References
8 A defense of absolute simultaneity
Michael Tooley
The basic thesis that I shall be defending in this paper is that events in the actual world do stand in the relation of absolute simultaneity, and in support of that thesis I shall offer two arguments. The first will be a metaphysical argument that focuses upon causation and space-time, while the second argument will appeal to quantum mechanics.1
The metaphysical argument: causation and space-time
This first argument involves four main steps. First, it will be argued that there are good reasons for rejecting a relationalist (or reductionist) view of space-time in favor of a realist account. Secondly, it will then be argued that once a realist view of space-time is accepted, the continued existence of space-time becomes a fact that stands in need of an explanation – and, specifically, a causal explanation. Thirdly, I shall then argue that the most plausible causal explanation is one that postulates a conservation principle for space-time itself, and, in particular, one that postulates non-branching causal processes. Finally, I shall then show that such a conservation principle enables one to define the notion of absolute location in space-time, and, thereby, the relation of absolute simultaneity.
One important feature of this argument, I think, is that it does not involve any special postulate whose only function is either to guarantee the existence of the relation of sameness of location, or to guarantee that events stand in the relation of absolute simultaneity. For the existence of both of these relations follows simply from the idea that parts of space-time are causally connected, together with the most plausible hypothesis concerning the conservation law that governs that connection.
Let us now turn to the argument. The first stage involves the claim that there are good reasons for accepting a realist view of space-time. This issue of the choice between an absolute, or realist, view of space-time, and a reductionist, or relational one raises, of course, some difficult questions. However philosophers of physics who reject the idea of absolute simultaneity do not in general rest their rejection of it upon a rejection of a realist view of space-time: they maintain, rather, that regardless of whether one accepts an absolute view of space-time or a relational one, there is no reason to accept the idea that events in our world stand in the relation of absolute simultaneity.
Because of this, I shall not attempt to offer a detailed defense of realism with regard to space-time. I shall, however, briefly set out what seems to me one of the strongest arguments for a non-relational view, and which runs as follows. First, consider the fact that there are locations where there could, at a given time, have been a physical object, even though, as a matter of fact, that was not the case. The possibility involved here is not that of a mere logical possibility: our everyday experience of the motion of objects, for example, makes it reasonable to believe that there are locations where there are, as a matter of fact, no physical objects, but where the existence of such objects is not only logically possible, but empirically possible.
Secondly, I think it is plausible that statements of empirical possibility – in contrast to statements of logical possibility – require truth makers in the world, and that the truth makers in question cannot consist of ontologically primitive, modal facts: any empirical possibilities must instead be grounded in non-modal, categorical states of affairs – together, presumably, with laws of nature.
If this is right, then consider any spatio-temporal location where there is, as a matter of fact, no physical object, but where it is empirically possible that there could have been such an object. What is the relevant categorical basis of the empirical possibility in question?
In response, it might be suggested that answers are certainly possible that do not involve a realist view of space-time. Perhaps, for example, it is the presence of some physical field in an otherwise empty location that is the ground of the empirical possibility of there being an object at that location. Or perhaps the empirical possibility is somehow grounded in the categorical properties of physical objects, events, or fields that exist at other locations than the one in question. I think, however, that it is fair to say that both of these hypotheses are extremely speculative: there is no evidence either for the view that what makes it possible for there to be an object at a given location is that there is already some field at that location, or for the view that the possibility is, instead, dependent upon fields or events or objects at other locations. But if these accounts are rejected, it is hard to see what plausible alternative there is to the view that the categorical properties that are the basis of the empirical possibilities in question are properties of the space-time points themselves, and, thus, properties that are in no way dependent upon the properties of physical objects, or events, or fields – there or elsewhere. If this is right, and there are no plausible alternatives, then the postulation of absolute, or substantival space-time is justified as providing a categorical ground for empirical possibilities concerning alternative locations of physical objects.
