Physics and Simultaneity

Presentism and Relativity

The longstanding debate over the A and B theories of time is often thought to have been closed by Einstein's theory of relativity. As the argument goes, according to A theories (or at least presentism), only a single present, consisting of a set of simultaneous events, exists. However, within the most straightforward interpretation of relativity, it is meaningless to talk about simultaneity except relative to a chosen reference frame, which is in clear conflict with presentism. I will argue that despite the conflict between presentism and relativity, it would be premature to conclude that presentism is in conflict with our broader understanding of physics. It is well known that relativity and/or QM is incomplete. Most interpretations of quantum mechanics have absolute simultaneity built in (though it’s often by design), and I will argue that there are some general problems with any method for making those interpretations Lorentz invariant. One could argue that this prima facie evidence in favor of simultaneity is at least as strong as the evidence from relativity against it. My point is not to reiterate the well known conflict between these two theories, but is instead to argue that the relationship between presentism and physics should remain open as long as relativity and QM remain unreconciled.

The Case Against Absolute Simultaneity

The argument against absolute simultaneity from relativity is familiar one. I will provide a brief overview of it here using Einsteins train as an example, and will later discuss alternative ways of interpreting the thought experiment, and reasons those interpretations might take precedence.

Consider a train moving at high velocity along a track. There are two observers, one inside the train, and one observing the track from a distance. As the center of the train passes the observer, he/she sees two lightning bolts strike the car simultaneously — one on the front, one on the back. The observer sees the two flashes of light at the same time, so he/she concludes that the strikes were simultaneous because the light traveled from two equidistant points at the same velocity. Now consider the perspective of the person on the train. A Newtonian would predict that the person on the train would see the light from the front bolt first, because they are travelling towards it and away from the rear bolt. However, a postulate of relativity, verified by experiment, is that the speed of light is constant for all observers. Because of this, the observer on the train would receive the light from each bolt simultaneously, and then conclude that the strikes were not simultaneous because of their relative velocity. This seems to show that the simultaneity is only an observer relative phenomenon. Relativity has encouraged a view that time is akin to an additional spatial dimension, which meshes nicely with an eternalist view where time and space are combined into a 4D space-time block. This is clearly in conflict with the standard presentist picture of time.

Absolute Simultaneity and Quantum Mechanics

Bell’s theorem was an important theorem concerning whether particles in an entangled state could be mutually dependant when separated at large distances. Bell showed that local hidden variable theories made, under certain conditions, make different predictions from standard quantum mechanics. The eventual experimental violation of Bell’s inequalities essentially ruled out any local hidden variable theories. Since Bell there have been a wide array of strategies for interpreting quantum mechanics without locality. I will attempt to show that most of these strategies point towards absolute simultaneity.

A full elaboration on the supposed conflict will require a discussion of specific interpretations. But first, we’ll get an intuition for the general problem by considering real collapse theories. Consider a pair of electrons, A and B, in the state ½( |+> |-> - |-> |+>).

At t1 particle A is measured for x spin and particle B is measured for z spin. By applying STR, we can see that there exist foliations of this space-time diagram where A is measured first, and others where B is measured first. This means we can trace at least two possible histories of the system. An example for each foliation is shown below.

OperationStateOperation 2State 2
Initial State 1/2(|+x> |-x> - |-x> |+x>) Initial State 1/2(|+x> |-x> - |-x> |+x>)
Ax Measured |+x>A |-x>B Bz Measured |-x>A |+x>B
Bz Measured |+x>A |+x>B Ax Measured |+x>A |+x>B
Because one measurement is happening along the x spin, while the other is happening along the z spin, the order of the measurements actually matters for determining the history of the particle. These two different histories disagree both on the intermediate states of the particles, and which measurements were actually chancy. There is no way that these two foliations can be seen as different descriptions of the same events.

