A relativistic framework in which the measurement event is modelled as a geometric incidence between a null quantum system (a photon, represented over projective null twistor space ℙN) and a timelike observer worldline in Minkowski space. The observer's forward temporal orientation is supplied not thermodynamically but as a discrete geometric datum fixed by the temporal orientability of Minkowski space. Global evolution remains unitary; the only irreversibility is a causal monotone of second-law type with no finite non-relativistic limit. The central claim — that the temporal arrow of collapse can be supplied purely geometrically while preserving unitarity — is stated as a falsifiable question with two valid answers, and the deciding experimentum crucis is specified but not yet executed. The claim is therefore left explicitly open.
A relativistic framework in which the measurement event is modelled as a geometric incidence between a null quantum system (a photon, represented over projective null twistor space ℙN) and a timelike observer worldline in Minkowski space. The observer's forward temporal orientation is supplied not thermodynamically but as a discrete geometric datum fixed by the temporal orientability of Minkowski space. Global evolution remains unitary; the only irreversibility is a causal monotone of second-law type with no finite non-relativistic limit. The central claim — that the temporal arrow of collapse can be supplied purely geometrically while preserving unitarity — is stated as a falsifiable question with two valid answers, and the deciding experimentum crucis is specified but not yet executed. The claim is therefore left explicitly open.
This work proposes a framework for wavefunction collapse based on temporal-orientation dynamics in an extended Hilbert-space structure. The model introduces asymmetric temporal sectors associated with observer-system interaction and derives irreversible collapse behavior through GKSL-consistent dynamics, stochastic unraveling, and observer-alignment mechanisms. The framework recovers Born-rule statistics while remaining operationally compatible with standard quantum mechanics in the appropriate limits. The paper distinguishes explicitly between formal theorems, operational propositions, and heuristic interpretations, and proposes numerical simulation protocols intended to assess empirical distinguishability relative to standard quantum theory. This preprint represents Phase II of a broader research program concerning temporal structure, quantum measurement, and relativistic extensions of collapse dynamics.
Why Quantum Superposition Cannot Be Observed: A Null–Timelike Regime Framework for Measurement and CollapseQuantum superposition is central to quantum theory, yet it is never directly observed as a physical state. Instead, it is inferred from interference patterns and statistical correlations of localized outcomes. This preprint proposes a relativistic–geometric explanation for this limitation by distinguishing two physically distinct regimes of quantum evolution: null (lightlike, ds² = 0) and timelike (ds² > 0).Core ClaimFree photons propagate as delocalized wavefronts on the light-cone boundary with no proper time, supporting persistent superposition without intrinsic decoherence. Measurement requires coupling to timelike matter that localizes energy, forms records, and completes history. The Null–Timelike Superposition Theorem formalizes this spacetime-causal distinction, reinterpreting collapse as a geometric transition rather than an ad hoc postulate.Key Contributions• Explains why superposition is inferred but never directly observed: null regime lacks proper-time evolution; observation demands timelike records.• Distinguishes boundary interactions (amplitude redistribution, no records) from measurement interactions (irreversible energy transfer).• Applies to double-slit: unobserved case preserves null coherence; which-path detection forces early timelike coupling.• History-completion view resolves delayed-choice without retrocausality.
Abstract This article presents a revised and conceptually refined formulation of a previously proposed Temporal Interpretation of quantum measurement, explicitly addressing the physical nature of wavefunction collapse. While the original proposal emphasised relativistic aspects of momentum superpositions, the present work clarifies the interpretation within the standard formalism of quantum mechanics, without introducing new dynamics or experimental predictions. Unitary evolution is read as a process of differentiated phase accumulation between branches of a quantum state. In relativistic contexts, phase differentials can be structurally related to effective proper-time differentials, allowing the introduction of a notion of temporal compatibility that provides a physically grounded account of decoherence. When such differentials exceed a characteristic scale, interference between branches becomes operationally inaccessible, while global unitarity is preserved. The observer is treated as a physical system endowed with an irreversible proper time associated with macroscopic, entropic dynamics. Within this framework, collapse is explained as an emergent physical phenomenon arising from the irreversibility of the observer’s proper time, which prevents the reconstruction of phase coherence after an interaction. Collapse is therefore neither a fundamental dynamical mechanism nor an objective event in space-time, but a necessary consequence of temporal irreversibility in physical observers. This formulation sharpens the distinction between decoherence and collapse, preserves full consistency with the Born rule, and positions the Temporal Interpretation as a competing interpretative framework that provides a concrete physical explanation for the quantum–classical transition, improving and clarifying the original proposal. This version clarifies the operational status of the interaction time, refines Sections 5.3 and 5.4, and standardises references and editorial structure. No changes to the formalism or conclusions.
