Special Relativity and Entanglement

[thenewmans]

I’ve been thinking about the implications of Special Relativity on Entanglement. Please tell me if I’m misunderstanding anything here. So let’s say an emitter is a light-year away and sends one entangled photon toward Earth and the other away from Earth. Just when the photon reaches Earth and we measure it, the other photon gets measured at the same angle. So the results match as expected (meaning one spins up and the other down.) We know that the spin was not set at the emitter because of Bell’s well tested theorem. But the photons are measured at the same time only from our inertial frame of reference. It seems to me that you could measure that other photon anywhere along its path and there exists some frame that preserves the two measurements as occurring at the same time. From our frame, the measurements could be years apart. So when a measurement causes wave collapse, you can’t really say which of the two measurements caused it.

Does all that make sense?

 

[DrChinese]

... So when a measurement causes wave collapse, you can’t really say which of the two measurements caused it.

Does all that make sense?

Sure.

 

[thenewmans]

Thanks Doc!

 

[DevilsAvocado]

thenewmans, I think 'someone' in this thread is having just a little too much fun... no names, no fingers.

Your question is excellent, and in fact – this is one of hardest problems to solve regarding entanglement and EPR-Bell experiments!

Why!?

Because, as you point out, the values of the photons cannot be set at the source, and the entangled pair share the same wavefunction, and this wavefunction can only decohere once, and then the entanglement is broken, once and for all.

As you see, either Alice OR Bob must set the outcome, and this just doesn’t work with our current understanding of Special Relativity and inertial frame of reference...

Anyone still smiling??

 

[K^2]

It's only a hard problem in Copenhagen Interpretation. Go to Many Worlds Interpretation and it's easy as pi. Since interpretations are actually equivalent, when you run into situation like this, choosing the right interpretation to use is very important.

 

[thenewmans]

thenewmans, I think 'someone' in this thread is having just a little too much fun... no names, no fingers.

Your question is excellent, and in fact – this is one of hardest problems to solve regarding entanglement and EPR-Bell experiments!

Why!?

Because, as you point out, the values of the photons cannot be set at the source, and the entangled pair share the same wavefunction, and this wavefunction can only decohere once, and then the entanglement is broken, once and for all.

As you see, either Alice OR Bob must set the outcome, and this just doesn’t work with our current understanding of Special Relativity and inertial frame of reference...

Anyone still smiling??

Well DrChineese has earned my respect. So if he has fun at my expense, I can accept that. So why must the outcome be set by either Bob or Alice? I'm hoping you can give me some clues I can follow up on and learn more. From what I've heard of Dirac, he did a good job at combining SR and QM. So I figure there must be something there for me to sink my teeth in. Plus, my understanding is that there really is no conflict between the two since no info travels FTL. I can accept that too.

 

[thenewmans]

It's only a hard problem in Copenhagen Interpretation. Go to Many Worlds Interpretation and it's easy as pi. Since interpretations are actually equivalent, when you run into situation like this, choosing the right interpretation to use is very important.

So K^2, How does MWI help me understand this? I know MWI only superficially. Just from guessing, from one world, the wave collapse is initiated from one end. And from the other world, it was initiated from the other end. Am I close?

 

[Alvasin]

Special relativity is bound up with the impossibility of transmitting messages faster than the speed of light. If special relativity is true, no material carrier of a message can be accelerated from rest to speeds greater than that of light. A message transmitted faster than light would, according to some clocks, be a message that arrived before it was sent, potentially unleashing all the paradoxes of time travel.

 

[K^2]

So K^2, How does MWI help me understand this? I know MWI only superficially. Just from guessing, from one world, the wave collapse is initiated from one end. And from the other world, it was initiated from the other end. Am I close?

In MWI, there is no such thing as wave function collapse. When you observe a state, you become entangled to that state. Think Shroedinger's Cat. Say you measured spin of a particle. The total state of the system is now (you measured "up" * spin is "up") + (you measured "down" * spin is "down"). Because of linearity, your state of having measured "up" cannot interact with state where you measured "down", so after the measurement, you can only observe the measured spin as being "up". And vice versa. If you measured down, you can now only observe it as down. Subsequent measurements don't make a change to this state. Result is apparent wave function collapse.

