preprints.org > physical sciences > theoretical physics > doi: 10.20944/preprints202209.0151.v4

Preprint Article Version 4 Preserved in Portico This version is not peer-reviewed

Version 1 : Received: 11 September 2022 / Approved: 12 September 2022 / Online: 12 September 2022 (13:03:22 CEST)
Version 2 : Received: 20 September 2022 / Approved: 20 September 2022 / Online: 20 September 2022 (11:21:14 CEST)
Version 3 : Received: 20 March 2023 / Approved: 21 March 2023 / Online: 21 March 2023 (15:15:29 CET)
Version 4 : Received: 27 September 2023 / Approved: 27 September 2023 / Online: 28 September 2023 (10:27:02 CEST)
Version 5 : Received: 18 March 2024 / Approved: 19 March 2024 / Online: 19 March 2024 (12:54:20 CET)

The time interval set approach depends on results for radiation propagation from star sources, where properties relate to sphere like propagation surfaces, finite for any realistic event and measurement. In contrast usually applied to stationary and parallel propagation is the traditional vector and one moment time coordinate kinematic approach from Newton’s laws. A time interval only description necessarily has to start from it's own definitions, and properties since time intervals have to be defined with time intervals. In this paper studied are time interval only set properties, commutation, addition and multiplication, and derivatives, and how to define these corresponding consistently with one moment time set properties. Time development and equilibrium within the time interval description depend on the well-known ‘mean velocity theorem’ and the time interval version of the Legendre transform. Radiation propagation ‘away from’ and gravitation ‘towards’ the star source are part of the one time interval description. In the second, discussion, part the time interval only set approach with only the fundamental properties is applied to radiation. Included is a derivation of star source radiation energy for both zero and non zero wave particle mass. The time interval set is not one of the usual sets encountered and the canonical property does not apply, the approach in this paper starts from commutation properties of one moment time coordinates and of time intervals and relates to Noether charges and structure constants. These are found to be equal to the radiation wave group-velocity, for photons the light velocity c, and, different from the usual derivative to one moment time, they equal specific arguments of the time interval only set derivative.

time interval; radiation; gravitation; commutations; derivatives; propagation surface; star groups; measurement event; (a-) symmetry; time development

Physical Sciences, Theoretical Physics

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