Relativity without miracles
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(2021) 11:3
PAPER IN PHILOSOPHY OF THE NATURAL SCIENCES
Relativity without miracles ´ Sus1 Adan Received: 27 January 2020 / Accepted: 11 September 2020 / © Springer Nature B.V. 2020
Abstract It has been claimed, recently, that the fact that all the non-gravitational fields are locally Poincar´e invariant and that these invariances coincide, in a certain regime, with the symmetries of the spacetime metric is miraculous in general relativity (GR). In this paper I show that, in the context of GR, it is possible to account for these so-called miracles of relativity. The way to do so involves integrating the realisation that the gravitational field equations (the Einstein field equation in GR) impose constraints on the behaviour of matter in a novel interpretation of the equivalence principle, which dictates the determination of local inertial frames through gravitational interaction. This proposed explanation of the miracles can also deal with the problematic cases for attempts at explaining them in the context of the standard geometrical perspective on relativity theory. Keywords General relativity · Spacetime symmetry · Dynamical symmetry · Equivalence principle · Miracles of relativity · Dynamical approach
1 Introduction What is postulated and what is derived in a physical theory is probably not an absolute matter: claims about the fundamentality or derivative character of some features denote different stances on the interpretation of the theory. Recently, it has been claimed that the fact that all the matter laws have the same local symmetries (local Poincar´e invariance) and that these coincide with the symmetries of the spacetime metric is miraculous in general relativity (GR). These two unexplained, and highly surprising, coincidences – of all the local symmetries of the matter laws and of them with the spacetime symmetries – are called in (Read et al. 2018) the two miracles of relativity. My aim in this paper is to argue that relativity theory, at least under a Ad´an Sus
[email protected]; [email protected]
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Department of Philosophy, University of Valladolid, Valladolid, Spain
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European Journal for Philosophy of Science
(2021) 11:3
certain interpretation, has the resources to account for these coincidences: to show that they can be seen as somehow derived instead of brute facts and therefore not as miraculous after all. As I will discuss, this does not mean that there is no contingent component in them. Let me be more specific. Read et al. (2018) and Read (2019) present the problem in the following way. Brown’s influential dynamical approach attempts to regard spacetime in special relativity (SR) as a codification of certain facts about the laws governing the matter fields. As a consequence of this, the symmetries of the metric are seen as accounted for by the Poincar´e invariance of matter laws which is seen, consequently, as a brute fact in SR. In GR things are a bit more complicated. The fact that the metric is itself a dynamical field seems to make the previous interpretation
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