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bobc2 Apr2-11 09:50 PM

Special Relativity and Enganglement
 
Here is an attempt at representing a two-photon enganglement situation as analyzed in spacetime for two observers (red and black in sketch below) moving in opposite directions at the same relativistic speeds with respect to the black rest system shown in the sketch.

Let's say that the photon moving to the left is found to be in the UP state at event A by an observer at rest in the red frame. Then the photon moving to the right snapes to the DOWN state at event B. I have the following puzzling questions:

1) If the right photon is in a DOWN state at event B, then in the blue coordinate system that would seem to snap the left photon into an UP state at event C. But that event precedes event A, implying a reverse causality, that is event A has caused the past event C.

2) Once event A has snapped the left photon into UP, how does nature decide which observer's frame of reference to snap the right photon into? The black reference frame would have the right photon snapping to DOWN at event D.

3) Would a chain of events be released, i.e., event C causes the right photon to snap to DOWN at event E, etc.?

http://i209.photobucket.com/albums/b...anglement3.jpg

DaleSpam Apr3-11 07:14 AM

Re: Special Relativity and Enganglement
 
Let's say that there was a measurment at B. Then (according to my knowledge) in the blue frame the wavefunction of the other photon collapses at C and in the red frame the wavefunction of the other particle collapses at A.

Calrid Apr3-11 07:25 AM

Re: Special Relativity and Enganglement
 
Yeah as long as the time line doesn't show a simultaneous or reverse causality and I can't see how it does here then that looks pretty much like the correct transform in that situation. I suppose technically the speed of transfer of information would have to be shown as less than c but I'm sure that would be a semantic issue unless the distance between entanglement was extremely large.

bobc2 Apr3-11 08:15 AM

Re: Special Relativity and Enganglement
 
Quote:

Quote by DaleSpam (Post 3226670)
Let's say that there was a measurment at B. Then (according to my knowledge) in the blue frame the wavefunction of the other photon collapses at C and in the red frame the wavefunction of the other particle collapses at A.

Your analysis seems right, DaleSpam. But when the two-particle system wave function collapses snapping the left photon into an UP state at C, then wouldn't that cause the right photon to snap into the DOWN state at E? But, that would be a reverse causality with the measurement at B causing the event E (before B had yet happened)?

Dmitry67 Apr3-11 09:18 AM

Re: Special Relativity and Enganglement
 
Yes, yes.
So if you accept Block Time, you have to abandon realism.

bobc2 Apr3-11 01:36 PM

Re: Special Relativity and Enganglement
 
Quote:

Quote by Dmitry67 (Post 3226807)
Yes, yes.
So if you accept Block Time, you have to abandon realism.

Dmitry67, could you explain that a little more?

DaleSpam Apr3-11 01:44 PM

Re: Special Relativity and Enganglement
 
Quote:

Quote by bobc2 (Post 3226726)
Your analysis seems right, DaleSpam. But when the two-particle system wave function collapses snapping the left photon into an UP state at C, then wouldn't that cause the right photon to snap into the DOWN state at E? But, that would be a reverse causality with the measurement at B causing the event E (before B had yet happened)?

Not according to my understanding (which is admittedly superficial on this topic). My understanding is that it is the interaction with the measuring device at B which causes the collapse. There is no measurement performed at C, so the wavefunction would not collapse at E in either frame. Due to the measurement at B the wavefunction collapses at C in the blue frame and at A in the red frame, and that is all.

bobc2 Apr3-11 02:17 PM

Re: Special Relativity and Enganglement
 
Quote:

Quote by DaleSpam (Post 3227227)
...My understanding is that it is the interaction with the measuring device at B which causes the collapse.

You are definitely correct about that.

Quote:

Quote by DaleSpam (Post 3227227)
There is no measurement performed at C, so the wavefunction would not collapse at E in either frame.

You bring up a very important point here, DaleSpam. My understanding would be that once the measurement is made at B (DOWN state) then the state of the left photon at C would instantly snap to UP. That would mean that the wave function for the two-photon system in the red frame of event C would require the right photon at E to be in the DOWN state.

Now, the only argument I can think of to avoid the state change at E would be the following (and I haven't found literature on this): Once the state is set for the two-photon system to UP and DOWN, coherence is destroyed so that the two photons are no longer entangled. Without specifying details of the measurement device at B, the photon is perhaps absorbed after detection.

Someone told me that Griffith's book (either the QM or QFT book) resolves this problem, but I wasn't told what the resolution was).

Quote:

Quote by DaleSpam (Post 3227227)
Due to the measurement at B the wavefunction collapses at C in the blue frame and at A in the red frame, and that is all.

I agree that once the measurement is made at B the wave function collapses. But once the wavefunction collapses, it's collapsed, and the photon at C is the UP state. But, that collapse event is also in the red frame at red's time of t1''. That's one of the fundamental problems I'm having here.

