Finding ‘Real’ Time in Quantum Mechanics



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Finding ‘Real’ Time in Quantum Mechanics



Craig Callender

Department of Philosophy, UCSD

La Jolla, CA 92093, USA
Quantum mechanics seemingly offers something to everyone. Some find free will in quantum mechanics. Others discover consciousness and value. Still others locate the hand of God in the quantum wavefunction. It may come as no surprise, therefore, to hear that many believe quantum mechanics implies or at least makes the world more hospitable to the tensed theory of time.1 Quantum mechanics rescues the significance of the present moment, the mutability of the future and possibly even the whoosh of time’s flow. It allegedly does so in at least two different ways:
A. Quantum non-locality is said to make a preferred foliation of spacetime into space and time scientifically respectable again. Tensers need worry no longer about ‘no-go’ theorems proving the incompatibility of the tensed theory with special relativity. Quantum non-locality provides them the foliation they need.
B. Wavefunction collapse injects temporal ‘becoming’ into the world.

The aim of this paper is to show that the kind of reasoning underlying these claims is at least as desperate as that finding freedom, value, the mind and God in quantum mechanics—which is pretty desperate. The bulk of the paper concentrates on A; discussion of B is reserved for the Appendix. After setting things up in section 1-3, section 4 develops what I call the “coordination problem” for tensers. The upshot of this problem is that if tensers escape the threat of relativity, they do so only by embracing conflict with the branch of physics they believed saved them, quantum mechanics. Section 5 briefly considers what lessons we might draw for tenses from quantum gravity. Finally, in section 6 I step back from the fray and examine some methodological issues, concluding that scientific methodology will always be “against” tenses as they are currently conceived.

1. Special Relativity against Tenses

The argument from special relativity against tenses is familiar, so I will be brief. The basic idea begins with the relativity of simultaneity in Minkowski spacetime, the spacetime appropriate to special relativity. A special relativistic world is a 4-dimensional manifold of spacetime events endowed with a Minkowski metric and matter fields. A foliation of this manifold carves up spacetime into space and time via an equivalence relation, simultaneity, and time is the 1-dimensional linearly ordered quotient set induced by this relation. The famous relativity of simultaneity implies that there are many different foliations of spacetime into space and time. Though a tension between relativity and common sense conceptions of time was recognized very early on, Putnam 1967 and Rietdijk 1966 were perhaps the first to set out the argument against tenses from relativity explicitly.




Figure 1.

The basic idea is as follows. (See Figure 1.) Consider two inertial observers, A and B, traveling in opposite directions but intersecting at some event e, and some distant inertial observer C. Simply put, using the standard Einstein-Poincaré synchronization, A has a different hyperplane of simultaneity than B does. Hence A and B will disagree about what events on C’s history are simultaneous with e. A will declare that event C1 is simultaneous with e whereas B will declare that event C2 is simultaneous with e. In typical terrestrial situations, C1 and C2 may be so close together that their difference is not subsequently noticeable to A or B. For C’s that are very far away (or for A’s and B’s with very high relative velocity with respect to one another), however, there can be great disagreement. Now take some event C3 such that C1 < C3 < C2. Since one’s simultaneity hyperplane divides the world into the future and past—and on any tensed view this has ontological repercussions—C3 is in A’s past but B’s future. Furthermore, the so-called “principle of relativity” asserts that neither A nor B are privileged in any way. If the future is ontologically unlike the past or present (i.e., non-existent, indefinite, etc.), as the tensed theory demands, then A judges C3 ontologically different than B judges C3. But why should C3’s ontological status be relative to one’s state of motion?

Scores of papers respond to this argument. I won’t summarize them all here, but let me comment on a few strategies of reply (see Savitt 2002). Some tensers have bitten the bullet and suggested relativizing existence to one’s state of motion. Others have flatly denounced special relativity as false (which it is, but they mean even if gravitational and quantum effects are negligible). These claims are obviously very radical. Others, like Stein (1991), have claimed that Putnam’s argument is wrong, that a “becoming” relation is perfectly well definable on Minkowski spacetime. The trouble with this claim is that Stein’s “tensed” theory is not remotely close to any tensed theory ever devised and lacks any philosophical virtues apart from being a relation definable on (temporally oriented) Minkowski spacetime (see Callender 2000 and Saunders 2002). Callender 2000, furthermore, argues that if one uses a relation remotely like those found in tensed theories (that is, where at least two events can be co-present), then one can invert Stein’s theorem and prove a “no go” theorem showing that becoming is incompatible with Minkowski spacetime (see also Clifton and Hogarth 1995, Dorato 1996 and Rakic 1997).

In my opinion, by far the best way for the tenser to respond to Putnam et al is to adopt the Lorentz 1915 interpretation of time dilation and Fitzgerald contraction.2 Lorentz attributed these effects (and hence the famous null results regarding an aether) to the Lorentz invariance of the dynamical laws governing matter and radiation, not to spacetime structure. On this view, Lorentz invariance is not a spacetime symmetry but a dynamical symmetry, and the special relativistic effects of dilation and contraction are not purely kinematical. The background spacetime is Newtonian or neo-Newtonian, not Minkowskian. Both Newtonian and neo-Newtonian spacetime include a global absolute simultaneity among their invariant structures (with Newtonian spacetime singling out one of neo-Newtonian spacetime’s many preferred inertial frames as the rest frame). On this picture, there is no relativity of simultaneity and spacetime is uniquely decomposable into space and time. Nonetheless, because matter and radiation transform between different frames via the Lorentz transformations, the theory is empirically adequate. Putnam’s argument has no purchase here because Lorentz invariance has no repercussions for the structure of space and time. Moreover, the theory shouldn’t be viewed as a desperate attempt to save absolute simultaneity in the face of the phenomena, but it should rather be viewed as a natural extension of the well-known Lorentz invariance of the free Maxwell equations. The reason why some tensers have sought all manner of strange replacements for special relativity when this comparatively elegant theory exists is baffling.

The main concern about the Lorentzian theory is that dynamical symmetries do not mirror spacetime symmetries on this view, or as Einstein said, there are asymmetries in the theory not found in the phenomena (Janssen 2002). The matter fields are Lorentz invariant but the spacetime is not. For this reason, all else being equal, one ought to prefer the Einstein-Minkowski interpretation to the Lorentzian interpretation. Positing otherwise unnecessary unobservable structure—absolute simultaneity—does violence to Occham’s razor. But is all else equal? If the case for tenses is elsewhere strong, that may tip the balance over to the Lorentzian interpretation. The Lorentzian picture is logically consistent and empirically adequate, after all. What are a few lost explanatory virtues in contrast to _______ (fill in the blank with whatever tenses explain)? There are many assumptions in our overall world picture, and we know from Quine-Duhem that there are many ways of organizing them. The no-go theorems focus on only a small piece of this theorizing and are only as good as their assumptions. In particular, what symmetries one takes a spacetime to have depends on prior assumptions about what one takes to be in the spacetime in the first place. If quantum non-locality spoils the Lorentz invarianceof Minkowski spacetime, then this would override the explanatory deficit of the Lorentzian view. Does quantum mechanics help tip the balance toward a spacetime structure more friendly to tenses?



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