Entanglement and special relativity : a paradox

[notknowing]

Suppose one prepares two particles in an entangled state (at point S) and that one has detectors (say A and B) at opposite equidistant positions, separated by a large distance from S. Now, if one makes a measurement of the spin at A, the spin at B should SIMULTANEOUSLY change to the opposite spin as A. These kind of spooky actions are by now a well established fact. Now, as we all know, according to special relativity, there is no such thing as absolute simultaneous events. What is simultaneous for one observer is not simultaneous for another one moving at constant speed relative to the positions of both events. This means that if one measures the spin at A, such that the spin changes at B, a fast moving observer can see the observation of the spin at B BEFORE the measurement is made at A ! So, this observer will see the effect before the cause ! Since both quantum physics and the special relativity are valid, one would expect that such a situation can really occur. This in turn would imply that one is dealing with signals which go back in time.

I thought to be the first one who thought of this, but this was unfortunately not true . One can find more on internet about this but I could not find or uderstand the solution to this apparent paradox. Has anyone figured out how to solve this ?

 

[pervect]

One way to resolve the issue is MWI or one of its variants, such as decoherence or Everett's original "relative state" hypothesis.

See for instance http://en.wikipedia.org/wiki/Many-worlds_interpretation.

 

[michael879]

Can you explain how someone could view B before A happens? I am not seeing it

 

[pervect]

There is no cause-effect correlation in the EPR "entanglement" experiments. Two distant outcomes are correlated, but there is no cause-effect type correlation in an EPR experiment. One cannot, for instance, send a signal from point A to point B faster than light using an EPR entanglement.

Explaining two different outcomes is of course not directly a problem, one can do so simply with a "common cause".

The interesting part of the EPR problem is that if one assumes local realism, the "common cause" explanation can be shown not to be sufficient to explain experimental results.

Thus EPR does not directly conflict with locality. It conflicts only with locality plus realism, i.e. it conflicts with "local realistic theories".

While it is possible to assume non-locality, it is at the very least an alternative (and in my opinion, a much more popular alternative) to get rid of the assumption of "realism". MWI is one example of how this can be done, an example of what is meant by a "non-realistic" theory.

 

[notknowing]

Can you explain how someone could view B before A happens? I am not seeing it

This is a standard item in special relativity: If A and B are simultaneous in the frame which is stationary to A and B, an observer in a moving frame will see the event at B at a time interval DT earlier where
DT = (v/c**2)*1/SQRT(1-v**2/c**2)*Dx in which Dx is the spearation between A and B (in the frame where A and B occur simultaneously). As v comes closer to c, this time difference can be made arbitrary large. Hence, the moving observer can see B much earlier than A.

 

[notknowing]

One way to resolve the issue is MWI or one of its variants, such as decoherence or Everett's original "relative state" hypothesis.

See for instance http://en.wikipedia.org/wiki/Many-worlds_interpretation.

I am familiar with the MWI and I follow your argument. But let us look again at the actual example (original question). The moving observer will really see the observer at B measuring one spin and only later the observer at A measuring the opposite one (so the opposite order as for the stationary observer). So, the moving observer will conclude that B (or the event at B) causes A, while the stationanry observer will conclude that A causes B. If I understand you correctly, both misinterpret the situation; in this situation there is no actual cause and no actual effect.
What a wonderfull world ...

 

[JesseM]

I am familiar with the MWI and I follow your argument. But let us look again at the actual example (original question). The moving observer will really see the observer at B measuring one spin and only later the observer at A measuring the opposite one (so the opposite order as for the stationary observer). So, the moving observer will conclude that B (or the event at B) causes A, while the stationanry observer will conclude that A causes B. If I understand you correctly, both misinterpret the situation; in this situation there is no actual cause and no actual effect.
What a wonderfull world ...

I think the basic idea is that in the MWI, when A makes a measurement, she splits into different versions, each of which saw a different outcome of her measurement; likewise, when B makes a measurement, he splits into different versions which saw different outcomes of his measurement. But the universe doesn't have to decide which versions of A are part of the same "world" as which versions of B until there's been time for a signal traveling at the speed of light to travel between them, and at that point the matching can happen in such a way as to give the observed correlations between the measurements at the two locations.

 

[nrqed]

I think the basic idea is that in the MWI, when A makes a measurement, she splits into different versions, each of which saw a different outcome of her measurement; likewise, when B makes a measurement, he splits into different versions which saw different outcomes of his measurement. But the universe doesn't have to decide which versions of A are part of the same "world" as which versions of B until there's been time for a signal traveling at the speed of light to travel between them, and at that point the matching can happen in such a way as to give the observed correlations between the measurements at the two locations.

It does solve some aspect of the problem but the creates other questions (which is not a bad thing in itself!). What is the actual "process" by which the entanglement between the different observers occur? How does the "Bob saw a spin up" gets entangled with only the "Alice saw a spin down" and no the other Alice? And does this entanglement occurs only if they physically get in contact (by meeting or calling each other) or does it occur even if they don't (this last question might be simply rhetorical but I am just wondering if there is an agreement on this). And then the question becomes one of consciousness. Once Alice measured the spin, even before she is within a time-like interval with Bob, she will be conscious of having measured a definite spin. So are there really two conscious Alice having experienced two different outcomes which will then go on to live their own existence? How can we say that this does not imply that a new Alice has beencreated at the instant of the measurement?

Just thinking aloud...

 

[pervect]

My impresssion is that the idea of "splitting universes" is not rigorously defined, but a convenient visualization device.

