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.?
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.
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.
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.
You are definitely correct about that. 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). 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.
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.
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.
Quantum Decoherence http://en.wikipedia.org/wiki/Quantum_decoherence had replaced the "mysterious" collapse. Copenhagen Interpretation is dead 15 y already...
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.
I have not yet finished reading about quantum decoherence, so my comments may be outdated. In the blue frame, yes. No, in the red frame the collapse of the other photon occurs at A, not C. In the blue frame, yes. But it doesn't collapse until A in the red frame.
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.
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.
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.
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?
Thanks a lot for your thoughts. I'll do some Bell's theorem study and also reflect on your well reasoned analysis. And that might be good advice, carrying the topic over to the QM guys. One critical point you've put your finger on turns on the question of whether, at the instant of measurement of photon 1, does photon 2 change state, regardless of whether it is observed or not? I take it that is really your key point--and a very good one. I've been assuming the answer to that is yes--and maybe that's out of my tendency to find as much realism in spacetime as possible (as opposed to being informed about QM theory). Of course the Aspect experiments always validated EPR by making that measurement on particle no. 2 and finding that sure enough it was opposite to particle no. 1. So, if he had not made the measurement of particle 2, how could he have known if its state had actually changed (although I've been betting on maintaining original system spin = zero, and how could that be maintained if particle 2 did not change even though it was not measured?).
At first, I wanted to add that historically Von Neumann had recognized the problem you are talking about. He developed his own 'flavor' of Copenhagen Interpretation, where "collapse" was just an information update, not a physical process, avoiding issues with relativity. After the death of Copenhagen Int. (and also Transaction Int) there are 3 viable Int, and they approach this issue differently. Stochastic Mechanics - macroscopic, not microscopic events are atomic. particles, fields etc are "just the math" to explain the correlations between the macroscopic events. So in SM it is non-issue: math gives you the formula which is in agreement with the reality - then shut up and calculate. Dont think how some weird stuff "propagates" from Alice to Bob. Neither real nor virtual particles exist in that Int - they are just math. On the contrary, particles tracks in cameras are real. Bohmian Mechanics - is non-local. Some versions even have a hidden preferred frame. Note that no matter how far particles are in real space, they can be very close in some other configurational space. So BM can be local - but not in our space :) BM also has some weird definition of reality, so I dont want to go further. MWI - is local, nonrealistic (becased on the commonly accepted definition of realism) but is realistic in a wider sense, because the global wavefunction of the universe is well defined in any point of spacetime. Also, in EPR experiment at least 2 copies of Alice and Bob are created independently. Later they synchronize their data using slow than light channels, and reveal the correlations. Nothing is transfered FTL in such case and ordering of events is well defined. In MWI there is just a unitary evolution of the wavefunction. There are no particles - just waves (even measurement create an illusion of them and even tracks). Ultimately, the whole world is just one big unbound Feynman diagram Personally, for me by EPR nature is crying that MWI is true, but not all people agree with me, of course. MWI is also deterministic, so God does not play dice after all..