Let us now move on to the second stage in the argument. It involves the claim that, once one accepts a realist view of space-time, it is very
reasonable to hold that there are causal relations between temporal slices of space-time. Why should this be so? One argument is as follows. Assume that a realist account of space-time is correct. Given that assumption, what external relations must obtained between different spatio-temporal regions? One external relation that must obtain between some spatio-temporal regions is that of temporal priority. Let us ask, then, what account is to be given of that relation.
One answer, which has been defended by a number of philosophers, is that temporal priority is to be analyzed in causal terms (Mehlberg 1935: 119–258; 1937: 111–231; Mellor 1981: Chapters 9 and 10; 1998: Chapters 10–12; Tooley 1997: Chapter 9). But if such an account is right, and if one accepts a realist view of space-time, then it seems that one may be able, by focusing upon the possibility that space-time might be completely empty, to argue that in order for different parts of space-time to be temporally related to one another, there must be causal relations between them.
But is this conclusion justified? An important challenge to it involves the point that causal theories of temporal priority have often been formulated, not in terms of actual causal connections between states of affairs, but in terms of possible causal connections, in terms of causal connectibility. Moreover, it may well appear, initially, that there is a very good reason for opting for a modal formulation, since there would seem to be possible worlds where the actual causal relations that obtain between events may not be sufficient to fix all of the temporal relations that obtain between events. So, for example, it may be that event C causally gives rise to two events – A and B – but that there is no causal process leading from A to B, or from B to A. The actual causal relations in such a case do not settle how A and B are temporally related. And given such possibilities, it is natural, if one is attracted to a causal account of temporal priority, to respond by appealing to possible causal connections, and to say, for example, that if A is temporally prior to B then it must be the case that there could have been an event in the immediate vicinity of A that would have given rise to an event in the immediate vicinity of B.2
If an account of temporal priority in terms of causal connectibility is correct, the argument mentioned above is undercut, for what makes it the case that one part of space-time is temporally prior to another need not be a matter of causal connections between the two parts: it could instead be a matter of causal connections that would have been obtained had there been events in the relevant parts of space-time.
In response, however, I think that it can be shown that modal formulations of causal accounts of temporal priority are open to a decisive objection – an objection that becomes evident once one focuses upon the concept of causal connectibility. For that concept presumably has to be analyzed in terms of counterfactuals, and then one is faced with the question of the truth makers for the relevant subjunctive conditionals: what makes it true that, although event A is not causally connected to event B, there could have been a causal process connecting those events, or, at least, connecting alternative events in the same spatio-temporal locations? It is hard to see what answer there can be, other than one that appeals not only to relevant laws of nature, and to the intrinsic properties of the events in question, but also to the temporal relation between those events. But if there is no other answer, then causal approaches to temporal priority that appeal to causal connectibility are unable, on pain of circularity, to specify truth makers for the relevant subjunctive conditionals.
The upshot is that the idea of focusing upon the possibility of a space-time that is completely empty, and then of appealing to a causal account of temporal priority to show that there must be causal relations between spatio-temporal regions themselves, cannot be undercut by arguing that a causal analysis of temporal priority should be formulated in terms of possible causal connections, rather than actual ones.
At this point, two other responses are possible. First, it might be suggested that there is simply no good reason to accept a causal account of temporal priority. But it is doubtful that that contention can be sustained, given that alternative accounts of temporal priority seem very problematic. Thus, on the one hand, other reductionist accounts of the direction of time fail to generate any direction at all in the case of some simple universes – such as a universe containing a single particle, or a universe containing two uncharged particles rotating about one another. They also generate the wrong direction in the case of universes where, because of unusual – but perfectly possible – initial conditions, the direction defined by such features as the direction of increase in entropy, or the direction of the expansion of the universe, or the direction of open forks, etc., are all opposite to that of the direction of time.3
On the other hand, if one opts instead for a non-reductionist account of the direction of time, then one encounters the problem that such an account cannot, apparently, provide any explanation of why it is that the things that we normally take as evidence of the direction of time are in fact evidence, and this in turn means that it becomes rather mysterious, given a realist account of temporal priority, how one can ever know what the direction of time is.
