One should be careful when using words, instead of doing calculations. Quantum mechanics does provide unambiguous prescriptions for doing all the calculations described here. That *historically* many, even famous, people, used words, like ``collapse'', that are ambiguous, doesn't mean that there isn't a way of doing the calculcations consistently and avoiding any technical issues. For an example, cf. the paper by Distler and Paban, http://arxiv.org/abs/1211.4169

Mainz, Germany

Dear Wechsler,

I think this a fascinating question, and I have some thoughts about it, though none that I think of as favoring any particular development of physical theory. But, as you seem to point out, the question of how to best understanding the correlation of entangled results is a problem common to various approaches.

First off, then I'm much disinclined to postulate faster than light signals. This idea seems too much at odds with SR and GR. I suspect, instead, that there is an assumption in play in the puzzle which needs to be questioned. The assumption is that the correlations involved in entanglement must be open to a causal explanation. I think there is reason to question that idea. Our ordinary conception of causality does involve uniform correlations, of course, and well as temporal sequence. But in the phenomenon of entanglement, we seem to have uniform correlations without definite temporal sequence, as you argue above.

This we might think of as something simply factual--something that physical theory simply needs to accommodate. As regards causality, we are already familiar with a basic randomness or probabilistic character of quantum measurement. Given the same experimental set-up we get different results on different trials, though over a longer series of trials, the statistical distribution of results is predictable. That is the way things go in QM. Its the kind of fact upon which the uncertainty principle depends as a matter of supporting evidence. "Hidden variables" have generally been rejected, and as concerns entanglement at astronomical distances, it is difficult to see how any supposed hidden variables could operate.

In general terms, it is sometimes possible to find an underlying mechanism explaining particular observed regularities. But it cannot be that every observed regularity depends upon a further underlying mechanism, on pain of infinite regress. In consequence, it appears that some observed regularities (including correlations) are simply basic, and there is no further underlying mechanism by reference to which they might be explained. Treating QM as fundamental in this sense, its correlations may plausibly be regarded as requiring no further explanation.

It is not that I think physics or science, generally, should give up on seeking mechanisms and explanations, of course. But I believe that seeing the correlations of entanglements as factual and basic is much in the spirit of Bohr, Born, Heisenberg & Co. This suggests to me that the correlations of entanglements are sub-causal--that is, factual and not open to causal explanation. An advantage of such a position is that it allows us to take QM and GR both, quite seriously. Whether physics will ultimately work out this way is, of course, a different question; and philosophical reflection on the results of science is ever subject to being overturned by empirical-theoretical developments in the sciences themselves. I propose no dogmas here.  

H.G. Callaway

In fact one *can* explain how entanglement occurs: the space of quantum states contains many more states, than just those that have a classical limit. That's all. Quantum mechanics provides an unambiguous description of them all. The difficulties arise, when trying to describe all these states, only in terms of states that *do* possess a classical limit-it's not possible. The other way around makes sense: showing that, within the quantum space of states, it is possible to define a subspace of states  that *do* describe classical physics, in the appropriate limit. Were this not possible, it would imply that quantum mechanics is incomplete, that there would exist classical states that can't be recovered from quantum states. One recovers classical physics as a limiting case of quantum physics. Incidentally, there's no point in appealing to the velocity of light, when discussing non-relativistic physics, whether classical or quantum. 

Dear users,

If you want to answer this question, please first READ it carefully, make sure that you understood the question. If you didn't understand something, please ask.

If somebody has a solution, please say the solution, don't say generalities and indications for other people how to find a solution. Please explain the solution in which you believe, in your own words. If one understands an idea, one is able to explain it in his/her own words in a few lines.That would help the person who answers to check if the answer addresses the question or not.

About articles, this question is not a call for references. There are thousands of articles, and NONE solved the problem.

The question is ``Any suggestions?'', along with many statements. The answer to the question is, yes, any *textbook* on quantum mechanics. The reason is that  the statements made in the text are either wrong, or can't be assigned any physically relevant meaning-namely there isn't any ``absurdity'', since the formalism of quantum mechanics *does* allow an unambiguous calculation. It *would* have been absurd, had the formalism led to calculations that required *additional* assumptions. This isn't the case. And using any argument about faster than light travel doesn't make sense within non-relativistic quantum mechanics. 

