# Entanglement Effects in Relativistic Reference Frames

1. Dec 19, 2007

### peter0302

Hello all -

New to the forums so let me start by saying hi to everyone. ;)

Something has always bugged me about considering entanglement effects as "instantaneous." As we all know from SR, moving observers do not agree on simultaneity between two space-separated events.

If we consider the entanglement effect to be "instantaneous" do we not have a problem when we consider the relativistic observer in the following thought experiment?

Say we have two entangled electrons (E1 and E2) moving in opposite directions, each at .9c relative to the lab. Observers A and B, however, are riding the particle accelerator with E1 and E2, respectively, matching their speeds perfectly. When A performs a measurement on E1, the "influence" is "instantaneously" felt by E2. But instantaneous for whom?? A? B? A stationary observer in the lab? All of the above?

And at the time A makes a measurement, believing it to travel "instantaneously" to B, in B's frame that measurement has not yet occurred. Thus, will the "influence" travel backwards in time for B? If B made a measurement BEFORE (in his frame) A did, will the Bell correlations hold? If not, can we not infer a "speed limit" for the quantum influence? If so, can we conclude anything other than non-causality or retro-causality?

Would love to hear your thoughts!

Peter

2. Dec 19, 2007

### cesiumfrog

Basically, this argument is moot because the "influence" does not convey any information. Specifically, nothing is "felt" by E2.

Think of it like a shadow: I can make my shadow move between stars faster than the speed of light. If observers from each star compare notes afterward, they will see a correlation between their measurements. But it doesn't bring causality into question.

Last edited: Dec 19, 2007
3. Dec 19, 2007

### peter0302

I disagree that it's moot, but in any event the question still has a yes/no answer. Will the Bell inequalities be violated with the same distribution in my thought experiment as they would for stationary observers? And how do we interpret either answer?

I'm not interested in conveying information; I'm interested in how entanglement relates to causality, and whether or not the influence is reverse-causal or non-causal.

4. Dec 19, 2007

### peter0302

Also, I might add, "information" and "influence" are different things. The assumption (well supported by the data) is that the measurement of E1 affects the outcome of the measurement of E2. Whether E2 is conscious of the influence does not change the fact that it happened, any moreso than my ignorance of my relative velocity with respect to a distant star affects that velocity.

Thus, my "argument" / question is whether it might be possible to, using relativistic observers, "beat" the speed of the influence? If not, must not the "influence" travel backwards in time?

5. Dec 19, 2007

### cesiumfrog

This should really be in an FAQ somewhere..

That sounds like a self-contradiction, I'm not sure quite what concept you're thinking of when you use the word causality.

When you say "affects", a physicist would only say "is correlated with". One reason for this choice of words is to emphasise the lack of any time directionality in the theory (well supported by the data).

I could answer this by returning to the shadow analogy. The results of the experiment do not depend on who makes the measurement first (correlation, not causation). Hence, the fact that they disagree on the order of the measurements does not affect the results nor the theoretical predictions. There is no speed for the observers to try to beat, and hence they cannot beat it. Nonetheless, this does not imply retro-causality (although some people have chosen to explore retro-causal models anyway.. these have generally been successful in reproducing existing features of QM, but have recently led to embarrassment instead of progress).

Last edited: Dec 19, 2007
6. Dec 19, 2007

### mgelfan

The entanglement "effect" is instantaneous because wrt quantum theory it's evolving in an imaginary space. You're considering global changes (the joint measurement of events at A and B) -- so if something at either A or B is changed, then the global situation is changed ... instantaneously.

Quantum entanglement has a technical (and not necessarily intuitive wrt real space and real time) definition, and this has to do with the mathematical (and probabilistic) nonseparability of events at spatially separated locations.

Experimental violations of Bell inequalities indicate that the data streams at A and B aren't statistically independent. What this means wrt the possible existence of superluminal or instantaneous causal influences in nature is a matter of speculation and interpretation.

As far as quantum theory is concerned, it's acausal.

7. Dec 19, 2007

### peter0302

Not sure if you're implying that the answer is obvious, but I do not think it is. Further, you still haven't answered my question. Does the correlation hold for very fast moving observers? I take it you're assuming the answer is yes and you believe the answer obvious.

