What Can We Learn about the Ontology of Space and Time from the Theory of Relativity? A Synopsis

John D. Norton
Department of History and Philosophy of Science
University of Pittsburgh
Pittsburgh PA  USA 15260

	What is the nature of space? What is the nature of time? These are the perennial questions of philosophy of space and time. A long standing tradition looks to our latest science for assistance in answering. In the seventeenth century, Isaac Newton redefined philosophy of space and time in introducing the notions of Absolute Space and Absolute Time. They were underwritten by the authority of the leading sage of his day and at least a century to come. In the twentieth century, Albert Einstein published his theories of relativity, the special and the general. Philosophy of space and time was transformed once again. Exactly how was it changed? What should we learn from Einstein's work? That is my concern here.
	The task proves to be a little different from what one might expect. The task is not to exercise one's philosophical creativity to generate these lessons. Rather it is to apply a critical filter to the plethora of morals already proclaimed. In repeated efforts to extract the philosophical bounty of Einstein's work, generations of philosophers have ended up proclaiming almost every conceivable thesis on Einstein's authority. The present task, then, is to sift through this abundance, discard the spurious morals and answer the question "What can we learn about the ontology of space and time from the theory of relativity?" This note is a synopsis of a lengthier study presented elsewhere. The reader is referred to it for citations and elaboration on the claims that follow.
1. Four Requirements for Any Moral
	How are we to sift? I propose that any candidate moral must satisfy four requirements if it is to count as a philosophical moral of Einstein's theories for the philosophy of space and time. They are:
Novelty:  The morals we draw should be novel consequences of relativity theory. They should not be results that could have been drawn equally from earlier theories.
In the exuberance engendered by Einstein's theories, it is easy to overlook what we already knew or could have known. If the moral was already known or knowable prior to Einstein's work, then we cannot claim it as a moral of the advent of relativity theory. We might be grateful that Einstein's work somehow brought the possibility to our attention and comforted that his work does not refute it. That should not be what we esteem Einstein most highly for. We seek those results which are genuinely novel with Einstein's theories.
Modesty: The morals we draw should be consequences of relativity theory. They should not be results we wish could be drawn from relativity theory, but are only suggested to us by the theory.
Relativity theory is often a part of a longer project that involves quite strong philosophical goals. In their confidence of ultimate success, proponents of such projects have proclaimed that relativity theory vindicates the principles expressed in their philosophical goals. That is premature.
Realism: Relativity theory is to be construed as literally as possible. 
We seek morals about the nature of space and time. If we are allowed to construe Einstein's theories metaphorically, then how do we distinguish the morals we draw from our metaphorical inventions from those resulting from the physical content of the theory? To preclude this difficulty we should construe the theories as literally as we can; in so far as it is sustainable, the content of the theories is just what the theories literally say.
Robustness: We should not draw morals in one part of the theory that are contradicted in others. In particular, the morals we draw from examination of special relativity should survive the transition to general relativity. 
Einstein developed the special theory of relativity before the general. That first theory has long enjoyed more detailed philosophical scrutiny, in part because it is the easier theory to learn and understand. However it deals only with a special case of the many spacetimes dealt with in general relativity. So it has proven possible to settle on philosophical morals in the special theory that do not survive in the general theory.
2. What’s IN; What’s OUT. An Opinionated Survey
	I have divided the morals that I urge can be drawn ("What's in") into three groups, all employing the banner of "entanglement". I list them below in three sections and also list related candidate morals in each that fail one of the four requirements above ("What's out"). A final section lists some miscellaneous morals that fail.
2.1 Entanglement of Space and Time
IN
	Relativity of Simultaneity. When Einstein presented his special theory of relativity, he began with an analysis of simultaneity. On the basis of his light postulate, he showed that observers in relative motion may disagree on the simultaneity of events at different spatial locations. This proved to be the conceptual key that enabled consistent development of his new theory of space and time. The result is threatened by robustness since it does not survive in Einstein's original form in general relativity. However it does depend on a form of the entanglement of space and time of importance to general relativity. It may be re-expressed in weakened form in infinitesimal regions that surround events. The entanglement it expresses is what makes the spacetime formulation of relativity theory so fertile.
