ilexa Yardley, Circular Theory.
This document is obsolete; its content has been fully integrated into the consolidated PSE manuscript. This document presents the foundational definitions of the Principle of Emerging Structure (PSE), a theoretical framework in which physical reality arises from a prespatial network of correlations governed by two fundamental principles: evolutionary coherence (E) and structural coherence (C).Within this framework, space and time are not primitive entities but emergent properties derived from the structural relations within the network. Particles are defined as stable, localized, and quantized configurations of coherence—stationary modes of the underlying structure—while fields correspond to diffuse, non‑localized modes of the same dynamics.Interactions are described as structural reorganizations that modify the stability of these modes, eliminating the need for fundamental forces. The wave–particle duality is resolved as an artifact of the emergent description: wave‑like and particle‑like behaviors correspond to different regimes of coherence. Measurement is interpreted as a structural reconfiguration induced by interaction, without invoking collapse or observer‑dependent mechanisms.The uncertainty principle emerges naturally from the impossibility of stabilizing incompatible structural modes simultaneously, providing a geometric rather than epistemic interpretation. Additional concepts such as decoherence and emergent gravity are defined in terms of changes in structural coherence and curvature of structural distance.This document establishes the conceptual and ontological basis of the PSE and serves as a reference for the other works in the series. This work complements the previous document published on Zenodo with DOI: https://doi.org/10.5281/zenodo.20218975. Andrea Toricelli - a.toricelli@hotmail.it