This example should provide some intuition for the problem. Few people would accept a collapse theory like this one anymore, so a more detailed discussion of different interpretations will follow. Bohmian Mechanics

Bohmian mechanics posits a non-local “pilot wave” that guides the motions of any particles in a system. The movement of the pilot wave according to some linear dynamical equation provides an explanation for some unusual quantum phenomenon observed in experiments (like interference in the double slit experiment), and the fact that we only interact with the particles that take the wave equation as an input velocity explains why there is only apparently a single state after “measurement”. The standard formulation of Bohmian mechanics is non-relativistic (this conflict with STR is unsurprising). There may, however, be a general property of the theory that gives reason to think it will always absolute simultaneity. Since Bohmian particles take their velocity as input from the pilot wave equation, the position of each particle can be derived from the spatial derivatives of the entire system evaluated at that point. The facts about a given particle’s position and velocity depend on the instantaneous positions of the other particles. This is because pilot wave is defined as an evolution on configuration space (the instantaneous state of the whole system as a single vector space).

This is essentially a more detailed reiteration of the fact that Bohmian mechanics is a non-local theory. However, it more clearly shows the root of difficulty with reconciling Bohmian mechanics and a traditional conception of relativity — in order to define a configuration space, a privileged frame must be chosen. This issue persists when substituting the Schrodinger equation for a relativistic equation. Predicting the position of a particle still requires a privileged frame at least over the portion of the pilot wave relevant to the motion of the particle in question. The difficulties posed by non-locality for Lorentz invariance were recognized early on by John Bell, who said that “if [physicists] want to talk about the problems of quantum mechanics—the real problems of quantum mechanics—they must be talking about Lorentz invariance”

It should noted that Bohmian mechanics can be made Lorentz invariant if an absolute frame is introduced. An example of this reconciliation has been performed by (Dürr 1999).

Modern Collapse Theories

Modern collapse theories avoid the more embarrassing problems of the Copenhagen interpretation. GRW proposes the wave function collapse happens spontaneously. For single particles, this happens extremely rarely, which is essential for the theory’s compatibility with experiments on individual particles. Another essential part of the theory is that collapse propagates amongst entangled particles. This means that when a system becomes entangled with a large number of particles (like a measuring device in a physics laboratory) the probability of a single particle collapsing, causing the entire system to collapse, is exponentially higher. This ensures the consistency of the theory’s compatibility with apparent wave function collapse when particles are measured. GRW is generally considered to be the preferred collapse theory because it avoids some of the vague talk of “measurement” associated with many alternatives.

GRW faces a problem similar to the one faced by Bohmian mechanics. While in the latter case the problem arose from entangled particles possessing a non-local state, in former case problems arise from the collapse process being causally non-local. While each “hit” happens locally, the collapse of an entangled system happens instantaneously. If this was interpreted as an instantaneous propagation of wave function collapse, it would be in clear violation of STR because the collapse process would exceed the universal speed limit. In light of this, the more common view is to treat causation in wave function collapse as non-local. The problem with this can be illustrated with a thought experiment. Consider again a pair of entangled particles A and B in the state ½( |+> |-> - |-> |+>).

Suppose when the particles have been sufficiently spatially separated, a measurement is performed on particle A. According to GRW, the entangled system will then collapse with high probability because of the entanglement with the large number of particles in the measurement device. Also, because collapse is a non-local process, the entire system will collapse instantaneously. If we assume it was a “hit” on one of the particles in the measuring device that caused the collapse, it means there is a real causal connection between that particle and spatially separate particle B. The idea that the collapse happens instantaneously across space is equivalent to the idea that the events happen simultaneously in both places. This poses a clear problem, because there simply isn’t a notion of simultaneity to be found in STR. In addition, different relativistic reference frames could disagree about the ordering of events. For example, an observer traveling quickly along a line between A and B, might conclude that B collapsed before the measuring device (assuming collapse was observable). Beyond this being inconsistent with the postulated notion of instantaneous collapse in GRW, it would then be possible for observers to reach different conclusions about the causal ordering of events. This is again in conflict with the postulates of GRW, which include a fact of the matter about which “hit” causes the collapse.