OUT
	Time is the fourth dimension. This tired slogan gains some credence since Minkowski's spacetime formulation of relativity theory proved to be the most insightful and fertile. However it is hard to see how it improves on the more precise notion of the relativity of simultaneity. The slogan that time is the fourth dimension either fails for its banality: one could always give spacetime formulations even of classical theories (violation of novelty). Or it fails for its pretentiousness, if it is read as saying that time is a fourth dimension just like space. It isn't in relativity theory (violation of modesty).
	Determinateness of the future. If we assume that simultaneous event are determinate with respect to each other, we can chain such events together and conclude that future events are determinate as well. The thesis does not survive transition from special to general relativity, since the geometric constructions it requires can no longer be mounted in general.  It violates robustness. In addition it is unclear that simultaneity does entail determinateness and that the requisite transitivity of determinateness obtains, a violation of modesty.
	Conventionality of simultaneity. Famously, Reichenbach urged that simultaneity is not only relative to the observer but, even for a particular observer, there is considerable freedom of choice in deciding which events are simultaneous. The thesis does not survive transition to general relativity. There is a unique relation of simultaneity in, for example, the Robertson-Walker spacetimes of standard cosmology. The thesis violates robustness. Whether the thesis is sustainable in the context of special relativity alone remains under debate; my view is that the issue is clouded by the lack of clear, independent meaning for the notion of simultaneity.
2.2 Entanglement of Spacetime and Matter
IN
	Spacetime loses absoluteness: In earlier theories and in the special theory of relativity, space and time or spacetime provided an immutable container for matter. That container had an absolute status in the sense that it was entirely unaffected by how matter may be distributed within it. Yet space and time themselves had a powerful causal effect on matter. They determine which are the inertial trajectories of free bodies, for example. As Einstein emphasized, general relativity altered that. Through his gravitational field equations, the distribution of matter determines the curvature of spacetime; so spacetime is now affected causally by matter and loses its absolute status.
	Failure of spacetime (manifold) substantivalism. Spacetime interacts causally with matter. Does it have an existence independent of that matter, as if it were a substance itself, as the doctrine of spacetime substantivalism says? A modernized version of Einstein's "hole argument" of 1913 and 1914 appears to show otherwise. If we assume that the events of a spacetime manifold have that independent existence, then we are forced to a conclusion most find unpalatable: we must accept that two spacetimes are distinct even when the difference between them transcends all possible observation and even the determining power of the equations of general relativity itself. It remains an open question, however, whether these results pertain to general relativity alone or whether they can be mounted in formulations of earlier theories as well. The latter case would be a violation novelty.
	Gravitational field energy and momentum compromised. In earlier theories, what was distinctive about matter was that it carried energy and momentum. In general relativity, however, the gravitational field (and thus the energy and momentum it carries) is combined with the geometry of spacetime, blurring the distinction between spacetime the container and matter the contained.. The outcome is that it is no longer possible to give an observer independent judgment of the gravitational energy and momentum density present at an event in spacetime or to say how much gravitational energy and momentum is present in a region of spacetime, except in special cases.
OUT
	Relational theory of space and time. Relativity theory has long been associated with a relational theory of space and time. According to it, there are no independent entities of space, time and spacetime. There are spatial points occupied by matter or spacetime events occupied by processes; space, time and spacetime are abstractions constructed from them. Popular as it is, this relational view violates a realistic interpretation of general relativity. It is a theory not of occupied events, but of a spacetime that may be entirely empty of matter. Thus realism is violated. Many theorists hope or have hoped that Einstein's theory is an intermediate in the development of a fully relational theory of space and time. That theory is not Einstein's, however, so we cannot claim the result for Einstein's theory without violating modesty.
	All is geometry. The striking novelty of Einstein's general theory is that it accounts for gravitation not as a force but as a part of the geometry of a curved spacetime. This raised the speculation that all known forces could be accounted for in some kind of spacetime geometry; such was the presumption of Einstein's long standing quest for a unified field theory. We cannot accept "all is geometry" as a moral of general relativity, however, since that quest was never completed. To do so would violate modesty.