Within non-relativistic physics it doesn't make sense to talk of space-like/light-like/time-like intervals-they aren't physically relevant labels in this case. Within quantum mechanics the issue of successive measurements is non-trivial, not due to any relativistic issues, however, but due to entanglement, the property that multiparticle measures do not factorize over one-particle measures, except in the classical limit, for the case of non-interacting particles. 

What's described in the text is, indeed, entanglement-that's not an impasse of any sort, but a property of quantum mechanics. 

And it can be proved, by an elementary calculation, that initial conditions that *are* factorized, one-particle measures, do evolve to non-factorizable measures. This is a property of the mathematics, it isn't an indication of any technical inconsistency, however, since the observables, anyway, involve averaging over the measure of the multiparticle configuration. The fact that these multiple integrals, do not become products over the configuration of each individual particle isn't something particularly astonishing-nor does it mean the integrals can't be calculated unambiguously. And the physical consequences can be studied, now, experimentally, thanks to the work of Aspect and Haroche and, now, many others.

Mainz, Germany

Dear Nicolis,

you wrote:

In fact one *can* explain how entanglement occurs: the space of quantum states contains many more states, than just those that have a classical limit. That's all. Quantum mechanics provides an unambiguous description of them all. The difficulties arise, when trying to describe all these states, only in terms of states that *do* possess a classical limit-it's not possible.

---end quotation

I like this, but it strikes me as something other than a causal explanation; it seems to be an alternative, general, statement of the facts involved --in terms of state space. I take it you are not claiming this is a kind of causal explanation of "collapse" or of entanglement. I take it that not all explanations are causal explanations.

Regarding the relevance of relativity, the point of this is just that entangled phenomena might reasonably be expected to play out over astronomical separations, and in consequence, we cannot reasonably think of the results of measurement as effecting distant, correlated results. QM, one assumes, must be consistent with GR whether relativity is normally invoked in QM or not.

H.G. Callaway

No, entanglement is the name of the causal explanation-not any alternative: it's the term that signifies the non-factorizability of the multi particle measure over one-particle measures, which is the technical description, of what's happening. And I'm saying that ``collapse'' is just a word, that means that the measure becomes localized on a particular subset of states. But, once more, the calculation is unambiguous.  That, historically, it took time for many people to understand this, doesn't mean that, now, it's not understood. 

If one does want to take into account relativistic effects, then one needs to work within the framework of quantum field theory, not one-particle quantum mechanics. And there the calculations are, equally, straightforward, at the level of principle, discussed here; one can compute transition amplitudes and  the corresponding probabilities and one does find that relativistic invariance is manifest and confirmed. And that the necessary intermediate states do, in fact, have the property that the measure doesn't factorize. Nonetheless, this isn't inconsistent with relativistic invariance, because the particles that are associated with these states are ``off-shell', i.e. the field configurations do not satisfy the classical equations of motion. (A fact, about intermediate states,  that was noticed, indeed, within quantum mechanics, by Dirac.). 

One doesn't require a unified framework of quantum mechanics with general relativity, if one can work in the approximation where astronomy is relevant and, thus, gravitational effects are classical.Then one studies quantum field theory on a fixed, eventually, curved, background. For astronomical purposes one then finds what's expected. 

One does require a, hitherto unknown, theory that does unify quantum and gravitational effects, if one wishes to study how entangled quantum measures affect spacetime, e.g. during the late stages of Hawking radiation, when the spacetime geometry changes ``rapidly'' with respect to the radiation rate. That's why it's not possible to describe what ``black hole evaporation'' really means, yet.

The solution is simple: one writes down the evolution of the 2-particle system, |A,B>(t). One can, thus, compute any transition amplitude of the 2-particle system.  If one is interested in one-particle transition amplitudes of particle A, one computes the transition amplitudes, by summing over the states of particle B; idem for the other case. Depending on the situation one inserts the corresponding projector, that expresses any additional constraints, like time ordering. That's all. 

