Abstract
Chapter 3 will introduce an interpretation of flat spacetime theories I call Primitive Motion Relationalism (PMR). According to this interpretation, motion should be thought of as a primitive entity, more fundamental than spatial points and temporal instants. Events are taken to be coincidences between motions; the identity of events depends on the identity of the underlying motions. The other main feature of this approach is that spacetime consists of a set of potential trajectories. The spacetime manifold and the metric defined on it should not be thought of as a field analogous to other material fields. Rather, spacetime determines the form of actual trajectories and relations between motions, in analogy with Aristotelian formal causes that determine the essence of a substance. One of the main advantages of PMR is that it explains the restricted Principle of Relativity (i.e., the equivalence between inertial reference frames), without presupposing the Principle of Relativity as a postulate.
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Notes
- 1.
This interpretation of the General Principle of Relativity was later contested by many physicists and philosophers, since the General Principle of Relativity is violated by some theories of spacetime that are nevertheless invariant under general coordinate transformations. I shall not pursue this interpretive problem here.
- 2.
A tacit assumption is that if rods in one coordinate system are boosted until they moved with uniform rectilinear motion relative to the first system, they would represent the same length in the new coordinate system. Similarly, the implicit assumption is that boosted clocks would also represent the same unit of time in the moving frame. See Brown (2005, p. 81) and footnote 41 for supporting quotations.
- 3.
In the following I replace Einstein’s notation with the more readable modern notation.
- 4.
Einstein justifies this conclusion as follows:
From reasons of symmetry it is now evident that the length of a given rod moving perpendicularly to its axis, measured in the stationary system, must depend only on the velocity and not on the direction and the sense of the motion. The length of the moving rod measured in the stationary system does not change, therefore, if v and −v are interchanged. Hence follows that \(\frac{l}{\phi(v)}=\frac{l}{\phi(-v)}\) and
$$\phi(v)=\phi(-v)=1$$ - 5.
Brown and Sypel (1995) argue that Einstein’s application of the Relativity Principle to derive the Lorentz transformations should not be surprising, since “the rods and clocks are themselves to be viewed not as primitive, structureless objects, but as solutions of the basic equations, treating clocks and rods as composite entities whose parts are governed by dynamic forces.” Thus given a dynamic approach to spacetime, Einstein’s application of the Principle of Relativity in this context is unproblematic. I shall consider dynamic approaches and their problems in Section 2.4.
- 6.
See Brown (2005, section 5.2).
- 7.
It took a while until the philosophical community came to grips with the status of the Lorentz-Fitzgerald contraction hypothesis (LCH). Popper (2003, p. 62) argued that the LCH is an ad-hoc hypothesis, since the prediction of Maxwell’s theory together with Newtonian mechanics regarding the motion through the ether was falsified by the Michelson-Morely experiment. The LCH was just introduced in order to avoid facing the falsification of accepted theories, and produced no new predictions. Grünbaum (1959) argued that the LCH in isolation was falsified by the Kennedy-Thorndike experiment. In this experimental setup, the interferometer used was similar to that of Michelson and Morley’s, only it had arms of different lengths. The difference in time between the two arms did not depend on the orientation of the interferometer. This shows that the LCH by itself is not sufficient to cohere with the data, and one needs to assume time dilation in addition to length contraction. See Grünbaum (1959), Evans (1969), and Erlichson (1971).
- 8.
- 9.
- 10.
For example, the analysis of the logical foundations of relativity theory shows that it is possible to replace the Principle of Relativity with a weaker axiom (i.e., that observers agree on which events take place). The price for weakening the relativity postulate is that it is necessary to add a reciprocity relation between frames, i.e., time dilation and length contraction must be the same for any boosted frame relative to the frame at rest.
- 11.
See Friedman (1983, chapter VII) for a similar complaint against conventionalism.
- 12.
- 13.
A reference frame F is defined by a time-like vector field X, i.e., \(dtX\neq0\). The trajectories of X could be interpreted as the worldlines of points in the spacetime. If there is a coordinate system \(\{x^\mu\}\) in which the components of the affine connection vanish, or \(\Gamma^\gamma_{\mu\nu}=0\), and the coordinate system is adaptable to F, i.e., the spatial coordinates \(x^{\alpha}, \alpha = 1, 2, 3\) of the trajectories of X are constant, then F is an inertial reference frame (Earman and Friedman, 1973, section 3).
- 14.
See Newton’s account of absolute space in the De Gravitatione, Newton (2004).
- 15.
Even though Einstein described the relation between spacetime and matter as causal, he also thought that having two independent fields existing side by side is problematic. This is one of his motivations for searching for a unified field theory. In a lecture delivered at the Nobel Prize ceremony, he asserted the following:
The mind striving after unification of the theory cannot be satisfied that two fields should exist which, by their nature, are quite independent. A mathematically unified field theory is sought in which the gravitational field and the electromagnetic field are interpreted as only different components or manifestations of the same uniform field … The gravitational theory, considered in terms of mathematical formalism, i.e., Riemannian geometry, should be generalized so that it includes the laws of the electromagnetic field. (Einstein, 1923, p. 489)
- 16.
In the following chapter I will argue for a different account of the mass parameter, which undermines the view that mass is an inherent property. However, I am using the popular (though false) understanding of mass to make a philosophical point.
- 17.
See Balashov and Janssen (2003) for a similar argument against Craig’s neo-Lorentzian interpretation of relativity.
- 18.
I should point out that Brown is not endorsing the adoption of an ether or an absolute frame of reference. Thus he is not attempting to resuscitate Lorentz’s specific strategy for explaining kinematic effects. Rather, he claims that dynamic laws should explain the kinematic effects of a set of rods and clocks moving relative to another system of clocks and rods. Brown argues that dynamics should explain kinematics, not that the Principle of Relativity is false.
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Belkind, O. (2012). Interpretations of Spacetime and the Principle of Relativity. In: Physical Systems. Boston Studies in the Philosophy of Science, vol 264. Springer, Dordrecht. https://doi.org/10.1007/978-94-007-2373-3_2
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