# Two entangled particles One on Earth, the other on a space ship

1. May 13, 2014

### Ragnor8

First off I'd like to say my understanding of physics isn't very good, so I'm sorry if this question is a non sequitur.

Suppose we have two entangled particles, one on Earth, and the other on a ship that is travelling away from Earth at near to light speed.

According to quantum entanglement, if we measure one particle, the other one correlates INSTANTANEOUSLY, at faster than light speed. However according to relativity, time will be passing at a slower rate on the ship than it is on Earth.

Does this mean that if we were to measure the particle on Earth, that the particle on the ship would actually correlate BEFORE we took the measurement? Surely not. However if it correlates "instantly", then in what sense can it be said that time is occurring at a slower rate on the ship?

2. May 13, 2014

### Staff: Mentor

Measurements cannot correlate until you make the measurements.

3. May 13, 2014

### Ragnor8

I thought the idea of quantum entanglement is that the second particle changes its state instantly.. regardless of whether you measure it or not?

4. May 13, 2014

### Staff: Mentor

The state does change instantly. That is different than measurements correlating. Measurements can only correlate after they are measured.

5. May 13, 2014

### Ragnor8

In that case I'll rephrase my question.

If the we measure the particle on Earth, then the particle on the ship changes its state instantly. We can't see this until we measure the particle on the ship, but the state DOES change.

Now if time is running slower on the ship than it is on Earth, how can the state of the particle change instantly?

How can there be such a thing as "simultaneity" if time is running at different speeds?

6. May 13, 2014

### Staff: Mentor

What would prevent it? In what way does the change of the state in the Earth's frame depend on the rate of the ship's clocks?

Simultaneity isn't something physical. It is merely a convention.

7. May 13, 2014

### Ragnor8

I mean, if you measure the particle on Earth, according to quantum entanglement the particle on the ship then immediately collapses in the same way it did on Earth.

How can something happen "instantaneously", if time is running at different rates? You say that simultaneity is just a convention. So in what sense can the particles be said to collapse simultaneously if there is no such thing as simultaneity in the first place?

8. May 13, 2014

### Staff: Mentor

You simply adopt a convention where they happen simultaneously. There is nothing physical, it is just a matter of convention.

I feel like I am playing a guessing game about what your concern is, so let me simply try to explain a little physics without directly answering your questions.

Suppose that you have an arbitrary quantum system. That system is described by a state, or a wavefunction. If you make a measurement on the system then the state collapses to the eigenstate corresponding to the measurement. Now, if you make another measurement with an operator that commutes with the first, then the outcome of the second measurement is certain.

Now, suppose that you have a pair of entangled particles. All that means is that the two particles together form a single quantum system with a single quantum state. As always, if you make a measurement on the system then the state collapses to the eigenstate corresponding to the measurement, and if you make another measurement with an operator that commutes with the first, then the outcome of the second measurement is certain.

So, if you measure the spin of one particle then the wavefunction of the whole system collapses and, since measurement of the spin of the other particle commutes, the outcome of the second measurement is certain.

If the two measurements are spacelike separated then the order of the measurements is frame-dependent. But in all frames, when one measurement is made the other is certain, since the operators commute.

The velocity is not relevant at all.

9. May 13, 2014

### Staff: Mentor

You stated this wrong; what you should have said is that according to non-relativistic quantum entanglement, the non-entangled particle's state changes instantaneously. In other words, if we measure particle A, particle B's state changes instantaneously, so that if we then measure particle B, the result we get must be correlated in a certain way with the result of the measurement of particle A. But this whole description is a non-relativistic approximation: it is not valid if the particles are moving at relativistic speeds.

The correct relativistic description of quantum entanglement states things differently: it says that, if two measurement events are spacelike separated, they must commute: that is, the results must be the same regardless of which order the measurements are made in. This is what ensures that the results will be the same regardless of which inertial frame we use to describe them. But it also means that there is no longer any way to determine, physically, which measurement "happened first", which means that there's no way to tell which particle's measurement "caused" the other particle to change state; in fact, the whole idea of the "change of state" being propagated from one measurement event to the other is not valid. All you have are quantum field operators at different events in spacetime.

10. May 13, 2014

### Staff: Mentor

I think this way of describing things is part of the non-relativistic approximation I referred to in my previous post. (If more detailed discussion of this is desired, it should probably be moved to the Quantum Physics forum.) In relativistic QM, i.e., quantum field theory, you can't really use an ordinary wavefunction to describe the "state" of a many-particle system where the particles are spacelike separated. (More precisely, you can, but doing so involves choosing a frame, so the wavefunction is really a frame-dependent variable and is not physically "real" in the way it's usually thought of in non-relativistic QM.)

A proper invariant description of a process involving spacelike separated measurement events in QFT would, AFAIK, either use a path integral or use quantum field operators that are tied to particular spacetime events, rather than wavefunctions that are tied to particular surfaces of simultaneity. Spacelike separated measurement events then simply have field operators that commute; there's no "collapse" that propagates from one to the other.

11. May 13, 2014

### Staff: Mentor

Yes, I believe so.