To Stam,

The "many statements" that you seem to dismiss, contain the PROBLEM. If one takes from my question only the "any suggestion?", one can suggest a solution to another problem than I pose. I am interested in answers that address the problem. By the way, the problem is pure quantum, classical limits is not an issue here.

I see your answers, and I repeat that you don't address the problem.

Do you need an example in order to understand the problem? Here it is: take the polarization singlet of two photons, A and B. If A is measured first, then the result of A is arbitrarily picked, but the result of B depends on what answered A. However, in another frame, B can appear as measured first. So, B should give an answer arbitrarily picked, and A's answer should be fitted to what answered B.

It can't be that for both A and B the answers are arbitrarily picked, such answers are UNCORRELATED.

I repeat, if one doesn't want to read the problem and dismisses it as "many statements", it's a bad service to the question, it deflects the attention of other users to non-relevant issues.

Also, the question is not HOW TO CALCULATE, but how to explain. As to relativistic fields that you recommend, what to do with them? Do they tell you which experiment is done FIRST?

Mainz, Germany

Dear Nicolis,

Thanks for your thoughtful reply.

you wrote:

No, entanglement is the name of the causal explanation-not any alternative: it's the term that signifies the non-factorizability of the multi particle measure over one-particle measures, which is the technical description, of what's happening. And I'm saying that "collapse'' is just a word, that means that the measure becomes localized on a particular subset of states. But, once more, the calculation is unambiguous. That, historically, it took time for many people to understand this, doesn't mean that, now, it's not understood.

---end quotation

So you do think that "collapse" and entanglement correlations are causal. I'm surprised. But I don't see anything in what you say that would tend to convince me of this--so far. You say, of entanglement that "it's the term that signifies the non-factorizability of the multi particle measure over one-particle measures, which is the technical description, of what's happening." I see nothing to dispute in that, but it doesn't seem to indicate anything causal, as the term is usually understood.

The way that causality is normally understood, you have regularity or uniformity of sequence and temporal order. But I don't believe there is any evidence of temporal ordering in entanglement phenomena. It just a matter of correlation between the measurements made on one element of the entangled ensemble and what may be found regarding the other elements. It is not that a measurement brings about something else in a temporal sequence. It is usually understood that a cause has to proceed its effect. I take it not all correlations are causal in character. 

Briefly, I'm aware of the difference between QM and QFT, in relation to relativity, but emphasis on the point seemed unnecessary to what I was saying in the note you replied to above. Nor do I think that a unified framework is require for this particular discussion and the questions at hand. Again, I have no doubts about the relevant calculations. I'm concerned with the relationship of QM to causality.

H.G. Callaway

Sorry, by ``causal explanation'' I mean that entanglement is the ``causal explanation'' of the effects, not that entanglement is ``causal''. 

Regarding the two-photon state, once more, this is elementary quantum mechanics-one has a two-particle state, |s1,s2>(t). To compute any property of photon 1, at time t, one computes 

sum_(over s2)(t)

where P is some operator. This is done in the frame of observer O1 (nothing to do with photon 1, of course!)  This operation induces a new probability measure, that one needs to use to compute subsequent transition amplitudes. So far for observer O1.

It's probably easier, technically, to take some fixed basis and let the operators evolve in time. 

Now take some other observer O2, in another reference frame. Within non-relativistic quantum mechanics, this means that one performs a change of basis and computes the corresponding quantities. The change of basis induces a corresponding change in the transition amplitudes and the probabilities. What's the problem? If the space of states has some non-trivial geometry, as is the case here, this will become manifest in the transition probabilities. Where's the problem of principle? There isn't any problem of principle at all, just a question of linear algebra and calculus.

The result of any measurement in quantum mechanics is NOT, ``picked arbitrarily at the time of the measurement''-that statement is wrong.  Quantum mechanics defines dynamics, a time evolution of dynamical variables, that induces a probability measure on any measurement. If one wishes to find a way to render such distributions sharply localized on configurations, one is looking for ``hidden variables''. And one can try to work out the consequences and finds either contradiction with experiment, or another, equally non-local, formulation (Bohm): the non-local correlations are simply repackaged. So it's a metaphysical question, whether one wants to use Schrödinger, Heisenberg, Feynman or Bohm's (cf. http://www.bohmian-mechanics.net/index.html ) formulation, since they all give the same results. 

