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| Format: | Recurso digital |
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Zenodo
2026
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| Online Access: | https://doi.org/10.5281/zenodo.19364368 |
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Table of Contents:
- <p><span lang="EN-US">We present complex-time (CT) theory, a framework in which the fundamental structures of quantum mechanics are <em>derived</em> 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 </span><span lang="EN-US"></span><span lang="EN-US"> fp); and (P3) the total temporal magnitude is conserved (pf</span><span lang="EN-US"></span><span lang="EN-US"> + fp</span><span lang="EN-US"></span><span lang="EN-US"> = 1). From these three postulates alone, we show that: (i) the state space is the unit circle </span><span lang="EN-US"></span><span lang="EN-US"> and the dynamical group is </span><span lang="EN-US"></span><span lang="EN-US">, so that the imaginary unit </span><span lang="EN-US"></span><span lang="EN-US"> arises as the <em>unique</em> generator of temporal evolution — not as a mathematical convenience but as a consequence of temporal geometry; (ii) the Schrödinger equation </span><span lang="EN-US"></span><span lang="EN-US"> follows from the identification of energy with the rate of phase rotation in the pf–fp plane, with the Planck constant </span><span lang="EN-US"></span><span lang="EN-US"> playing the role of a natural constant intrinsic to the pf/fp structure; (iii) the de Broglie–Einstein relation </span><span lang="EN-US"></span><span lang="EN-US"> 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 </span><span lang="EN-US"></span><span lang="EN-US"> is a geometric consequence of the impossibility of fully eliminating fp while preserving </span><span lang="EN-US"></span><span lang="EN-US">; (v) the complex structure of Hilbert space, the inner product, and the Born rule </span><span lang="EN-US"></span><span lang="EN-US"> all follow from the geometry of fp </span><span lang="EN-US"></span><span lang="EN-US"> 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.</span></p> <p><strong><span lang="EN-US">Keywords:</span></strong><span lang="EN-US"> complex time; temporal structure; imaginary unit; quantum mechanics derivation; past-fixed / future-pending decomposition; Born rule; energy quantization; measurement; irreversibility; arrow of time</span></p> <p> </p>