# Quantum entanglement vs relativity of time

I looked into quantum entanglement thing last days and I think I got it right. At least the basics.

Just one thing. Quantum entanglement concept says that when I measure the state of one particle, it affects the entangled one's state instantly.

But what does this have to do with the relativity of time? If one measuring device (and the particle) is moving very very fast, so the time is slowing down on it from the viewpoint of the second, how will the results correlate, since there's no absolute time and simultaneity is relative?

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And one more thing. There's a popular analogy of quantum entanglement with classical mechanics, which goes like this: "Alice and Bob have a coin, and they slice it along the circumference into two half-coins, in such a way that each half-coin is either "heads" or "tails". They then put each half-coin in an envelope, one for Alice and the other for Bob, randomly. Alice then measures her half-coin, by opening her envelope. For her, the measurement will be unpredictable, with a 50% probability of her half-coin being "heads" or "tails". However, if she compares the side of the coin she obtained with the side of the coin Bob measured in his half-coin, she will see that they are always opposite, hence perfectly anti-correlated."

As I pictured to myself, this analogy ends when we do a measurement of the same parameter the second time and get the other results. Though http://en.wikipedia.org/wiki/Quantum_entanglement#Concept" states that it breaks down even earlier: "To see the power of entanglement, Alice and Bob have to measure the spin of their particles in other directions than just up or down. ... Now the classical simulation of entanglement breaks down―there are no "directions" other than heads or tails to be measured. One could imagine that upgrading the coins to dice could solve the problem, but this is hopeless."

Is it correct? Even if we work with probabilistic values here. What makes it impossible to simulate the experiment with dice? Aren't we gonna see anti-correlation anyway? Just can't get what creates a difference here. Or should I look into the Bell's inequality in order to understand this?

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Demystifier
Gold Member
Quantum entanglement concept says that when I measure the state of one particle, it affects the entangled one's state instantly.
Not necessarily. That is so in the collapse interpretation, but not in the interpretations without the collapse, such as many-world interpretation or pilot-wave interpretation. In the latter interpretations, measurement of one particle does not influence the "state" (more precisely - density matrix) of the other particle.

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A. Neumaier
Quantum entanglement concept says that when I measure the state of one particle, it affects the entangled one's state instantly.

But what does this have to do with the relativity of time? If one measuring device (and the particle) is moving very very fast, so the time is slowing down on it from the viewpoint of the second, how will the results correlate, since there's no absolute time and simultaneity is relative?

See the entry '''Is there a relativistic measurement theory?' in Chapter A4 of my theoretical physics FAQ at http://www.mat.univie.ac.at/~neum/physfaq/physics-faq.html#relMeas

DrChinese
Gold Member
I looked into quantum entanglement thing last days and I think I got it right. At least the basics.

Just one thing. Quantum entanglement concept says that when I measure the state of one particle, it affects the entangled one's state instantly.

1. But what does this have to do with the relativity of time?

If one measuring device (and the particle) is moving very very fast, so the time is slowing down on it from the viewpoint of the second, how will the results correlate, since there's no absolute time and simultaneity is relative?

--
And one more thing. There's a popular analogy of quantum entanglement with classical mechanics, which goes like this: "Alice and Bob have a coin, and they slice it along the circumference into two half-coins, in such a way that each half-coin is either "heads" or "tails". They then put each half-coin in an envelope, one for Alice and the other for Bob, randomly. Alice then measures her half-coin, by opening her envelope. For her, the measurement will be unpredictable, with a 50% probability of her half-coin being "heads" or "tails". However, if she compares the side of the coin she obtained with the side of the coin Bob measured in his half-coin, she will see that they are always opposite, hence perfectly anti-correlated."

As I pictured to myself, this analogy ends when we do a measurement of the same parameter the second time and get the other results. Though http://en.wikipedia.org/wiki/Quantum_entanglement#Concept" states that it breaks down even earlier: "To see the power of entanglement, Alice and Bob have to measure the spin of their particles in other directions than just up or down. ... Now the classical simulation of entanglement breaks down―there are no "directions" other than heads or tails to be measured. One could imagine that upgrading the coins to dice could solve the problem, but this is hopeless."