All the confusion in the text is due to the lack of any attempt to actually calculate anything. Classical mechanics, also, describes probability distributions in phase space-the evolution equation is Liouville's equation. It's instructive to compare the two. If one does attempt to calculate the evolution of the probability distribution of any quantity and tries to study how average values behave and when they can become typical values, using standard techniques from probability theory, one will find Ehrenfest's theorem and so on and find just what a single trial means and how all this differs from classical, non-commuting, degrees of freedom, in contact with a noise bath. When one does take into account the fluctuations of the noise, one will find quantum mechanics, once more, where the noise fluctuations describe the quantum fluctuations and, for non-commuting variables, one will find matrix quantum mechanics. And one will not come to any sort of impasse whatsoever, when one tries to perform a change of reference frame. 

All this, in fact, has been done in studying the classical limit of quantum observables and, also, when studying how thermodynamics emerges as the macroscopic description of statistical mechanics. Quantum mechanics introduces certain new features, that's all, namely non-factorizable states. These appear due to interference effects, that aren't present elsewhere. And the stochastic formulation avoids them, because it computes the distribution directly. 

Stam,

If you want to answer, please focus on the question. You systematically introduce alien issues. I don't agree that my question be flooded with unrelated talks: statistics, Liouville, Ehrenfest, classical limit, quantum fields, noise,... A whole safari.

It's not a question about statistical experiments, but about SINGLE TRIALS. I gave you the most known example. Given the polarization singlet of two photons, A and B, and given that both are measured along the same axes, x and y, the state can be written as

|ψ> = (|x>|x> + |y>|y>)/sqrt(2).

So, whenever A responds x, so does B, deterministically. And whenever A responds y, so does B, also deterministically. Which statistics do you need?

But, I repeat, there are frames by which A is measured first, and frames by which B is measured first. So, each particle should produce the result independently because it is measured first. But the results are deterministically correlated, see above. 

How so? Is some information transmitted from future to the past? Or, could there be a PREFERRED frame? Are there, in the quantum mechanics, some other hints that a preferred frame should be considered?

As to quantum noise, the results are not determined by quantum noise. Noise was proposed by Ghirardi, but doesn't help. Does the noise in a future measurement influence a past measurement? No!

Mainz, Germany

Dear all,

Here follows a video backgrounder on the present topic:

https://www.youtube.com/watch?v=sAXxSKifgtU

There are actually two connected videos, and they add up to about a half-hour. The second follows automatically after the first. They seemed to me very clear--concerned with the EPR argument, Bell's inequalities, and experiments connected with the theme.

I thought the videos well worth the time. Technicalities are minimized.

H.G. Callaway

Photons are indistinguishable particles in quantum mechanics, so the statement photon A is measured first, then photon B is measured afterwards doesn't make sense in this context: one photon of the two was measured the first time around, one photon was measured the second time around, but it's not possible, in quantum mechanics, to say *which* of the two photons was measured, that's why one traces over all configurations of one photon to recover the one photon state from the two photon state.  Some operator contains the information about the probability for measuring a photon in a given polarization state; if spatial information is available, the operator will project on the state at some position of a detector. The fact that a one-photon state *was* measured has consequences, that are discussed in Distler and Paban. And to compute what some other observer measures, one performs the corresponding transformations on the states, once one has specified how they evolve in time-which is missing here, still. 

One way would be to take the classical equations of motion for the polarization, replace the dynamical variables by operators, in the appropriate representation of spin,  impose Weyl ordering and solve the Heisenberg equations of motion for the operators, that act on the two-photon states. These operators transform appropriately under spacetime transformations and one goes on with the calculation. No problem of principle, no impasse, a nice exercise in practice. This doesn't have anything to do with any notion of single trial, it computes the usual transition amplitudes and probabilities, in any frame desired. Standard stuff. The subtlety here resides in ``inserting'' the fact that a measurement took place, within the evolution. That's all.

