We develop a record-based account of internal time in quantum mechanics. Persistent records first define an ordinal chronology through inclusion of their accumulated Boolean algebras. On a specified record filtration, we prove that, under three minimal consistency requirements, namely dependence only on conditional Born weight, invariance under sequential refinement of the same recorded fact, and continuity, the actualization of each outcome contributes an internal time proportional to its \textit{surprisal}, defined as the negative logarithm of that probability. A certain outcome therefore contributes no duration, whereas less probable outcomes contribute larger increments. The mean and variance of the accumulated clock are governed by the Shannon entropy and varentropy of the record process, its moment-generating function is related to the R'enyi entropy spectrum, and its pathwise fluctuations admit a Doob decomposition into a predictable entropic compensator and a martingale. Two further results provide independent consistency checks. Within the stated class of finite-dimensional bipartite states, universal additivity of local clock readings across all admissible local record contexts is equivalent to the absence of entanglement. In the quantum Zeno regime, the number of monitoring rounds may diverge while the expected accumulated surprisal tends to zero. The construction therefore supplies a canonical internal-time functional for a specified quantum record process without presupposing an external clock. It does not by itself identify which physical record processes constitute material clocks; determining their production rates and dynamical realization remains a separate problem.
We develop a record-based account of internal time in quantum mechanics. Persistent records first define an ordinal chronology through inclusion of their accumulated Boolean algebras. On a specified record filtration, we prove that, under three minimal consistency requirements, namely dependence only on conditional Born weight, invariance under sequential refinement of the same recorded fact, and continuity, the actualization of each outcome contributes an internal time proportional to its \textit{surprisal}, defined as the negative logarithm of that probability. A certain outcome therefore contributes no duration, whereas less probable outcomes contribute larger increments. The mean and variance of the accumulated clock are governed by the Shannon entropy and varentropy of the record process, its moment-generating function is related to the R'enyi entropy spectrum, and its pathwise fluctuations admit a Doob decomposition into a predictable entropic compensator and a martingale. Two further results provide independent consistency checks. Within the stated class of finite-dimensional bipartite states, universal additivity of local clock readings across all admissible local record contexts is equivalent to the absence of entanglement. In the quantum Zeno regime, the number of monitoring rounds may diverge while the expected accumulated surprisal tends to zero. The construction therefore supplies a canonical internal-time functional for a specified quantum record process without presupposing an external clock. It does not by itself identify which physical record processes constitute material clocks; determining their production rates and dynamical realization remains a separate problem.
Description This work develops a foundational reformulation of quantum measurement by treating physical time as an emergent, dynamically produced quantity rather than as an external background parameter. Within the Discrete Expansion and Emergent Time (DEET) framework, physical duration is generated by the spacetime gradient of a scalar phase field, \Theta(x), with the local time flow defined by u_\mu = \nabla_\mu \Theta. Once time is produced rather than assumed, the weighting of mutually exclusive quantum outcomes requires a new structural interpretation. The paper introduces a time-production (allocation) density \rho(\psi), defined as a bookkeeping quantity for realized physical time rather than a probability postulate. By imposing only minimal and physically unavoidable requirements—global phase invariance, locality, separability under independent composition, and additivity under coarse-graining over exclusive alternatives—it is shown that this density is uniquely fixed (up to normalization) as \rho(\psi) \propto |\psi|^2. Measurement is modeled dynamically as a phase–gradient locking process, in which interaction with a macroscopic record sector enforces a shared realized time flow. Total time production is conserved during measurement, but redistributed across exclusive record sectors. Defining outcome weights as ratios of allocated time production yields the Born rule uniquely, without introducing stochastic collapse postulates, subjective probability, or additional interpretive assumptions. In this framework, state reduction corresponds to dynamical stabilization of a single record-compatible time flow rather than non-unitary projection, and apparent randomness arises from coarse-graining over inaccessible microscopic phase configurations. The work clarifies the structural origin of the Born rule, unifies time-dependent and timeless regimes of quantum theory, and identifies conservative falsifiability targets, including finite-time locking dynamics and correlated phase/timing residuals during measurement.
We present the foundational layer of a research program that derives quantum-mechanical, relativistic, and thermodynamic structure from a single ontology: a ledger of sealed records. The ledger is governed by three axioms: R, laws are laws of whole sealed histories; S, no distinction without a record; and C, couplings are fixed by self-consistency under refinement. The program builds on the stochastic-quantum correspondence of Barandes' indivisible processes, replacing configuration trajectories by committed records as the primitive. The main results, each at stated scope and with machine-verified receipts, are as follows. First, the Born layer: record weights compose through square roots, and tame-class reconstruction recovers the Weyl algebra and the Schrodinger representation, via Stone-von Neumann, from record towers, with ladder operators, selection rules, and exact continuum targets approached at machine precision. Second, Lorentz signature: the commitment structure of records forces a Lorentzian (1,d) split with derived orientation classes. The spatial dimension d = 3 is selected by a minimality principle graded as input in the text, not derived. The operational identification lapse = local clock rate is verified to 3.7 x 10^{-8} in curved record geometries as a model-internal consistency receipt, with first 3+1-dimensional cosmological checks presented qualitatively and no cosmological number claimed in this batch. Third, the arrow of time: reflection positivity is a theorem for eventless sectors with finite primitive Markov presentations, the entropy-production functional is the path-measure relative entropy sigma = D(P_AB || P_BA), the classical identity of stochastic thermodynamics in record-pair form, and the presentation hypothesis is sharp. An explicit reversible, valid, finite-rank process, the "record clock", fails reflection positivity, separating record laws from general reversible processes. Fourth, thermality: horizon temperature T = kappa / 2 pi is recovered in exact lattice constructions, presented in full in the companion horizon paper and cited here only as a consistency credential. We state precisely what is axiom, what is theorem, what is named identification, and what is imported mathematics; the full dependency audit is part of the paper. We also delimit the program's frontier: the tame class, the regularity stratum of the emergent continuum, and continuous sector families.
