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Problems by considering that a measurement produce a collapse. (causality violation) 
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#1
Jun2411, 06:55 PM

P: 59

Introduction: (can be skipped)
We know the problems around the collapse of the state (specially that we don't know how an outcome is selected from the preferred states). Now thousand of experiments shows us that this strange not unitary transformation of the states occurs when a measurement is made. Also Quantum mechanics is not local and there are many experiments of quantum entanglement that can argued in favor of this strange behavior (there is a debate about the validity of this experiments). The paradox between the intrinsic local nature of special relativity and the nonlocal nature of quantum mechanics is solved because a measurement will destroy the state. This mean that if a guy measure one of the entangle particle he will force the state of the other particle (we are assuming a collapse again) to some state, but the guy that have the other particle have no means to know in which state is his particle, then he will ignored the fact that the other particle was measured. No transfer the information, then no contradiction with special relativity. Now to the key point of this post. (paradox) Suppose that both entangled particles are measured and the differences between this events is spacelike. That mean that for some inertia frame both measurement were made a the same time. My question is which one of the measurement produce the collapse of the state? A person can answer that both measurement produced the collapse. That is wrong because in another inertia frame we can see that a measurement was made before the other and by conventional quantum mechanics was this measurement the one that produced the collapse. But in another inertia frame the order of the measurement is the other way around then the other measurement was the one that produced the collapse. The result of the experiment is the same and not information could be transferred, then in this sense there is not a violation to causality, except for the collapse. If we related the collapse as a effect of the measurement, then there is a problem here, causality is violated. I think that the reason of this paradox is that the collapse is not well defined. The paradox is that the collapse was produced by different measurements depending of the inertia reference frame, then we expect from a relation of cause and effect that the order of the events should be invariant, this is not the case. Then how can we said that the measurement cause a collapse? I hope to see some replies. 


#2
Jun2411, 07:16 PM

P: 59

Another argument that can be made is that a collapse in the case of entangled particles will happen in some inertia frame, before a measurement was made. The argument is the same. Suppose that you did a measurement of one of the entangled particles, then by the collapse postulate the state of the other particle collapsed. Now like these two events are simultaneously, then there is an inertia frame in which the particle collapse before the measurement and another in which the particle collapse was not simultaneously with the measurement. This is a problem because is impossible to define two events that are simultaneously in any inertial reference frame.
Now the collapse between entangled particles and the measurement should be simultaneously, because if not then we can measure the first particle and like the second will no collapse instantaneously we can measured the second particle before the collapsed happened and have another result. That is an horrible contradiction. Then both should be simultaneously, but at the same time they can't be simultaneous in any inertia reference frame. 


#3
Jun2411, 08:50 PM

P: 59

another case that I can imagined and we don't need to go to the collapse to see a problem is the case in which to incompatible states are measured at the same time is two entangled particles. Suppose you have the case of aup up>+down down> in the z direction. Now you measurement the spin in the z direction of the first particle at the same time you measure the spin in the x direction of the second particle. Using einslection we have two different sets incompatible sets of results of the measurement and that is a contradiction.
Now returning to the collapse of the state we can see that up up>+down down> in the z direction can be written as up up>+down down> in the x direction. Now is both measurement are spacelike we have that in one inertial frame one is done before the other. Suppose in this inertia frame the particle one was measured first as was up, then both particle are are up in z and after that you measure the spin in the x direction of the second particle and was up and you have the result first particle up in z and second up in x. if we see this from other reference frame in which the second was measured before the first one we have the same result. now that implies that if we measure both particle at the same time we will have the same result? I think that is a nice question. Some people can argued that I am using the collapse of the state and related it to some interpretation. What I am using is that when we measure a observable the result is an eigen state of the observable. This is not an interpretation, this have been confirmed by thousands of experiments. Now what is part of interpretation is that this measurement will affect also the state of the other particle instantaneously (non locality of the collapse) that concept is the one that I argued is problematic in the sense of causality. Now that doesn't mean that entaglement cannot happen ( I believe it happen) and local unitary transforms can affect the global state and bla,bla,bla. Now the crucial problem about entanglement and the nonlocal effects of a local measurement are accepted by many in quantum mechanics and for me that is problematic. 


