| viXra.org > Mathematical Physics > 2508 |
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| viXra.org > Mathematical Physics > 2508 |
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[6] viXra:2508.0181 [pdf] submitted on 2025-08-31 20:11:56
Authors: Pedro A. Kubitschek Homem de Carvalho
Comments: 4 Pages.
The quantum harmonic oscillator is traditionally formulated under the assumption of continuous time, leading to well-known eigenstates and energy spectra. However, when extended to cosmological scales, the same formalism contributes to divergences such as the vacuum energy catastrophe (10120 discrepancy in the cosmological constant). In this paper, we propose a reinterpretation: the oscillator is reformulated using the "time-of-time" formalism, where time itself oscillates over the Planck area scale. A new constant, αU = keAP (Coulomb’s constant multiplied by Planck area), emerges as the measure of vacuum rigidity. We show how this modification regulates divergences, unifies the interpretation of vacuum tension across quantum and cosmological domains, and provides a physical ontology to the notion of time in quantum mechanics.
Category: Mathematical Physics
[5] viXra:2508.0180 [pdf] submitted on 2025-08-31 20:15:00
Authors: Pedro A. Kubitschek Homem de Carvalho
Comments: 4 Pages.
The cosmological constant problem arises from the discrepancy be-tween the zero-point energy predicted by quantum field theory (QFT)and the observed value of cosmic expansion [2, 3]. We propose thatthe fundamental oscillation of time-of-time, together with the constantαU = keAP (the product of Coulomb’s constant and the Planck area),provides a natural regularization for this divergence. We show that,instead of summing over all quantum modes, the oscillatory residueleads to a finite effective cosmological term Λeff ∼ α2U /AP , eliminatingthe 10120 mismatch.
Category: Mathematical Physics
[4] viXra:2508.0145 [pdf] submitted on 2025-08-25 03:09:21
Authors: Bin Li
Comments: 22 Pages. (Note by viXra Admin: For the last time, please submit article written with AI assistance to ai.viXra.org)
We ask how Lorentzian causal structure can emerge from a pregeometric substrate. For arigorously defined class of finite—range, ferromagnetically coupled "chronon" models with quartic norm pinning, we prove the existence, with strictly positive Gibbs probability, of a macroscopic percolating domain D ⊂ M on which the coarse—grained field Φµ is smooth, future—directed,unit—norm timelike (ΦµΦµ = −1, Φ0 > 0) and twist—free. We work on a smooth differentiablemanifold but do not assume Lorentzian signature or a global time field a priori; these arise onD from the dynamics. Under four operational axioms—well-posed local dynamics, finite-speed signalling, acyclic causal order, and stable memory/records—we further prove that no alternative (Euclidean orultrahyperbolic) signature, nor a Lorentzian background lacking a globally unit—norm time field,can sustain such behavior; the Lorentzian, unit—norm phase is therefore exclusive. Finally, we show that "measurement" acts as a boundary-induced selector of this phase: an interface coupling to an aligned apparatus field ΦA admits a unique minimizer, pins the norm and alignment, suppresses twist, and drives any initial state to the aligned phase with exponential convergence; large-deviation bounds quantify high-fidelity selection.Our theorems hold for general (1, d) signatures with d ≥ 1. While the proofs are dimensionagnostic, heuristic coarse-graining and stability considerations suggest d = 3 as the most probable large-scale outcome. Together, these results provide a mathematically controlled foundationfor the emergence and exclusivity of Lorentzian causal structure and for boundary-driven selection (measurement) in pregeometric ensembles.
Category: Mathematical Physics
[3] viXra:2508.0130 [pdf] submitted on 2025-08-20 21:24:22
Authors: Pedro A. Kubitschek Homem de Carvalho
Comments: 17 Pages. In Portuguese (Note by viXra Admin: All entries on the Submission Form should be English)
We present the derivation of the inverse-square law and the acceleration of gravity g from the Geometric Principle (GP). Space is treated as a mesh of minimal areas A_P, whose rigidity is regulated by alpha_U = k_e A_P. The derivation shows that g emerges naturally and reproduces the value measured at the Earth's surface. The generalization to two bodies leads to an emergent form of the gravitational constant G.
Category: Mathematical Physics
[2] viXra:2508.0114 [pdf] submitted on 2025-08-17 22:43:19
Authors: Vicente Pedro Diogo
Comments: 14 Pages.
The present article aims to present an extension of the Fourier dualityto non-commutative groups and algebraic structures,analyzing thenon-commutative Fourier transform on one dimensional structures alongwith their unitary representation. This approach gives a comprehensiveinsight into the harmonic analysis of operator-valued functions, providingmathematical foundations for analyzing physical systems that exhibitnon-commutative symmetries. Hence the article discusses applications ofnon-commutative harmonic analysis into emerging fields of physics such asquantum mechanics and models of quantum gravity , opening paths forexploration of the connections between non-commutative algebras, harmonicanalysis, and theoretical Physics.
Category: Mathematical Physics
[1] viXra:2508.0095 [pdf] submitted on 2025-08-14 20:30:37
Authors: Igor Tkachenko, Victoria Miroshnichenko, Kostiantin Tkachenko, Sergiy Miroshnichenko, Yuriy Miroshnichenko
Comments: 6 Pages.
We applied early developed analytic approach for analysis of third order non-stationary stochastic processes (NSPs) to consider the second order ones. A new constitutive differential equation for the NSPs was derived, and its analytic solutions were obtained. Possibility of periodic combination of nonperiodic analytic solutions of the equation was shown. Development of a 2-nd order NSP long before its macroscopically fixed beginning was shown and a possible explanation of the corresponding negative probability values for the time period was proposed. Necessity of further fine tuned experimental investigations is noted.
Category: Mathematical Physics
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