This paper argues that amplitude calculus is not an auxiliary quantum construction but the relational coordinate framework forced into existence when the Lorentzian chart collapses at the null boundary. Within the causal domain accessible to a massive probe, the coordinates (x,t) retain clear geometric meaning: worldlines exist, proper time accumulates, and classical trajectories are well defined. At the null boundary these structures fail simultaneously. The invariant interval vanishes, the Lorentzian chart reaches its degenerate limit, and no geometric observable survives. Beyond this boundary the analytic continuation of (x,t) is not spacetime but the diagrammatic overreach of a coordinate system that has exhausted its operational content. Three structural consequences follow. First, null propagation carries no proper time: the boundary is a zero--interval relation, not a limit of motion. Second, the null boundary is not a worldline and admits no geometric in--between. Third, once (x,t) loses operational meaning, only a relational description is possible. In this regime Feynman's amplitude assignments are not postulates but the unique Lorentz--invariant extension assigning complex weights to admissible relational configurations whose coherent aggregate replaces the classical trajectory. Quantum mechanics is thus the relational mathematics demanded by Lorentzian geometry once its coordinates collapse. The non--spacetime domain is not an extension of spacetime but the region where geometry terminates and amplitude begins. This is version 1.1: This version corrects minor structural issues and removes an obsolete appendix; no scientific conclusions are changed. Authors' note (October 2026). This paper is preserved as an exploratory precursor to our later research, not as a validated derivation of quantum mechanics. Several central geometric claims are incorrect: a null interval does not collapse spacetime coordinates to (0,0) or make the Lorentzian metric degenerate, and spacelike-separated events remain part of ordinary spacetime, not a non-spacetime exterior. The further claim that quantum amplitude calculus and complex amplitudes are uniquely forced by null geometry is not established. In particular, the proposed weight e^(−mℓ/ℏ) is a positive real exponential that does not supply the oscillatory relative phases needed for the claimed interference construction; for massless particles (m = 0), this weight is identically one. The original manuscript is retained unchanged as a historical record of the questions that motivated our subsequent investigations. Our later paper, The Lorentz-Analytic Exterior: A Conditional Mathematical Framework (Version 2, October 2026), revisits the geometric and analytic questions under explicit mathematical assumptions, without relying on the coordinate-collapse argument. https://doi.org/10.5281/zenodo.23400176
The fundamental laws of classical mechanics, quantum mechanics, and general relativity are time-symmetric, yet macroscopic experience is irreversible without exception. Standard physics bridges this gap with statistical argument: reversal is treated as merely improbable, not physically inadmissible. This paper argues that the gap is an artifact of treating space as a continuum, and that it closes once space is treated as discrete, as in Quantum-Geometry Dynamics (QGD). Two independent grounds are identified for the categorical, non-statistical irreversibility of every elementary interaction in discrete space: a local ground, the loss of individual addressability when one particle's constituent preon(+)s merge into another upon absorption; and a global ground, the irreducible universal gravitational trace left by any positional change, given that gravity in QGD is instantaneous and universal in scope. Applied across four domains, this single result dissolves the arrow-of-time problem, grounds the second law of thermodynamics in dynamics rather than probability, dissolves the apparent asymmetry between unitary evolution and measurement collapse, and shows the reversible/irreversible distinction in quantum gate theory to be a feature of the abstract computational model rather than of physical mechanism. The result is shown to be compatible with, and silent on, whether a finite deterministic system's forward dynamics eventually revisit an earlier configuration by a non-retracing causal path. No new axiom or free parameter is introduced: the result follows from elements of QGD already established for independent reasons.
We develop an information-geometric framework for analyzing quantum state-update processes generated by explicit collapse dynamics. Whereas a purely geometric description characterizes collapse as a finite displacement between an initial and a final statistical state, the present approach incorporates the dynamical law governing the intermediate evolution. A quantum state is represented by a density operator ρ(t) satisfying a specified dynamical equation, dρdt=C[ρ,t], or, more generally, by a unitary-plus-collapse evolution in which the collapse contribution is explicitly identified. The resulting trajectory is embedded in the statistical manifold of quantum states and analyzed using the quantum Fisher information metric. This allows one to define the instantaneous Fisher speed, the information-geometric length of the collapse trajectory, and an integrated geometric cost associated with the dynamical state change. The framework also permits comparison between the actual trajectory generated by a collapse model and the corresponding Fisher-geodesic trajectory connecting the same initial and final states. Relative entropy provides a complementary global measure of the distinguishability generated by the evolution, while the quantum Fisher metric characterizes its local statistical structure. The formalism is constructed so that different dynamical collapse proposals can be analyzed within a common geometric language without assuming that the geometric quantities themselves constitute a collapse mechanism: this is a diagnostic framework rather than a mechanism. In particular, once a specific collapse generator is supplied, the framework can determine how its parameters, localization properties, stochasticity, and time scale are reflected in the geometry of the associated state trajectory. The resulting formulation therefore provides a bridge between dynamical models of wave-function collapse and the information geometry of a quantum state space, while preserving the distinction between a physical collapse law and its geometric characterization.