Causality:
"Cause" affects "Outcome" if:
p(Outcome|Cause) != p(Outcome|!Cause)

I do not see how you can interpret the correlations seen in Bell experiments as anything other than causality. If you measure one particle in one way, the results of the both measurements, including the distant one, will be different than if you had measured the first particle in a different way. The results are predictalbe. It is clearly not random. That the final results depend upon both measurements, or that the correlation is only evident in large statistical samples and calculated after-the-fact does not change this.

There is a cause and effect; the question is what sequence in time those occur. You say there is no temporal sequence and therefore the quesiton is moot. I say that the lack of a temporal sequence is anything but moot. My argument, I guess, if I have one, is that entanglement must more than non-local; it must be non-temporal as well. Is that obvious? If so, it wasn't to me.

You say lack of time directionality is well supported by the data. May I ask to what you are referring? Experiments such as the delayed choice quantum eraser suggest to me that there is either 1) backwards-in-time influence upon the ealrier photon when the latter photon is detected _or_ 2) hidden information, in the form of a newly "collapsed" wavefunction, that is bestowed upon the latter photon while en route to the detector after the earlier one is detected, implying a message sent by the earlier detected particle to the second informing it how to behave. Both ideas seem absurd, yet I do not know either interpretation to have been proven or disproven.

You choose to argue mootness because the results are always the same regardless of who is believed to make the first observation. Yet what you are saying, in fact, is that the outcome is dependent upon two events, irrespective of their spatial OR temporal separation and sequence. How can you argue that this does not imply non-local AND non-temporal influence!?

Are you referring to the Cramer experiment? If so I had not heard of any negative result, and as I look at the experiment, I cannot see the flaw. What other embarassing events are you referring to?

Last edited: Dec 19, 2007
8. Dec 19, 2007

### kdv

very good questions. Basically, the way I see it, causality and entanglement can'tbe reconciled. Causality is a classical concept that must be dropped in the quantum world. All theer are are correlations between the two measurements and everybody agrees on those. Trying to identify a cause and an effect (is it the measurement at A that causes the collapse at B or vice versa?) is pointless since, as you said, one cannot even say which event occurred first in an invariant way.

I personally think that there is something deep behind this, that it is a fact that points to more fundamental laws of physics that what we have now but most people react by saying "There is nothing to it, there is no actual propagation of energy or information so that does not bother me". It's a bit like the equivalence of the gravitational and inertial masses. Many people knew about that before Einstein but just thought "So what?". It took Einstein to dig more and realize it led to a totally new view of the gravitational force. I think that the entanglement/causality issue points to a need for a reworking of our fundamental notions of space, time and interactions. But Most physicists seem to feel that there is no big deal.

9. Dec 19, 2007

### peter0302

Yes, that is exactly my point, made much more succinctly than I was able to do. ;) Assuming the correlations hold true for fast-moving observers, one simply cannot reconcile "classical" causality and quantum mechanics. Perthaps my error was calling it "retrocausation" - it is non-causal.

Agreed completely, and with due respect to the other poster, I don't see how this question is moot, nor how any retrocausality experiments (even unsuccessful ones) can be "embarassing," any more so than questions about the invariance of the speed of light were "moot" following Michelson-Morley's "embarassment". This is my single biggest criticism of Copenhagenists - their answer to everything is "the wave function isn't real, so who cares".

Unfortunately it will probably take a mind on par with Einstein's to resolve the issue, which I could never hope to possess. I will say this, though - Einstein had a hunch something was "spooky" about this entanglement business before anyone else did. While the EPR paper obviously has its weaknesses, Bohr's response was incoherent, and EPR's basic argument has yet to be proven wrong. And I, for one, will take Einstein's hunches over just about anyone else's "facts".

10. Dec 19, 2007

### cesiumfrog

There should be a (long and detailed) FAQ on this issue, because it is a very frequent cause of misconceptions. I'm not certainly not implying that the answer (viz. yes) is obvious, but it is well known. (Perhaps if you concentrated on the DCQE, you would repeat one of the exact proposals we've shot down before, and you could just search for the archived thread..)
This is a fundamental mistake. The results of the distant measurement *do not depend* on the manner in which the other particle is measured. (They are strongly correlated, even more so than the many similar classical examples we could give. If you so choose, you may validly "interpret" this as being due to retro-causal influences, but such is not the only valid interpretation, and experiments do not distinguish between interpretations, by definition.)

