Open Access
2017 Is Spacetime as Physical as Is Space?
Mayeul Arminjon
J. Geom. Symmetry Phys. 46: 1-24 (2017). DOI: 10.7546/jgsp-46-2017-1-24


Two questions are investigated by looking successively at classical mechanics, special relativity, and relativistic gravity: first, how is space related with spacetime? The proposed answer is that each given reference fluid, that is a congruence of reference trajectories, defines a physical space. The points of that space are formally defined to be the world lines of the congruence. That space can be endowed with a natural structure of 3-D differentiable manifold, thus giving rise to a simple notion of spatial tensor -- namely, a tensor on the space manifold. The second question is: does the geometric structure of the spacetime determine the physics, in particular, does it determine its relativistic or preferred-frame character? We find that it does not, for different physics (either relativistic or not) may be defined on the same spacetime structure - and also, the same physics can be implemented on different spacetime structures.


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Mayeul Arminjon. "Is Spacetime as Physical as Is Space?." J. Geom. Symmetry Phys. 46 1 - 24, 2017.


Published: 2017
First available in Project Euclid: 14 February 2018

MathSciNet: MR3791928
Digital Object Identifier: 10.7546/jgsp-46-2017-1-24

Rights: Copyright © 2017 Institute of Biophysics and Biomedical Engineering, Bulgarian Academy of Sciences

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