Chapter 4: Minkowski Space-Time: A Glorious Non-Entity

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Abstract

It is argued that Minkowski space-time cannot serve as the deep structure within a “constructive” version of the special theory of relativity, contrary to widespread opinion in the philosophical community. This paper is dedicated to the memory of Jeeva Anandan.

Section snippets

Einstein and the space-time explanation of inertia

According to Einstein, special relativity (SR) and Newtonian mechanics share a defect. They both violate the action–reaction principle.

Leibniz held that a defining attribute of substances was their both acting and being acted upon. It would appear that Einstein shared this view. He wrote in 1924 that each physical object “influences and in general is influenced in turn by others.” (Einstein, 1924, p. 15) It is “contrary to the mode of scientific thinking”, he wrote earlier in 1922, “to conceive

The nature of absolute space-time

The second point made in the previous section about the derivations of the geodesic principle was that they demonstrate its limited validity. In particular, it is not enough that the test particle be force-free. It has long been recognised that spinning bodies for which tidal gravitational forces act on its elementary pieces deviate from geodesic behaviour4

The principle versus constructive theory distinction

In recent years there has been increasing discussion of the role that thermodynamics played as a methodological template in Einstein's development of SR, and of his characterization of SR as a “principle” theory, as opposed to a “constructive” theory like the kinetic theory of gases8

The explanation of length contraction

How are we to explain length contraction in SR? One needs to be careful about what, exactly, is taken to stand in need of an explanation.

Balashov and Janssen's (2003, p. 331) initial characterization of the constructive-theory explanation of the space-time interpretation runs as follows:

length contraction is explained by showing that two observers who are in relative motion to one another and therefore use different sets of space-time axes disagree about which cross-sections of the ‘world-tube’

Minkowski space-time: the cart or the horse?

But if it is often sufficient to appeal to Lorentz covariance to give a dynamical explanation of length contraction, is that where explanations should stop? It is here that Balashov and Janssen see a further, constructive role for the geometry of space-time. They ask:

 does the Minkowskian nature of space-time explain why the forces holding a rod together are Lorentz invariant or the other way around? Our intuition is that the geometrical structure of space(-time) is the explanans here and the

Acknowledgments

We are grateful to Michel Janssen and Simon Saunders for discussion, and to an anonymous referee for very helpful comments that led to significant clarifications of our arguments. This paper was composed during Oliver Pooley's tenure of a British Academy Postdoctoral Fellowships; he gratefully acknowledges the support of the British Academy.

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