Yes, I did refer to Cramer's experiment. He apparently intends to publish a work of fiction rather than a negative result. The embarrassing flaw in his proposal is basically that his design is based on a previous experiment, but presumes the incorrect outcome from that experiment. (I actually once contacted him to ask for details of his apparatus, because I suspect that, with a corrected application of his own interpretation, even he would concede that his FTL communication will only give the same results that preceding experimentalists have already published.)

I am sorry.

11. Dec 19, 2007

### peter0302

I will perform that search, thanks for the info.

I may be wrong, but I feel you're taking more issue with my languange than my point. Let me try to be more precise:

First, again, all I mean by depend/cause is:

p(Effect|Cause) != p(Effect|!Cause)

So, if I send photon A through a 0 degrees polarizer and I send entangled twin B through a 90 degrees polarizer, there is no chance they will both emerge.

p(Both Pass|Polarizers at 0, 90) = 0

If I send photon A through a 0 degrees polarizer and B through a 45 degrees polarizer, there is a 50/50 chance they will both emerge.

p(Both Pass|Polarizers at 0, 45) = .5.

Clearly, moving polarizer 2 from 90 to 45 caused the probability of "both pass" to change, based on my definition of causality.

So at the very least, we can all agree, I think, that the choice of polarizer angles affects the probability of a correlation. No shock there. And that is all I mean by cause and I don't exclude the possibility of there being a common cause. Perhaps this is what you mean by correlation, and if so, I'll use that language instead.

Anyway, back to QM, we also should be able to agree that if photon A passes through a 0 degrees polarizer, the probability that photon B will pass through a 45 degree polarizer is different than if photon A had passed through a 22.5 degree polarizer.

p(B passes 45|A passes 0) != p(B passes 45|A passes 22.5)

So then we turn to the "interpretation." It may well be that the likelihood of B's passage through a 45 degree polarizer and A's passage through a 22.5 degree polarizer have a common cause C, and that the likelihood of B's passage through a 45 degree polarizer and A's passage through a 0 degree polarizer also have a common cause, C'. In fact, maybe C and C' themselves have a common cause. Maybe it was all determined at the time of the Big Bang, or maybe this can be explained by an as-yet undeveloped hidden variable theory, some variation on chaos theory, or world-splitting - I don't know. Or maybe whether A passed the polarizer did cause the probability to change, and I use the word cause intentionally.

What I do know is that the Copenhagen answer is essentially useless to an understanding of the nature of the universe, and all of the other theories I've seen would make Bill Occam wish he had a chain saw! But to reiterate the point of my first post: the thought experiment involving relativistic observers is meant to emphasize what the other poster said, that classical causation cannot be reconciled with quantum mechanics because there is no way to agree on the sequence of events in an invariant way. You say it's moot, but I believe that these phenomenon might help us better understand causality on all levels and COULD lead to breakthroughs in communication or in other areas. It certainly doesn't hurt to explore!

Well that is certainly disappointing and, may I say, downright crappy considering the donations from the public he received.

I'll search here for threads on this experiment because I'm quite curious what the flaw is - perhaps it would aid my understanding as well because, as I said, I didn't see it.

LOL. This is what I love about physics - the more things change, the more they stay the same. Men become giants, then get discredited by the next generation of giants, only to be vindicated by the third generation!

Last edited: Dec 19, 2007
12. Dec 19, 2007

### colorSpace

No, Peter is right, and that is why there is "non-locality" at all. For example, for the spins of two entangled particles, the spins will always be opposite, when measured along the same direction. If measurements at B were independent of A, they would sometimes be the same, but they are never. While it is possible to construct local-realistic models that could explain this for measurements along the same direction, these models will fail when using different directions, as the Bell-theorem-related experiments have proven. Otherwise there would be no point in talking about "non-locality".

However, it turns out that this influence is symmetrical, that is, an observer who will see B as being measured first, will see a similar influence, but causally backwards.

So it is not "acausal", but "symmetrically-causal", so to speak. Weird...

