Entangled particles and the Andromeda paradox experiment

Question

I know there are other questions linking the two subjects. I am not asking about an explanation, rather I am curious whether an experiment would be possible.

To explain the experiment let's start with two entangled particles, one here and one in the Andromeda galaxy. If I measure the direction of the spin here, and someone measures the direction of the spin there, they will always be one up and one down. Say there is a second pair of entangled particles. The two on Earth are close to each other so I can do the measurement at the same time (close, locality is preserved), however one is moving towards Andromeda. This should imply that the two particles on Earth will have spin up or down defined pretty much at the same time on Earth, but the scientist on Andromeda should not see the ones entangled in Andromeda with defined spin up or down at the same time (again, for the person on Andromeda the two particles are near each other), because of the movement of one particle and the fact that simultaneity for the two pairs is different. Basically, the second particle on Andromeda should have spin up or down simultaneously with the one on Earth, but, since one is moving, it may be days after the first one.

Obviously we cannot send anyone on Andromeda, but we don’t need a delay of days, also, the particle will not walk but move faster, so, we do not need to go to Andromeda.

Can this thought experiment be validated at shorter distances with particles moving faster? Has this experiment ever been attempted?

CLARIFICATION*****

I am going to clarify my question:

1. I have two pairs of entangled particles x and y, and w and z.

2. x and w are in one location, y and z are in a different location

3. x and w are local and are measured simultaineously

4. x is not moving while w is moving

5. Depending on how far y and z are, and since w is moving, the measuring should not be simultaineous for the local observer in the location where w and z are

Can this experiment be performed and confirmed?

Answer 1

There's no way to tell whether two particles are still entangled or not, except by comparing the results after measuring them. There's also no way to tell which measurement "collapsed" the wave function. That is, all you can tell in your experiment is that when the Earth particle and Andromeda particles are measured they will have opposite spins. It doesn't matter which order the particles are measured in, the results will be the same. So all observers will agree on the outcome regardless of their relative motion. If they subscribe to an interpretation of QM in which measurements collapse wave functions, they may disagree about which of the two measurements "caused" the colllapse, but since the experimental result is the same either way it physically doesn't matter.

Answer 2

Without disagreeing with anything in Eric's answer and comment, I will add a bit to hoping to clarify the situation.

1. The issue of simultaneity of measurement does not enter into the equation at all. Strictly speaking, most would say that it is not even possible to determine that two entangled particles were measured at the same time. That is simply because the detections cannot be resolved well enough using today's technology - even with the incredible advances that have bee made in recent years. But even if you could measure simultaneously, theory says that nothing special happens at that point. Simultaneous or not, the results appear the same for entangled systems.

If you want to read about entanglement experiments where the measurements are as near-simultaneous as possible, I would recommend studying what is called the Hong-Ou-Mandel effect. In experiments, it is often called the HOM dip and is characterized by a graph with a dip in the middle. Here is the original HOM paper (see Figure 2). But please understand this subject - measuring time to the level of femtoseconds or even attoseconds - is extremely complex for even the most well-studied (which I am not lol).

2. Likewise, the issue of moving reference frames does not enter into the equation at all. Nor does direction of movement (closer or farther) have any observable impact. For entangled photons, many experiments have been performed with such pairs. Obviously, their velocity is c. But they are measured going in all kinds of directions relative to each other. There is no change to the quantum predictions required for this scenario. Same applies for entangled systems of other particle types.

3. Your question actually asks whether this experiment can be performed and confirmed. The answer is sure, it can be done and has been done in many ways. But there's nothing specific to confirm, you didn't actually provide a prediction of something you expect to witness one way or the other. But again, there is nothing to see when it comes to reference frames or simultaneity when it comes to entangled systems.

If you want to read about entanglement experiments from Earth to space, this has actually been done with satellites in orbit: Ground-to-satellite quantum teleportation

4. Not only does special relativity not enter into the quantum predictions in any way, neither does the order of measurement - which might otherwise lead you to believe the earlier measurement is the cause and the later one is the effect. In the so-called "delayed-choice" experiments on entangled pairs: cause-and-effect are demonstrated to be in reverse. Keep in mind that most interpretations of QM do not consider this to be evidence of the future changing the past; but certainly there is no apparent difference when order is reversed.

If you want to know more about delayed choice: Delayed-choice gedanken experiments and their realizations

While it may not be entirely clear how these references apply to your question: they actually are the experimental pieces that when put together, provide the answers you seek. And the experimental results match the quantum mechanical theory extremely well.

Answer 3

Relativistic quantum theories have been invented and used extensively, see books on quantum field theory such as "Quantum Field Theory for the Gifted Amateur" by Lancaster and Blundell. If you have entangled particles in motion relative to detectors and each other you can observe Bell correlations between them though the measurement settings required to produce the maximum possible correlations will in general require transforming observables for particles in motion relative to one another and the measurement devices:

https://arxiv.org/abs/2008.03317