If one is worried about causality issues, it suffices to take an even simpler model: one free particle, compute its evolution and then state that, in frame F1, a measurement of momentum was done at time t1 and another measurement of momentum was done at time t2 > t1, in that frame and compute the state at time t3 > t2, in that frame. Now take another frame, F2 and compute what would be registered by that observer. 

This calculation can be done for the free relativistic particle, too, which can be consistently quantized, also. 

However for the dynamics of the polarization states considered here, one is, really, studying a 2-level system, the Lorentz transformations of the polarization 4-vectors are ``internal'' transformations. We have two 2-level systems in interaction, that's it, so it's a situation that can be described within non-relativistic quantum mechanics. 

So, if one does want to do single trials, one is doing *classical* electrodynamics, solving the classical equations of evolution for the polarization states and is describing the polarization states of the superposition of two electromagnetic waves.  There's no issue with quantum mechanics, so-called collapse and measurement problems.  One transforms the polarization vectors in the requisite configuration and finds the classical solution, in any frame desired. This situation is the classical limit of the situation mentioned in the beginning. That's why it's useful to describe a concrete calculation and not indulge in metaphysics-one then realizes fairly quickly why certain terms require clarification.

In quantum mechanics it's perfectly possible to say which photon was measured first if one indicates the frame of coordinated according to which one describes the experiment.

It's the relativity which creates a problem, because if the two measurements are separated by a space-like interval, if according to some frame the photon A was measured first, another frame exists by which the proton B appears as measured first.

And it seems that some people refuse to understand that the particle which is measured first, produces a result independent and unconstrained by any correlation with the other particle, the latter being measured in the FUTURE.

But if one believes that writing classical e.m. equations can help, one has to decide according to which frame of coordinates to write the equations, and one has also to explain why he chose that frame and not another frame.

Whether in non-relatvistic or relatvistic mechanics, classical or quantum, coordinate frames are not physical, so it is pointless to seek for any physical effect that is sensitive to a particular choice and it is pointless to discuss the physical meaning of any intermediate calculations that depend on it. It can be proved that there exist quantities that are independent of such choices. And this is so well-known, that it's surprising it's being discussed at this level at all. 

And photons, by definition, are indistinguishable particles, so it's, simply, meaningless to talk about photon A and photon B, when discussing a multiphoton state;  that makes sense when treating them classically, which is a shortcut for talking about polarization states of classical electromagnetic fields, that satisfy classical equations of motion. When talking about the one-photon subspace of multiphoton state spaces, one projects on the one-photon state by appropriate operators, that express the experiment-but this doesn't mean that it's possible to say *which* photon has been measured, just that *one* photon has been measured.  That's a consequence of the fact that  photons obey Bose-Einstein statistics, not Boltzmann statistics, like the modes of the classical electromagnetic field.

The constraints for the future come from the fact that future evolution depends on the fact that a measurement has occurred-that's new information and is realized through an appropriate projector. (A projector isn't invertible, by definition, that's how certainty is expressed. But, in quantum mechanics, the states are fixed and probabilities can be computed, only, nevertheless.) However, there isn't any problem, because an explicit calculation shows how the state of the system, measured at a time t3 > t2 = measurement of one photon > t1=measurment of one photon in one frame, can be expressed in terms of the state of the system measured in another frame, when ALL effects have been transformed appropriately and vice versa. So there isn't any issue.  The reason is that in the relativistic setting Poincaré invariance is a global symmetry, so causality is globally defined-it's not possible, by a Lorentz transformation, to violate causality, because that would mean that one has changed a time-like interval to a space-like interval and that's impossible. Therefore, events that are separated by a time-like interval in one frame, are separated by a time-like interval in any frame, if covariant quantities are calculated. Non-covariant quantities don't have any invariant meaning and no physical conclusion can be drawn from examining them. So, in relativistic mechanics, the intervals are the relevant quantities, not the time-components themselves. This is the mistake that has been made in many comments here. 