And by the way, thanks for your ideas and help in sorting this out.

DrGreg Apr3-11 02:35 PM

Re: Special Relativity and Enganglement
 
Like Dale, my knowledge of quantum theory is limited too, but it is wrong to think that measuring one photon causes the other one to change its state in some way. "Collapse of the wavefunction" refers to the knowledge that an observer has of the system. The result of an experiment causes the observer's knowledge to change and therefore the wavefunction has to be replaced by another wavefunction. (Note there is a single wavefunction that describes both photons, and the before-measurement wavefunction specifies that the probability of two UPs is zero.) Measurement of one photon doesn't cause the other photon's state to change, it causes the observer's knowledge of the other photon's state to change.

When two experiments independently measure the UP/DOWN state of each photon, the temporal order of those experiments depends on the choice of inertial frame (assuming spacelike separation of the two measurement events) so that makes even less sense in terms of one measurement influencing the other. Don't confuse correlation with causation.

Dmitry67 Apr3-11 02:40 PM

Re: Special Relativity and Enganglement
 
Quote:

Quote by bobc2 (Post 3227221)
Dmitry67, could you explain that a little more?

Based on the Bell's theorem, realism cant be local.

If you accept realism, in EPR you have to ask weird questions like "does Alice affect Bob's measurement or vice versa" knowning that in different frames order of measurements is different. In Block Time (wiki it) there is no difference between FUTURE and the PAST, everything is just a static solution in 4D spacetime. Hence it is meaningless to ask if Alice affects Bob or Bob affect Alice.

P.S. I assume you are also aware that 'wavefunction collapse" is an abandoned concept since min 90x, so you had used it as just an example/simplification.

DaleSpam Apr3-11 02:49 PM

Re: Special Relativity and Enganglement
 
Quote:

Quote by Dmitry67 (Post 3227326)
P.S. I assume you are also aware that 'wavefunction collapse" is an abandoned concept since min 90x, so you had used it as just an example/simplification.

I was not aware of that. What has replaced the concept or how has it been modified or superceded?

Dmitry67 Apr3-11 02:55 PM

Re: Special Relativity and Enganglement
 
Quantum Decoherence
http://en.wikipedia.org/wiki/Quantum_decoherence
had replaced the "mysterious" collapse.
Copenhagen Interpretation is dead 15 y already...

bobc2 Apr3-11 07:41 PM

Re: Special Relativity and Enganglement
 
Quote:

Quote by Dmitry67 (Post 3226807)
Yes, yes.
So if you accept Block Time, you have to abandon realism.

I'm thinking you may have intended to say it the other way around. If you accept the block universe model (All 4 dimensions of the universe exist as a real material space/structure) then you can't have the picture I've presented representing the entanglement dilemma. In other words you have to abandon EPR (at least the mechanism depicted here) if you are to retain the block universe with all of the photon world lines in place as static 4-dimensional objects.

DaleSpam Apr3-11 07:58 PM

Re: Special Relativity and Enganglement
 
I have not yet finished reading about quantum decoherence, so my comments may be outdated.

Quote:

Quote by bobc2 (Post 3227284)
You bring up a very important point here, DaleSpam. My understanding would be that once the measurement is made at B (DOWN state) then the state of the left photon at C would instantly snap to UP.

In the blue frame, yes.

Quote:

Quote by bobc2 (Post 3227284)
That would mean that the wave function for the two-photon system in the red frame of event C would require the right photon at E to be in the DOWN state.

No, in the red frame the collapse of the other photon occurs at A, not C.

Quote:

Quote by bobc2 (Post 3227284)
I agree that once the measurement is made at B the wave function collapses. But once the wavefunction collapses, it's collapsed, and the photon at C is the UP state.

In the blue frame, yes.

Quote:

Quote by bobc2 (Post 3227284)
But, that collapse event is also in the red frame at red's time of t1''. That's one of the fundamental problems I'm having here.

But it doesn't collapse until A in the red frame.

bobc2 Apr3-11 08:01 PM

Re: Special Relativity and Enganglement
 
Quote:

Quote by DaleSpam (Post 3227341)
I was not aware of that. What has replaced the concept or how has it been modified or superceded?

I think "collapse" is still used, but the context has to be understood. If one has a precise context in mind, then the concept is used with refinement and the "collapse" term might not be used. That is, the electron, in the time neighborhood of the measurement apparatus, participates in a more global wavefunction along with elements in its measurement environment.

If you were able to follow a very slow motion movie of the electron as it participates in an ever larger encompasing time varying system wave function as it approaches close proximity to the measurement system and ultimately interacts with it, you would see that the contribution of the original electron pair coupling becomes small compared to the new evolving coupling to the larger system having a more global wave function. This means that at some point the two original electrons are decoupled--or coherence is lost (decoherence).

