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Addendum 3 – On Standing Waves, Intrinsic Change, and the Nature of Measurement in SCG

Rasky, Thomas Zigmond

Published Dec 6, 2025• 0 citations
Publisher

Abstract

This addendum clarifies two core elements of Space-Change Geometry (SCG): internal change and measurement. It argues that a particle is a self-sustaining wave-pattern existing only because imaginary curvature supports intrinsic α-rotation. The measurement process is reframed as sampling one instant of a system’s real–imaginary evolution: a definite position arises from the real coordinate plus the instantaneous projection of the CPW coupling term. Absorption does not freeze the wave-pattern; it ends it, transferring its energy into a new configuration.

DOI
10.5281/zenodo.17839365

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This addendum clarifies two core elements of Space-Change Geometry (SCG): internal change and measurement. It argues that a particle is a self-sustaining wave-pattern existing only because imaginary curvature supports intrinsic α-rotation. The measurement process is reframed as sampling one instant of a system’s real–imaginary evolution: a definite position arises from the real coordinate plus the instantaneous projection of the CPW coupling term. Absorption does not freeze the wave-pattern; it ends it, transferring its energy into a new configuration.
Abstract This paper extends the framework developed in Part I: Complex-Time Geometry and Phase Symmetry by examining the ontological origin and physical meaning of the imaginary rotation eiθeiθ that sustains temporal continuity.While Part I defined time as an intrinsic complex-phase rotation linking quantum mechanics and relativity, the present work investigates what the imaginary component ii itself represents in the emergence of temporal direction and measurement. It is proposed that ii introduces an orthogonality between “being” (real component) and “becoming” (imaginary component).Temporal flow is interpreted as the continuous projection of undetermined future phases into determined past fixation.The increase of entropy and the arrow of time naturally arise as the cumulative effect of these projections—the gradual loss of imaginary-phase freedom. Within this complex-time geometry, quantum measurement is redefined as past fixation, the act that converts potential states within the imaginary domain into realized events on the real axis.A superposed quantum state therefore does not lack existence; rather, it exists within the imaginary-phase continuum as an undetermined future.Observation performs the transition Im(ψ)→Re(ψ)Im(ψ)→Re(ψ), turning potentiality into actuality. Quantum entanglement is reinterpreted as a temporally coherent relation already realified at its creation.Because the correlation itself is fixed in the real domain, no information transfer or superluminal signaling is required—the apparent simultaneity is the result of a shared past fixation.Once realified, the relation loses its imaginary component (dτ=0dτ=0), existing as a null-temporal entity outside ordinary spacetime.Consequently, the problem of nonlocality dissolves as a misunderstanding of temporal structure rather than spatial distance. At the macroscopic level, matter experiences time as the aggregate rhythm of countless microscopic realificationsamong interacting particles.Each crossing of eiθeiθ through the real axis imprints a discrete mark of actuality.The apparent continuity of classical time emerges as the statistical accumulation of these quantized projections—a self-recording process through which the universe continuously writes its own history. Ultimately, this study concludes that time is not an external parameter but the internal oscillation of existence itself—the ongoing conversion between potential and actual that underlies all physical and informational processes. Keywords:complex-time geometry; temporal projection; quantum measurement; entropy; arrow of time; quantum entanglement; nonlocality; ontology of time; self-recording process of reality
Abstract This paper develops a unified theoretical framework in which time is formulated as an intrinsic complex-phase rotation eiθeiθ within an imaginary extension of spacetime.In this formulation, the imaginary unit ii is not a mere mathematical symbol but the operator of indeterminacy, representing the undetermined future phase of physical existence, while the real component corresponds to the determined and fixed past.Temporal continuity arises from this internal oscillation, and both the light limit (v=cv=c) and the rest limit (v=0v=0) emerge as degenerate boundaries of the same rotation. This Complex-Time Geometry (CTG) provides a geometric basis that links quantum mechanics, relativity, and thermodynamics under a single structure.The flow of time is interpreted as a continuous projection Im(ψ)→Re(ψ),Im(ψ)→Re(ψ), transforming potentiality into actuality.Within this framework, entropy increase corresponds to the progressive fixation of imaginary freedom, and the arrow of time naturally arises as the geometric direction of realification.Measurement is redefined as a temporal projection from the imaginary to the real domain, resolving the conceptual gap between quantum indeterminacy and classical determinacy. The theory further interprets Schrödinger’s iℏ∂ψ∂t=H^ψiℏ∂t∂ψ=H^ψ as the mathematical manifestation of orthogonal evolution in complex time, where ii ensures reversible continuity.Ultimately, time is not an external parameter but the internal oscillation of existence itself—the mechanism through which the universe continuously writes its own history. Keywords complex-time geometry; temporal projection; quantum measurement; relativity; entropy; arrow of time; ontology of time; self-recording universe
This paper overall treats the timeless mind-body problem. Descartes said: “I think, therefore I am.” This suggests the existence of life in a non-material world, specifically, a spacetime that is devoid of particles, which then evokes the equally celebrated theme of the wave-particle duality, which is the foundation of quantum mechanics. Correspondingly in mathematics, there is a dichotomy of the real number 1, and the imaginary number i - - which has however presented itself as a mystery for centuries. Here, we maintain that a 1-dimensional manifold is either a line or otherwise with curvatures and any curvature can be locally fitted by a circle, i.e., either a line with unit 1 or a unit circle expressed by exp(it), such as in the contrast between a linear calendar time t and a circular clock time it, or a linear expansion versus a rotational motion as indicated by the eigenvalues of a linear operator in a dynamical system. As such, the imaginary number i is just a periodic motion, or a wave. While Maxwell’s electromagnetic wave has energy, the quantum wave is yet a probability; we unify these two treatments of the wave by equating the quantum wave with Maxwell’s electromagnetic wave. The wave-particle duality logically leads to a diagonal spacetime manifold containing {(particle, its associated electromagnetic wave)}. In literature, a particle wave has its energy E distributed into (3E/4, E/4) respectively. Experimentally, a 50/50 beam splitter has been found to split half of the E/4 into a particle-less wave, evidencing the existence of a separate but coincidental wave universe; it is here that we define a living element as a set of particle-less electromagnetic waves that adds life to a set of molecules in the particle universe. We will present the mathematical formulation of the above and examine its implications and applications.