About quantum entanglement and relativity of simultaneity

[Ookke]

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.

 

[Nugatory]

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.

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".

 

[phinds]

Alice and Bob approach each other, synchronize their clocks when they meet, then drift away from each other with relative speed 0.8c.

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"

 

[zonde]

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.

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.

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.

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.

 

[Dale]

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.

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.

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?

Nature doesn't care as far as I can tell.

 

[bobc2]

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.

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.

http://i209.photobucket.com/albums/bb185/BobC_03/Entanglement_SpaceTime.jpg

 

[Aimless]

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.

 

[zonde]

A mirror copy of a random result is also a random result.

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.

 

[Dale]

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.

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.

 

[Ookke]

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?

 

[DrGreg]

It's defined if the other particle has already been measured by someone, undefined otherwise.

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.

 

[Dale]

shouldn't it be clear whether the state is defined of undefined

No, it is not clear. There is absolutely no way to know.

 

[bobc2]

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.

[PLAIN]http://i209.photobucket.com/albums/bb185/BobC_03/Entanglement_SpaceTime.jpg[/QUOTE]

Let's separate two issues here. One issue is a strictly special relativity issue and the other is a QM issue.

First, the SR issue: The sketch above could apply for two arbitrary events, A and B. The situation is well known to folks dabling in special relativity and has been fairly well clarified in some of the earlier posts in this thread. Let's say that, in the above sketch, the two events A and B have nothing to do with QM, particularly entanglement. Thus, whether the A event occurs before the B event or the B event occurs before the A event depends on whose inertial reference system you are using for defining "before" and "after." So, I think at this point we can all pretty much agree on the situation. Different observers will not necessarily agree on which event occurred first. But, we avoid any QM implications for this case since particles are not entangled.

But, now the QM entanglement case: First, we choose which special relativity concept for use in proceeding with our analysis (Einstein-Minkowski or Lorentz). We choose the Einstein-Minkowski for this example. The trouble here is that the QM language doesn't seem suited for this model--particularly if you are picturing a block universe. In this special relativity model the 4-dimensional objects are what they are--they are all there as 4-D objects associated with their worldlines. If event A represents a measurement of an entangled particle in the UP state, then we have the intersection of the worldline of the particle and the worldline of the measurement instrument.

Now comes the problem. The usual QM language for the entangled experiment has a global wave function collapsing, yielding the particle states, UP at A and DOWN at B (but, in our SR model we must deal with the question of "where in the 4-dimensional universe is B?"). QM would use a description that envisions the measurement at A that induces ("causes") a collapse of the wave function. But viewing the entire 4-dimensional world, where in that 4-D world would nature locate the event B? Some will argue that event B does not occur without a measurement, but others insist the particle must pop up somewhere along with the collapse. How would nature come up with a preferred location for event B in all of 4-D space-time? Some suggest that the worldline of the two particles do not initiate until events A and B (there is only the wave function in space-time between the creation event and the collapse events of A and B, and the Einstein-Minkowski model has no way of representing the wave function, i.e., as a physical object--of course you can have a mathematical 4-dimensional wave function).

Some have suggested that the B event would have to be located in the same inertial frame as the instrument performing the measurement at A. Then you still have the basic problem of which event really occurred first (as considered in the strictly SR context and discussed in the previous posts). Others have said that the two entangled particles are associated with worldlines having the fixed UP and DOWN states from the point of the creation of the entangled particles. Others object to this, claiming that the particles do not exist (no worldlines are defined) until a measurement is made and that having particles existing in their states from creation is in complete conflict with the usual understanding and application of wave functions. Some seem to feel that the reality of the particles is actually vested in the wave function.

A straghtforward interpretation in the context of block universe asserts that that fundamental problem is the habit of requiring events to be "caused." Configurations of 4-dimensional worldlines will always manifest a 4-dimensional organization consistent with whatever "measurement events" show up when doing physics. You may develop subjective impressions of a wave collapse resulting in a particle with UP state at A and "causing" a DOWN state particle at B. But, in the 4-dimensional view of the universe there was no causality involved. The 4-dimensional objects are just all there. Any observations of the continuous sequence of instantaneous 3-D worlds performed by any observer will be fully consistent with the static 4-dimensional universe.

Without fully and carefully thinking this through, I would suspect that you would have consistency with SR and entanglement if you do the analysis, using a universal proper time measured from the big bang, The wave function would collapse over the entire universe simultaneously (in the universal time sense) over some 3-D cross-section. Everyone can agree on which 4-dimensional proper time lapse is greater. The proper time lapse from the event at the big bang to event A will be the shorter proper time for all observers, assuming the B event is measured at a later universal proper time (although both particles are created simultaneously with the wave function collapse--unless you prefer to have the 4-D particles with their worldlines there at the start of the experiment). It doesn't matter at all what the local time coordinate values are for various boosted inertial coordinates--it's just irrelevant--the only thing that matters is that there be consistency between SR and entanglement in terms of where the events are located in 4-dimensional space.

So, this is a very interesting topic in physics, one that I've never been able to resolve. I missed homework assignments in grad school due to the distraction of this problem. Someone told me that the Griffiths QM textbook has the best explanation. I'd be interested to hear from anyone who has that text.

[Edit] Text inserted at two or three places from last night and getting up this morning.

 

[zonde]

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 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.

 

[bobc2]

Let's say that you have an entangled particle at hand...

If you have it in hand, then you have collapsed the wave function and the particle now exists in an UP or DOWN state.

 

[Ookke]

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.

 

[bobc2]

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.

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 occurred 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 occurred 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).

 

[harrylin]

[..]
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.

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.