Continuous quantum measurements and geometry of the universe

Joel Monasterial

Paper 10.11S formalizes the quantum substrate as the continuity geometry of pre‑identity state‑flow, establishing the invariant that continuity becomes identity only through constraint. The paper reframes superposition, entanglement, and measurement as continuity primitives—unbroken possibility, cross‑boundary coherence, and constraint‑induced collapse. It defines the continuity→constraint→collapse→identity sequence as universal geometry across quantum behavior, classical physics, epistemic architectures, and the cyber–fusion–QC triad. Paper 10.11S serves as the canonical substrate spine for the entire 10.x series.

E.G. Eberle

Mikio Namiki, Y. Aizawa, Kei‐ichi Maeda +1 more

Ishibashi, Toru

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

Richard Phillip Gilliard

The historical statistical interpretation of measurement in quantum mechanics, attributed to Max Born, has generally been that it is governed by pure probability. In this paper, it is shown that this probability is equivalent to that governed by the statistical distribution of the energy from continuous spacetime into a pixelated Planck canvas. It should be noted that all units in this paper utilize the cgsrev system, a system entirely isomorphic to standard Gaussian cgs. By demonstrating that the discrete micro-world and the continuous macro-world are dual expressions of a single unified manifold, gravity and quantum probability are revealed to be intrinsic structural features of a completely geometrized universe. The implementation of the cgsrev framework within the scaffolding of discrete differential geometry completes a rigorous re-architecture of theoretical physics.

James Thomas Wheeler