Abstract We take physical distinguishability as the sole primitive of physics: two states are distinct if and only if some measurement can tell them apart. From this single principle, a geometry emerges on the space of all physical states. Its universal threshold — the point where the rate of change of distinguishability saturates — is simultaneously the quantum speed limit, the event horizon of a black hole, and the critical point of a thermodynamic phase transition. Quantum mechanics, general relativity, and thermodynamics are three expressions of the same geometric threshold on different state spaces; the constants ℏ, c , and k B are conversion factors between them. Within this structure, we identify a parameter-free geometric mechanism that yields the Schrödinger equation; the Einstein field equations both on the horizon (exactly) and in the bulk (to corrections smaller than 10⁻³² at all accessible energies); the Lorentzian signature of spacetime; and a structural resolution of the cosmological constant problem, reducing the standard discrepancy of 10¹²³ to order unity. Consequently, the framework evaluates a vacuum length scale of 88 μm and energy 2.25 meV from the observed dark-energy density, placing the dominant source in the lightest neutrino sector. The framework further suggests that macroscopic quantum coherence suppresses geodesic distinguishability — the Bose–Einstein condensate (BEC) analogue of the Meissner effect — with a predicted breathing-mode shift of ~1.5 mHz in ⁸⁷Rb. IBM Quantum experiments on three independent 156-qubit Heron processors show excitation probabilities differing by a factor of 3.8 across protocols with identical control parameters but different geometric paths, consistent with the prediction that endpoint distinguishability governs the outcome. Cross-backend transfer errors remain below 1%. Physical reality is what is distinguishable. The laws of nature are the geometry of distinguishability.
Abstract We take physical distinguishability as the sole primitive of physics: two states are distinct if and only if some measurement can tell them apart. From this single principle, a geometry emerges on the space of all physical states. Its universal threshold — the point where the rate of change of distinguishability saturates — is simultaneously the quantum speed limit, the event horizon of a black hole, and the critical point of a thermodynamic phase transition. Quantum mechanics, general relativity, and thermodynamics are three expressions of the same geometric threshold on different state spaces; the constants ℏ, c , and k B are conversion factors between them. Within this structure, we identify a parameter-free geometric mechanism that yields the Schrödinger equation; the Einstein field equations both on the horizon (exactly) and in the bulk (to corrections smaller than 10⁻³² at all accessible energies); the Lorentzian signature of spacetime; and a structural resolution of the cosmological constant problem, reducing the standard discrepancy of 10¹²³ to order unity. Consequently, the framework evaluates a vacuum length scale of 88 μm and energy 2.25 meV from the observed dark-energy density, placing the dominant source in the lightest neutrino sector. The framework further suggests that macroscopic quantum coherence suppresses geodesic distinguishability — the Bose–Einstein condensate (BEC) analogue of the Meissner effect — with a predicted breathing-mode shift of ~1.5 mHz in ⁸⁷Rb. IBM Quantum experiments on three independent 156-qubit Heron processors show excitation probabilities differing by a factor of 3.8 across protocols with identical control parameters but different geometric paths, consistent with the prediction that endpoint distinguishability governs the outcome. Cross-backend transfer errors remain below 1%. Physical reality is what is distinguishable. The laws of nature are the geometry of distinguishability.
Abstract We take physical distinguishability as the sole primitive of physics: two states are distinct if and only if some measurement can tell them apart. From this single principle, a geometry emerges on the space of all physical states. Its universal threshold — the point where the rate of change of distinguishability saturates — is simultaneously the quantum speed limit, the event horizon of a black hole, and the critical point of a thermodynamic phase transition. Quantum mechanics, general relativity, and thermodynamics are three expressions of the same geometric threshold on different state spaces; the constants ℏ, c , and k B are conversion factors between them. Within this structure, we identify a parameter-free geometric mechanism that yields the Schrödinger equation; the Einstein field equations, exactly on the horizon and in the bulk to corrections below 10⁻³² for stationary configurations (the fully dynamical case is not established here); the Lorentzian signature of spacetime; and a structural mechanism that reduces the standard 10¹²³ discrepancy of the cosmological constant problem to order unity, conditional on two framework-internal postulates (Section 13.8). Applying this, the framework evaluates a vacuum length scale of ~88 μm and energy ~2.25 meV from the observed dark-energy density, placing the dominant source in the lightest neutrino sector. The framework further suggests that macroscopic quantum coherence suppresses geodesic distinguishability — the Bose–Einstein condensate (BEC) analogue of the Meissner effect — with a predicted breathing-mode shift of ~1.5 mHz in ⁸⁷Rb. IBM Quantum experiments on three independent 156-qubit Heron processors show excitation probabilities differing by a factor of ≈3.7 across protocols with identical control parameters but different geometric paths, consistent with the prediction that endpoint distinguishability governs the outcome. Cross-backend transfer errors remain below 1%. Physical reality is what is distinguishable. The laws of nature are the geometry of distinguishability.
