"If a piece of knowledge is calculated about a system with certainty then such knowledge is intrinsically represented by the system in the form of a physical reality without the need for a verifying measurement." Please Register or Log in to view the hidden image! There exists a classic conflict (a conflict in appearance only, IMO) between QM and SR of which I am convinced that not all Physicists/students/posters on this forum are aware. (If you are aware of this problem you don't need to tell me so!) The attached picture contains two entangled photons in an EPR experiment, as seen from the perspective of two different observers moving relative to one another. Analyze the picture and reconcile it with the above statement with consideration to "when" each photon's wavefunction has collapsed. That there are only two observers here should be irrelevant to your answer; the Universe is plenty full of potential "observers" of the experiment from an infinite number of perspectives in the form of planets, meteors, stars, traveling aliens, etc which are all moving in myriad directions with myriad relative speeds to each other and to each of these particles. The point is that the wavefunction supposedly collapses "simultaneously" between the photons, yet simutaneity is meaningless in a Relativisitic world. As can be seen in the picture each photon's wavefunction has collapsed before it is measured. IMHO there is an explanation in Block Time but I am open to alternatives (of which I have yet to find any that are intellectually satisfying).
Ben, I felt I did a much better job explaining the problem here, don't you think? This thread frames the same problem but in a slightly different way, and is simpler. You had threatened to lock my survey because I was unable to understand your responses, and I'm hoping that with this simpler scenario your answer will be correspondingly simpler (for my simple mind Please Register or Log in to view the hidden image!)
RJB--- I am now fully confident that my answer is the correct one, after talking to a few of my friends. Once a measurement is made of the particle's spin, in any frame, the wavefunction is collapsed, and future measurements produce correlated results.
No, it hasn't. The word "before" depends on the frame. There is no frame in which the wavefunction has collapsed before being measured.
There are several things wrong here. First of all, simultaneity isn't meaningless in str, but it is relative. Second of all, it doesn't make sense make sense to talk of "each photon's wavefunction", even less so if they are entangled. There's only one wavefunction, which evolves according a time parameter. If I've understood the popular QFT accounts I've read correctly, this time parameter is the time parameter of the frame you're considering. That is, if you want to say "the wavefunction collapsed at this time", then, in a relativistic framework you have to specify a frame as well. Third, you're saying that the wavefunctions both collapse before measurement, but you are relying on notions of "before" from two different frames! That's a big no-no in relativity theory, and I suspect the same is true in QFT.
Ben said I was going to point out that the squishy definition of "once" in Relativity is the crux of this problem. However after giving your post some thought we are in complete agreement - since you said once the measurement is made (and not "once the observer in a given frame takes a measurement"), assuming that we agree there are an infinite number of possible frames, from every conceivable angle and speed, from which to view the measurement of either particle then we would also both agree that both particles possess a definite spin at a point arbitrarily close to their emission event. Ergo the wavefunction never exists in any physically real sense. Iceaura, are you claiming that the left particle in the top picture has a definite spin before it is measured, but only for the top observer? So it is your position that a particle can have a definite spin and continue to exist in a state of superposition at the same time in it's own timeline? Please remember that the "state jumps" point that the top observer sees for the left particle is an event which occurs before that particle is measured for all frames of reference. Similarly, funkstar, what you are saying is that even if we "gave a clock" to each of the particles their wavefunction either has or has not collapsed depending upon which frame we are referring to. Please study the picture again because this would lead to a situation where at, say, t=100 for the left particle, that particle possesses a definite spin and also remains in a state of superposition from various frames of different observers. Please note that t=100 for a given particle would be a discrete point in it's timeline regardless of frame of reference. In other words, if this is true: "When particle B's clock reads 100 it can be proven from my POV that particle B has a definite spin." Then this is true: "Particle B's spin is intrinsically and physically real when its clock reads 100." To claim otherwise is to take issue with the original premise at the top of the OP. I'm discouraged that I can't make things more clear. If you want some heady reading check out the following which I found this morning: http://cosmology.princeton.edu/~mcdonald/examples/QM/aharonov_prd_24_359_81.pdf
No. Your logic is flawed. The particle has a spin, but you don't know it's spin until you measure it. It doesn't matter B's relative velocity to A---he still measures the spin of the particle either simultaneously with A or after A. His results will still be correlated, no matter how much he is boosted relative to A. You are making the mistake, I think, of assuming that the wavefunction collapses more than once. That is, the wavefunction of the two particles collapses only after a measurement is made, period. Once A has made his measurement, it is only then that B, in whatever frame he happens to be in, "knows" what the spin is (in reality, he must first ask A). What does A's clock read? Why would the spin not be real before his clock read 100? Has A made his measurement already? As am I, considering every physicist I have talked to about this problem has come to the same conclusion (i.e. mine). It is only "armchair" physicists who seem to take issue with the explanation.