#4
Jun2511, 02:14 AM

P: 113

Problems by considering that a measurement produce a collapse. (causality violation)
The paradox is solvable by saying there is no real seperation to begin with.



#5
Jun2511, 10:00 AM

Sci Advisor
PF Gold
P: 5,299

I think it is easiest to consider the overall "context" of an observation, which may involve spacelike or timelike separated components. I.e. the context itself is not restricted to what is local even though the individual components traverse a local timeline. You can see this with entanglement swapping, in which particles become entangled which have never existed in a common light cone. http://arxiv.org/abs/quantph/0201134 


#6
Jun2511, 11:40 AM

P: 59

I know the concept of entanglement swapping and in general I am not attacking the nonlocal behavior of quantum mechanics. The reason is that this nonlocal behavior can be used to explain how classical mechanics can emerge from quantum mechanics and that topic is one of my favorites.
Now I am attacking with this paradox three features. First that the interpretation that a measurement produce a collapse instantaneously is contradictory because cause and effect relation cannot be sustained in spacelike separations (the better example is my second post). I know this also attack the nonlocal behavior of quantum mechanics and I am trying to seek how i can safe this by attacking the collapse. (any idea is appreciated). The paradox here is that a collapse can happen before the measurement. The paradox can be safe by saying that it doesn't matter because the result is the same. I can debate this concept, but for the moment I am more interested in the following concept. The other point is what happen when we measure the two entangled particle at the same time. basically we have two collapse happening at the same time. Using lorentz invariance with respect to the result of the measurement I found out that is the local collapse (the one produced by the local measurement of each particle) the one that dominates. (this is my second post). This results can be derived also if we assume that there is not a nonlocal collapse. Now if we assume that there is nonlocal collapse, then why a measurement is preferred over the other. Quantum mechanics doesn't need to agree with special relativity. Quantum mechanics was created from a nonrelativistic point of view, for example in QFT the interactions are local by default following relativity and in my experience with QFT I have never observe a nonlocal behavior as in traditional quantum mechanics. My plan right now is to use premeasurement and eniselection to study formally these cases. Probably I am just confused, but I really don't see how can we ignore the last post that i did. Now is not something that is happening and we can't measure. Now we are measuring to stuff at the sametime and by relativity one of this measurement is preferred. I think this can solve by einselection and that is the apparatus the one that produce this. In that sense I probably can solve the last post, but anyway I have a lot of problem with the first two(not matter that the result is the same), but there somethings that we need to accept as weirdness of nature and other that are unacceptable as part of nature(mean the theory is wrong). I need to decide in what list i should put the firsts two posts. 


#7
Jun2511, 12:25 PM

Sci Advisor
PF Gold
P: 5,299




#8
Jun2511, 02:34 PM

P: 59

yes I agree if we throw the concept that a cause precede a effect there is not paradox. Then if we do that special relativity is doom and our daily experience is just a huge coincident. I don't want to created example of how the word will be if the cause precede the effect, but some of them is the conversations laws(a particle doesn't need a force acting on it to change momentum), the principle of relativity (how can we define an inertial frame) and particle physics (we are going to have production of particle before the particle collided). That is not a solution, if that is the case what is the point to study physics.