Is it correct? Even if we work with probabilistic values here. What makes it impossible to simulate the experiment with dice? Aren't we gonna see anti-correlation anyway? Just can't get what creates a difference here.

2. Or should I look into the Bell's inequality in order to understand this?

Welcome to PhysicsForums, jackfield!

1. The collapse of a quantum system wavefunction operates "as if" it is instantaneous by any frame you care to consider. No one really knows the physical mechanism, there is only a more formal mathematical mechanism in use to explain. There is no technical conflict between quantum mechanics and relativity per se. The conflict is more one of semantics when you interpret the theories.

2. Yes, I highly recommend learning more about Bell and the underlying argument. It is really not very complex (once it is pointed out). I have several related web pages which go through the math, see my tag line for the link. Also:

http://drchinese.com/David/Bell_Theorem_Easy_Math.htm

Essentially, you discover that the correlation function is solely dependent on the relative angle between Alice and Bob's measurement devices. Further, because the relationship is non-linear, it leads to the conclusion that the results are dependent on Alice knowing Bob's setting (or vice versa). Which of course seems impossible by our ideas of spacetime.

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"In which Lorentz frame is this instantaneous? In any frame!"
DrChinese saying the same as I see. Hm interesting. So does it mean that in Twin paradox if I'm travelling in a superfast spacecraft, at the time when I'm doing a turn back with one entangled particle (let's say this back turn takes an hour or smth) our results will be instantaneous in the way that 1 second for me is 1 minute (for example) for my partner on the Earth? So if we do measurements every 10 seconds in our time, 1 my measurement will correlate with one of 10 measurements of my partner? Is my understanding correct? I was looking at http://en.wikipedia.org/wiki/File:Twin_Paradox_Minkowski_Diagram.svg" [Broken] graph.

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A. Neumaier
"In which Lorentz frame is this instantaneous? In any frame!"
DrChinese saying the same as I see. Hm interesting. So does it mean that in Twin paradox if I'm travelling in a superfast spacecraft, at the time when I'm doing a turn back with one entangled particle (let's say this back turn takes an hour or smth) our results will be instantaneous in the way that 1 second for me is 1 minute (for example) for my partner on the Earth?
What is instantaneous in the frame of an observer has nothing to do with what that observer can measure. All information an observer has comes from its past causal cone. (For example, we don't see what happens at the sun now, only what happened 8 minutes ago.)

The instantaneous frame is only a fiction that allows one to think of a relativistic situation in a more nonrelativistic way it the frame of a particular observer.

Demystifier
Gold Member
"In which Lorentz frame is this instantaneous? In any frame!"
For a critique of it see
http://xxx.lanl.gov/abs/quant-ph/0109120 [Phys.Rev. A64 (2001) 066101]

For example, we don't see what happens at the sun now, only what happened 8 minutes ago.
...
The instantaneous frame is only a fiction that allows one to think of a relativistic situation in a more nonrelativistic way it the frame of a particular observer.
Yep I understand this. But hard for me to bring facts together, feel kinda lost. Could you just say what correlations will look like when we do measurements of entangled particles in the light of Twin paradox?

A. Neumaier
Yep I understand this. But hard for me to bring facts together, feel kinda lost. Could you just say what correlations will look like when we do measurements of entangled particles in the light of Twin paradox?

This cannot be answered without saying much more about the set-up. Usually, entangled particles are produced somewhere in pairs, flying in opposite directions (which can be deflected later); then they are measured somewhere.

I wouldn't know how to arrange things such that the twins could make enough measurements on such pairs to get a reasonable coincidence statistics while one of them is moving. But without coincidence statistics, nothing predictable can be measured. Thus your question seems to be without content.

Oops I think I found a flaw in my understanding. Previously I thought that when we measure one particle, the measurment on other side will be opposite of last that we measured here. BUT this way we could send information by measurement (one measures a particle, tells second the result, and if the second sees other result than the first has told him, then we know for sure the first has made another measurement, sending information by the very fact of it!).

Damn, these popular explanations of "measurement affects the measurement" led me astray. My question loses sense, since the sequence of results is the only that makes sense in quantum entanglement.

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