By contrast, these difficulties that confront alternative accounts do not pose any problems for a causal approach. Thus it can be argued, for example, that any simple universe that one would naturally classify as a temporal universe also contains causal relations. Nor is there any problem concerning the epistemology of our temporal judgments, since it can be argued that the facts that we take as evidence for the direction of time are evidence for the direction of causation. And finally, provided that one adopts a realist account of causation, one can handle without difficulty cases where, because of extremely improbable initial conditions, the direction of time is opposite to that indicated by various processes taking place in time – such as increase in entropy.
There are, then, a number of considerations that provide strong prima facie support for a causal account of temporal priority. But that still leaves a final response that needs to be addressed – namely, that whatever advantages such an approach may have, it must still be rejected, since it is exposed to decisive objections.
One of the most detailed and careful statements of the case against a causal approach to temporal priority has been given by J. J. C. Smart in his article ‘‘Causal Theories of Time’’ (Smart 1971: 61–77), where he argues that causal theories of time are exposed to a number of very strong objections. I believe that it can be shown, however – as I have argued elsewhere (Tooley 1997: Chapter 9) – that while Smart’s objections do tell against causal theories of time that are conjoined with relational theories of space-time, the objections have no force if a causal theory of temporal priority is embedded in an absolute theory of space-time.
In view of the above, I believe that there are good reasons for thinking that one is justified in appealing to a causal account of temporal priority as part of an argument for the conclusion that, given a realist account of space-time, some parts of space-time must stand in causal relations to one another. But I also want to argue that one need not, at this point, rest everything upon an appeal to a causal theory of time, since there are at least two other reasons that can be offered for holding that there are causal relations between spatio-temporal regions. Thus, another line of argument is as follows. First, if space-time is a continuant, an account is needed of its identity over time, of what it is that makes spatio-temporal regions, existing at different times, part of a single space-time. Secondly, any satisfactory account of identity over time for ordinary entities must involve causal relations between temporal slices (Armstrong 1980: 67–78). Hence, thirdly, if space-time is a continuant, its unification into a single persisting entity should, presumably, be explicable in parallel fashion: different spatio-temporal regions are part of a single, persisting space-time because of causal connections between them. Therefore, it is reasonable to hold that there are causal relations between different temporal parts of space-time.
A final consideration that also supports the idea of causal connections between spatio-temporal regions is this. It is not a necessary truth that space-time continues to exist. How, then, is this contingent state of affairs to be explained? If one accepted a relational account of space-time, then the continued existence of space-time would be reducible to the continued existence of objects in space-time, and that, in turn, could be explained by relevant conservation laws. But this type of explanation is ruled out if one adopts a realist account, since then one is saying that space-time could exist even if it were totally empty. So what explanation can be offered, given a realist view of space-time? It is hard to see what alternative there is to the idea that the continued existence of space-time is to be explained by the hypothesis that spatio-temporal regions existing at one moment causally give rise to spatio-temporal regions existing at later moments.
But might not one perhaps respond as follows at this point: ‘‘why think that there has to be any explanation at all for the continued existence of space-time? After all, explanation has to stop somewhere.’’
This attempt to blunt the present argument involves, however, a confusion – namely, that between explanations of laws, and explanations of temporally located states of affairs. In the case of laws, the idea that one will ultimately arrive at basic laws that cannot be further explained – rather than there being an infinite regress of more and more basic laws – is very plausible. But when it is a question of the existence of some temporally located state of affairs, one does not appeal to the idea that explanation has to stop somewhere. In that case, one attempts, whenever possible, to explain the existence of a state of affairs at one time in terms of the existence of a state of affairs at an earlier time, and so on, in principle, back forever, if time has no beginning.
