Abstract
In this paper we argue that structural explanations are an effective way of explaining well-known relativistic phenomena like length contraction and time dilation, and then try to understand how this can be possible by looking at the literature on scientific models. In particular, we ask whether and how a model like that provided by Minkowski spacetime can be said to represent the physical world, in such a way that it can successfully explain physical phenomena structurally. We conclude by claiming that a partial isomorphic approach to scientific representation can supply an answer only if supplemented by a robust injection of pragmatic factors.
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Notes
- 1.
- 2.
A categorial framework is the set of fundamental metaphysical assumptions about what sorts of entities and what sorts of processes lie within a theory’s domain (Hughes 1989).
- 3.
Recall that there is a relational and objective matter of fact for all observers about the contraction of a ruler relative to an inertial wordline O(see above).
- 4.
- 5.
“One can distinguish various kinds of theories in physics. Most of them are constructive. These seek to construct a model of the more complex phenomena out of a relatively simple formalism taken as a basis. Thus the kinetic theory of gases seeks to reduce mechanical, thermal, and diffusional processes to the movements of molecules\tilde{n}i.e., to construct them out of the hypothesis of molecular motion. When one says that we have succeeded in understanding a group of natural processes, one always means that a constructive theory has been found that comprehends the relevant processes” (Einstein 1919, transl. by Don Howard). It is possibly not irrelevant to remark that none so far has been able to provide any such constructive theory, neither for SR nor for GR.
- 6.
For the discussion of another improper, metaphysical use of Minkowski spacetime, see Dorato (2006).
- 7.
Given that also the metric field is causally inert even though it is surely correlated to matter (a causal reading of the metric field is very controversial to say the least), how could one regard a causal reading of Minkowski spacetime as plausible?
- 8.
- 9.
Batterman (2010) argues that asymptotic behaviour cannot be captured by any kind of isomorphic relation.
- 10.
Whether it is also neutral toward a form of spacetime structural realism is of course much less clear. But see below.
- 11.
One can recognize this charge against the effectiveness of geometrical explanations also in Brown’s works (see Felline Forthcoming).
- 12.
For problems with the isomorphic approach, see Batterman (2010).
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Acknowledgements
The authors thank Vesselin Petkov for his careful reading of a previous version of this paper, which eliminated a mistake. Laura Felline’s research is founded by a Master and Back scholarship from Regione Sardegna. She would also like to thank all the members of Alophis – Applied Logic and Philosophy of Science – group for daily support and help.
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Dorato, M., Felline, L. (2010). Structural Explanations in Minkowski Spacetime: Which Account of Models?. In: Petkov, V. (eds) Space, Time, and Spacetime. Fundamental Theories of Physics, vol 167. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-13538-5_9
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