Quantum Entanglement & Relativity: Time Dilation Effects

[serp777]

Lets say two particles are entangled with each other. One particle is put in a spaceship, while the other remains on Earth. The spaceship then increases its speed till it is nearly at the speed of light. How does the time dilation effect influence the properties of entanglement? How does relativity interact with quantum entanglement in this situation?

 

[gork]

Various experiments of varying lengths have shown that distance has no effect on entanglement, and all entanglement experiments are done over space-like (superliminal) distances, so the particles would remain entangled no matter how fast they were going or how far apart they are. In fact, entangled particles used in experiments are already moving away from each other at a relative velocity of 2c, so the conditions you put forth are exactly what has been tested for the last 40 years.

 

[serp777]

but let's say that on earth, an observer looks at the entangled particle every nano second, thus changing its state every nano second. However, now say that the spaceship is traveling at a speed so close to light that time nearly stops. If both entangled particles are updating at the same time regardless of the distance, then a observer on the spaceship (who is traveling through time very slowly relative to earth) would notice the entangled particle changing states faster than the plank constant of the universe, because of the time dilation effect, which is impossible. Also, if the person on the spaceship observed the entangled particle to change its spin or something, then would an observer on Earth notice the entangled particle changing spins very slowly? Also if the spin updates more slowly, then couldn't you interrupt the entangled process by observing it while it is changing?

 

[serp777]

I don't mean to be annoying, but bump.

 

[DrChinese]

but let's say that on earth, an observer looks at the entangled particle every nano second, thus changing its state every nano second. ...

Welcome to PhysicsForums, serp777!

Entanglement is not as you imagine it in your examples. When you first observe entangled Alice here on Earth, she is still entangled with far away Bob. But that entangled state ends at that time. So the idea of repeatedly observing Alice and trying to determine the connection to Bob will not be meaningful. There is no way to observe Alice's momentum, for example, and expect Alice and Bob to remain entangled as to momentum. (They will instead go into individual eigenstates.)

Doing something to Alice does not necessarily change Bob in any way. Better to say that any measurement done on Alice will yield information about far away Bob. Of course, that "information" is redundant so it is not very useful.

 

[serp777]

Thank you; I appreciate you spending your time to help me understand entanglement.

 

[alphawolf50]

Entanglement is not as you imagine it in your examples. When you first observe entangled Alice here on Earth, she is still entangled with far away Bob. But that entangled state ends at that time.

Are you saying entanglement is only good for one observation? If Alice sees "clockwise" on her first observation, she knows that Bob is counter-clockwise -- but if she observes her particle a second time she knows nothing of Bob's particle?

 

[e.bar.goum]

Are you saying entanglement is only good for one observation? If Alice sees "clockwise" on her first observation, she knows that Bob is counter-clockwise -- but if she observes her particle a second time she knows nothing of Bob's particle?

Well, that's quantum mechanics, isn't it? Making the measurement of "clockwise" has "collapsed the wavefunction" (to use an imprecise phrase) of Alice's particle, and it is no longer in an entangled state with Bob's. Thus, making another measurement of her particle (it would still read "clockwise", unless you mean, say, measuring it's position) can't tell you about Bob's.

 

[DrChinese]

Are you saying entanglement is only good for one observation? If Alice sees "clockwise" on her first observation, she knows that Bob is counter-clockwise -- but if she observes her particle a second time she knows nothing of Bob's particle?

Generally, the answer is yes (as e.bar.goum indicates).

There is a theoretically possible situation in which a little more can be learned. Polarization entangled photons are usually also entangled as to wavelength. If the first measurement did not reveal any information about wavelength (directly or indirectly), then you could use that to learn about Bob.

 

[e.bar.goum]

f the first measurement did not reveal any information about wavelength (directly or indirectly), then you could use that to learn about Bob.

I might be totally wrong, but wouldn't the interaction with the environment made by taking the first measurement break the entanglement anyway?

 

[DrChinese]

I might be totally wrong, but wouldn't the interaction with the environment made by taking the first measurement break the entanglement anyway?

Entangled photons can be entangled on one or more bases. Essentially, each could be independently collapsed.

Not sure if this exactly represents this condition, but it certainly discusses some of the issues:

http://arxiv.org/abs/quant-ph/0406148

 

[e.bar.goum]

Cool paper, thanks DrChinese. I knew that entanglement can occur in many bases, but I didn't realize it had been experimentally realized. I just skimmed the paper (clearly, very quickly) and it doesn't appear that *sequential* measurements were taken, but simultaneous ones. That is, it's not quite the situation we're concerned with here, where we get information about polarization (say) then momentum. (I could be wrong, I just skimmed)

My concern is with interactions with the environment. Entangled states are coherent, yes? In which case, interactions with a measuring device/environment will result in decoherence (off diagonal terms in the density matrix will go to zero, to use some jargon) and thus a breaking of entanglement. Or have I mis-represented the connection between entangled and coherent states?

 

[kith]

My concern is with interactions with the environment. Entangled states are coherent, yes? In which case, interactions with a measuring device/environment will result in decoherence (off diagonal terms in the density matrix will go to zero, to use some jargon) and thus a breaking of entanglement.

The question is in which basis? If your environment is such that it only destroys the coherences in one basis (polarization), but doesn't destroy them in the other (wavelength), entanglement with respect to the second basis is preserved. This is probably difficult to achieve experimentally and I don't know if it has been done.

Also note that the best phrasing is "coherent superposition". "Coherent state" has another meaning when it comes to quantum mechanical oscillators.

 

[e.bar.goum]

The question is in which basis? If your environment is such that it only destroys the coherences in one basis (polarization), but doesn't destroy them in the other (wavelength), entanglement with respect to the second basis is preserved. This is probably difficult to achieve experimentally and I don't know if it has been done.

Also note that the best phrasing is "coherent superposition", because "coherent state" has another meaning when it comes to quantum mechanical oscillators.

True enough, I hadn't considered that decoherence was basis dependent. It would depend on the coupling strength though.

In this situation, "coherent superposition" and "coherent state" can be used pretty much interchangeably. I didn't want to introduce extra jargon. But yes, sorry for any confusion caused.

 

[alphawolf50]

I think I get the general idea of what you fine fellows are saying. Nearly everything I know of quantum mechanics comes from watching the Science Channel, and one program used a coin-tossing analogy to describe entanglement. It left the impression that, while each toss was random and you couldn't possibly know the result beforehand, the coins would always land with the opposite face up. They did not indicate that it was a one-time affair :(

Thanks for the clarification, we amateurs truly appreciate it :)