This preprint introduces the concept of the Relativistic Halting Problem, proposing that the operational impossibility of constructing inverse quantum evolutions under relativistic and computational constraints leads to effective non-Hermitian dynamics in macroscopic systems. The work argues that standard quantum mechanics implicitly assumes a “Mirror Fallacy”: that inverse operators are ontologically given independent of physical realizability. By treating operators as physically constructed processes bounded by causal horizons, the paper provides an operational account of the emergence of the arrow of time and macroscopic irreversibility. This work is intended as a conceptual and foundational proposal rather than a complete formal theory.
This preprint introduces the concept of the Relativistic Halting Problem, proposing that the operational impossibility of constructing inverse quantum evolutions under relativistic and computational constraints leads to effective non-Hermitian dynamics in macroscopic systems. The work argues that standard quantum mechanics implicitly assumes a “Mirror Fallacy”: that inverse operators are ontologically given independent of physical realizability. By treating operators as physically constructed processes bounded by causal horizons, the paper provides an operational account of the emergence of the arrow of time and macroscopic irreversibility. This work is intended as a conceptual and foundational proposal rather than a complete formal theory.
We propose a unified operational framework for the emergence of irreversibility in physical systems. Building on the Relativistic Halting perspective, we introduce the dimensionless Relativistic Information Ratio, Ω, defined as the ratio of the causal time window available to an observer to the computational time required to reverse the system's instantaneous dynamics. Crucially, we argue that the quantum-to-classical transition is not a consequence of accumulated historical complexity, but a property of the current action: quantum behavior corresponds to actions where the complexity generation is reversible (Ω >> 1), while classical behavior corresponds to actions where the generated complexity renders the state effectively undecidable (Ω << 1). This framework explains the stability of macroscopic quantum states (e.g., superconductors) as systems where the "action of complexity generation" is suppressed.
This preprint is part of a three-paper series exploring physical realization as a temporally organized process constrained by relativistic causality. The present paper addresses quantum outcome realization. Standard quantum mechanics provides a complete and accurate description of state evolution but does not specify how physical outcomes are realized within an already structured world. In this work, a strict separation is made between quantum dynamics and realization. No modification of the Schrödinger equation, operators, or measurement formalism is introduced. A minimal global temporal constraint, T= L / c, is proposed as an organizational condition on realization, arising directly from finite causal connectivity. Quantum states are interpreted as spaces of possible realizations, while actual outcomes emerge through selection constrained by global phase compatibility with previously realized structure. Within this framework, the Born rule appears as the unique statistically stable distribution of realizations required for consistency across composite systems, rather than as a postulate of dynamics. The approach preserves quantum indeterminacy, introduces no hidden variables, and provides a unified account of realization across quantum and macroscopic regimes.
We propose a kinematic criterion for the emergence of irreversibility in extended physical systems. By integrating the Quantum Lyapunov Exponent (λL)—characterizing the rate of information scrambling—with the relativistic causal bound (c), we derive a dimensionless stability parameter Ω. We demonstrate that when the scrambling rate exceeds the system’s internal causal synchronization bandwidth (Ω > 1), the physical reconstruction of an inverse time-evolution operator ˆU † becomes operationally impossible within the causal horizon. This work provides a unified, first-principles derivation for the quantum-to-classical transition, verifying experimental decoherence thresholds in mesoscopic interferometry and superconducting qubit arrays. We propose Ω as a candidate universal instability parameter marking the breakdown of operational unitarity.
Hermiticity of the Hamiltonian is a foundational assumption of standard quantum mechanics, guaranteeing real eigenvalues, unitary evolution, and a consistent probability interpretation. We argue that this assumption, while epistemically indispensable in the low-energy limit, may not be ontologically fundamental. Working within the Quantum Reality Framework (QRF), in which physical structure is derived from a causal set (E, ≺, A), we propose to identify the relational amplitude kernel A(x,y) with the Benincasa–Dowker operator and suggest a route toward recovering aspects of the kinematical structure of quantum theory — Hilbert space, dispersion relation, and momentum operator — in the continuum limit. A fundamental tension then arises: the BD kernel is intrinsically time-directed and non-symmetric, while quantum mechanics requires a Hermitian kernel. We propose that Hermiticity is an emergent approximate symmetry valid in the limit E ≪ E_P, and that the appropriate mathematical framework is pseudo-Hermitian quantum mechanics (Bender & Boettcher 1998; Mostafazadeh 2002). This leads to potentially falsifiable consequences, partly model-dependent in their precise form: a qubit/qutrit decoherence ratio τ(qubit)/τ(qutrit) = 3/5 in a minimal implementation, quadratic Lorentz invariance violation δv/v ∼ −(E/E_P)²/6, mass-dependent deviations in matter-wave interference, and possible CPT violation at order (m/m_P)². Keywords: causal sets · quantum foundations · Hermiticity · PT-symmetry · time asymmetry · emergent quantum mechanics
Quantum Incompleteness presents an ontological interpretation of quantum mechanics in which physical systems are objectively under-specified prior to irreversible interaction. The theory rejects hidden variables, parallel worlds, and observer-dependent collapse, proposing instead that definite outcomes emerge through irreversible information-theoretic constraints that physically exclude alternatives. The wavefunction is treated as a real but non-material structural entity that defines the space of admissible outcomes rather than pre-existing values. Measurement, entanglement, classical definiteness, and the arrow of time are unified under a single completion mechanism grounded in thermodynamic irreversibility, while preserving the standard mathematical formalism of quantum mechanics. This work is empirically equivalent to standard quantum theory and is intended as a foundational clarification of what quantum mechanics describes rather than a modification of how it computes predictions.