In the paper you posted, I think Figure 7 directly confirms my interpretation of the experiment. See Eq. (7) for notation. In this case, a state is prepared of, say, two (entangled) electrons, with spin 0 (cf equation 7). When the spin of one electron is measured, it is found that it is spin +1/2. The spin of the other electron is automatically known whether (I quote) "the collapse is taken along t [which you can think of as B2] or along t' [which you can think of as B2]".
Ben, we're in agreement that the wavefunction collapses only once and because we agree on that I believe we are in agreement on everything. I've labelled the observers, particles and events in this picture. Do you agree with me that A collapses at Ta=70 and that B collapses at Tb=70 for all frames? Please Register or Log in to view the hidden image!
Excellent, now it's just a matter of settling what "observing" the measurement means. Imagine a galaxy 500,000 light years away moving relative to this experiment in such a way as to calculate that Tb = 100 and Ta = 25 are simultaneous. The information carried about the experiment (in the form of traveling light) is spread throughout this galaxy. Let's say it's "observed" by the following: Please Register or Log in to view the hidden image! 1) A child who understands what he sees but does not understand its meaning 2) An alien who is very advanced 3) An astronomer 4) A meteor whose trajectory is infinitesimally altered by the absorption of the photons 5) A brick wall which is heated very slightly by the photons 6) A very advanced light sensitive camera recording everything it sees, left on a desolate planet by an ancient race of beings 7) A potential life form in the middle of abiogenesis sitting in a pool of "life soup" whose process of becoming alive is disrupted (ala Star Trek) 8) ETC... You see, I agree with you that if X and Y were the only two observers (or actually if X and Y's frames were the only ones that existed) then I guess it could be said that the wavefunction would collapse at Ta=70 and Tb=70. But I am saying that it is not possible for these to be the only frames which are affected by this experiment. Even if you tried to "block all escaping photons" you're going to have a hard time blocking all influence (gravitational and otherwise; all forms of information!) from escaping the lab area, not just at the time of the experiment but for all time into the future! At some point, Observers X and Y would leave the lab and discuss their results (presumably) and now THIS discussion can be considered the measurement event which will be able to be calculated as simultaneous with some Ta < 70. It boils down to the measurement problem which I am convinced only ceases to be a problem if one accepts block time. :bawl:
Now you're playing games with what "observer" means, which is outside the scope of the discussion. The only people who have a problem with measurement are philosophers, so maybe you'd better take the discussion there. And, you haven't explained to me why my interpretation is wrong, still. I come to the conclusion that there's no contradiction, people who I trust about Quantum Mechanics come to the same conclusion that there's no contradiction, and the paper you posted a link to comes to the same conclusion that there's no contradiction. Apparently, there's no conflict between SR and (specifically) wavefunction collapse. This is the conclusion I've come to, and you have failed to convince me why this thought experiment is in contradiction to special relativity, or the idea of wavefunction collapse.
I think the solution is obvious. The problem is being over thought. Observers A and B agree only because they're moving in the same fashion. The observers in the galaxy c disagree with observers A and B because they're in a different reference frame from the experiment (even though they are still observers of the experiment. All any of this actually means is that Observes A & B would disagree with the observers in Galaxy C as to when they made the measurement (and how fast their clocks are ticking etc).