The way I think about it is that the phase space of the universe is very very big - big enough to contain an infinite number of "realistic" universes.

Physics doesn't define when a universe "splits", this is still done by the observer, so its a mental sort of split, not a physical one.

An example might help. Note that this is the way I think of it, not something from a textbook, and that it's going to be described in lose language rather than math. In short, it's basically "philosophical rambling".

Suppose we have a two slit experiment. If the universe really split when the photon went through the slit, we'd have one universe where the photon went through the left slit, and another universe where the photon went through the right slit. If the universes never interacted after the "split", we wouldn't have the fun quantum phenomenon of the photons interferring with each other.

But the whole point of the two slit experiment is that the photons can interfere after one of them went through the "left" slit and the other went through the "right" slit. At least that's the point if you use Feynman's "sum of paths" interpretation. The particles follow "all possible paths" and interfere with each other under this interpretation.

So the situation as I interpret it is that the photon goes through both slits. In terms of multiple universes, the "two universes" still interact, so no definite split has been made.

Eventually, however, the state of the system evloves to a point where quantum interference phenomenon can no longer be observed. At that point, we can effectively approximate the very large phase space universe as two separate, smaller, "realistic" universes which have split apart. They are split just because they don't interact. At this point, things behave clasically, rather than in the very-large-phase space that we need to use when we apply quantum mechanics.

 

[JesseM]

And then the question becomes one of consciousness. Once Alice measured the spin, even before she is within a time-like interval with Bob, she will be conscious of having measured a definite spin. So are there really two conscious Alice having experienced two different outcomes which will then go on to live their own existence? How can we say that this does not imply that a new Alice has beencreated at the instant of the measurement?

It does, according to the many-worlds interpretation--the interpretation says there really are different versions of you experiencing different outcomes of any given measurement, all equally real, although of course none is aware of any "world" but their own. This is one of the reasons that some people find this interpretation hard to swallow, although this seems like more of an aesthetic objection than a philosophical or scientific one.

 

[michael879]

I think the basic idea is that in the MWI, when A makes a measurement, she splits into different versions, each of which saw a different outcome of her measurement; likewise, when B makes a measurement, he splits into different versions which saw different outcomes of his measurement. But the universe doesn't have to decide which versions of A are part of the same "world" as which versions of B until there's been time for a signal traveling at the speed of light to travel between them, and at that point the matching can happen in such a way as to give the observed correlations between the measurements at the two locations.

The universe would only split once actually, after whichever measurement came first. Once A (or B) is measured, the universe splits into one where A is + and B is - and one where A is - and B is + (or --,++ w/e). This does seem like a paradox however since a moving observer would observe the universe splitting before the observer measuring A (A would see it split when he took his measurement while the mover would see it split when B took his measurement). I am a little tired right now but I am sure I could come up with a very good paradox with that situation. Two observers seeing their universe split at different times?

 

[JesseM]

The universe would only split once actually, after whichever measurement came first. Once A (or B) is measured, the universe splits into one where A is + and B is - and one where A is - and B is + (or --,++ w/e).

No, the "splitting" in the MWI is local, the entire universe does not split all at once.

 

[michael879]

o really? I thought the theory was that the whole universe split.

 

[michael879]

No, the "splitting" in the MWI is local, the entire universe does not split all at once.

http://en.wikipedia.org/wiki/Many-worlds_interpretation
according to that the MWI theory says that the whole universe splits. The "universal wave function" is a real deterministic wave that splits into two.
http://en.wikipedia.org/wiki/Many-minds_interpretation
this one says that it is just the "observer" who splits which is what your saying. In this theory only the outcome of the observation splits and the rest of the universe stays the same.

if the MWI theory is true this seems like an interesting paradox. The moving observer could see himself in a different, and split universe while the A observer still sees himself in an unsplit one.

 

[JesseM]

o really? I thought the theory was that the whole universe split.

Ya really! Check out the Everett Interpretation FAQ:

Q12 Is many-worlds a local theory?

The simplest way to see that the many-worlds metatheory is a local theory is to note that it requires that the wavefunction obey some relativistic wave equation, the exact form of which is currently unknown, but which is presumed to be locally Lorentz invariant at all times and everywhere. This is equivalent to imposing the requirement that locality is enforced at all times and everywhere. Ergo many-worlds is a local theory.

Another way of seeing this is examine how macrostates evolve. Macrostates descriptions of objects evolve in a local fashion. Worlds split as the macrostate description divides inside the light cone of the triggering event. Thus the splitting is a local process, transmitted causally at light or sub-light speeds. (See "Does the EPR experiment prohibit locality?" and "When do worlds split?")

For some more technical discussions on how the MWI can be a local theory, here are a few papers:

http://www.arxiv.org/abs/quant-ph/0003146
http://www.arxiv.org/abs/quant-ph/0103079
http://www.arxiv.org/abs/quant-ph/0204024

By the way, where in the wikipedia article did you think it was saying the whole universe was instantaneously split? I looked it over and it only seemed to talk about individual systems splitting, for example:

The many-worlds interpretation is DeWitt's popularisation of Everett's work, who had referred to the combined observer-object system as being split by an observation, each split corresponding to the different or multiple possible outcomes of an observation.

and later

One consequence is that every observation can be thought of as causing the combined observer-object's wavefunction to change into a quantum superposition of two or more non-interacting branches, or split into many "worlds".

(note that they only talk about the "observer-object's wavefunction" splitting into multiple branches, not the entire universe)

 

[michael879]

hmm maybe I read it wrong sorry. They seemed to make a point that MWI wasnt MMI which sounds a lot like what you were talking about.