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arXiv:1111.0457 · Springer eBooks

The Emergent Nature of Time and the Complex Numbers in Quantum Cosmology

Gary William Gibbons

Published Oct 12, 2011• 32 citations
arXivHTMLPDF
DOI
10.1007/978-3-642-23259-6_6

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For over a century, physics has pursued a unified description of nature linking quantum mechanics, relativity, and cosmology, yet consciousness—our direct window into existence—remains unaccounted for. This review proposes that consciousness continuity is not an emergent accident of neural complexity but a quantum informational invariant, conserved across transformations of its physical substrate. Grounded in the empirical absence of “zombie” organisms and extended through a synthesis of quantum information theory, cosmological logic, and the author’s previous Two-Particle Quantum Bonding Hypothesis (TPQBH), the framework introduces a Quantum Informational Bonding (QIB) mechanism operating within a universal Hilbert space. This mechanism preserves an identity parameter (𝓘₍C₎) analogous to conservation laws in physics. The resulting cosmological model implies an infinite, centre-less universe and a unidirectional arrow of time emerging from informational continuity. The theory reframes the “hard problem” of consciousness as a missing symmetry in fundamental physics—one connecting subjective experience, information, and spacetime structure.

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Relativistic quantum mechanics was developed to reconcile the principles of quantum mechanics with Einstein’s theory of relativity. Despite its success in describing high-energy particles, the theory continues to face unresolved conceptual and mathematical difficulties, particularly in relation to the nature of time, causality, and relativistic consistency. In recent years, the idea of extending space-time into the complex domain has emerged as a useful and potentially meaningful approach to these problems. In this work, a theoretical synthesis is presented to examine the role of complex space-time in relativistic quantum mechanics. The study discusses how complex time arises naturally in relativistic wave equations, quantum field theory, and path integral formulations. Established methods such as Wick rotation, complex coordinate transformations, and non-Hermitian but parity–time (PT) symmetric Hamiltonians are reviewed to illustrate how complex space-time contributes to mathematical stability and clearer physical interpretation (Dirac, 1928; Wick, 1954; Bender & Boettcher, 1998). The relevance of complex space-time is further explored in the context of relativistic particle dynamics and quantum cosmology, where it helps address, issues related to vacuum structure, time evolution, and causality (Feynman & Hibbs, 1965; Hartle & Hawking, 1983). The paper suggests that complex space-time should be viewed not only as a computational technique, but as a framework that may reflect deeper features of relativistic quantum phenomena.

Recent Trends in Mathematics•Jan 1, 2026•0 citations
For over a century, physics has pursued a unified description of nature linking quantum mechanics, relativity, and cosmology, yet consciousness—our direct window into existence—remains unaccounted for. This review proposes that consciousness continuity is not an emergent accident of neural complexity but a quantum informational invariant, conserved across transformations of its physical substrate. Grounded in the empirical absence of “zombie” organisms and extended through a synthesis of quantum information theory, cosmological logic, and the author’s previous Two-Particle Quantum Bonding Hypothesis (TPQBH), the framework introduces a Quantum Informational Bonding (QIB) mechanism operating within a universal Hilbert space. This mechanism preserves an identity parameter (𝓘₍C₎) analogous to conservation laws in physics. The resulting cosmological model implies an infinite, centre-less universe and a unidirectional arrow of time emerging from informational continuity. The theory reframes the “hard problem” of consciousness as a missing symmetry in fundamental physics—one connecting subjective experience, information, and spacetime structure.
We present a relational framework in which temporal structure is not fundamental but emerges from correlations within a globally stationary quantum state. Each subsystem includes an internal clock, and conditional states evolve effectively with respect to these internal readings. The construction naturally extends to relativistic motion, gravitational redshift, and cosmological expansion, leading to a unified emergent-time functional valid across diverse physical regimes. The theory reproduces classical time dilation, predicts correlation-dependent deviations from standard evolution, and suggests that non-interacting or massless particles exhibit negligible internal time. These consequences open directions for conceptual and experimental investigations in the foundations of temporal physics, from multi-clock quantum systems to precision metrology and cosmological settings. In particular, the framework suggests measurable deviation from standard quantum evolution for highly entangled systems and predicts negligible internal time for massless particles.
Relativistic quantum mechanics was developed to reconcile the principles of quantum mechanics with Einstein’s theory of relativity. Despite its success in describing high-energy particles, the theory continues to face unresolved conceptual and mathematical difficulties, particularly in relation to the nature of time, causality, and relativistic consistency. In recent years, the idea of extending space-time into the complex domain has emerged as a useful and potentially meaningful approach to these problems. In this work, a theoretical synthesis is presented to examine the role of complex space-time in relativistic quantum mechanics. The study discusses how complex time arises naturally in relativistic wave equations, quantum field theory, and path integral formulations. Established methods such as Wick rotation, complex coordinate transformations, and non-Hermitian but parity–time (PT) symmetric Hamiltonians are reviewed to illustrate how complex space-time contributes to mathematical stability and clearer physical interpretation (Dirac, 1928; Wick, 1954; Bender & Boettcher, 1998). The relevance of complex space-time is further explored in the context of relativistic particle dynamics and quantum cosmology, where it helps address, issues related to vacuum structure, time evolution, and causality (Feynman & Hibbs, 1965; Hartle & Hawking, 1983). The paper suggests that complex space-time should be viewed not only as a computational technique, but as a framework that may reflect deeper features of relativistic quantum phenomena.