Quantum Entaglement and EPR

Question

I was studying the EPR Paradox and Bell's theorem . My question is how does this information travel between two entangled particles, has there been any research into this?

Answer 1

This is not the conclusion of EPR, where FTL information travel is still impossible.

Say 2 particles are prepared in an EPR state and are traveling in opposite directions. The paradoxical quantum mechanical conclusion that makes it almost seem like there's information being passed faster than light is that the system as a whole while unperturbed is described by a highly non local wave function. To say this concretely, in the EPR state, we can measure the spin projector along a given axis of one particle and simultaneously we must find the other particle in the other state no matter how separated they are.

The thing which makes FTL information travel still impossible is that we can not do anything "new" to either particle and preserve the entangled state. We can't make particle A do something completely new and have that be reflected in the state of particle B for someone way over there to measure.

Answer 2

It's not a question that's subject to scientific investigation, because the information that travels faster than light (if it happens at all) is experimentally unobservable. We can't see wavefunction collapse. We can't test to see if it has happened yet. There are other interpretations of quantum mechanics that make all the same predictions about experiment without wavefunction collapse, or anything moving FTL. There is no way to tell.

We can only judge the theory on more aesthetic grounds: simplicity, parsimony, completeness, ease of calculation, and so on. And there is no doubt that FTL propagation of the wavefunction collapse introduces some tricky conceptual difficulties when combined with relativity. The problem is there is no absolute objective definition of 'instantaneous' propagation. It can be instantaneous in the frame of some particular observer, but other observers can see the events happening in either order. That leads to situations like this:

Two entangled particles are separated to Earth and Alpha Centauri. The two observers are moving relative to one another. Each measures their own particle, and the wavefunction collapses 'instantaneously' in their own frame of reference. In both cases this FTL collapse hits the other particle's worldline before it gets measured. So each particle collapses the other before it can trigger the collapse itself.

If you want there to be one objective history of the relativistic universe (which is pretty much the raison d'etre for collapse theories) then this cannot happen. The collapse must propagate along a definite path in spacetime, which means it cannot be 'instantaneous' for all observers, and for at least some observers must propagate backwards in time.

The only reason that's not a problem is that the collapse is unobservable. The wavefunction changes on collapse, so that information is being propagated, but you are free to be as vague and mystical as you like about when and how it does so because the consequences are only apparent in the long-range correlations between measurements, which are only observable when you get the information from both those measurements together at the same place, at the speed of light or slower.

We can explain the observations without FTL effects with a different interpretation. (Even if you choose not to believe it's true, the fact that it's possible to interpret experiment without FTL still means that the FTL collapse effect cannot be observable.)

Here we show the spacetime diagram for the EPR experiment. The particles are prepared in a superposition of orthogonal 'red' and 'blue' states and separated. The two observers each interact with their local particle, and the interaction causes their own wavefunction to enter a superposition of orthogonal states correlated with that of the particle: one of the states being that of an observer seeing red, the other being that of an observer seeing blue. (For a very high level outline of how this is thought to happen, see here.)

After the observations have been made, the observers return home, and compare notes. The parts of each superposition can only see the corresponding correlated part of the other observer. Observers seeing the same colour can interact. Observers seeing different colours are mutually invisible.

Nothing has to travel faster than light. Observer A becomes correlated with particle A through the measurement interaction, which is correlated with particle B through the way they were initially prepared, which is correlated with observer B through the other measurement. The causal path leads from one measurement back in time to when the particles are made, and then forwards in time to when the other measurement is made. Everything happens at no more than the speed of light.

At the end of the journey, the two observers who saw red cannot see any sign of the other observers who saw blue. They must have disappeared somewhere along the journey. Where might they have done so? One possibility you might think is right at the beginning :- when the particles were prepared, the matter was decided. This is the 'hidden variables' theory that Einstein tried to construct. It turns out that this cannot work, because the two observers can decide what type of measurement to make, and it is impossible to set up the initial state so as to recreate the correlations that quantum mechanics predicts for all combinations of measurement types - this is Bell's theorem.

However, the disappearance can happen any time after the decisions have been made. That looks a bit like this:

Since red cannot see blue, there is no way for the red observer to tell if the other state is still there or not. It has to happen after the choice of measurement axes has been made, as the uncollapsed joint state is needed to generate the right correlations in all circumstances, but before the observers get back together, where those correlations can be observed. Otherwise, we are free to make it up. But we cannot make up any FTL transfer of information that the no-collapse interpretation cannot explain.

And since the collapse is unobservable, when and how and how fast it happens, or if it does at all, is not a scientific question. It's really a question of metaphysics, or aesthetics, or utility.