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Journal Articles journal of geometry and symmetry in physics Year : 2017

Is spacetime as physical as is space?


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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Dates and versions

hal-01454865 , version 1 (03-02-2017)
hal-01454865 , version 2 (04-05-2017)
hal-01454865 , version 3 (17-11-2017)



Mayeul Arminjon. Is spacetime as physical as is space?. journal of geometry and symmetry in physics, 2017, 46, pp.1-24. ⟨10.7546/jgsp-46-2017-1-24⟩. ⟨hal-01454865v3⟩
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