Notice, in addition, what is involved in the suggestion that one should make no attempt to explain the continued existence of space-time. It is very different from saying, for example, that perhaps some small event that is highly localized in space-time has no explanation. For if one holds that there is no explanation of the continued existence of space-time, then one is accepting an accident of cosmic proportions, since it involves a non-denumerably infinite sequence of states of affairs of the same type. If there were no explanation for such a sequence of states of affairs, the sequence would be massively improbable – indeed, its probability would be infinitesimally close to zero. To treat the continued existence of space-time as not in need of any explanation is, accordingly, not a rationally defensible position.
What account can be offered, then, of the continued existence of space-time? If one accepted a relational account of space-time, then, as noted earlier, the continued existence of space-time would be reducible to the continued existence of objects in space-time, and that, in turn, could be explained by relevant conservation laws. But this type of explanation is ruled out if one adopts a realist account, since then one is saying that space-time could exist even if it were totally empty. So what explanation can be offered, given a realist view of space-time? It is hard to see what alternative there is to the idea that the continued existence of space-time is to be explained by the hypothesis that spatio-temporal regions existing at one moment causally gives rise to spatio-temporal regions existing at later moments. This hypothesis, of course, does not generate very exciting predictions; however the same is true of conservation laws in general. But it does generate predictions that, although unexciting, are massively confirmed, and so, unless some better explanation of the continued existence of space-time can be advanced, there would seem to be excellent reason for accepting this hypothesis.
To sum up this second stage in my argument: we have seen that there are at least three substantial reasons for holding that parts of space-time stand in causal relations to one another. One of the arguments does involve the claim – which many philosophers would either question or reject – that temporal priority is to be analyzed in causal terms. In response, I indicated briefly some reasons for thinking that a causal account of temporal priority deserves serious consideration. In any case, the other two arguments for the claim that parts of space-time stand in causal relations to one another did not involve any particularly controversial assumptions.
The third and final step in the argument involves asking how, exactly, different parts of space-time are causally related to one another. This question cannot be answered, of course, by experimenting with space-time to determine what causal connections are present: answering the question will be a matter, rather, of determining what hypothesis provides, overall, the best explanation of the continued existence of space-time.
What hypothesis, then, does so? The candidate that I wish to propose is the following: ‘‘The Principle of the Parallel, Non-Branching Conservation of Space-Time’’:
How do the different clauses in this conservation principle function? The answer is that clauses (1) and (2) capture the general idea that space-time is a persisting entity, while clause (3) imposes the requirement that all space-time points on any line containing two causally connected space-time points must also be causally connected, with the result that there is no causal gappiness. Finally, clause (4) ensures that appropriate betweenness and congruence relations are preserved, and that the causal relations involved in the continuing existence of space-time are non-branching ones, with the result that what one has is a strict conservation of space-time.
But what grounds can be offered for thinking that this particular principle provides the best explanation of the continued existence of space-time? Is it clear that there are no alternative hypotheses that are preferable?
What alternatives need to be considered? First of all, in view of the fact that it is an absolutely central principle within the Theory of Special Relativity that nothing can travel faster than the speed of light in a vacuum, any conservation principle for space-time that allowed the existence of one space-time to be caused by the existence of a space-time point to be that was not in the past light cone of that space-time point, or, equivalently, that allowed the existence of a space-time point to cause the existence of a space-time point that was not in its future light cone, should presumably be excluded.
Secondly, once one departs from the conservation principle formulated above, and allows non-parallel causal processes, and possibly also branching causal processes, the only non-arbitrary way of allowing the existence of a space-time point to be causally connected with the existence of some, but not all, of the space-time points within its past and future light cones, is via principles that distinguish between space-time points on the surface of the light cones, and space-time points in the interior of the light cones. It would seem, then, that, as regards alternatives to the Principle of the Parallel, Non-Branching Conservation of Space-Time, there are only three possibilities that are serious candidates, since there are only three alternatives that neither entail the existence of causal processes that are faster than those involved in the transmission of light, nor suffer from arbitrariness. First, there is an expansive, ‘‘conservation’’ principle according to which the existence of a space-time point is causally connected to the existence of every space-time point to which it is connected via optical lines: ‘‘Expansive Conservation of Space: Principle I’’:
Every space-time point is such that its existence is a cause, via a straight-line causal process, of the existence of every space-time point on the surface of its future light cone.