2.3 Entanglement of Spacetime and Causation
IN
	New forms of causal isolation. That causation is tied up with space and time has been long known. It has long been suspected that causal action must be contiguous is space and time, although the action-at-a-distance accounts of Newtonian gravitation and other forces did present awkward challenges. The general theory of relativity brought forth a new repertoire of ways in which causal isolation might arise. Certain spacetimes, such as those associated with black holes, involve the existence of worlds causally isolated from our own on the other side of the black hole. Formerly, talk of worlds that are both real but causally isolated from us would have been dismissed as confused metaphysics; Einstein's theory gave them a serious physical foundation. Even within our world there might be unexpected horizons for causation. For example, in big bang cosmology, all matter issues forth from a past in which is was compressed to together to arbitrarily high density as we approach the big bang. One might suppose that, as we approach these times of arbitrary high compression, all matter must have been in causal communication. That proves not to be so. In some cosmologies, our matter remains causally isolated from all but a small part of the matter of the universe however far back we go in time.
	New forms of causal entanglement. If general relativity provides further ways that causal connections may fail, it also supplies the possibility of richer forms of causal contact. There are many universes that solve Einstein's equations and admit causation into the past, that is, time travel. The simplest is the Goedel universe in which all matter is in cosmic rotation. Other spacetimes allow us to see the infinite lifetime of some entity; they are now called "Malament-Hogarth spacetimes." So if ever we could construct a simple computing machine that could compute for an infinity of its own experienced time, in the right spacetime, we could find an event from which we could view the entire calculation. As long as a suitable protocol for communication by signals is set up, we could know whether an arbitrary program halts on some nominated input.
OUT
	Constancy of speed of light . This constancy is the most conspicuous result one first encounters in learning special relativity. Whether we want to count this as a philosophical moral of relativity becomes moot when we realize that it does not survive into the general theory. To proclaim it would violate robustness.
	Causal theory of time. Reichenbach advocated a celebrated reduction of time to causal relations. To say event E is earlier that event F means, in his theory, that event E can causally affect event F. In its original form, the theory depended on a simple result in special relativity. Events are causally connectible if a signal proceeding at or less than the speed of light can connect them. If we specify which pairs of events are causally connectible in spacetime, then it is possible to recover the full structure of a Minkowski spacetime. That recoverability fails in the transition to general relativity and with it the project of the causal theory of time in its original form; there are many geometrically distinct spacetimes that share the same causal structure.  The causal theory of time fails robustness. In addition we may doubt the prudence of trying to account for something relatively well understood, spacetime, in terms of notoriously poorly understood, causation.
2.4 Other Morals
OUT
	All is relative. Einstein's theories are often called upon to license a relativity that extends well beyond the relativity that Einstein advanced, the relativity of physical quantities to observers' states of motion. We are urged to accept a relativity of truth, beauty and the good. Whatever merit there may be in these further relativities, they have no special relation to Einstein's theories, which can be recast equally effectively as a theory of certain absolutes. To draw these further relativities as morals violates modesty.
	Relativity of geometry. Following arguments of Poincaré and Einstein, Reichenbach urged that there was a considerable conventional freedom in our choice of geometry. We cannot know the true geometry without interpreting the results of operations with measuring rods. We cannot interpret those results without a theory of measuring rods. So we can insist upon just about any geometry as long as we make compensating changes in our theory of measuring rods. This thesis has been subject to much debate. While it was advanced in the context of discussion of relativity theory, for our purpose, what matters is that the arguments that support it can be mounted in a fully classical setting. So to claim it as a moral of relativity theory would violate novelty.
	Relativity of all motion. The novelty of Einstein's special theory of relativity was the principle of relativity of inertial motion. In developing the general theory Einstein hoped to extend this relativity to accelerated motion. Whether he succeeded or not remains a matter of some debate. A considerable body of opinion denies his success and even suggests that his general theory has no relativity of motion in it at all. If the latter is correct, the relativity of motion cannot be drawn as a moral without violation of robustness.
	Arbitrariness of coordinate systems. In his efforts to generalize the principle of relativity to accelerated motion, Einstein was drawn to a formalism that employed arbitrary spacetime coordinate systems, even suggesting controversially that this fact alone assured a generalization of the principle of relativity to acceleration. While Einstein was one of the first to use formalisms that admitted arbitrary spacetime coordinate systems, such coordinate systems could have been employed in earlier theories. Shortly after Einstein's work, simple ways of doing it were displayed. A spacetime coordinate system is merely a convenient way of labeling events in spacetime in a continuous manner, so classical theories place few constraints on how this might be done. To see novel philosophical import in the use of these arbitrary coordinate systems would violate novelty.