One possible strategy for reconciling GRW with relativity is to postulate that particles only have determinate locations after collapse vents. This “flashy” formulation of GRW, avoids the problems discussed above with different folations disagreeing on particle histories because entire systems do not have enough location properties at any time for the system to be non-local. However, upon closer examination there are some problems with this approach. In order to match with experimental data, the theory has to give up agreement between foliations about which “hit” causes the collapse. Another important issue is that when relativizing causal explanation between two measurements, there will always be reference frames for which there is faster-than-light causation. (Lewis, 2016) One might think this makes the theory untenable. However, there will always exist one set of coordinates for which the causation is instantaneous rather than superluminal. One could use this coordinate set to reconcile the theory with a neo-lorentzian view (discussed more below). A flashy GRW formulated this way would be lorentz invariant but would have the addition of an undetectable standard for absolute simultaneity.

Many Worlds

The interpretations discussed above encompass most common positions on the measurement problem with the exception of the Many Worlds Interpretation. MWI can easily be made relativistic by substituting the Schrodinger equation for the Dirac equation. The presentist could, however, reject MWI for other reasons. These objections are outside the scope of this paper, so I’ll redirect an interested reader to David Albert’s “Interpreting the Many Worlds Interpretation”.

The More General Argument

A more general argument can be derived from the individual arguments I have made from the perspective of several interpretations of QM. In order to explain the experimental data, each interpretation postulates some phenomenon like: instantaneous collapse, non-local causation, etc. These related notions all have simultaneity built in. For example, the idea of an instantaneous wave function collapse across space is equivalent to the idea of collapse happening simultaneously in all these locations. They all face a similar problem when combined with relativity. Relativity is supposed to preserve the causal ordering of events, regardless of reference frame. Combining non-locality with relativity provides a reliable way to violate this causal ordering, which leads to disagreements about the state of a system between reference frames that cannot be explained by mere descriptive differences. These issues can all be solved by adding a (possibly undetectable) privileged reference frame.

Another important point is that these phenomena like instantaneous collapse and non-local causation seem to be indispensable to each interpretation. Of course, it is not surprising that these interpretations (most of which which were designed to be non-relativistic) have simultaneity built in. The key point, however, is that simultaneity is built into the essence of the way each interpretation attempts to solve the measurement problem. This poses a significant problem for making any of these interpretations compatible with relativity in the future, and at least partially explains why many of the interpretations have remained stubbornly non-relativistic for over 50 years.

Interpreting Relativity

Even if one accepted absolute simultaneity because of QM, this would not necessitate taking an anti-realist view towards relativity. There are other ways to interpret relativity, most notably a neo-Lorentzian view. This view preserves some important phenomenon in relativity like time dilation and length contraction, but does so within the addition of a privileged reference frame. Many interpretations of QM, like Bohmian mechanics and GRW, can be reconciled with a neo-Lorentzian scheme.

Concluding Remarks

It wouldn’t be prudent to draw strong conclusions from the various formulations of quantum mechanics discussed above, as most of them are almost certainly false — to one day be replaced by a more fundamental theory that includes gravity. However, at first glance, it does appear that there are some common pattern between the different interpretations of QM that provide at least prima facie evidence for simultaneity. QM and relativity both have the support of rigorous verification by scientists over the past century. When considered in opposition, however, one might think that relativity is the approximate theory given that quantum mechanics has much stronger verification at smaller scales, while relativity has only been tested in high energy/mass systems. At the very least these arguments should provide some reason to believe that the relationship between presentism and physics is an open question, at least until there is more scientific progress.

Citations

Lewis, Peter J. “Quantum Ontology: A Guide to the Metaphysics of Quantum Mechanics” Stanford Encyclopedia of Philosophy. “Bohmian Mechanics”