Ben, the paradox lies in the fact that it is claimed the wavefunction collapses "simultaneously" between both entangled particles when "simultaneously" has no absolute meaning. I also said it was an APPARENT paradox. I don't remember saying that YOUR interpretation is wrong or contradictory - if I did it was before I realized that you agree the wavefunction collapses only once (at the earliest time possible for each particle). Now I just need you to see that taking that stance implies that the wavefunction collapses immediately upon emission. BTW, I won't allow you to wave your hand and gloss over my definition of observer - this is critical step in my argument! Read my last post and you will see that I agree with you that if X and Y were the only observers of the experiment then A and B would collapse at Ta = 70 and Tb = 70, respectively - I'M AGREEING WITH YOU. Then I try to explain why they cannot be the only "observers", and that anywhere the photons of the experiment travel they are carrying the results of the measurement with them in such a way that manifests itself into a macro-level result which would differ with different measurement results. If you can accept the above point and my various anecdotal definitions of observer (slim chance that you will admit it, I know) then the final step is to point out that it is trival to prove the virtually infinite number of frames from which to "observe" any experiment in the Universe...
Think of it this way. In S.R., "simultaneous" means to "happening at the same time". You make constant time slices across the diagram, and where the slices intersect the world-lines is where simultaneous events take place. In RJB's experiment, observer B is boosted wrt observer A, which means that the constant time slice is not perpendicular to the `t' axis. Then your argument is flawed. The electron could scatter off of a photon, say, and that would change it's wavefunction. In this sense of the word, the photon is an "observer". So your argument is that there are an infinite number of observers observing the wavefunction at any time. This is not really how gendanken experiments work (i.e. usually you separate the experiment from the rest of the universe). We don't really expect quantum mechanics to work differently in a completely empty universe in which there are only two observers. In that case you cannot argue that there are any ambiguities. And even in this universe there are not an infinite number of observers, because our Hubble volume (i.e. the volume of space in which we are causal contact with) is finite. And "virtually infinite" and "infinite" are COMPLETELY different quantities. One is quantifiable and one is not. This means that, supposing I COULD know the positions and relative velocities of all of the observers in the universe, there still exists a frame, infinitessimally close to the original particle decay, in which the wavefunction has not collapsed. To me, this is enough to kill your conclusion. But that's a bit hollow, because I feel like I am arguing using your (wrong) understanding of how special relativity works. There is still no paradox, because you are forgetting all of your special relativity. Special relativity says that there is no universal time, and that what each observer sees is relative. Each observer sees the experiment happening in a different way---there is really nothing new or ground shattering about this, because it's one of the first things you learn when you learn how to do scattering experiments which are consistent with special relativity. Each observer is in a different frame, relative to the experiment, with their own clock. This means that the wavefunction can collapse in my frame, but not in another frame. So let's review: 1.) Even if your intuition is correct, there is no contradiction, because I can, in principle, construct a frame from which the wavefunction is not being observed. In fact, I can construct an infinite number of such frames. 2.) The ultimate resolution lies in the fact that the collapse of the wavefunction is a "simultaneous" event, and "simultaneous" is a frame dependent statement in special relativity.
OK Ben let's try a different tack. I said: You responded: Now, Ta =70 and Tb = 70 would be considered a simutaneous event from event E (the emission point of A and B). This knowledge is not available to an observer at event E, nevertheless the particles both possess a definite spin BEFORE EITHER IS MEASURED in this frame. If you are arguing that the wavefunction (and superpositions in general) have a physical reality, then this scenario is contradictory to the typical QM interpretation! OTOH, if you argue that wavefunctions only exist when there is a lack of knowledge (by a conscious observer, or whatever [see my above post]) then you are stuck defending the position that at Ta=70 the A particle has both collapsed and has not collapsed. Do you still insist that your view (although correct, IMO) does not hold an apparent paradox?
