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About quantum entanglement and relativity of simultaneity

  1. Sep 6, 2012 #1
    This looks more like a relativity question, so let's post it here. I try to keep it short.

    Alice and Bob approach each other, synchronize their clocks when they meet, then drift away from each other with relative speed 0.8c. No acceleration involved here. There is an entangled particle, Alice having one piece, Bob the other.

    Both of them measure the particle's quantum state when their own clock shows 60 minutes. The one that performs the measurement first, gets the actual random result, and the one that does it later, gets just a mirror copy of this result.

    In Alice's frame, Bob's clock shows only 36 minutes when Alices clock shows 60 minutes, so Alice thinks that she is the first to do the measurement. With similar argument, Bob thinks he is the first.

    Do you think there is some way to solve the question who is actually first, within SR/GR or QM, or does the nature just not care about the order? Thanks.
  2. jcsd
  3. Sep 6, 2012 #2


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    There is not, and indeed you're falling into a very common trap when you use the word "actually" above - there's no such thing as "actually first" or "actually second. One observer sees the events in one order and the other sees them in the other order, and both views are equally good and just as "real" and "actual".
  4. Sep 6, 2012 #3


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    That's going to be QUITE a trick to synchronize clocks as they pass each other at a "drifting" speed of .8c --- that's quite a "drift" :smile:
  5. Sep 6, 2012 #4


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    SR does not care who is "actually first".
    It's a bit trickier with QM. While minimal formal framework does not care who is first some interpretations of QM might care.

    Basically your formulation cares who is first because the first one gets random result and the other one gets certain result. But it might be quite tricky to formulate experimental test that would tell apart random from certain result when according to your formulation the same result can be random or certain depending on who tells it first.
  6. Sep 7, 2012 #5


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    A mirror copy of a random result is also a random result. So each experimenter gets a random result, and each random result is perfectly anti correlated with the other. That much is completely symmetrical, regardless of who measures first.

    Nature doesn't care as far as I can tell.
  7. Sep 7, 2012 #6
    I've sketched a Loedel (symmetric) space-time diagram for two entangled photons in an attempt to illustrate this time issue arising with entanglement and special relativity.

    A red guy moving along his X4'' world line at some relativistic speed (with respect to stationary black reference coordinate) while a blue guy moves in the opposite direction at the same relativistic speed as red. Red measures an UP state of the left moving photon at event A. And a short instant later red measures a DOWN state of the right moving photon at event B.

    But the event at B occurs in the blue's instantaneous 3D cross-section of the 4-D universe at t'B, whereas the original event A does not occur for Blue until t'A, much later than event B. So, for the blue guy, event A happened after event B, whereas for the red guy event A was first followed an instant later by event B.

  8. Sep 7, 2012 #7
    In a sense, the concept of "simultaneity" is meaningless from a relativity standpoint. For any two events A and B, there are only three possible descriptions one can give which will be agreed upon by all observers: that the events are space-like separated, time-like separated, or null-separated.

    Space-like separation means that there exists a class of inertial observers which will record A and B as being simultaneous; likewise, there is a class of observers which will record A as having preceded B, and B as having preceded A. All of them, however will agree that the two events are space-like separated (which means that light emitted from event A will reach an observer passing through event B after B has occurred, and light from event B will reach an observer passing through A after A has occurred).

    Null-separation means that event B is located on either the past or future light cone of event A (that is, there exists a light ray which passes through both events A and B).

    Time-like separation means that all observers will agree that either A preceded B or B preceded A.

    Beyond that, there is nothing one can say about the timing of the two events which does not depend on choice of an observer. Thus, asking which event was "actually first" is an ill-defined and meaningless question.

    Edit: As this applies to entanglement: unless there really is some quantum-mechanically preferred reference frame (and I see no evidence that there is), then entanglement in this case is just a correlation between space-like separated measurements. So, there's still no meaning to the question of who measured first.
    Last edited: Sep 7, 2012
  9. Sep 8, 2012 #8


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    This is not so simple. Copy is not random, it is exactly the same as original and that makes it predictable and compressible i.e. non random.
  10. Sep 8, 2012 #9


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    I think you misunderstand what it means for a result to be random in QM. It means that if you repeat the experiment multiple times no amount of knowledge about the previous experiments nor about the state of the experimental apparatus will allow you to predict the outcome of the next experiment. This holds true for both the "original" and the "copy" in any frame, so both are random in the meaning of QM.

    Furthermore, even in the looser meaning of random which I think you are using, the "copy" is random. Specifically, the "copy" is not predictable at the event of its measurement since no information about the "original" is available. The "copy" is post-dictable, but that doesn't seem to be the same as predictable.
  11. Sep 8, 2012 #10
    Let's say that you have an entangled particle at hand, but you haven't measured its state yet. Maybe this is only my intuition, but shouldn't it be clear whether the state is defined of undefined, is there some other options? It's defined if the other particle has already been measured by someone, undefined otherwise. Even if you cannot test how it is, and even if it doesn't really matter, it is there.

