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MINKOWSKI’S SPACE-TIME

AND THE INTERPRETATION OF PHYSICAL THEORY

by Robert DiSalle

The theory of relativity might not appear to pose profound questions of

interpretation of the sort that are posed by quantum mechanics. On the one hand, there

are continuing metaphysical debates about the nature of relativistic space-time

(concerning, e.g., whether it is “substantival” or “relational”), and methodological

questions about the role played by conventions. On the other hand, however, the theory

does not appear to allow the variety of fundamentally different interpretations that one

finds in the case of quantum mechanics. For, in the case of quantum mechanics, different

interpretations represent profoundly divergent conceptions of what the theory “is about”.

In the case of relativity, a peculiarly compelling conception of what the theory “is about”

was expressed in Minkowski’s (1908) account of Einstein’s theory as a theory of spacetime

geometry founded on Lorentz invariance.

It might appear to be surprising, therefore, that in recent literature the

interpretation of relativity has become a matter of controversy. This controversy arises in

part from a penetrating and subtle re-examination of the meaning of Lorentz invariance

(cf. Brown 2005), from which a re-examination of the nature, and the ontological

significance, of Minkowski’s space-time inevitably results. On what once seemed an

obvious interpretation, Lorentz invariance is a central part of what, according to Einstein,

characterizes special relativity as a “principle-theory”: a theory that expresses “general

characteristics of natural processes, principles that give rise to mathematically formulated

criteria which the separate processes or the theoretical representations of them have to

satisfy” (Einstein 1919). On Lorentz’s theory, by contrast, Lorentz invariance is to be

explained by a “constructive theory,” i.e. a theory that “builds up a picture of the more

complex phenomena out of the materials of a relatively simple formal scheme.” That is,

where Einstein’s theory derives Lorentz invariance from fundamental empirical

postulates, Lorentz’s explains it “constructively” as the dynamical effect of interactions

between moving particles and the ether. According to Brown, the dynamical,

“constructive” account of Lorentz invariance deserves a careful reconsideration.

Such a reconsideration crucially depends, I suggest, on a particular understanding

of the distinction between principle and constructive theories. It construes the distinction

as something very much like the distinction between theories that are fundamental and

those that are merely phenomenological, a construal encouraged by Einstein’s

characterization of principle-theories as expressing “empirically-discovered” principles.

On this account, Einstein accepted Lorentz invariance as something fundamental—that is,

as not further explicable by any “constructive” account—only provisionally, in the

absence of the deeper understanding that a constructive account ought to provide. It

follows from this view that Minkowski space-time cannot be regarded as the ontological

basis of special relativity, or as in any way explanatory of Lorentz invariance; it is instead

merely a “codification” of the behavior of moving bodies and clocks that still awaits a

proper explanation.

This view is challenged by (among others) Janssen (2007), who defends the view

of special relativity as a fundamental theory and articulates a sense in which Minkowski

space-time is indeed explanatory. While I am in broad agreement the force of this

challenge, I offer a different account of the explanatory role of Minkowski spacetime. In

this account, particular attention is paid to one aspect of principle theories, that they

express “criteria” which natural processes “have to obey.” The question I consider is how

certain principles come to have the force of

explanation of how processes or systems come to satisfy these criteria at the

phenomenological level, or even a deductive-nomological explanation of how they

follow from an underlying structure, I consider the sense in which these criteria are

criteria in this sense. Instead of a dynamical

definitive in turn, requires us to reconsider the epistemological arguments given by Einstein in

1905, and the role that they play in Minkowski’s arguments of 1908. These arguments

concern

, or constitutive, of fundamental physical properties of dynamical systems. This, how well defined  are the fundamental concepts presupposed by Lorentz’s theory, explain the Lorentz invariance, in the sense of specifying an underlying

and what physical assumptions are required in order to construct a framework of space

and time in which such a theory can make sense. If these arguments are compelling, then

the principle-theory is not merely a phenomenological description whose deeper

explanation is wanting; it is the demand for a dynamical explanation that is wanting, in

the sense that the concepts of the spatio-temporal framework that it presupposes—the

concepts of simultaneity, length, and time—require a physical interpretation that has yet

to be adequately defined.

This analysis provides a perspective on what Minkowski’s space-time theory

accomplishes as an interpretation of special relativity. In one sense Minkowski spacetime

does not

reality of which the latter is a phenomenological consequence. In another sense,

Minkowski’s space-time explains the significance of Einstein’s theory for our

understanding of the world, and of the nature of space-time; it explicates the conceptual

revision that Einstein’s theory forces upon us. This, I suggest, is at least one useful way

of thinking about the interpretation of a physical theory: a compelling interpretation is

one that is, at the same time a compelling explanation of the ways in which the theory

forces us to re-conceptualize our experience of the physical world, and to revise our

fundamental physical concepts.

 

Robert DiSalle

Professor, Department of Philosophy

University of Western Ontario

 

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