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 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 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 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.
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.
Physics is written in mathematics, and at the base of mathematics lies distinction: yes or no, identical or different, one or zero. A bit is the minimal written form of such a distinction. Physics can therefore measure only what can become distinguishable. What cannot be distinguished cannot yet appear as a physical record. From distinguishability comes information; from the registration of information comes physical time. Unified informational Theory (UiT) presents a unified physical framework in which time, mass, force, thermodynamic directionality, electromagnetic coupling, nuclear structure, and horizon physics are expressed through one informational registration mechanism: closed phase becoming physical record. The central object is a closed-light phase carrier: a closed photon-like phase structure carrying informational increments of ℏ, rotating on a complex phase surface at the Compton frequency, with a Planck-scale phase radius. It is not treated as a point mechanically moving through ordinary three-dimensional space. Before measurement, its structure exists in the complex phase domain as physical distinguishability: real, active, and capable of producing measurable effects, but not yet written as an ordinary 3+1 record such as position, trajectory, detector event, clock reading, or linear-time history. Measurement is the operation that projects and registers part of this complex phase structure into ordinary record-space, using energy and carrying a thermodynamic cost. In UiT, linear physical time is the ordered registration of physical change into record. A record may be a clock reading, track, pointer state, detector click, environmental correlation, thermodynamic trace, or any stable physical mark. Time is not a passive background parameter. It is the informational order produced when phase structure becomes registered reality. The same principle also defines force. All forces are gradients of one underlying registration object, read under different load conditions, geometries, and coupling branches. A force appears where an invariant closed phase carrier is placed in a field whose time-registration rate varies across record-space. The carrier cannot change its own invariant Compton phase throughput, so the mismatch between invariant internal phase and local registration capacity becomes a physical force. Inertia and gravity are therefore not separate mysteries at the deepest level: both are responses of the same closed phase throughput to different ways of limiting temporal registration. Special relativity arises when recorded motion consumes part of the available registration bandwidth. Motion requires information about position and change of position, and this cost enters quadratically. The carrier phase itself never stops moving; what changes is how much of its invariant phase throughput can be written as linear time rather than as recorded motion. Lorentz time dilation is therefore read as a registration-budget partition: motion spends part of the time-writing capacity. Gravity arises from the same Compton throughput read radially. A mass is not merely an object placed inside space. It is closed-light Compton sampling of a Planck registration-stiffness update. Around it, record-space has reduced capacity to write distinguishable temporal information. Less capacity remains for writing time, and the radial gradient of that capacity is read as gravity. In this view, space is not a rubber sheet that literally bends. Space is the local capacity to register distinguishable physical alternatives. Changing the time-registration capacity also changes the spatial registration structure, so the same geodesics are obtained, but their ontology changes: curvature is the metric bookkeeping of variable registration capacity. This same capacity logic leads directly to thermodynamics and entropy. Entropy counts the available or dispersed ways in which distinctions can be written, stabilized, erased, hidden, or made inaccessible. Thermodynamic directionality is not added from outside. It is the cost and irreversibility of registering physical distinction into stable record. Horizon entropy is the saturated boundary count of the same closed phase surface: the point where ordinary exterior registration reaches its limiting boundary. Electromagnetism is read as a phase-connection branch of the same object. Charge is not introduced as an unrelated primitive substance, but as a coupling orientation of phase registration. Electric and magnetic effects are different record-space readouts of this phase connection under different motion and registration conditions. The weak sector gives UiT its primary empirical handle. Radioactive decay is treated as a finite identity-rewrite process. In order for a decay path to be environmentally perturbable, the environment must couple to degrees of freedom required for reverse daughter-to-parent reconstruction. This requires local reverse temporal registration: a limited branch in which identity is locally unwritten and rewritten. From this postulate, UiT produces a taxonomy of radioactive-decay perturbability, functioning like a periodic table of decay influence. The table does not merely classify known decays by name; it identifies which decay channels can be perturbed and why, according to the informational variables required by the reverse reconstruction path. The strong sector is expressed through closed multi-carrier phase geometry. Three phase carriers form a zero-sum closure in the complex plane. What appears outwardly as fractional charge is a projection of a deeper internal closure: one-third is externally read, while two-thirds remain internally locked within the phase structure. This gives a geometric and numerical account of fractional charge weights, confinement architecture, and the Cornell-potential structure, while leaving full QCD dynamics and detailed coefficients as completion targets. UiT is not presented as a theory of everything, and it does not discard established physics. It proposes a deeper informational primitive from which quantum phase, relativistic time, gravitational distortion, thermodynamic irreversibility, electromagnetic coupling, weak decay, strong closure, and horizon counting arise as different expressions of one closed phase-registration object. The empirical content is twofold. The primary tested layer is the weak-sector perturbability table, which organizes radioactive decay channels according to the informational degrees of freedom required for reverse daughter-to-parent reconstruction. A second prospective discriminant predicts photon arrival-time delay with no linear Planck-energy term and leading quadratic Planck suppression. The compact unification principle is this: physical law is the geometry of informational registration. Time is the written order of phase registration; mass is closed-light Compton throughput; force is the gradient of registration mismatch; entropy is the count and cost of distinguishable writing; and the apparent separation between relativity, thermodynamics, electromagnetism, nuclear structure, and horizon physics reflects different readout conditions of the same underlying closed phase surface.