    If Alice and Bob both are first to measure the entangled state, as they are in their own frames, wouldn't this mean that both of them fix the quantum state from undefined to defined?
  12. Sep 8, 2012 #11


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    The problem is that the phrase "has already been measured" makes no sense in relativity. In the context being discussed you can't say for sure which of the two measurements happens first; different observers disagree over this, and all points of view are equally valid.
  13. Sep 8, 2012 #12


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    No, it is not clear. There is absolutely no way to know.
  14. Sep 9, 2012 #13
    Last edited by a moderator: May 6, 2017
  15. Sep 9, 2012 #14


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    It can be sort of "defined" right from the start. This is called local hidden variable hypothesis.
    There are a lot of people who claim that Bell test experiments have ruled out that hypothesis but that is actually not true as loophole free Bell test has not been performed yet (despite considerable effort).
    What actually is true that local hidden variable hypothesis has not produced any viable explanation for entanglement. And yet it remains as a theoretical possibility how to explain entanglement without magic. :wink:
  16. Sep 10, 2012 #15
    If you have it in hand, then you have collapsed the wave function and the particle now exists in an UP or DOWN state.
  17. Sep 11, 2012 #16
    Let's imagine that the question "who is first" is really just a point of view in all aspects.

    Because Alice is first in her frame, Alice has a particle in undefined quantum state before measurement. She performs a measurement. The particle gets defined quantum state. Because the state was undefined before measurement, the probability of UP state is 50% and DOWN state also 50%, without any bias.

    Because Bob is first in his frame, Bob has a particle in undefined quantum state before measurement. He performs a measurement. The particle gets defined quantum state. Because the state was undefined before measurement, the probability of UP state is 50% and DOWN state also 50%, without any bias.

    Sorry about the repeat, but I think it's kind of illustrative. So there is 25% probability that both Alice and Bob get UP state, the same with both DOWN state. That would be bad for conservation laws, but something that we may need to accept, if the quantum state really is undefined before both measurements, both Alice's and Bob's viewpoint is equally valid, and there is nothing behind the scenes that is missing from this setup.

    But maybe entanglement is just a correlation between separate measurements, as suggested in some replies, with hidden variables or with magic. I tend to think there is more behind the scenes, but it's only a feeling (although there came up some interesting ideas to study in this thread). "Just a correlation" is a bit of disappointment, but at least it's reasonably simple way to solve, or workaround, this problem. I can live with that.
  18. Sep 11, 2012 #17
    Ookke, the wave function should be thought of as a global function which provides the amplitudes for states of a SYSTEM. Thus, the particles participate in the state of a SYSTEM. The wave function could collapse into a system of UP at A & DOWN B, or else DOWN at A and UP at B. But the thing to grasp is that the wave function describes the amplitude for a SYSTEM state (the conjugate square of the amplitude describes the probability for collapsing into a particular system state).

    It's not like the measurement at A collapses the wave function into a particle and then the particle at A "causes" a particle at B to pop up--or that the wave function decides what to produce at A and then decides what to produce at B. The wave function collapses into a system of particles--and particles pop up consistent with SYSTEM states. If A is UP and B is DOWN it's because that's the SYSTEM state that happened to pop up.

    Now, as far as the results from the standpoint of special relativity, we then consider the implications that have been discussed in the earlier posts on your thread. Repeating one speculation (which we don't like to do on this forum), one could consider a universe "NOW" concept in the following way: Imagine all observers on worldlines that could be traced to the big bang. All observers move along their worldlines at the speed of light, and if you imagine tracing out a network of lines throughout a 3-D cross-section of the universe, connecting all events in the universe that share the same proper time (regardless of velocities and as reckoned from the big bang) you then have the universe "NOW" that we imagine ourselves living in at this instant (not to be confused with local inertial coordinate time axis "NOWS" involving time dilation, etc.). Then we imagine the wave function collapsing across the universe at this "NOW" 3-D instant of "universe proper time." Different observers will not agree on whether event A occured before event B (using their local inertial time axis values, etc). But, that does not matter. All observers can agree on whether a measurement at event A occured before event B based on proper time. Please do not take this description as a popular view among physicists. I haven't even considered all of the implications of it myself. One problem is that the worldline of the particle at A may not have the same proper time as the proper time associated with the instrument collapsing the wave function (the two worldlines intersect much like the worldline intersection of twins in the twin paradox). But, you might be able to make a case for the wave function collapses over a 3-D cross-section of the universe associated with the proper time of the measuring instrument.

    Do not feel like the Lone Ranger with your sentiment that there is more behind the scenes. You are in good company there with physicists like Einstein and Nobel physicist Gerard 't Hooft (myself as well, but my sentiments are certainly not worthy of attention).
    Last edited: Sep 11, 2012
  19. Sep 12, 2012 #18
    Yes, that's perhaps the pertinent point that came up in other discussions of this topic. Post-diction takes place at the speed of light or less.

    Ookke, did you search this forum? I'm sure that your question comes up regularly.
    Last edited: Sep 12, 2012
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