Abstract We propose physical distinguishability as the fundamental primitive underlying quantum mechanics, general relativity, and thermodynamics. A state is defined operationally: two states are physically distinct if a physical interaction or measurement can reveal a difference between them. From this principle, a geometric structure emerges on the space of physical states, generating a universal accessibility measure and a geometric notion of time. A single threshold condition appears across all three domains, corresponding to the quantum speed limit, event horizons in gravity, and critical phenomena in thermodynamics. Within this framework, the standard Schrödinger equation is recovered in the quantum sector, while Einstein gravity emerges in the thermodynamic horizon sector. The framework also provides a geometric origin for the Lorentzian structure of spacetime and identifies the roles of Planck’s constant, the speed of light, and Boltzmann’s constant as conversion factors linking different physical realizations of distinguishability dynamics. The theory predicts a characteristic vacuum distinguishability scale of approximately 103 μm and an associated energy scale of approximately 7.6 meV. These quantities connect quantum-vacuum physics, neutrino-scale phenomena, and cosmological scales within a single geometric description. The framework is tested experimentally on IBM Quantum superconducting processors. Across one-qubit, two-qubit, 127-qubit, and 156-qubit experiments performed on three independent Heron-generation backends, excitation probabilities collapse onto universal curves when parameterized by endpoint distinguishability. Protocols with identical control parameters but different endpoint distinguishabilities produce outcomes differing by up to a factor of 3.8, while protocols with identical endpoint distinguishabilities yield consistent results across independent processors. Cross-backend transfer errors remain below 1%. In addition to quantum-computing experiments, the framework suggests new tests in precision metrology, including atomic-force and scanning-tunneling microscopy, where large probe displacements may provide an independent route for testing vacuum distinguishability effects. Taken together, the theoretical construction, vacuum-sector predictions, and quantum-hardware experiments support distinguishability geometry as a unified and experimentally testable framework for physical dynamics.
Abstract We propose physical distinguishability as the fundamental primitive underlying quantum mechanics, general relativity, and thermodynamics. A state is defined operationally: two states are physically distinct if a physical interaction or measurement can reveal a difference between them. From this single principle, the distinguishability divergence D generates a smooth state space endowed with a Riemannian metric , a geometric velocity, an accessibility scale Λ, an accessibility ratio , and a geometric time . The framework provides a unified geometric description of the three major domains of physics. Quantum mechanics emerges through the Fubini–Study geometry of projective Hilbert space, thermodynamics through Fisher–Rao and Ruppeiner information geometry, and general relativity through the geometry of geodesic deviation. The threshold condition A=1acquires a universal physical meaning and appears in all three realizations as the boundary between physically accessible and inaccessible evolution. Variational formulations of both the Einstein and Schrödinger equations are constructed within the same geometric framework. The Lorentzian signature of spacetime emerges from a single sign reversal associated with the geometric-time direction, while the coupling constant of the distinguishability action is connected to the observed vacuum energy density. The framework further predicts a characteristic vacuum distinguishability scale ≈8.8×10^(-5) m, corresponding to an energy scale≈2.25" " meV. The theory is tested experimentally on IBM Quantum superconducting processors. Across one-qubit, two-qubit, 127-qubit, and 156-qubit experiments performed on three independent Heron-generation backends, excitation probabilities collapse onto universal curves when parameterized by endpoint Fubini–Study distinguishability. Protocols with identical laboratory control parameters but different endpoint distinguishabilities produce excitation probabilities differing by up to a factor of 3.8, while protocols with identical distinguishability produce identical outcomes across independent processors. Cross-backend transfer errors remain below 1%, providing direct experimental support for endpoint distinguishability as a universal physical variable. Taken together, the theoretical construction, variational formulations, vacuum-sector predictions, and large-scale quantum-processor experiments support distinguishability geometry as a unified and experimentally testable foundation for physical dynamics.
