ABSTRACT In this paper we analyze whether a universe governed exclusively by local, time-propagated dynamics can remain internally consistent when exact quantum conservation laws are imposed. Starting from a minimal rule-set incorporating special relativity, quantum mechanics, and conservation of angular momentum, we show that any non-zero temporal delay in conservation enforcement renders the dynamical evolution ill-defined as an operator identity. We demonstrate that consistency requires conservation to be enforced as a non-temporal constraint on admissible states — a structure recognized in Dirac’s constrained Hamiltonian formalism and in the timeless formulation associated with the Wheeler–DeWitt equation — and that this correction introduces secondary causal ambiguities. These ambiguities are resolved by imposing a boundary condition on irreversible information recording. The resulting architecture exhibits structural features analogous to integrity-preserving correction in engineered systems. No assumptions are made regarding agency or intent; conclusions follow from mathematical consistency alone.
The mathematical structure of quantum theory is usually postulated rather than explained—Hilbert spaces, operators, and probabilistic structure—without explaining why this arena should exist in the first place. In this work we address a more primitive question: starting from the absence of any prior structure, what conditions must be satisfied for coherent persistence to be possible at all? We begin from a state of zero determination (the Void), understood not as physical emptiness but as the absence of admissibility constraints. From this starting point, we show that the possibility of persistence forces a minimal triadic structure consisting of reference, transformation, and return. This structure enables self-verification without external supervision and distinguishes genuine continuity from accidental resemblance. The requirement of self-verifying persistence forces deviation to be representable quantitatively and to compose across histories. This necessity leads uniquely to a linear vector space structure. Stability further imposes a knife-edge viability condition: identity-preserving and identity-violating contributions must equalize at closure. From this condition, an inner product and norm are forced, yielding Hilbert space geometry and operator representations as consequences of viability rather than axioms. Within this framework, familiar features of quantum kinematics—such as uncertainty, unitary evolution, and probabilistic weighting—arise as structural necessities rather than postulated rules. The present work establishes the kinematic foundations of coherence, deriving the mathematical arena of quantum theory from the requirement that something persist at all. Applications to mass relations, symmetry, temporal ordering, and composite systems are developed separately.Version 1.0. This preprint establishes the structural foundations of Coherence Algebra and derives Hilbert space from self-verification and persistence.
We propose a preliminary mathematical framework for physical theories based on experimentally grounded constraints. A physical theory is represented as a structured object (S, O, D) consisting of a state space, a set of observables, and a dynamical law. We introduce constraint operators acting on the space of candidate theories, encoding symmetry, causality, quantum, and dynamical requirements. The space of physically admissible theories is defined as the intersection of constraint-defined subsets, leading to a constraint-based interpretation of physical laws as consistency conditions. This framework provides a unified mathematical perspective in which classical mechanics, relativity, and quantum theory can be understood as different realizations within a common structure. This work presents a preliminary but structured conceptual and mathematical framework.
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 argue for the universality of quantum theory using a dynamical consistency argument, within a specific Hamiltonian setting. We analyse two different types of coupling between simple quantum harmonic oscillators. Each illustrates an aspect of the free and interacting quantum fields and shows the inadequacy of semiclassical models. In particular, we establish that requiring the canonical algebra to be preserved under joint unitary dynamics rules out specific hybrid classical-quantum models. We apply our reasoning to the gravitational field in the linear regime, coupled to the quantised electromagnetic field and, separately, to quantised matter. We conclude with a comparison to DeWitt's analysis of quantum measurement, in which the apparatus, if classical, must be at least stochastic to preserve the Heisenberg Uncertainty Principle. We also note that stochastic models are inconsistent with the strict version of conservation principles, even if they comply with a probabilistic (on average) conservation.
Quantum mechanics is traditionally formulated using the reversible coordinate time
t, which enforces a globally reversible unitary group structure and time‑symmetric propagators. This conflicts with physically irreversible processes such as decoherence, measurement, entropy production, causal propagation, and curvature‑driven focusing in general relativity. We resolve this mismatch by replacing
t with the monotonic temporal field
T, previously developed in the context of global causal structure, temporal focusing, and worldline ordering in curved spacetime. Once
T is taken as the fundamental evolution parameter, quantum dynamics cannot be reversible: the inverse operator
U−1 is not physically realizable, and unitary evolution becomes a forward‑directed semigroup. We formulate **forward unitarity**, in which physical evolution is generated only by forward‑directed operators
Uphys(T2,T1) with
T2>T1. Pure states evolve according to a forward Schrödinger equation with an intrinsic, monotonic decoherence functional
D(T), while mixed states evolve under a forward Lindblad structure. Probability is conserved, but coherent recoverability is forbidden by geometric irreversibility, causal structure, and temporal focusing. We construct a Forward‑QM Lagrangian, a forward Heisenberg picture, and a forward path integral restricted to histories with non‑decreasing
T, showing how operator algebras, propagators, correlation functions, and creation/annihilation operators inherit the arrow of time. Forward‑QM provides a unified, forward‑directed formulation of quantum mechanics compatible with general relativity, causal geometry, and the irreversible structure of spacetime. It replaces reversible unitary groups with physically meaningful semigroup evolution, aligns quantum dynamics with measurement, decoherence, and entropy production, and establishes the foundation for Forward Quantum Field Theory (FQFT). The extension to FQFT—covering forward propagators, interacting fields, renormalization in the presence of monotonic decoherence, and causal compatibility in curved spacetime—will be developed in future work.