Secondly, there is an expansive, ‘‘conservation’’ principle according to which the existence of a space-time point is causally connected to the existence of all and only space-time points that lie on the inside of its future light cone: ‘‘Expansive Conservation of Space: Principle II’’:
Every space-time point is such that its existence is a cause, via a straight-line causal process, of the existence of every space-time point in the interior of its future light cone.
Thirdly, there is the expansive, ‘‘conservation’’ principle that postulates both the causal connections involved in Principle I, and those involved in Principle II: ‘‘Expansive Conservation of Space: Principle III’’:
Every space-time point is such that its existence is a cause, via a straight-line causal process, of the existence of every space-time point in its future light cone.
How does the Principle of the Parallel, Non-Branching Conservation of Space-Time compare with these three alternatives? It seems to me that it is superior, for at least three reasons. In the first place, that principle is simpler with respect to the number of states of affairs that it postulates. For whereas the Principle of the Parallel, Non-Branching Conservation of Space-Time does not entail anything beyond the existence of non-branching causal chains connecting some space-time points, all three of the expansive conservation principles entail that every space-time point is causally connected, via non-denumerably many causal chains, with every space-time point on the inside of the relevant forward and backward light cones. In addition, each of those causal chains branches infinitely often at every point, whereas, according to the Parallel, Non-Branching Conservation Principle, the causal chains connecting space-time points never branch. The latter theory is therefore vastly simpler with respect to the actual causal connections that it postulates.
Secondly, and as an immediate consequence of the preceding point, the three expansive conservation principles involve massive causal over-determination, since, for every space-time point, there are non-denumerably many, causally unconnected space-time points such that the existence of any one of those points is a sufficient cause of the existence of the space-time point in question. By contrast, no such overdetermination exists in the case of the Parallel, Non-Branching Conservation Principle.
Finally, in adding new laws to a scientific theory, it seems reasonable, other things being equal, to assume that new laws will be similar in mathematical and causal form to known laws that deal with comparable phenomena. Thus, in particular, if the goal is to arrive at a law dealing with the continued existence of space-time, a plausible initial hypothesis is that the law in question will be parallel in form to laws dealing with the conservation of matter and energy, momentum, electrical charge, etc. The latter, however, are conservation laws. It is therefore likely that the law governing the continued existence of space-time will also be a conservation law. The Principle of the Parallel, Non-Branching Conservation of Space-Time, in postulating non-branching causal connections between space-time points, entails that space-time, rather than increasing or decreasing, is strictly conserved, and so it is a law of the relevant form. By contrast, the other three proposals, in entailing the existence of branching causal processes – indeed, infinitely branching ones – are not conservation laws, and therefore are radically different in form from the laws dealing with the continued existence of matter, energy, momentum, and electrical charge.
The conclusion, in short, is as follows. First, the Principle of the Parallel, Non-Branching Conservation of Space-Time both predicts and causally explains the continued existence of space-time, so that, in the absence of a superior hypothesis, its acceptance can be justified via an inference to the best explanation. Secondly, it is superior to the three alternative hypotheses with regard to simplicity, both because it postulates far fewer causal processes, and because it avoids massive causal overdetermination. Thirdly, it is a hypothesis that is parallel in form to other central, conservation principles of physics, whereas the other three alternatives are not. There would seem to be excellent grounds, therefore, for regarding that principle as more plausible than its competitors.