You can actually demonstrate an analogous situation classically with vibrating structures. Start with a cantelever beam vibrating in an eigenstate corresponding to its first resonance frequency. Then have a second very complex system of many vibrating masses and springs, and first couple the two systems together with a light spring so that there is very slight coupling (the first cantelever frequency shifts just a little). Then progressively connect more and more springs of increasing stiffness between the two systems until the identity of the original cantelever eigenstate is completely buried in the new global modes of vibration.

My point is, in spite of this, the entanglement phenomena are well established, and when the measurement is made on the first electron, it's state is established and the other electron snaps to the opposite state (in my example the original coupled electron pair system spin was zero, so the final states had to take on + and - to conserve the original two-particle system state). So, your original language is really understood and doesn't really affect your analysis.

bobc2 Apr3-11 08:20 PM

Re: Special Relativity and Enganglement
 
Quote:

Quote by DaleSpam (Post 3227828)
But it doesn't collapse until A in the red frame.

Please don't take this to be argumentative. I'm still struggling with the concept that when an event occurs in 4-dimensional space, it is there as a 4-dimensional event and is not subject to moving to different 4-D positions. That's how an event is described. We can identify the event, C, in our case using a 4-vector (a displacement vector), call it C. Then that is the same 4-D object (vector), no matter whose coordinates are used:

Cred = Cblue

The X1 and X4 components are different, but the vector is the same, and that 4-D event for the left photon changing to the DOWN state is the same event for both red and blue coordinates.

The photon at event C cannot simultaneously have two different definite states of UP and DOWN. It can only be one or the other. And that state exists in both the blue coordinate system and the red coordinate system at event C.

Now, Dimitry67 may be telling us that the event C cannot exist as a real event. That's another ball of worms that might push us over to a QM thread. It's been a long time since I've studied Bell's theorem, so I'll have to do some side bar on that.

DaleSpam Apr3-11 08:32 PM

Re: Special Relativity and Enganglement
 
Quote:

Quote by bobc2 (Post 3227867)
Please don't take this to be argumentative. I'm still struggling with the concept that when an event occurs in 4-dimensional space, it is there as a 4-dimensional event and is not subject to moving to different 4-D positions. That's how an event is described. We can identify the event, C, in our case using a 4-vector (a displacement vector), call it C. Then that is the same 4-D object, no matter whose coordinates are used:

Cred = Cblue

The X1 and X4 components are different, but the vector is the same, and the 4-D event for the left photon changing to the DOWN state is the same event for both red and blue coordinates.

I don't think that the collapse of the wave function is an event in this sense. It is not something that can be observed or recorded on its own in any way. It is only something which you can get by comparing data after the fact.

You see similar things in other situations, e.g. when you are doing EM in a gauge other than the Lorentz gauge. You can get dramatic changes in the potentials in one frame that do not happen in another frame. If you called the change in the potential an event, then you might suffer this same confusion. But the potential is not observable, nor is the collapse.

You may want to ask this in the QM section, I am way beyond the limits of my understanding here, and I could very well be completely wrong.

bobc2 Apr3-11 08:34 PM

Re: Special Relativity and Enganglement
 
Quote:

Quote by Dmitry67 (Post 3227326)
Based on the Bell's theorem, realism cant be local.

If you accept realism, in EPR you have to ask weird questions like "does Alice affect Bob's measurement or vice versa" knowning that in different frames order of measurements is different. In Block Time (wiki it) there is no difference between FUTURE and the PAST, everything is just a static solution in 4D spacetime. Hence it is meaningless to ask if Alice affects Bob or Bob affect Alice.

P.S. I assume you are also aware that 'wavefunction collapse" is an abandoned concept since min 90x, so you had used it as just an example/simplification.

Thanks a lot for your input, Dmitry67. Good work. I answered your earlier post a while ago, and thought you may have communicated the opposite of what you intended, but now I see that I misinterpreted your meaning. I see what you are saying now and will review Bell's theorem since it has actually been at least three years since I've thought about it.

And yes, I was aware of the decoherence considerations and the imprecision in using "wavefunction collapse" (you are of course correct with that).

I'm still troubled with the apparent conflict between QM and special relativity on this entanglement issue, notwithstanding Bell's theorem. I don't see how you deny realism in QM (but then maybe that's the essense of QM) and yet we would still like to include elementary particle world lines in the spacetime diagrams--we would like for them to be real (should we instead have wave functions in the spacetime diagrams?). Feynman diagrams seem close to a representation of reality (being sure to include the W boson in the beta decay pictures, etc.).

Spacetime pictures are consistent with tracks in particle accelerators. And the entanglement phenomena are adequately demonstrated experimentally. So, where are we?


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