#9
Jun2511, 03:56 PM

Sci Advisor
PF Gold
P: 5,299




#10
Jun2611, 09:53 AM

P: 59

Sorry you comment doesn't make sense. In special relativity the four space have embedding an arrow of time (really is an embedding from R to the four space) and this arrow of time is the time coordinate. Now is this embedding was not there then we don't need relativity because it mean the time is not a coordinate, but a parameter. In that case what we can have a is path (obviously is also an embedding). Now this features have nothing to do with cause and effect. Cause and effect is a relation between two events. Now one feature that we related to cause and effect is that the projection of the path to the time coordinate is monotonic increasing. That mean that preserve the given order. Now you are telling me that this is not necessary the case. No if you for example in QFT want to calculate the propagator you put a time ordering operator just to insure that this projection is monotonic increasing, now you are telling me that there is not reason for it. That mean that when we calculate a scattering amplitude the result will be wrong because we force an order in cause and effect. Now if a field in the past can affect a particle in the present then obviously the local conversations are wrong. The reason is that this conservation cannot be written in an simply deferential form as a continuity equation (or divergence of an energystress tensor) that is well know. That is exactly the reason that the concept of field is some important and is because of the local conservation. For example if we accept the nonlocal behavior of classical mechanics we will find that at considering electrodynamics the conservation of momentum is not true (the magnetic term is the one that is responsible). how the problem is solved considering locality of the field and assigning a momentum to this field. This is equivalent to assume cause and effect (by my comment before). Also if the order of cause and effect was not invariant for the trajectory of a particle, then need to correct calculate the effect of a field over it to integrate over all times. This is equivalent to put the green function and not the retarded green function (what is the point of the theta(step) function if you are.) We are assuming that the order of cause and effect doesn't change probably in any calculation in physics. If our calculations are not wrong then we are doing something right.
Now also apart that the monotonic behavior of cause and effect is used like one of the most sacred principles of physics (really this is in any area of science.) we have also that cause and effect is not symmetric. if A cause B then is not true in general that B cause A. This strange fact was discovered because of the CP violation and The CPT theorem. Then we have a T violation. From a mathematical point of view it means that the relation fo cause and effect is not a relation of equivalence (equivalence need symmetry) and for that reason cause and effect are not interchangeable. 


#11
Jun2611, 10:06 AM

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P: 1,395




#12
Jun2611, 11:01 AM

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PF Gold
P: 5,299

a) I think it is something that is speculated by many that the arrow of time we see is a consequence of some initial conditions. In other words, the laws of physics are essentially symmetric with respect to the direction of time and there is nothing per se that prevents us from saying: would we notice any difference if the time direction was reversed for everyone? At any rate, I am not aware of any evidence either way on this. b) Is there really a thermodynamic arrow of time? I would argue NO, and here is my reasoning. I completely agree that the evidence is that entropy increases to the future. But I would argue that entropy ALSO always increases to the past. In other words, any experiment measuring a thermodynamic state involves us starting at T=0 and moving to T=1. T=0 represents a local maximum of our knowledge to the state of the system (which is also to say that the number of possible states it could be in is a local minimum). What happens if you move from T=0 to T=1? I think a careful analysis will demonstrate that the number of possible states (entropy) increases in BOTH directions from this minimum. The reason you never witness this is that the T=1 to T=0 region is not a closed system, which it is from T=0 to T=1. On the other hand, I would not say this is a generally accepted viewpoint. 


#13
Jun2611, 11:14 AM

P: 59

SpectraCat
I will try to understand what you are telling me (sorry for my ignorance). Are you telling me that the projection of a path of a particle over the time coordinate is not monotonic increasing? Really I don't see how is that possible, but also my field is not GR. Mathematically time is a coordinate then obviously we can have any kind of path, but the constraints make by physics really permit to go backwards in time? Probably I am confusing it, but that doesn't implies that time reversal is a symmetry of nature (which is not the case, then one direction of the flow should not be prefered)? Now suppose that the backwards flow if possible the by time ordering it should be also monotonic decreasing? That mean we don't have a same particle going forward and backward in time or is possible? The only thing that I need to know is if a effect can precede a cause (that's Drchinese argument). For example is an object will start moving in an inertia reference frame (SR) before a force act on it and is that is possible how this is not a violation of conservation of momentum. I mean we describe physics in terms of field to make sure that all the interaction are not spacelike and to preserve causality. My argument is that to have an interaction that is spacelike is against physics. Not only in classical mechanics(relativisctic) but also in QFT. Now for what I understand the only thing that I need to preserve causality is an ordering of event and that this ordering should be lorentz invariant (reduce lorentz group (time reversal is not included)). Now the two most important question that I need the answer is: Is physical possible an spacelike interaction? there is not contradiction with a spacelike interaction? That is the only thing that we need to preserve causality. Doesn't matter the direction of the time flow the ordering of cause and effect events should be lorentz invariant if the interaction is timelike. If you need to choose to answer one question please answer one of the two last question. DRchinese Well there is a theorem in QFT that said that CPT is a symmetric of physics. That mean that is there is a CP violation, then we have a Time reversal violation( physics is not the same to both flow of time) This violation is in the weak interaction and have been confirmed experimentally. Now if we limited ourselves to study gravity, electrodynamics and the strong force then there is not Time reversal violation, but there is one force that violates it (weak foce). if that not enough to said that time reversal is not a symmetry of nature? Also this time reversal violation theoretical are needed to explain what we observe more matter than antimatter in the universe. 


