In the quantum world, the future causes the past

How Bell’s Paradox is solved by Retrocausality

Two particles affecting one another faster than light seemed unimaginable but there is no denying the facts. This mystery has inspired much skepticism from lay folk and Nobel prize winners alike.  But how do we solve this? Emily Adlam argues, that retrocausality, the idea the future can affect the past, is the key to solving this quantum enigma.


One of the most famous and puzzling features of quantum mechanics is the fact that it exhibits what Einstein called ‘spooky action at a distance, - correlations between measurements performed on particles very far apart in space. Now, of course distant correlations in and of themselves are nothing surprising. For example, suppose I take a pair of socks out of my drawer, separate them, and then send one off to my friend Alice in London and the other to my friend Bob in Auckland. If my friends observe the socks and then compare their results and discover that they both have socks of the same colour, there’s no mystery about that - the socks are the same colour because of a common cause in their shared past, i.e. the fact that they both came from the same pair. But the correlations appearing in quantum mechanics are special because they cannot be explained in this way. For example, distant quantum correlations are typically demonstrated in a ‘Bell experiment,’ in which I prepare a pair of quantum particles and send one to Alice and another to Bob, and then Alice and Bob both choose a measurement and perform that measurement on their particle. A famous theorem due to the physicist John Bell tells us that in this scenario, correlations explained by a common cause in the past must obey a certain inequality - but it turns out that we can choose preparations and measurements in quantum mechanics which lead to a violation of Bell’s inequality. This seems to indicate that Alice’s decision to make one measurement rather than another has an instantaneous influence on Bob’s particle and thereby affects the results that Bob obtains in his own measurement, regardless of how far apart they are.


It’s troubling to think that the deep structure of quantum mechanics violates such a foundational principle of relativity.


These instantaneous nonlocal influences are troubling to many physicists, not least because they seem strongly in tension with our understanding of spe- cial relativity. The problem is that special relativity tells us that there is no fact of the matter about what is ‘instantaneous’ - to determine whether two distant events are simultaneous we must choose a reference frame relative to which we can assess simultaneity, but special relativity ultimately says that no reference frame is preferred and therefore there are no observer-independent facts about simultaneity. Now, quantum nonlocality doesn’t produce any observable contra- dictions with this relativistic principle, since the instantaneous influences work in a subtle way which means they are only detectable after the results of the measurements on both particles have been compared, and therefore we can’t ex- perimentally detect any preferred reference frame. But still, if the influences are instantaneous there must be some preferred reference frame, even if observers like us can’t detect it, and it’s troubling to think that the deep structure of quantum mechanics violates such a foundational principle of relativity. This seems particularly problematic if we hope to one day unify quantum mechanics and relativity in a theory of quantum gravity, for it seems unlikely we will be able to do this if the two theories are incompatible in such a foundational way.

Consequently, a number of physicists have sought to understand if there is any way we can explain these distant correlations without ‘spooky action at a distance.’ In order to do this, we will necessarily have to deny one of the assump- tions going into Bell’s theorem, and most work on the topic has focused on an assumption known as statistical independence, which simply says that the state of the two particles together at the time that I prepared them is independent of the later choices that Alice and Bob make about which measurements they are going to perform. This assumption is clearly necessary to prove the existence of non-locality, because if we know in advance what measurements Alice and Bob are going to perform, we can just pre-program the particles with outcomes which will give the appearance of non-locality even though everything is com- pletely local. So if there is any plausible way to deny statistical independence in a Bell experiment, that would allow us to resist the existence of spooky action at a distance.

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However, we can’t simply stipulate that statistical independence is violated - that would amount to simply switching one spooky nonlocal influence for an- other. Rather we will have to come up with some local mechanism by which the state of the particle could come to be correlated with the later measure- ment choices. And there are two obvious ways to do that. The first, known as superdeterminism, involves suggesting that there is some common cause in the past of the measurement choices and the preparation events which results in correlations between them. The second, known as retrocausality, involves sug- gesting that the measurement choices have a backwards-in-time causal influence on the state of the particle at the time of its preparation.

Superdeterminism might at first sound like the more natural approach, but it actually has some very strange consequences. For Alice and Bob can make their measurement choices in any way you can possibly imagine - flipping a coin, as a function of the date of their birthdays, by observing the light from distant galaxies, and so on. So superdeterminism regards us to suggest that there is some common causal factor which always influences the measurement choices, regardless of whatever weird and wonderful method Alice and Bob might use to make their choice. Moreover, we will probably have to just stipulate that the desired correlations are simply written into the initial state at the beginning of time, and that seems problematic, since our current understanding of statistical mechanics and thermodynamics suggests that we can only make sense of the arrow of time if we assume that the initial state of the universe does not contain too many fine correlations. Therefore adopting superdeterminism seems to create serious tensions with well-established scientific methodology.