Given the Principle of the Parallel, Non-Branching Conservation of Space-Time, it is possible to give an account of sameness of location. The idea is the very natural one of offering the same sort of analysis of the identity of locations over time that can be offered of the identity of physical objects over time. The latter, however, can be analyzed – and very plausibly – in terms of causal relations between temporal parts. Paralleling such an analysis for the case of sameness of locations relative to substantival space-time gives one the following analysis:
Two distinct space-time points P and Q are part of one and the same spatial location at different times
means the same as:
The Principle of the Parallel, Non-Branching Conservation of Space- Time is true, and P and Q are space-time points such that either the existence of P causes the existence of Q, or the existence of Q causes the existence of P.
The relation of sameness of location need not, then, be taken as a primitive relation, since it can be analyzed in terms of the ontologically fundamental relation of causation. Nor is there any need for an independent postulate that deals with sameness of location, in order to ensure that there are space-time points that are in the same location at different times, since given the above analysis of sameness of location in terms of causation, the existence of space-time points that are in the same location at different times will be entailed by a very plausible principle concerning the conservation of space-time.
Given an account of sameness of location, together with the idea of simultaneity relative to a frame of reference, the idea of absolute simultaneity can be defined very simply as follows:
Two events, E and F, are absolutely simultaneous
means the same as:
E and F are simultaneous relative to some frame of reference that is at rest with respect to absolute space-time – that is, which is such that no part of it is ever in different spatial locations at different times.
The upshot is that there is no need to postulate a relation of absolute simultaneity, since the existence of that relation follows very quickly from the existence of the relation of simultaneity relative to a frame of reference, together with the Principle of the Parallel, Non-Branching Conservation of Space-Time.
The scientific argument: quantum mechanics and absolute simultaneity
The second, and very different argument for the thesis that events in our world do stand in the relation of absolute simultaneity involves an appeal to quantum mechanics – and specifically, to an idea that is absolutely central in quantum mechanics, namely, that of the collapse of a wave packet.
Intuitively, the argument can be put as follows. Consider an electron that has been fired towards the screen of a cathode ray tube. According to quantum mechanics, the initial conditions do not causally determine what point on the screen the electron will strike. All that follows from the laws of quantum mechanics is that there are various non-zero probabilities of the electron’s striking different parts of the screen. But once the electron strikes the screen, the probabilities of it hitting other parts of the screen must change from having non-zero values to being equal to zero. But then must it not be the case that all of these changes are absolutely simultaneous with the event that consists of the electron’s hitting the screen in a certain location?
The idea of the collapse of the wave packet thus seems very clearly to involve the notion of absolute simultaneity. Put in such a general way, however, the force of this point may seem open to question, since one might well respond that, if quantum mechanics is inconsistent with the Special Theory of Relativity, then perhaps one should conclude, ‘‘So much the worse for quantum mechanics.’’ How does one know that it is the Special Theory of Relativity, rather than quantum mechanics, that needs to be modified?
This is a perfectly reasonable response to the argument as I have formulated it above. However, what we shall now see is that we can recast the argument in terms of a very famous theorem of quantum mechanics, and certain crucial experiments associated with it, and that, when we do so, it becomes clear that it is the Special Theory of Relativity that must be rejected, rather than quantum mechanics.
The story begins with a famous argument advanced by Albert Einstein, Boris Podolsky, and Nathan Rosen (Einstein et al. 1935: 770–80). Their argument involves a thought experiment designed to show that quantum mechanics does not provide a complete description of the world. In outline, the structure of the argument is this. On the one hand, quantum physics does not attribute any properties to an object until a relevant measurement has been made. So an electron, for example, does not have any definite position until a measurement of its position is made, nor any definite momentum until a measurement of its momentum is made, and so on. But, on the other hand, an experimental situation can be described in which there will be a correlation that can be satisfactorily explained only on the assumption that objects do have properties before any relevant measurement on them has been carried out. So the description of the physical world provided by quantum physics must be incomplete.
