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.
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.
This paper develops a consistent and self-contained formulation of external (physical) time as an emergent quantity, arising from the internal temporal evolution of correlational sites within the Universal Correlational Lattice (UCL) framework. Rather than assuming time as a fundamental background parameter, the theory distinguishes between: Internal times, defined locally at each correlational site through intrinsic dynamical evolution, and External time, which emerges relationally from the synchronization, ordering, and stability of correlations among multiple sites. The work formalizes how a coherent, observer-independent notion of temporal flow can arise without postulating a pre-existing global clock. External time is shown to correspond to a coarse-grained, effective parameter that captures persistent, ordered correlations across the correlational network, while remaining compatible with regimes where no global time is well-defined. Key results include: A precise definition of temporal evolution along internal time without reference to external time units. The emergence of a one-parameter effective temporal ordering from correlational dynamics. A clear separation between pre-geometric (timeless or multi-temporal) regimes and geometric regimes where an effective spacetime description becomes valid. Conceptual and mathematical consistency with relativistic causality, decoherence, and macroscopic temporal stability. This framework provides a natural resolution to longstanding tensions between quantum theory and general relativity regarding the status of time, without invoking collapse postulates or external observers. Time is not fundamental, but real and physical as an emergent, relational structure. The paper is intended for researchers interested in foundational questions of time, quantum gravity, emergent spacetime, and relational approaches to physics.
We establish two foundational results concerning time and irreversibility within an operational framework where physical measurements correspond to distinguishable, persistent record states. First, we prove that no physical clock can ground time as a fundamental parameter: any clock-induced ordering necessarily reduces to a preorder defined by reachability among record states via admissible transformations. Second, we prove that bounded recording capacity forces accessible irreversibility: any system capable of recording more distinct events than its accessible register capacity must exhibit non-invertible operations at the accessible level. These results are derived without assuming time, entropy, or thermodynamic principles as primitives. Together, they establish that temporal structure and irreversibility are not independent physical laws but emerge from operational constraints on physical memory and distinguishability. The framework is compatible with globally unitary microscopic dynamics while explaining effective irreversibility for bounded observers. We conclude that time is a representational index for record structure rather than an ontological primitive , establishing the necessary foundation for the failure of deterministic prediction addressed in companion work [3]
Abstract The ontological status of time remains unresolved in fundamental physics. In quantum mechanics, time appears as an external classical parameter, whereas in general relativity it is dynamical and intertwined with spacetime geometry. Canonical approaches to quantum gravity, most notably the Wheeler–DeWitt formulation, eliminate time altogether, leading to the well-known “problem of time.” These tensions motivate frameworks in which time is not fundamental but emergent. In this work, we propose a discrete, update-based framework in which the universe evolves through a sequence of global quantum states indexed by an abstract update parameter rather than by a physical time coordinate. Evolution is formulated as a completely positive, trace-preserving (CPTP) quantum channel acting on the universal density operator, ensuring exact conservation of probability and global quantum information at every update. The framework is deliberately conservative: it preserves the formal structure of quantum mechanics and quantum field theory, enforces vacuum stability, and supports global conservation laws without introducing new dynamical postulates. Within this setting, time emerges relationally at the level of subsystems. As subsystems become increasingly entangled with their environments, entropy gradients arise that define an effective arrow of time, closely aligned with the thermodynamic arrow. The resulting temporal flow is relative, statistical, and observer-dependent, while the global evolution remains information-preserving and, in the closed-system limit, reversible. We explore the implications of this framework for cosmology and black hole physics. The Big Bang is reinterpreted as an initial quantum state rather than a singular beginning of time, avoiding temporal singularities. Black hole evaporation is shown to be compatible with unitary evolution when the full quantum state is considered, naturally reproducing the expected Page curve and resolving the apparent information paradox. Overall, the framework provides a coherent, minimal setting in which time, irreversibility, and cosmological history emerge from quantum correlations rather than from a fundamental temporal background.
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.
A key conceptual achievement of special relativity was the abandonment of absolute time and the introduction of an operational definition of simultaneity through clock synchronization. Building on Einstein’s operational treatment of simultaneity, we extend the logic of clock synchronization to the quantum domain. Within the Overtime interpretation, quantum systems evolve in an internal time τ that becomes related to the observer’s time t only through synchronization. Measurement is thus understood as a temporal embedding rather than a physical collapse. Crucially, this resolution requires no new ontological entities—no additional state vectors, hidden variables, collapse mechanisms, or cosmological boundary conditions. The parameter τ is simply the standard ordering parameter of the Schrödinger equation, reinterpreted as system-intrinsic. This approach preserves all standard quantum predictions, maintains relativistic causality, and offers a unified conceptual framework for superposition, entanglement, delayed-choice phenomena, and the apparent discontinuity of measurement. The interpretation naturally aligns with the operational logic of special relativity and clarifies the role of entropy and the arrow of time in distinguishing macroscopic and microscopic systems.
The Entropy Footprint Hypothesis proposes that the universe does not exist as a continuously persisting background, but is instead constituted by discrete generative events. Each generative event actualizes a single physical state from a quantum probability cloud of multiple potential states. This act of actualization is fundamentally irreversible, as unrealized possibilities cannot be restored to their original probabilistic structure. The loss of inaccessible information resulting from each generative event is defined as an entropy footprint. Within this framework, entropy is reinterpreted not as a passive byproduct of physical evolution or disorder, but as the intrinsic informational cost of reality generation. Time is not treated as a flowing dimension, but as an ordered sequence of generative events. The arrow of time emerges from the accumulation of entropy footprints rather than from macroscopic thermodynamic asymmetry alone. This work integrates concepts from quantum mechanics, statistical physics, information theory, and philosophy of time to formulate a generative universe model. The hypothesis offers a unified explanatory perspective on entropy increase, temporal directionality, irreversibility, and quantum state actualization, while remaining compatible with established physical theories. Potential implications for cosmology, black hole entropy, decoherence, and the ontology of time are discussed.