What if the black-hole information problem begins with the wrong primitive? Rather than treating information as a substance that must be stored, hidden, destroyed, or recovered, this research reframes the problem around Realised Physical Distinguishability (RPD): the physically actual capacity to discriminate between alternative states by operations performed with finite energy, finite time, finite resolution, and access to a specified algebra of observables. Two states belong to the same operational class when no admissible measurement can distinguish them above a fixed threshold. The resulting structure is RPD(M) := 𝒮(M) / ~, while information appears only as the derived quantity I(M) := log₂ |RPD(M)|. From this perspective, a black hole is not primarily a container of inaccessible bits. It is a horizon-mediated transformer of distinguishability classes. The event horizon changes which operations remain available to an exterior observer. Because the exterior algebra 𝒜_ext is only a restricted part of the global algebra, states that remain globally distinct may become operationally indistinguishable from outside. This produces the observer-dependent quotient RPD_𝒜(M) := 𝒮(M) / ~_𝒜 and motivates a time-dependent transformation of the form T_H(t): RPD_𝒜₁(M,t₁) ⇝ RPD_𝒜₂(M,t₂). Horizon crossing therefore need not mean the destruction of physical distinctions; it may instead mean their removal from one accessible channel and their redistribution into others. The paper identifies three candidate channels: null-wave delocalisation, in which causal structure and redshift carry distinctions beyond ordinary localisation; gravitational-geometric re-expression, in which mass, angular momentum, multipole structure, gravitational waves, and memory preserve aspects of the preceding configuration; and quantum-radiative redistribution, in which correlations among Hawking radiation, residual geometry, and possible topological sectors may progressively restore exterior-accessible distinctions. Unitarity is consequently interpreted not as the miraculous reconstruction of a former macroscopic object, but as the possible lawful continuity of distinguishability through changing physical forms. The framework is developed on a compact or effectively compact S³ carrier, while Schwarzschild-, Kerr-, or de Sitter-type horizons remain local models of operational inaccessibility. A quantitative selector branch compares the causal-spectral capacity of S³ with explicitly declared external ceilings such as Bekenstein or holographic bounds. Its central filter is Σ_grav^(P) = min(1, B_ceil / (b_P Γ_R(T) N_P(ε))), where Γ_R(T) describes the causally accessible fraction of the compact carrier and N_P(ε) counts distinguishable spectral modes at resolution ε. In the local regime, a notable cancellation gives B_causal^(P) ~ (2b_P C_P / 3π)(cT/ε)³, removing the carrier radius R from the leading term and producing the threshold relation (ε_*^(P))³ = (2b_P C_P ln 2 / 3π²)cTℓ_P². This selector is not proposed as a force law or a complete microscopic theory; it is a disciplined diagnostic of how causal access, spectral resolution, and gravitational ceilings constrain physically realisable distinctions. The work further introduces topological horizon capacity as an open research object and explores whether holonomy, Berry phases, the Hopf fibration S¹ → S³ → S², and sectors labelled by Q_H ∈ ℤ could protect or transform distinguishability during collapse and evaporation. No final solution of the black-hole information paradox is claimed. The research contribution is a sharper foundational question: not “Where are the bits?”,but “Which physical differences remain realisable, for whom, through which channels, and under what geometric and topological limits?”