Now suppose you have two people making measurements on two particles from entangled pair. Each person is now entangled to his own particle, but because the particles are entangled, so are now the two persons who measured the states. They both end up measuring "up" or "down" with equal probability, but if they happen to exchange information about the experiment, the person that measured "up" can only interact with the state of the other person who also measured "up". Hence both particles appearing to collapse, and it doesn't matter which person started the experiment and even if they did it at the same time.

 

[DevilsAvocado]

It's only a hard problem in Copenhagen Interpretation. Go to Many Worlds Interpretation and it's easy as pi.

Sure, I have always been a big fan of physical proofs. If you just show me which of the many doors to enter, I’ll go check it out...

 

[DevilsAvocado]

Well DrChineese has earned my respect. So if he has fun at my expense, I can accept that.

DrCheese?? Who is that!?

Serious, we are all a bunch of old laughing farts in this forum, and I was joking as well. DrC has taught me almost everything I know about EPRB, and I think he can "take it".

So why must the outcome be set by either Bob or Alice? I'm hoping you can give me some clues I can follow up on and learn more.

Entanglement is the translation of Erwin Schrödinger’s term Verschränkung. According to Anton Zeilinger, entanglement is not as describing as the German term:

I.e. the objects that make up an entangled system (pair) are linked in such a way that the system cannot be adequately described without full mention of the other members of the system – they are a part of the same system even if the individual objects are spatially separated.

Think of the shared wavefunction as a "virtual rubber band" that 'carries' this link between the objects.

Q: How many times can you cut a rubber band before it becomes useless?

Plus, my understanding is that there really is no conflict between the two since no info travels FTL.

That is correct. The outcome in EPRB is always 100% random = 50/50 = random noise. This cannot be used to send "messages". The key point in EPRB is correlations, and these are always checked afterwards, when the data is in the in same spatial location.

But, there must be "something going on", that travels much faster than the speed of light, and this is when you get into conflict with SR...

 

[DevilsAvocado]

How does MWI help me understand this?

http://en.wikipedia.org/wiki/Many-worlds_interpretation"

[PLAIN]http://upload.wikimedia.org/wikipedia/en/thumb/b/b7/MWI_Schrodingers_cat.png/500px-MWI_Schrodingers_cat.png

 

[DrChinese]

Well DrChineese has earned my respect. So if he has fun at my expense, I can accept that. So why must the outcome be set by either Bob or Alice?

I promise I was not making fun of anyone... except maybe myself, DrMac&Cheese.

Seriously, you cannot strictly say that either Alice or Bob collapse the wave function unless you postulate a physical mechanism to go with it. So it is easy for me to agree with what was said in the first post. It is "AS IF" there is a hypersurface in which Alice and Bob participate in the collapse simultaneously. That hypersurface would not correspond to spacetime as envisioned by SR or GR.

 

[thenewmans]

Serious, we are all a bunch of old laughing farts in this forum, and I was joking as well. DrC has taught me almost everything I know about EPRB, and I think he can "take it".

DevilsAvocado, thank you for helping me with this. Where would we all be without DrChinese? I hope he feels the appreciation.

But, there must be "something going on", that travels much faster than the speed of light, and this is when you get into conflict with SR...

You have said a key phrase for me here. Sometimes I hear myself saying something similar and I feel as if I'm painting myself into a corner. And this is the essence of my original post. It seems to me that your statement implies things like a direction, simultaneity and a preferred inertial frame of reference. From an SR point of view, describing events usually requires selecting an inertial frame of reference. But changing that frame does not change what actually happened. In other words, if someone travels past Alice at 95% C just as Alice measures the photon, does that “something” (wave collapse?) travel FTL from his point of view as well? As I follow this line of reasoning, it only gets worse. Keep in mind that the 2 photons are traveling in completely opposite directions. That puts them both completely outside of each other’s past and future cones. It seems to me like the only solution is to say that there’s no way to determine which measurement was done first.

At a philosophical level, I understand that QM must break some classic principal we hold dear. But why must local realism be the most common victim? I get the feeling it's a popular whipping boy simply out of some lack of knowledge. It seems to me like an unnecessary assumption.

