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Time, Equilibrium, and General Relativity
Version 1
: Received: 24 June 2020 / Approved: 24 June 2020 / Online: 24 June 2020 (13:45:16 CEST)
Version 2 : Received: 9 August 2020 / Approved: 10 August 2020 / Online: 10 August 2020 (15:15:45 CEST)
Version 2 : Received: 9 August 2020 / Approved: 10 August 2020 / Online: 10 August 2020 (15:15:45 CEST)
How to cite: Hollestelle, H.H. Time, Equilibrium, and General Relativity. Preprints 2020, 2020060298. https://doi.org/10.20944/preprints202006.0298.v1 Hollestelle, H.H. Time, Equilibrium, and General Relativity. Preprints 2020, 2020060298. https://doi.org/10.20944/preprints202006.0298.v1
Abstract
Considered is “time as an interval” including time from the past and from the future, in contrast to time as a moment. Equilibrium as the basis for a description of changing properties in physics is understood to depend on the “mean velocity theorem”, while a “time” of equilibrium resembles a center of weight. This turns out to be a good method to derive properties for any function of time t including space coordinates q(t) and expressions for the time dependent Hamiltonian. Introduced are derivatives depending on time intervals instead of time moments and with these a new relation between the Lagrangian L and the Hamiltonian H. As an application introduced is a step by step method to integrate stationary state “local” time interval measurements to beyond “locality” in General Relativity. Because of limits on the measures of the resulting time intervals and their asymmetry, this allows for a probabilistic interpretation of quantities that have these intervals as time domain in QM. Their asymmetry also questions the time reversal symmetry of GR. Another application of time intervals is the discussion of the measurement of starlight radiation energy and QM wave packet collapse as an example of a time dependent Hamiltonian. Finally a relation between starlight frequency, metric and space- and time intervals is found. Discussed is how finite and asymmetric time intervals correspond to time dependent H and symmetric infinite time intervals to a time independent H. From there, in cosmological perspective, finite time intervals can help to describe how entropy change could relate to dark energy.
Supplementary and Associated Material
Keywords
time interval; equilibrium; graphs; derivative; metric; general relativity; starlight radiation; qm wave packet collapse; cosmology
Subject
Physical Sciences, Mathematical Physics
Copyright: This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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DOI: 10.24940/theijst/2020/v8/i5/ST2003-035