On the other hand, retrocausality does not require any special adjustments to the initial state of the universe: it allows us to say, as we would naturally be inclined to, that Alice and Bob’s choices of measurements are independent of the rest of the variables involved in the experiments, but nonetheless the state of the particles does end up correlated with the measurement choices. A number of interesting retrocausal models of the Bell experiments have thus been proposed, including proposals by Wharton and Schulman - these models demonstrate that it is indeed possible in principle to account for the Bell experiments in a local way by allowing retrocausal influences.

However, it’s important to note that there are two importantly different conceptions of retrocausality that one might adopt here. The first is the ‘two arrows’ approach, which is perhaps what most people think of first when they hear the term ‘retrocausality’ - it suggests there are literally two distinct arrows of causation pointing in opposite directions, so we have evolution both forwards in time and backwards in time. The alternative is the ‘all-at-once’ approach, in which there is no process of evolution at all, and instead the laws of nature work in an atemporal way to pick out the whole course of history at once, in much the same way as the rules of sudoku constrain the whole grid at once rather than starting at one side and moving to the other side. In all-at-once models the past and future influence each other in a mutual and reciprocal manner, and therefore in such models it is natural to expect that there will be correlations which appear from our internal point of view to involves something like backwards-in-time causal influences. So we could certainly get violations of statistical independence in an all-at-once model.

Which of these conceptions of retrocausality should we choose? Well, there is an obvious problem with the ‘two arrows’ conception: it seems liable to produce logical paradoxes. For example, consider the ‘grandfather paradox’ in which a time traveller goes back in time and kills her own grandfather before he can father any children - so then the time traveller will not be born, but then of course she can’t kill her grandfather, so it seems that there is no logically con- sistent way to resolve this course of events. We can easily imagine a retrocausal analogue of this paradox in which the time traveller uses a backwards-in-time causal influence rather than a time machine to kill her grandfather, ultimately producing the same paradoxical result. Since the universe presumably can- not contain logical paradoxes, it seems that this kind of composition of causal processes cannot be possible. But this is hard to achieve in the ‘two arrows’ conception of retrocausality - it seems that we have to add some kind of con- sistency conditions, and in order to fully rule out logical contradictions these conditions will have to apply all at once at a global level, and once we allow that it seems we are really moving towards the all-at-once picture rather than two arrows picture.


In an all-at-once account of the Bell experiments, we have no need to say that there is an instantaneous influence from one particle on another.


The all-at-once picture, meanwhile, can’t possibly produce logical contra- dictions, because the whole point of this approach is that the entire course of history is selected all together, in a logically consistent way. But there’s a catch - it’s not entirely clear that an ‘all-at-once’ model is really local in the ordi- nary sense. For in an all-at-once model, the correlations between distant events are brought about by constraints imposed directly on the whole of history, so there’s really no need for information to be carried from one point to another by a local process.  In such a model events at distant points can depend directly on each other via the global constraints, and thus in we should expect to see many strong correlations which are not mediated by any physical system carrying information between their locations.

Therefore one may worry that using retrocausality to avoid nonlocality will ultimately be self-defeating, since the most reasonable kind of retrocausal model turns out to be non-local in any case. But that depends on the reasons one has for wanting to get rid of nonlocality in the first place. Someone who simply thinks that nonlocality is ‘spooky’ will perhaps not be happy with an all-at- once model, but someone who merely worries about nonlocality because of the issue of consistency with relativity can happily accept an all-at-once model. For all though all-at-once models are generically very non-local, they don’t imple- ment that non-locality in a way that requires a preferred reference frame. For example, in an all-at-once account of the Bell experiments, we have no need to say that there is an instantaneous influence from one particle on another: we can simply impose a global constraint which requires that the results of the two measurements are correlated in certain ways, regardless of when and where the measurements are performed. There is no temporal process by which the information is carried from one particle to another, and thus there is no need to identify a preferred reference frame on which that happens.

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Ultimately, it seems the contradiction with relativity in the Bell correlations arises because we are trying to fit these correlations into a model based on time evolution, which forces us to pick a reference frame on which the correlations take effect. If we stop trying to do that, much of the tension with relativity goes away, so we end up with a model which is non-local but still entirely in line with the underlying principles of special relativity. Thus introducing retrocausality in the all-at-once sense offers a very interesting route to reconciling the Bell ex- periments with relativity, and we are just beginning to explore the implications of this possibility for our ideas about time, causation and gravity.

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