The EPR Paradox and Special Relativity

I'm in the middle of taking the free course on Special Relativity over on worldscienceu.com. I've already taken the simple version that doesn't include any math, and now I've just started the technical version that has all the math. It's a challenge since I haven't done complex math in years.

One of the things that I was already familiar with in relativity is how the EPR paradox kind of throws a challenge to the notion of the relativity of simultaneity. The EPR paradox is basically quantum entanglement. When two quantum particles become entangled, they can be separated at great distances and when one of the particles is measured and it becomes known that it has a certain spin, the other particle instantly becomes affected and will spin in the opposite direction. That won't become known until the other particle is measured of course, and any information about the spin of the first particle that was measured won't be able to travel faster than the speed of light. This seems to preserve Einstein's Special Relativity (SR) very well that no information can travel though space faster than light.

But this is not what bugs me. What bugs me is how if two distant particles can "instantly" affect one another, and if according to SR our reference frame that determines what is "now" depends on our velocity relative to other objects, how can the two entangled particles instantly affect one another? Suppose one of the particles was on a space ship travelling at 80% the speed of light and moving towards the other entangled particle that is a million light years away. According to SR the reference frame of the particle on the ship would require that its "now" slice contain the future events of the other distant particle. So if the particle on the moving ship is measured, does the other distant particle's spin change "instantly" or does it change in the far future, according to the measured particle's reference frame on the moving ship?

I asked physicist Brian Greene a similar question to this and this was the answer he gave me. I asked:

How does the relativity of simultaneity affect quantum entanglement where two entangled quantum particles instantly affect one another at great distances? If the reference frame of the measured particle is taken into affect and let's say it's moving at a high speed, how can it be instant if there's a relativity of simultaneity?

And Prof. Greene answered:

Good question. And one we can answer with the material covered in this module. (For those who have not encountered entangled particles of quantum mechanics, don't worry about this question.)

So, imagine that the two presidents each have one member of a pair of entangled particles, whose properties they measure simultaneously (from the perspective of all those on the train). Then, according to those on the platform, they do NOT measure their particles at the same moment. Instead, those on the platform would say that it is the President of Forwardland who measures the particle first (if the train is moving as in the lecture--so that the President of Forwardland is facing forwarding, in the direction of the motion). And if the train were moving in the opposite direction, those on the platform would say that the President of Backwardland carried out the measurement first.

He was referencing the scenario given in the course of two presidents signing a document when they're sitting at each end of a moving train car and they are set to sign a document when the light reaches them from a light in the middle of the train car. If you were a passenger on the train, according to SR they'd sign the documents at the same time. But if you were a spectator on a platform, (and if the train were travelling at near the speed of light) then you would see the president who is sitting and facing towards the direction that the train moving to have signed first, and the president sitting and facing away from the direction the train is moving to have signed last. (This is not due to the speed of light being faster or slower, it's due to the distance that the light has to travel. The president who is moving towards the light has less distance between him and the source of the light than the president who is moving away from the light. Less distance means the light hits him faster, but this is seen only from the perspective of the spectators, not anyone on the train due to the relativity of simultaneity.)

According to Greene, the relativity of simultaneity holds even for entangled particles, although the scenario he described is not exactly like mine. I still need an expert's opinion on this because it is one of those things that's been on my mind for months and I've been shit out of luck finding an answer to it. The EPR paradox is supposed to be one of the challenges to the idea of a block universe that theists like William Lane Craig have used, and that's why this fascinates me so deeply.