According to what I read about entanglement, when you measure the spin of one of the entangled particles all the possibilities collapse to one value immediately and the other particle will give the opposite result when measured. My question is about introducing special relativity concepts to this experiment. If we somehow tuned the velocities of the particles so, particle one will be moving with relativistic speed and get its spin measured and then particle 2 will move relativistically and be measured. That is the order of actions at the observer frame of reference. However, by adjusting the velocity, the frame of reference of the second particle will see particle 2 being measured first. The idea behind doing so is the observer will see particle 1 being measured then particle 2, But particle 2 will experience himself being measured first. Will that affects the results of the experiment. Making particle 2 not affected by particle 1 results.
1 Answer
If you have a non-local entangled state of two particles, such as two spin particles being entangled and whose spins are anti-aligned (as you describe), then nothing you do locally to one particle has any experimental effect on the other. This is due to the fact that even though the two measurement outcomes are correlated when measured in the correct way, they are also always completely random.
This result is known as the no-communication theorem, due to the fact that if you could create an experimentally measurable difference in the other particle, you could use this to communicate (possibly faster than the speed of light which is forbidden by special relativity).
However, what is true is that if you have two distant observers that share an entangled pair of particles, the story of what quantum state the particles are in at different points of time can be different. For instance, due to special relativity, there may not be an agreement of which particle was measured first (and therefore which particle was already collapsed when it was measured). This relativity of quantum states is taken very seriously by certain philosophical interpretations of quantum mechanics, notably Quantum Bayesianism (QBism) which treats the quantum state as a purely subjective statement of your particular information/knowledge of some quantum system, and Everett’s Relative-State Formulation of Quantum Mechanics where quantum states don't actually collapse but instead your relative quantum state is a statement of which universe you randomly find yourself in (with new universes created with each quantum interaction).
