Updated 21 Nov 2022

Recent experiments in quantum entanglement are leading to a reappraisal of the principle of causality, that any event must come after its cause in time.

Causality is fundamental to the laws of thermodynamics, which explain the "arrow" of time's forward progression in terms of cause-and-effect on dynamic systems. But strangely, there is no such absolute arrow of time in either Relativity or quantum mechanics.

In Relativity the flow of time is relative to the observer and will point in different directions or flow at different speeds within spacetime according to how the observer is moving or how their local spacetime is bent by gravity. One consequence is that the idea of simultaneity, of different events in different places happening at the same time, is similarly relative. One observer might see one event happening before the other, another at the same time, a third the other happening after the other. However, because any influence from one event to the other can not travel faster than the speed of light, this limited violation of simultaneity does not violate causality: a cause will never happen after its effect, no matter how you observe it.

In quantum mechanics all observers are alike and simultaneity is upheld. But the flow of time is not; time is symmetrical, with no preference for which way is forwards and which backwards. If you draw a diagram of a sequence of quantum interactions, you can run time forwards or backwards as the experiment demands and it all works fine. Well, almost. Sometimes you may need to swap a particle for its antiparticle or similar when you reverse time (something called CPT conservation), but that is not relevant here because the shape of the diagram does not change and the particle appears to have the same properties when observed.

Entanglement is a phenomenon where some property of two quanta is described by a single wave equation. In the classic case two photons are entangled so that their polarisations are opposite. However the wave is otherwise the usual superposition of all possible states so we do not know which is polarised which way.^{[1]} When we measure one particle, the state of the other is instantaneously determined. This really is instantataneous, the speed of light is no barrier. However in the macroscopic world it cannot be used to transfer information faster than light because, due to the statistical nature of the wave function, further information is required to decode the information it contains, and that further information can only travel at light speed (it is also borne out by the No Cloning Theorem and other such niceties).

But it does open the way to a paradox. A physicist sets up an experiment to measure the polarisations of entangled photon pairs. One observer (who might or might not be the same physicist) sees one detector trigger first and knows that this will cause the other detector to measure the opposite polarisation. But another observer is travelling at relativistic speed and sees the other detector trigger first, immediately deducing that this will cause the state of the second to be determined. The two observers see different measurements as determining the other. Who is right?

If either observer is wrong then, for them at least, entanglement has propagated an effect backwards in time before its cause. On the other hand, if both observers are right then causality itself becomes relative to the observer and no longer absolute.

Either way the principle of causality, the foundational principle of thermodynamics, is called into question. But which is it? Can causality run backwards in time, to the uncommunicative extent allowed by quantum entanglement? or, is causality in fact relative to the observer and not an absolute property of the physical world? In the worst case, might both be true?

A small variation on the experiment sheds some light on this. In essence the experimenter is given a switch which forces the quantum state of the particle at one detector, while the other particle is still in flight. They arbitrarily set the switch while both particles are in flight. Now, one of the relativistic observers sees the free detector triggering first and apparently causing the choice of setting for the switch. Short of granting an inanimate detector some psychic power of telekinesis, that impression has to be a mistake. The idea that causality might be relative to the observer has such unacceptable consequences that we may safely discard it. The conclusion seems inescapable that the setting of the switch caused the remaining chain of events even though its effect on the other detector appeared to occur first, a phenomenon known as retrocausality.

This drives us back to the only remaining possibility, that quantum entanglement must indeed be able to propagate backwards in time. We should not be too distressed at this possibility in principle, for it has a long heritage in the sum-over-histories derivation of the quantum wave function and its classical predecessor Wheeler-Feynman absorber theory. That the standard equation evolves forwards in time is a consequence of these fundamentals: change the histories to be summed by adding entanglement to the mix and we cannot be too surprised if the temporal as well as the spatial locations of the two quanta stop obeying the old rules. In essence, it is just the acknowledgement that quantum nonlocality is a nonlocality in time as well as in space. To a relativist, space and time are not wholly distinguishable anyway, so anybody hoping one day to reconcile the two theories will more likely feel relief than distress at this news.

What then of that other key quantum weirdness, the superposition of states made famous by SchrÃ¶dinger's alive-and-dead cat^{[2]}

But what then are the implications for thermodynamics? The link between causal and temporal ordering is inherent in its Second Law, that entropy never decreases. It is still so ingrained in many physicists that they regard it as a law of nature, even the definition of what we mean by cause and effect, and cannot countenance any of what has just been said. To them, either the experiments demonstrating nonlocal entanglement must somehow all be flawed, or some alternative more akin to hidden variables may be found, which is nevertheless compatible with the results. But for the rest of us, the underpinnings of thermodynamics in statistical mechanics deserve a closer look.

