preprints.org > physical sciences > astronomy and astrophysics > doi: 10.20944/preprints202009.0215.v7

Preprint Article Version 7 Preserved in Portico This version is not peer-reviewed

Version 1 : Received: 8 September 2020 / Approved: 10 September 2020 / Online: 10 September 2020 (03:54:27 CEST)
Version 2 : Received: 21 February 2022 / Approved: 22 February 2022 / Online: 22 February 2022 (08:23:27 CET)
Version 3 : Received: 3 June 2022 / Approved: 6 June 2022 / Online: 6 June 2022 (09:27:33 CEST)
Version 4 : Received: 25 August 2022 / Approved: 26 August 2022 / Online: 26 August 2022 (11:33:29 CEST)
Version 5 : Received: 7 November 2022 / Approved: 7 November 2022 / Online: 7 November 2022 (10:59:26 CET)
Version 6 : Received: 4 December 2022 / Approved: 5 December 2022 / Online: 5 December 2022 (10:32:03 CET)
Version 7 : Received: 7 April 2024 / Approved: 8 April 2024 / Online: 8 April 2024 (11:40:23 CEST)

Differences between the quantum mechanical and relativistic concepts of time observed in GPS satellites are accounted for by applying the equivalence principle to the transitioning electron of an atomic clock. It allows a differential equation of motion to be derived for the electron in the Minkowski space between electron shells. Using Hamilton’s principle we transform the differential equation relativistically into an integral equation of motion, the time integral of a Lagrangian. This newly derived equation accounts for the abstract mathematics of the more familiar non-relativistic model by means of a physical interpretation. Abstract rotations in Hilbert space are replaced by the rotations of real particle field geometries in Minkowski space. Because the properties of energy are universal the same equations are then used to describe the field geometry of galaxies despite vast differences in lifetime. They reveal a symmetry between the electromagnetic fields of atoms and the gravitational fields of galaxies due to similarities in the exchange of energy by radial and transverse fields. Our analysis reveals that the conjugate variables energy and time permit differences between atomic and galactic structure to be compared in a more intuitive way than by means of the differential equations of motion which use the conjugate variables position and momentum.

time; clocks; quantum mechanics; relativity theory; conjugate variables; space-time linearity; energy; quantum gravity

Physical Sciences, Astronomy and Astrophysics

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