Last edited: Dec 19, 2007
13. Dec 20, 2007

### cesiumfrog

Yes, but I wanted to emphasise this:
p(B passes 45|A passes 0 or gets blocked) == p(B passes 45|A passes 22.5 or gets blocked)

So although the two data streams are non-classically correlated, the link is not causal (analogous to how flies on a wall might make superluminally correlated light measurements as a shadow passes by, despite there being no possibility for the flies to communicate superluminally).

What doesn't change is the result of past experiments, so as long as you trust experimental facts before opinions (even of old "giants") you can't go too far wrong. Ciao.

14. Dec 20, 2007

### colorSpace

The example with the flies suggests that the "two data streams" could have a common classical source, but these possibilities have meanwhile been experimentally ruled out.

One example is entanglement-swapping, where two pairs of entangled particles, which have no common source, are entangled via one of the particles of each pair, resulting in the other two particles of each pair being entangled as well, and showing conforming results, reflecting their measurement angles, even though they have never met nor do they have a common source.

[Edit-added:] And since they have no common source, the (often 100%) correlation must be a result of the two particles communicating, or being connected, with each other.

Last edited: Dec 20, 2007
15. Dec 20, 2007

### peter0302

Agreed that B's pass rate correlates to both the direction of A's polarizer AND whether A passes through it. But that does not contradict mine and colorSpace's point - there is a correlation between two events regardless of their spatial separation AND temporal sequence. Absent a common cause, non-local / non-temporal influence cannot be ruled out.

I hesitate to use the word "must" but I certainly agree that cannot be ruled out!

16. Dec 20, 2007

### colorSpace

It wasn't quite clear that quote is from me. Now that you point it out, I'm looking for a better word as well, but knowing about the many experiments etc, that have been made meanwhile (in the last decade), it seems the only plausible explanation.

Another (small) point is that cesiumfrog uses the expression "data streams" as if the particles were simply producing data that always corresponds in the same way. But if one measures them in different directions (relative to each other), then their "output" will correspond much differently (less) then if one measures them in the same direction (relative to each other). This means the "data" produced depends on the relative direction of measurement, it is not always the same data. Even though that should be already obvious, I wanted to point out that this interpretation isn't possible. (Or doesn't seem to be :) )

17. Dec 20, 2007

### peter0302

Well, the fact that the correlation is influenced by the measurement angles, in itself, is nothing revolutionary. If I cut a coin in half and set up one detector to only let through heads and the other to only let through tails, 100% of the time they'll either both pass or both fail. If I set the detectors both to heads or both to tails, the detectors will never both get the same result. Just changed the correlation by changing the measurement apparatuses.

The reason the qm behavior is so wierd is not because the correlations change but because they change exactly according to the cosine of the angle between the detectors for _all_ delta-thetas, not just 0 and 90 degrees. This forces one to conclude that it is at least _possible_ that the angle of a detector is influencing and, hence, causing the result of the other. As I said, other explanations exist, but are either useless (Copenhagen), self-proving (many worlds), or a downright mess (TI).

There's a talk of Bell's printed in "Speakable and Unspeakable" that was given at a Symbosium on Frontier Problems in High Energy Physics in 1976. In that talk he explains quite eloquently (and mathematically flawlessly as far as I can tell) why the correlations cannot be reproduced in any local realistic way and just how close you can get to reproducing them. The closest you can get, he argues, is essentially a discontinuous saw-tooth wave, whereas the q-m predictions are obviously sinoid. Definitely worth checking out for anyone who hasn't already.

18. Dec 20, 2007

### peter0302

You know, while I'm at it, I was thinking about one of the first criticisms Einstein gave to Bohr, which is widely ridiculed but I suspect the key to unraveling this nonsense.

He essentially said take a single electron and shoot it through a slit with a detector on the other side. Before impact, for every atom in the detector there is a non-zero probability of impact. But after the impact, the probability of the electron hitting any other atom of the detector instantly becomes zero. How do the other atoms in the detector "know" the electorn didn't hit them if the electron existed as a probability wave at every point on the detector prior to the impact? Can't we say that the electron is entangled with the entire detector, and therefore the observer and, indeed, the whole universe, simply by virtue of its existence? Doesn't its existence affect the wave function of the entire universe, even if slightly?