What experimental situation did Einstein, Podolsky, and Rosen have in mind, as posing a problem for quantum mechanics? It was one based upon the fact that it is possible to create a pair of particles that are correlated in the sense that there is some determinable property such that, if the value of that property is fixed for one of the particles, it must also be fixed for the other. So, for example, a pair of electrons can be created in such a way that the total spin of the two electrons along a given axis must have a certain value, and, if this is the case, then, once the spin of either of the electrons, along the given axis, is measured, and so has a determinate value, the spin of the other electron, along the same axis, must also have a determinate value. Suppose, then, that such a pair of electrons is created, that they are then separated, and that at time t a measurement is made of the spin, along a given axis, of one of the electrons. Then, at least from that time onward, the spin of that electron, along the given axis, has a determinate value. But what about the other electron? When does it have a determinate spin, along the axis in question?
Only two views seem possible. The one is that neither electron acquires a determinate spin as the result of measurement, since both electrons have a determinate spin, along the axis in question, from the time that they are created. Measurement merely enables us to know what those determinate values are; it does not bring those determinate values into existence.
This is the view favored by Einstein, Podolsky, and Rosen. It implies, of course, that the description of the electrons given by quantum mechanics is incomplete, since quantum mechanics does not attribute determinate spins to the electrons prior to a measurement being made.
The other view is that the two electrons acquire a determinate spin, along any given axis, only when a measurement is made on at least one of the electrons. But if this is right, a crucial question arises – namely, what is the relation between the time of the acquisition of a determinate spin by the electron on which the measurement is carried out, and the time at which the other electron acquires a determinate spin?
Since the second electron surely does not acquire a determinate spin at an earlier time, either it comes to have a determinate spin only later, or else it acquires a determinate spin at the same time. If it has a determinate spin only later, there are two possibilities. One is that there is a temporal gap between the time at which the first electron acquires a determinate spin, and every moment at which the second electron has a determinate spin. But surely this cannot be possible, since it would imply that, if a measurement were made on the second electron during the temporal gap in question, then it would be possible for the measurement to yield a value for the spin along the axis in question that, in conjunction with the value of the spin of the first electron, would imply a violation of the principle of conservation of spin. So there cannot be any temporal gap.
Alternatively, it may be that, while the second electron does not acquire a determinate spin when the first electron does, it has a determinate spin at every time throughout some immediately following, open temporal interval. This possibility is best addressed, however, after we have considered the third possibility – namely, that the second electron acquires a determinate spin at precisely the same time as the first electron. The question that immediately arises, of course, is what is meant by ‘‘at the same time’’ in this context. In particular, can it be interpreted merely as simultaneity relative to some inertial frame, F? It would seem that it cannot, since if it were true merely that the acquisition of a determinate spin by the second electron was simultaneous with the acquisition of a determinate spin by the first electron relative to some inertial frame, F, then there would be another inertial frame, F*, such that, relative to that frame, the second electron acquires a determinate spin after the first electron does, and with an intervening gap, so that we would be confronted, once again, with the possibility of a measurement being made on the second electron during the gap between the moment when the first electron acquires a determinate spin and the moment when the second electron would otherwise acquire a determinate spin, in virtue of the measurement made on the first electron. Thus, if simultaneity is merely relative simultaneity, there will be inertial frames where there is a temporal gap, and so, from the perspective of those inertial frames, there will be the possibility of pairs of measurements generating values that violate conservation principles. Only if simultaneity is absolute simultaneity will such a possibility be excluded.
Finally, what about the possibility that, while the second electron does not have a determinate spin at the time when the first electron acquires one, it has a determinate spin at every time throughout some immediately following, open temporal interval? The answer is that precisely the same problem arises as in the case when the two electrons acquire a determinate spin at the same time, for, in characterizing the relevant open interval, one has to make use of the idea that the instant that immediately precedes that interval is simultaneous with the instant at which the first electron acquires a determinate spin, and, once again, it will not do to interpret the simultaneity as simultaneity relative to a frame of reference: only absolute simultaneity will do.