#14
Jun2611, 12:07 PM

Sci Advisor
P: 1,395

Anyway, I am not sure what a "spacelike interaction" would be, other than some sort of FTL effect between lightcones. I am not an expert on this stuff, but I would tend to agree with you that such a thing is impossible according to relativity. Actually, this line of questioning makes clear to me in a new way why so many people have a problem accepting the nonlocality implied by QM entanglement. However, as far as we can tell, the collapse of entangled states is a phenomenon that does not result in any violations of relativity that we can detect through experiments on entangled states. The best guess I can give for why this might be is that there ARE things that can propagate faster than light in physics. For example, the "FTL scissors problem" where the intersection point between two blades whose tips are approaching at near light speed can be made to "move" arbitrarily fast by increasing the lengths of the blades. Group velocity and phase velocities of propagating waves can also assume supraluminal velocities .. a list of allowable FTL phenomena that do not violate relativity is available here: http://en.wikipedia.org/wiki/Fasterthanlight. So, the preponderance of evidence suggests that collapse of entangled wavefunctions is another example of an allowable FTL phenomenon (i.e. one that does not allow FTL propagation of information), and as such, does not correspond to the kind of relativityviolating phenomenon implied by the "spacelike interaction" you mentioned. 


#15
Jun2611, 12:57 PM

P: 59

Thank You for the advice I will check the list.
I know I am hunting ghost here, but if quantum mechanics is based in a nonrelativistic classical mechanics then is surprising that the nonlocality of quantum mechanics cause not problem with relativity. now the assumptions that came from directly from classical mechanics (as symmetries and nonlocal potential) are a problem and the no conservation of particle number. The quantum mechanic in general is not a relativistic theory and doesn't need to agree with relativity (it doesn't) but this peculiar features does. I think that the nonlocal behavior of quantum mechanics can be constrained in some way (not eliminated) by examining it carefully which at the moment is impossible because the collapse is just a crazy nonunitary evolution that during a century have not shown their cards. I will try to work some of this using decoherence (decoherence need entanglement, but entanglement and nonlocality are not equivalent, that's something that many people ignore). Also returned to the last topic. To have flow of time in any direction then we are saying that the system is invariant with respect to time reversal. Now nature in general is not invariant with time reversal, for example the weak interaction. Gravity, ED and CD are invariant under T, but that doesn't mean that nature is. Then you think that still accurate to say that the flow of time can be in any direction or is not related at all to T symmetry. 


#16
Jun2611, 08:36 PM

P: 59

Is not a complete solution to the problem but I think the following article is interesting
http://prl.aps.org/abstract/PRL/v88/i1/e017901 


#17
Jun2811, 10:34 AM

P: 59

Now I am seeing it from a different point of view. First the result will not present difference in the experiments and that can be shown using quantum mechanics (not matter spacelike interaction), the real contradiction is that there are instantaneous transfer of information. That is exactly what a change in state means. The basics features that permit entanglement is the superposition and the tensor product. This features are basics in any quantum theory including QFT. Now there is two ways to solve the problem. First to assume that nonlocality is true in QM and latter to show that locality is because of decoherence (I am currently working in it). Second to show that the collapse can be constrained by relativistic consideration. The question here which of the two theories is more fundamentally. Originally is was guessing that was SR, but now I will try to guess the other way around. I think this paragraph is incomprehensible, but really there is hope. Now the problem of the non unitary and not deterministic transformation that we call collapse still present and until it is not solve or understood in a scientific way, then there is not a completely satisfactory explanation.



#18
Jun2811, 01:17 PM

P: 380

collapse via EPR correlation: http://arxiv.org/PS_cache/arxiv/pdf/...005.5092v2.pdf and the conflict between decoherence and special relativity http://www.tandfonline.com/doi/pdf/1...00340108230961 . 


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