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Synchronization and Fundamental Time: A Connection Between Relativity and Quantum Mechanics

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Abstract

An interesting connection between special relativity and quantum mechanics was put forward by Louis de Broglie, about 60 years ago, who focused on the link between synchronization in a rotating frame and the quantization of the angular momentum. Here we generalise his approach to curved spacetime, using the gravitoelectromagnetic analogy, which can be applied to describe the weak gravitational field around rotating sources, and give a new interpretation of the results.

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Notes

  1. We use the following notation: Greek (running from 0 to 3) and Latin (running from 1 to 3) indices denote spacetime and spatial components, respectively; letters in boldface like \(\textbf{x}\) indicate spatial vectors.

  2. Up to linear order in the gravitoelectromagnetic potentials.

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Acknowledgements

The author acknowledges the contribution of the local research project Modelli gravitazionali per lo studio dell’universo (2022)—Dipartimento di Matematica “G.Peano”, Università degli Studi di Torino; this work is done within the activity of the Gruppo Nazionale per la Fisica Matematica (GNFM). The author thanks Dr. Antonello Ortolan for useful discussion.

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  1. Dipartimento di Matematica “G.Peano”, Università degli studi di Torino, Via Carlo Alberto 10, 10123, Turin, Italy

    Matteo Luca Ruggiero

  2. INFN - LNL, Viale dell’Università 2, 35020, Legnaro, PD, Italy

    Matteo Luca Ruggiero

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Ruggiero, M.L. Synchronization and Fundamental Time: A Connection Between Relativity and Quantum Mechanics. Found Phys 53, 83 (2023). https://doi.org/10.1007/s10701-023-00724-8

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