Historically, thermodynamics is a macroscopic theory of energy flow and its key concept, entropy, is measured in units of energy per degree of temperature. Spontaneously changing from one state to another more stable one increases the entropy of the system and, since the initial state was the cause of the change and the subsequent state its effect, the arrow of time ensures that entropy will always increase over time. As our modern understanding of temperature as energetic particles developed, a theory of statistical mechanics arose describing the motions of those particles and deriving the laws of thermodynamics from them. In this, the number of possible "microstates" of every particle in a system is key, with entropy being defined in terms of this number: as time goes by, the number of possible states available to a system inexorably increases and there is no going back. For example a broken glass has many more possible states than a glass in one piece, so it is not possible for the glass to reassemble itself. To put it another way, the number of possible microstates is driven inexorably to increase by the arrow of time.

Can quantum entanglement turn this arrow backwards and force entropy to decrease? The easiest way to answer that is to consider the amount of information involved. The number of possible microstates is closely linked to the amount of information that a system can contain. Quantum entanglement certainly reduces it, in that an entangled pair can contain only one bit of information, representing the total quantum state of the pair, rather than the default of one bit per particle making two bits in all. But that limitation lasts throughout the life of the entanglement, neither measurement triggers any reduction in the potential to hold information. So it does not matter which measurement, the first or the second, is caused by the other since neither will cause a decrease in microstates and the laws of thermodynamics are unaffected. It seems that thermodynamics is no barrier after all.

Quantum retrocausality is here to stay. Causality in time is no more (nor less) set in the fabric of the universe than are locality in space, simultaneity, and the separation of space and time.

We are perhaps moving towards an understanding where, as with so many things quantum, a causal sequence may be undefined at the quantum level and is only established when a measurement "collapsing" it is made. Perhaps, as with entanglement, a retrocausal collapse is not able to transfer information or, consequently, to pass entropy backwards.

A wild idea to reconcile these emerging paradoxes has recently occurred to me, so I am adding it here as an afterthought.

Two time dimensions are sometimes suggested as a way out of some of the paradoxes of causality. But such theories tend to lead to unstable physics in which reality collapses or even more paradoxical phenomena become possible. Might there rather be two independent flows of causality, one thermodynamic and the other informational?

The familiar kind of causality is based on the arrow of time, the principle that any effect must follow its cause in time. It is the foundational principle which gives rise to the thermodynamic arrow of time.

The other kind of causality is logical, being the transformation of one piece of information into another. Examples include the step-by-step synthesis of a logical argument from hypothesis to theorem, or the state transformation from input to output of a digital logic circuit. Another example lies in the way that quantum information can never be destroyed, but only transformed; for example what ultimately comes out of a black hole is the same amount of information that fell in, but transformed and unrecognisable.

My proposition here is that these two kinds of causality, temporal and logical, are essentially independent. Temporal causality applies only at the classical level, and in consequence is subject to Relativity. Logical causality also applies at the quantum level, which is famously open to time-reversal. While classical transformations are bound by thermodynamics, and hence also in time, logical or transformations may in principle be effected transformations across time and space without restriction.

Why then is most information as time-bound as we are? The supposition implied in this question is not quite true. Information can only be transformed, or made available to us, via some physical carrier or substrate; it does not exist in isolation. The majority of information we encounter, such as any physical measurement, is carried on a classical physical substrate and is therefore necessarily as time-bound as its substrate.

It is only recently, and in carefully contrived circumstances, that we have been able to tease out information carried by time-symmetric quantum phenomena such as entanglement, and observe it breaking temporal causality.

One consequence of this quantum view is that every quantum wave is carrying an information transformation. Or rather, it is carrying a superposition of possible transformations. During this phase of its existence, the information is bound in space and time to the precise extent that its substrate is bound. This is what reconciles the fact that quantum interactions are time-symmetric yet they mostly appear Relativistic. It also allows the apparent causal paradoxes of quantum weirdness.

The act of measurement collapses the superposition to the transformation we observe. For the most part the quantum information was bound to the substrate, say a photon or an electron, and hence is also spacetime-bound. But certain aspects of the information, carried say by an entanglement between two photon polarisations or two electron spins, are spread without such restriction across spacetime: on measurement and collapse, these aspects are not explicable in terms of thermodynamic time.

Thus, for the most part the logical causal flow is carried on the temporally-bound substrate and we have traditionally missed the distinction between the two. This short-sightedness is especially evident in information theory, and especially communications theory, which is concerned with moving information around but assumes it to be bound to its substrate. It is only on those rare occasions where a quantum phenomenon such as entanglement has macroscopic consequences that we have caught logical causality in any other setting.

Anyway, that is the gist of the idea. I think you will agree that it is wild. Is it testable or falsifiable, just another impotent quantum interpretation, or not even that? I hope to work on it and see if I can make anything of it but, as ever with me, don't expect things to happen fast.

1. Some physicists still argue for "hidden variable" models in which the quantum state of a particle is always determined but hidden from us until we observe it. However if it is to agree with experimental results, any such model must still include nonlocality, for example as the accompanying "pilot wave" of Bohm & Hiley.

2. Kelly Oakes; "When causality Breaks", *New Scientist*, 18 January 2020, pp.34-7.