Whether time possesses an ontological status independent of physical-state evolution remains an open question in foundational physics. We propose a fundamental framework in which a local intrinsic time scale τ emerges as a direct consequence of information-entropy evolution. We demonstrate that in the absence of an absolute background clock, time must be defined operationally through internal state transitions. By identifying information entropy as the unique measure of state distinguishability and irreversibility in probabilistic dynamics, we propose the constitutive relation dτ = α dSlocal. Motivated by the Kubo Martin-Schwinger (KMS) condition and Wick rotation, we scale the factor as α = ℏ/(kBT), establishing temperature as the derivative of entropy with respect to intrinsic time: T = (ℏ/kB)(dS/dτ ). Bridging the microscopic and macroscopic realms via the Boltzmann relation, we obtain a parameter-free integral kB 2 ℏ ∆τ = ∫︁ d T Q 2 . The framework yields profound predictions for extreme physical regimes, including a holographic geometric factor (4π) in black hole time dilation, the intrinsic-time freezing at zero temperature, and a discontinuous step-jump in cumulative intrinsic time during the first-order phase transition of real materials. Consistency checks using the quantum Zeno effect and the quantum eraser demonstrate how local entropy suppression and postselected information recovery correspond to dynamical freezing and negative time increments.
Physics describes evolution, causal structure, and measurement outcomes, but lacks an accepted physical account of why one outcome-conditioned quantum situation is actual as the present. This article develops a conditional account within the reconstruction program, which places a premetric selection layer prior to spacetime dynamics. The Indefinite Reconstruction Stability Principle requires identities and readable relations to survive admissible continuation and to ignore unobservable distinctions. A present is proposed to be the outcome-conditioned quantum read-out of an IRSP-stable, history-bearing reconstruction boundary. Because the underlying relational record need not factorize, its read-out is generally entangled rather than a classical instantaneous configuration. Admissible successors are represented by a quantum instrument; present actualization postulates that one stable record sector becomes definite with its conditional probability, without an external observer. An explicit event-identity bridge identifies operationally equivalent realizations of the same descended event, and observable descent then makes its weight independent of reconstruction representative and unread embedding context. Given positivity, normalization, exclusive additivity, and a Hilbert-space read-out, Gleason representation fixes the Born form. Linear history composition implies no genuine third-order successor interference. Proper inheritance of the complete ancestry class supplies a conditional acyclic reconstruction order, stable small-step channels recover standard effective dynamics, and spacelike confluence replaces a preferred global simultaneity surface. The result is a conditional quantum architecture of present actuality and becoming, with explicit premises and failure conditions but no fitted collapse rate.
Quantum mechanics lacks a physical definition of measurement, observer, probability, and experienced time. These notions are instead treated as primitive or interpretation-dependent, leading to persistent foundational problems including the measurement problem, the origin of the Born rule, observer disagreement in Wigner’s Friend scenarios, the arrow of time, and apparent information loss in black hole evaporation. In this work, we show that these problems share a single missing ingredient: the absence of an operational definition of observers as bounded physical systems. We define observers as physically realizable systems capable of forming irreversible internal records under unitary dynamics. Measurement is identified with record formation, probability with record redundancy, experienced time with record accumulation, and irreversibility with computational inaccessibility rather than non-unitarity. Using decoherence and quantum Darwinism, we show that the number of accessible, decoherence-stable records associated with an outcome scales with the squared amplitude, yielding the Born rule from record counting without invoking collapse, subjective probability, or additional axioms. Observer-relative paradoxes dissolve once outcome definiteness is indexed to record formation rather than to the global quantum state. Reconstruction of global quantum information is shown to require exponential resources, rendering measurement and black hole evaporation operationally irreversible despite global unitarity. The resulting framework closes quantum mechanics conceptually by eliminating undefined primitives, without modifying its mathematical structure or introducing new dynamical postulates.
Duration can be reconstructed from finite physical records through the dynamics and calibration of internal clocks. Finite classical, relativistic, and stationary quantum models show how the available records and clock interactions affect this reconstruction. For a prepared oscillator, exact optimal error bounds identify when adding a record combining position and momentum improves the duration estimate, while a coupled pointer provides a consistency test for sampled readings. Separatrix passage, Sagnac returns, and quantum backflow illustrate the construction across these settings. The calibrated predictions agree with conventional descriptions without an independently supplied time interval.