Can we perhaps explain the apparent non-local interaction of two distant particles using the knowledge that the probability of a local, deterministic interaction between them, while infinitessimally small, is still non-zero, and, since an interaction, unlikely as it may be, is the only way to preserve the laws of physics, the interaction nonetheless must occur?

Another random, perhaps even more useless thought. The idea of photons "communicating" with each other across vast distances of space and time really should cause us no diffulty, as a photon, travelling at c, essentially exists simultaneously at all points in the universe for an instant in time. Perhaps there is only one photon, just as there is only "one electron."

19. Dec 20, 2007

### colorSpace

No, that is not revolutionary at all, but it does counter the (perhaps superficial) impression that the two particles might simply produce data streams which are correlated in any case, completely independent of the measurement angles.

It is, so to speak, a trivial disproof of one of the most simple local hidden variable theories possible, and I'm mentioning it only to keep quick readers from getting a wrong impression of the nature of the phenomenon.

It seems that in Internet discussions the edge cases which are considered to disprove (using Bells theorem) even very complex local hidden variable theories, are often confused with the phenomenon of entanglement itself.

Entanglement also works in much simpler ways than in those edge cases, and that's one of the points I'm trying to make here, as I see that often being confused.

20. Dec 20, 2007

### colorSpace

I'm not sure I'm getting your point, but there is 3 major ways (AFAIK) to "trivialize" or "overcomplexify" entanglement:

1. The assumption that there could be information from a common source.
2. The assumption that there is a classical communication between the particles or measurement apparatus (or via a third party).
3. The assumption that there isn't anything interesting going on, in the first place.

Each of these have been disproved, but often the disproof of one increases the likelihood of a misunderstanding that one of the other could be the case.

21. Dec 20, 2007

### peter0302

I'm not sure I have a point. ;) But if I do, it's that the wave function itself allows for the possibility (albiet EXTREMELY remote) of even distant particles interacting in a seemingly local way, simply by virtue of the probability wave being non-zero everywhere. Similar in concept to tunnelling. Just throwing that out there, for what it's worth.

22. Dec 21, 2007

### colorSpace

That's actually something I was wondering about many times, though I didn't read about it recently anymore. Do you have a link? Is tunneling exactly this, or is this more general?

BTW, there are recent reports that enzymes might do their work using tunneling, to speed up biological processes by a factor of more than a million. But it didn't seem to be confirmed yet.

23. Dec 22, 2007

### mgelfan

When one side, say A, records a detection event, then this affects the sample space at B, limiting it to a certain coincidence interval surrounding the detection at A. The size of the interval is determined by a number of factors including the distances of A and B from the emitter, the type of effects being produced (optical or whatever), etc.

The probability of detection at B, for an observer at B having no knowledge of the axis of detection at A (eg., the setting of a polarizing filter), remains .5. Same for an observer at A who has no knowledge of B's setting. But if both settings are known, then it might be said that the conditional (or joint) probability of detection is proportional to
cos^2 theta, where theta is the angular difference between the settings at A and B.

The probability of joint detection has no physical meaning for individual detections. The probability of individual detection at either A or B remains .5 for any and all future measurements at A or B.

The probability of joint detection has no physical meaning for individual joint detections either. These probabilities are statements that only become physically meaningful when related to large statistical samples.

It's unknown whether an interaction between a disturbance incident on the filter at A has any physical affect on the disturbance incident on the filter at B for the same coincidence interval. However, a subsequent detection does cause (instantaneously ) some changes. It's assumed that, given a detection at one end, say A, then only disturbances impinging on B during the interval associated with detection at A are related to events at A -- all others are screened out via coincidence circuitry.

24. Dec 22, 2007

### colorSpace

I'm not sure what you are saying here, but if it is the question of whether there is a non-local effect even when the measurements are performed at exactly the same time, then I'd think that the answer needs to be, in theory, that the non-local effect needs to take place even then. For example in the case of entanglement via spin, the declared "motivation" for the effect is to conserve momentum, the spins need to add up to zero, so they are always opposite when measured along the same direction. This would have to be the case, it would seem to me, even if the measurements are performed 'exactly' at the same time. This also seems to be the general concept of entanglement as an immediate connection, rather than as a transmission in time.

However, if that is what you meant with the last paragraph, then I'm also not sure how it would be related to the original question, if it is.