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