What the Einstein-Podolsky-Rosen thought experiment shows, in short, is this. Either particles have determinate states prior to measurement, in which case quantum mechanics does not provide a complete description of physical reality, or else correlated particles must acquire corresponding determinate properties simultaneously, in the absolute sense – or at least without there being an intervening temporal gap – in which case the Special Theory of Relativity does not provide a complete description of the spatio-temporal relations between events.
Given the argument to this point, I think it is fair to say that it would be plausible to back the Special Theory of Relativity, and so to conclude that quantum mechanics fails to provide a complete description of reality. But there is more to the story. In 1964 a physicist, John S. Bell, published a paper in which he showed that the quantitative predictions generated by quantum mechanics logically preclude there being properties that make it the case, for example, that an electron possesses determinate spins along various possible axes before any measurements are made (Bell 1964: 195– 200).4 So the thrust of the Einstein-Podolsky-Rosen thought experiment is no longer merely that either the Special Theory of Relativity, or else quantum mechanics, is incomplete. It is rather that either the Special Theory of Relativity is incomplete, or quantum mechanics is false.
When it was a matter merely of the incompleteness of quantum physics, that option was not too difficult to accept. But with Bell’s theorem on board, it became rather more difficult to hold that the Special Theory of Relativity provides a complete description of the spatio-temporal relations between events, since one could do so only by holding that quantum mechanics, which is very well confirmed indeed, is false.
The crucial point, however, is that, with the proof of Bell’s theorem, it becomes possible to put the question to an experimental test. It is no longer a matter for speculation which view should be adopted. What happens, then, when the relevant experiments are performed? The answer is that the predictions of quantum mechanics in this area are correct (Aspect et al. 1981: 460–67; 1982: 91–94). But this means, as we have seen, that it will not do to say, for example, that the electron on which the measurement is not made has a determinate spin from the time that the two electrons are created. It must be the case, rather, either that there is a time at which it acquires a determinate spin, and which, for the reason indicated earlier, must be absolutely simultaneous with the time at which the other electron acquires a determinate spin, or else it has a determinate spin at every moment after a time that is absolutely simultaneous with the time at which the first electron acquires a determinate spin. Both possibilities presuppose absolute simultaneity. The conclusion, accordingly, is that there are experimental grounds for holding that absolute simultaneity is a relation that obtains between events in our world.
Summing up
The question of whether the relation of absolute simultaneity is a relation that is present in our world is a metaphysical question of considerable interest, especially given that tensed or dynamic accounts of the nature of time typically involve the idea of a present that is universe-wide, and that is not relative in any way to frames of reference. What I have tried to do here is to show that there are good reasons to believe that absolute simultaneity is a relation that holds between events in our world. For that view can be supported by at least two arguments, one which is a metaphysical argument that focuses upon the best explanation of the continued existence of space-time, realistically conceived, and the other of which turns upon appeal to quantum mechanics, and, in particular, to Bell’s Theorem, and the experimental results connected with it.
Notes
1 These two arguments were first set out in Chapter 11 of Tooley (1997). The metaphysical argument is there embedded, however, in a modified version of the Theory of Special Relativity. Here I am setting it out as an independent argument.
2 Compare the view advanced by Robb (1914).
3 For additional discussion, see Tooley (1987): especially Section 7.4, pp. 221–28.
4 For clear formulations of Bell’s theorem which do not presuppose any specialist background, see d’Espagnat (1979: 158–81), and Mermin (1981: 397–408; 1985: 38–47).
References
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Aspect, A., P. Grangier, and G. Roger (1982) ‘Experimental Realization of Einstein-Podolsky-Rosen-Bohm Gedankenexperiment: A New Violation of Bell’s Inequalities’, Physical Review Letters 48, 91–94.
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