We develop an extended formulation of Universal Modular Dynamics (UMD) in which physical law is organized as a hierarchy of nested, renormalization-stable informational phases emerging from a pre-quantum domain of distinguishability. The construction does not assume spacetime, locality, quantum fields, or graph structure as fundamental. Instead, the primitive level is defined through relations of distinguishability between pre-physical configurations, whose dynamically persistent sectors provide the substrate from which effective operator states and subsequent physical structures emerge. Within this architecture, previously derived pre-string configurations are interpreted as a particular low-dimensional stable sector of the broader UMD pre-quantum state space, rather than as the universal starting point of the theory. Their collective scaling behavior admits an effective graph limit, providing a controlled route from pre-string organization to relational connectivity and, subsequently, to operational subsystem structure. This graph limit is therefore emergent and sector-dependent, rather than ontologically primitive. At the operator level, the density matrix ρ becomes the carrier of distinguishability and generates modular structure through K = −log ρ, Kρ|σ = −log ρ + log σ. Relative modular dynamics, together with completely positive open-system flows, defines a sequence of scale-dependent transformations through which stable subsystem decompositions, operational locality, and finite-speed information propagation emerge. The resulting causal structure is established before continuum spacetime geometry and is governed by Lieb– Robinson-type bounds on the transport of quantum correlations. A central aim of the present work is to sharpen the transition from discrete relational organization to continuum spacetime. We explicitly distinguish the geometry of quantum state space from physical spacetime geometry and formulate the intermediate coarse-graining and scaling conditions required to connect Bogoliubov–Kubo–Mori information geometry, correlation-based relational distances, and an effective continuum metric. Einstein-type dynamics is then interpreted as an entropic consistency condition of the emergent geometric phase, arising from local information balance and variational stability rather than from a fundamental spacetime background. The same hierarchical framework is extended to access-relative vacuum structure and hidden-sector dynamics. Dark-energy-like behavior is associated with stable entropic vacuum drift relative to an observer-accessible algebra, while dark-matter-like effects arise from correlations and backreaction between visible and inaccessible sectors. These mechanisms are embedded within the same renormalization hierarchy rather than introduced as independent cosmological components. We further characterize regimes in which metricity, causal ordering, and stable factorization fail, defining non-geometric phases relevant to the breakdown of the spacetime description in extreme gravitational and early-universe regimes. Throughout the construction, we distinguish theorem-level results, conditional emergence statements, numerical evidence, and phenomenological predictions, and we identify explicit falsifiability conditions for the principal UMD claims. The resulting picture is that physical law is not represented by a single primitive dynamical equation imposed on a pre-existing arena, but by a recursively organized hierarchy of informational structures whose stable renormalization sectors generate quantum states, locality, causality, geometry, gravitation, and effective dark-sector phenomena.
Fire a single particle at a barrier with two slits. An interference pattern emerges even when particles are sent one at a time. Introduce which-path detection and the pattern disappears. Quantum mechanics predicts these outcomes with extraordinary accuracy. What it does not provide is a widely accepted physical account of the underlying mechanism. We present Binding Geometry, a framework that proposes such a mechanism. In this view, a particle corresponds to a locally jammed region within a frustrated geometric lattice. Each particle carries delocalized geometric slack—void degrees of freedom distributed through the surrounding structure. Because this slack is a property of geometry rather than a localized object, it can extend through both slits simultaneously. Overlapping slack configurations give rise to interference. Introducing a detector adds constraints to the local geometry, forcing the slack to localize into a single configuration and suppressing interference. This behaviour is one instance of a broader proposal: physical reality can be understood as a packing problem in which degrees of freedom arrange under geometric constraints. The structure of those constraints determines coordination numbers, phase thresholds, and the numerical values of physical constants. Established physical theories accurately describe the observable consequences of this packing. Binding Geometry aims to describe the underlying structure from which those consequences arise. The framework leaves all experimentally verified equations of the Standard Model and General Relativity intact. It instead addresses a class of open questions left unresolved by current theory, including the origin of the fine-structure constant, the smallness of the cosmological constant, the existence of three particle generations, and the physical interpretation of quantum measurement. Binding Geometry has been examined across more than forty domains spanning physics, computation, and biology (enumerated in Supplement B), where thresholds and transition points consistently align with predictions derived from packing geometry. The framework also yields falsifiable predictions, including the persistence of evolving dark energy in continued DESI releases and a correlated drift between cosmological parameters and the fine-structure constant.