We propose that irreversibility is the primitive physical fact from which the central formal features of quantum theory emerge. Quantum mechanics is formulated over the complex numbers, the Born rule is imposed by postulate, and the arrow of time is added by hand — yet each of these features, we argue, follows from a single foundational axiom: that the probabilistic information released by an interaction cannot be reabsorbed into the forward causal chain.
We propose that irreversibility is the primitive physical fact from which the central formal features of quantum theory emerge. Quantum mechanics is formulated over the complex numbers, the Born rule is imposed by postulate, and the arrow of time is added by hand — yet each of these features, we argue, follows from a single foundational axiom: that the probabilistic information released by an interaction cannot be reabsorbed into the forward causal chain.
The quantum measurement problem arises from a structural asymmetry in standard formulations of quantum mechanics: while unitary evolution is treated as fundamental, irreversible events are introduced only through ad hoc postulates. As a result, measurement, decoherence, and probability appear conceptually disconnected. In this work, we propose a minimal reformulation in which irreversible interaction events are taken as ontological primitives. An event is defined as a completely positive, trace-preserving map that is not equivalent to any unitary transformation. Unitary evolution emerges as an effective description valid between events. Within this framework, quantum measurement is not a special process but a particular class of irreversible events with outcome-resolving structure. The Born rule arises naturally from the statistical structure of event realizations, and environmental decoherence is reinterpreted as a high density of irreversible events. No collapse postulate, observer-dependent rule, or modification of quantum dynamics is required. This formulation provides a unified and physically grounded resolution of the measurement problem and establishes a conceptual foundation for event-based extensions connecting quantum theory with spacetime and gravity.
We present complex-time (CT) theory, a framework in which the fundamental structures of quantum mechanics are derived from three physical postulates concerning the internal structure of time. The postulates are: (P1) physical time possesses two orthogonal components — past-fixed (pf), representing actualized, irreversible records, and future-pending (fp), representing physically real but undetermined possibilities; (P2) pf and fp are orthogonal (pf fp); and (P3) the total temporal magnitude is conserved (pf + fp = 1). From these three postulates alone, we show that: (i) the state space is the unit circle and the dynamical group is , so that the imaginary unit arises as the unique generator of temporal evolution — not as a mathematical convenience but as a consequence of temporal geometry; (ii) the Schrödinger equation follows from the identification of energy with the rate of phase rotation in the pf–fp plane, with the Planck constant playing the role of a natural constant intrinsic to the pf/fp structure; (iii) the de Broglie–Einstein relation holds universally — for massive and massless particles alike — because the wave structure belongs to time itself, not to any particular particle; (iv) the uncertainty principle is a geometric consequence of the impossibility of fully eliminating fp while preserving ; (v) the complex structure of Hilbert space, the inner product, and the Born rule all follow from the geometry of fp pf projection; and (vi) energy quantization emerges from a “real-axis sampling” rule without imposing discreteness on the underlying dynamics. We further show that the CT framework provides unified descriptions of double-slit interference, quantum tunneling, unstable-state decay widths, and the structural origin of the arrow of time. Preliminary experimental predictions for quantum-circuit observables are stated, and applications to cosmological dark-energy phenomenology, galaxy rotation curves, and Lorentzian path-integral contour selection are outlined with references to dedicated companion papers. The central thesis is that quantum mechanics is not a theory of particles with mysterious wave-like properties, but a consequence of the internal structure of time — time whose wave-like phase (fp) is projected, irreversibly and discretely, onto the real axis (pf) in every act of measurement. Keywords: complex time; temporal structure; imaginary unit; quantum mechanics derivation; past-fixed / future-pending decomposition; Born rule; energy quantization; measurement; irreversibility; arrow of time
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.
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.
This paper is the third installment (Part III) of a research series dedicated to the geometric and algebraic foundations of higher-derivative scalar theories. Following the structural uniqueness of the □2 operator (Part I: arXiv:2512.16955) and the emergence of spin-analogous dynamics (Part II), this work addresses the most fundamental axioms of quantum mechanics (QM). Key findings presented in this manuscript: Geometric Origin of Complex Numbers: We demonstrate that the standard complex field C of quantum mechanics is not a fundamental postulation but an emergent infrared (IR) feature. In the Split-Quaternionic Krein Algebra (PQA), the decoupling of heavy indefinite-metric modes at the Lee-Wick scale (M≈11.3 TeV) naturally reduces the internal degrees of freedom to a complex subalgebra isomorphic to C. Derivation of the Born Rule: We show that the Born rule (P=∣ψ∣2) emerges as the unique, positive-definite inner product consistent with the internal Krein metric η after projecting out ghost-sector excitations. Algebraic Necessity of the Quadratic Form: The paper provides a rationale for the second-power dependence of probability, linking it to the conservation of the bilinear form under pseudo-unitary time evolution. By reframing standard QM as a low-energy manifestation of PQA geometry, this study provides a consistent "Why" for the mathematical structure of our quantum reality, suggesting that the "ghosts" of higher-derivative theories are the very keys to understanding the origin of quantum axioms.
This paper is the third installment (Part III) of a research series dedicated to the geometric and algebraic foundations of higher-derivative scalar theories. Following the structural uniqueness of the □2 operator (Part I: arXiv:2512.16955) and the emergence of spin-analogous dynamics (Part II), this work addresses the most fundamental axioms of quantum mechanics (QM). Key findings presented in this manuscript: Geometric Origin of Complex Numbers: We demonstrate that the standard complex field C of quantum mechanics is not a fundamental postulation but an emergent infrared (IR) feature. In the Split-Quaternionic Krein Algebra (PQA), the decoupling of heavy indefinite-metric modes at the Lee-Wick scale (M≈11.3 TeV) naturally reduces the internal degrees of freedom to a complex subalgebra isomorphic to C. Derivation of the Born Rule: We show that the Born rule (P=∣ψ∣2) emerges as the unique, positive-definite inner product consistent with the internal Krein metric η after projecting out ghost-sector excitations. Algebraic Necessity of the Quadratic Form: The paper provides a rationale for the second-power dependence of probability, linking it to the conservation of the bilinear form under pseudo-unitary time evolution. By reframing standard QM as a low-energy manifestation of PQA geometry, this study provides a consistent "Why" for the mathematical structure of our quantum reality, suggesting that the "ghosts" of higher-derivative theories are the very keys to understanding the origin of quantum axioms.