EPR communication with double slit

Question

I know this is probably not possible to use to communicate via EPR, so my question is why?

I create electron entangled pairs using pair production or some other method, (each color pair is an entangled pair) we send millions of those pairs toward two double slits separated far from each other. The person on the right side can decide to measure which slit the electron went through using detector D (which ruins the interference pattern) or they can decide to not measure which retains the interference pattern. This would seemingly also ruin or maintain the interference pattern for the person on the left side. If the source of electrons is streaming continuously, the person on the right could send a message by using dot dash for "interference on" or "interference off" during short 1 second intervals.

Again, I presume this would not work, so why exactly? And please don't say "because you can't communicate faster than light." What would specifically go wrong in this set up that would not make it work as described? Thanks!

Answer 1

Look at this double slit experiment one electron at a time:

The few electrons at a time, top frame, look random, there is no interference. The interference appears with the accumulations of same boundary conditions scatters ( double slits given width given distances) and verifies that the wave part in the wave-particle duality is a probability wave given by the $Ψ^*Ψ$ of the wavefunction $Ψ$, the solution of the quantum mechanical problem.

So whether there are two entangled particles in opposite direction, they will show no interference pattern. It is in the accumulation of events that the destruction of interference will appear when one tries to see which slit the particle went through, which is completely unsuitable for signaling anything. See the single photon at a time double slit experiment here.

Answer 2

I think there is some confusion with just what "entanglement" here is which can be cleared up. It refers to the outcomes of certain experiments being correlated. Two particles interacted in isolation and a certain quantity is conserved, then measuring the quantity in one of the particles, you will know the value of the quantity in the other.

This happens in non quantum systems and doesn't create any mystery --> grandpa dies leaving his fortune of 1 million dollars split between you and your cousin --> you get a check for $450k, how much did your cousin get? (he was always the favorite).

With QM, this gets fuddled because of the whole "measured values don't actually exist until measured" thing. But if you "detect" on the right hand side slits, you don't disrupt the interference pattern on the left, you simply get information of what would have been measured if you had also detected on the left slits.

If your cousin and you both decide to gamble your inheritance on lottery tickets, it will change the distribution of your wealth (disrupt the "interference patterns" by analogy), but your distributions will still be correlated (entangled). But you deciding to gamble it doesn't make your cousin do the same, so you can't send a signal via repeated gamble/no gamble actions on repeated inheritance (if that makes sense, and you have enough rich old relatives). If you gamble and he doesn't, the entanglement (correlation) is broken.

Answer 3

This would seemingly also ruin or maintain the interference pattern for the person on the left side

This is where your misconception lies. The interference pattern would show up on the left every single time, regardless of whether or not you placed a detector on the right hand side. Collapsing/observing one particle in an entangled pair does not collapse the other particle, thus it is still a wave on the left when it passes through the slits. Whether or not a wave-function has collapsed is not an enatanglable property. Like Peter Shor said in the comments, "Why do you think making the interference pattern on the right go away also makes the interference pattern on the left go away? It doesn't; that's not how entanglement works."

Let's reframe this experiment to understand why entangled pairs don't allow for faster than light communication. Let's say Alice and Bob entangle two coins in separate boxes. They know with 100% certainty that one of them will have a coin facing heads, and the other will have on facing tails. Now Alice and Bob get in separate spaceships and travel several lightyears apart from each other. Right now, their coin are in a state of superposition, where the coins are each 50% heads and 50% tails. Lightyears apart from Bob, Alice opens her box and she sees that it is heads. Now, let's shift to Bob. Since Alice opened her box and it became heads, "spooky action at a distance" occurred and Bob's box has a 100% chance of being tails, but he has no way of knowing this. He has no way of knowing that Alice has already opened her box and found heads, because he cannot detect that his chances of opening tails moved from 50% to 100%. Your hypothetical experiment is predicated on the notion that when Alice opens her box, Bob's box would magically open which would then alert Bob that Alice opened hers. This does not happen, Bob's box remains closed until he feels like opening it. When Bob opens his box, he observes tails. But he has no way of knowing if this was because of a 50-50 chance, or a 100% chance because Alice already opened her box. Thus no information was transmitted from Alice to Bob. The only "faster than light communication" that occurred was the spooky action at a distance, where Alice's particle "told" Bob's particle it had to be tails, but this information is impossible for Bob to measure. If entangled particles could allow Alice and Bob to communicate instantaneously across lightyears, it would lead to all sorts causality violations and time paradoxes.