 

[DevilsAvocado]

... except maybe myself, DrMac&Cheese.

You’re the BEST!

Kindest Regards
SatansGuacamole

 

[DevilsAvocado]

... there’s no way to determine which measurement was done first.

Absolutely right! According to SR there is no universal NOW and hence it’s impossible to decide which comes first and after.

As far as I understand this matter, QM and EPRB needs that universal NOW to determine when the entanglement is no more, so to speak, and BOOM there you have a BIG (and very interesting) conflict.

But why must local realism be the most common victim?

Well, Local + Realism is dead, stone dead. If you take only one of them, it’s okay, if the other is killed. You could say: Okay, then I take locality and kill realism! This will mean we have something called non-separability and I am not the man to explain exactly what this means, but you can read more about it here:
http://plato.stanford.edu/entries/physics-holism/"

 

[thenewmans]

As far as I understand this matter, QM and EPRB needs that universal NOW to determine when the entanglement is no more, so to speak, and BOOM there you have a BIG (and very interesting) conflict.

Wait, so you're saying that there is a preferred inertial frame of reference in QM? I thought ideas like that died out 100 years ago with Lorentz. Are you coming at this from a particular interpretation or is that the case for all interpretations?

Oh, and maybe I should ask what EPRB is. All this time I thought you were mistyping EPR. I can't find EPRB in wikipedia.

 

[K^2]

As far as I understand this matter, QM and EPRB needs that universal NOW to determine when the entanglement is no more, so to speak, and BOOM there you have a BIG (and very interesting) conflict.

No. EPR works in RQFT, where NOW depends on the frame of reference.

 

[thenewmans]

In MWI, there is no such thing as wave function collapse. When you observe a state, you become entangled to that state. Think Shroedinger's Cat. Say you measured spin of a particle. The total state of the system is now (you measured "up" * spin is "up") + (you measured "down" * spin is "down"). Because of linearity, your state of having measured "up" cannot interact with state where you measured "down", so after the measurement, you can only observe the measured spin as being "up". And vice versa. If you measured down, you can now only observe it as down. Subsequent measurements don't make a change to this state. Result is apparent wave function collapse.

Now suppose you have two people making measurements on two particles from entangled pair. Each person is now entangled to his own particle, but because the particles are entangled, so are now the two persons who measured the states. They both end up measuring "up" or "down" with equal probability, but if they happen to exchange information about the experiment, the person that measured "up" can only interact with the state of the other person who also measured "up". Hence both particles appearing to collapse, and it doesn't matter which person started the experiment and even if they did it at the same time.

Thanks K^2. I meant to ask you a follow-up. In MWI, let’s say Alice measures spin up. In that case, we know Bob will measure spin down or has already measured spin down. (My understanding is that the measurements should turn out opposite if done at the same angle.) So they’re both in the same MWI “state”. So does MWI have anything to say about who measured first? Or which measurement caused the world to split into two MWI states? Or am I correct in saying that there’s no way to determine that?

 

[yuiop]

No. EPR works in RQFT, where NOW depends on the frame of reference.

Please elaborate. How does EPR work in RQFT. Does that require non-localism or non-realism? I guess non-realism, as you seem to be advocating the MWI.

 

[DevilsAvocado]

No. EPR works in RQFT, where NOW depends on the frame of reference.

Please elaborate.

(I guess you just dismiss the whole EPR-Bell question thru MWI, but when do we get the physical proof for this interpretation?)

 

[DevilsAvocado]

Wait, so you're saying that there is a preferred inertial frame of reference in QM? I thought ideas like that died out 100 years ago with Lorentz.

And a lot of things that lived 50 years ago are dead today, like Local Realism.

I’m usually very careful to not come up with "personal speculations" and the tension and incompatibility Bell's theorem creates between QM and SR comes from the man himself http://en.wikipedia.org/wiki/John_Stewart_Bell" .

I’ve seen him on a video from 1990 (shortly before he died) saying these words, so there’s no guessing on my behalf.

You got to realize that these questions are not settled yet. We could have non-locality + realism, or locality + non-realism, or non-locality + non-realism. We just don’t know the correct answer yet.

Furthermore, logic says that either QM or SR must be 'slightly' wrong, but at the moment we have no idea which. They are both very solid theories and to my understanding – there must be "a big prize" waiting around the corner for the person(s) who crack this nut...

Oh, and maybe I should ask what EPRB is.

Sorry, my fault: EPRB = EPR-Bell = EPR-Bell experiments = http://en.wikipedia.org/wiki/Bell_test_experiments"

 

[DevilsAvocado]

So they’re both in the same MWI “state”. So does MWI have anything to say about who measured first? Or which measurement caused the world to split into two MWI states? Or am I correct in saying that there’s no way to determine that?

You should also ask K^2 this question: In MWI, when there’s a 50/50 outcome both always gets 'materialized' in different branches (worlds). Now, if you toss a coin a 100 times you expect to get approx 50 heads & tails, right?

But in one of these MWI branches some poor bastard will always get 100 tails, every time he performs this 'experiment'!

What is K^2’s advice to this guy? Just forget about it?? Or rewrite all laws on probability?? Or just show the "MWI-sign" if anybody ask 'difficult' questions??

 

[yuiop]

You should also ask K^2 this question: In MWI, when there’s a 50/50 outcome both always gets 'materialized' in different branches (worlds). Now, if you toss a coin a 100 times you expect to get approx 50 heads & tails, right?

But in one of these MWI branches some poor bastard will always get 100 tails, every time he performs this 'experiment'!

What is K^2’s advice to this guy? Just forget about it?? Or rewrite all laws on probability?? Or just show the "MWI-sign" if anybody ask 'difficult' questions??

If each time Bob tosses a coin the universe splits into two universes, one where Bob got a head and one where he got a tail, then after 100 coin tosses there will be 2^(100) = 1.267E30 new universes. MWI is not very economical on resources.

However, MWI does not defy the laws of probability as far as I can tell. The probability of getting 100 tails is 1/2^(100) but if you have 2^(100) universes, then yes there will be one universe that contains a version of Bob that got a hundred straight tails in a row. If the experiment is repeated there is a 1/2(100) chance that the Bob that got 100 tails the first time around will get 100 tails the second time around which is (very) far from saying that the same Bob will get 100 tails every time the experiment is carried out.

 

[K^2]

There is a 1/10^30 chance that you'll get heads 100 times in a row. There is a 1/10^30 chance that you'll observe a world where 100 heads come in a row. Either way, you just won some cosmic lottery. (And all you got was this lousy t-shirt.)

How does EPR work in RQFT

Same way it does in classical QM. You can have entangled states, and you collapse both by measuring either one. If both are measured, which measurement results in a collapse depends on your frame of reference.

 

[A. Neumaier]

logic says that either QM or SR must be 'slightly' wrong, but at the moment we have no idea which. They are both very solid theories and to my understanding – there must be "a big prize" waiting around the corner for the person(s) who crack this nut...

Maybe your logic says so, but there is no conflict between QM and SR. Our best theory, QED, combines QM and SR to produce the most accurate predictions we ever had. And QED is the basis of quantum optics, the discipline which performs all these wonderful experiments on entanglement. Nothing wrong there, only somewhat of a no man's land at the very foundation (just as in most disciplines if you dig deep enough).

http://arxiv.org/pdf/quant-ph/9906034
shows how measurements in a relativistic context are compatible with SR and QM.There seems to be a conflict between QM and _general_ relativity, but even this is not clear cut.

 

[DevilsAvocado]

There seems to be a conflict between QM and _general_ relativity, but even this is not clear cut.

Okay, give me a link to the final solution of Quantum Gravity, and then we can start to discuss what’s seems logical or not.

 

[K^2]

Quantum Gravity is a proposed resolution to conflict between Quantum Mechanics and General Relativity. Resolution to conflict between classical QM and SR is called Relativistic Quantum Field Theory, and it works. I deal with RQFT on daily basis, because without that we wouldn't really have particle physics.

 

[A. Neumaier]

Okay, give me a link to the final solution of Quantum Gravity, and then we can start to discuss what’s seems logical or not.

http://lanl.arxiv.org/pdf/2504.0375

 

[DevilsAvocado]

http://lanl.arxiv.org/pdf/2504.0375

That looks real promising.