These statements are true in classical and quantum physics; relativistic quantum mechanics is an example, classical electromagnetism another.

The evolution equations are, typically, written in the Hamiltonian formalism. This is non-Lorentz-covariant. In the non-relativistic setting there isn't any problem.  In a covariant setting, it's known how to ensure that the results of the Hamiltonian formalism can be expressed in covariant form, which is that needed for discussing physical results. Any non-covariant effects can be proved to not contribute to any physical quantity and, indeed, make as little sense as in asking which coordinate frame is more or less physical than another. It's a meaningless question, that can only have a meaningless answer.

To Stam Nicolis,

If this question shouldn't be asked, according to your "enlightened" opinion, then please be kind and DON'T ANSWER IT. After endless explanations of mine, you still didn't understand the question although I said again, and again, and again what is the problem.

The most eminent physicists, Abner Shimony and his celebrated co-workers, Asher Peres, Giancarlo Ghiradi and his famous co-workers, the great experimentalist Nicolas Gisin, seek for decades an answer.

Didn't you read the articles of the above people? Didn't you hear about Gisin's experiments with devices that implement moving frames? Then READ! Get acquainted with the material before talking! What you think, that all these illustrious people are stupid? That universities pay such big money for such expensive experiments as Gisin's, out of stupidity?

If, as you say "it's a meaningless question", then please be so kind and GET DOWN FROM IT.

What they ask isn't any question that depends on the choice of any frame-that's the difference, that one, usually,  learns in freshman physics courses,and is then used everywhere else,  that one can choose any frame and write the answers in an invariant way.  

And simply dropping names of people that aren't involved in the discussion doesn't lend any credibility to an argument, but detracts from it-it, simply, means, one hasn't understood the issues oneself-which is obvious by any statement that implies that the choice of any particular frame can have any physical effect.  So it's actually awful to take their names in vain, this way. They don't deserve it. Apparently, beyond appealing, falsely, to authority, nothing of any content is proposed. The illustrious people aren't stupid-those that appeal to them and hide behind their names, are. 

Leave my question and don't dare to talk to me anymore ! I will complain to the moderators of your insult. !!!!!!!!!!!!!!!!!!!!

The problem isn't with the two-photon state-it's with the one-photon states. If one does consider a *one-photon* state, in spacetime region A and another *one-photon* state, in spacetime region B, where regions A and B are space-like separated, then one can ask, whether the dynamics of each one-photon state is always local, in the sense that it can be described in a covariant way, within each region.  After all, one expects such a covariant description, of local measurements. The surprising answer is that it can happen that such a covariant description isn't, in fact, possible, if it transpires that the one-photon state one is studying, in fact is derived from a multi photon state. In that case, one will find that, indeed, the one-photon dynamics isn't local-the reason is that the multi photon state is described by Bose-Einstein statistics. This produces a non-local interaction between the one-photon states one thinks one is studying in regions A and B, so the information about the original multi photon state is required. That's the problem. In the approximation when Bose-Einstein statistics can be described by Boltzmann statistics, this problem doesn't occur, since, in this approximation, this interaction is absent. On the other hand, if one does know what the original multi photon state is, one can describe the one-photon states, obtained by tracing over the residual states and one has a consistent description. It's non-local, too, but that's a fact of life, due to Bose-Einstein statistics of the multi-photon state and the fixed number of photons in that state.

These worries, in fact, can be seen to stem from the fact that, in relativistic mechanics, whether classical or quantum, in fact, it is not possible to describe the interaction of a *fixed* number of more than one particles in a covariant way, the so-called ``no interaction theorem'', apparently first formulated and proved by H. Leutwyler in 1964. This issue is resolved in quantum field theory, where a field describes, in a covariant way, an indefinite number of particles. The only exception is when the multi-particle dynamics is integrable, which means that the putative interaction is an artifact and the invariant description is that of non-interacting particles-that can be very hard to obtain, in practice, of course, from the original description. 

Of course the same reasoning applies to any one-particle state in quantum mechanics: for fermions, Fermi-Dirac statistics, similarly, leads to a putative non-local correlation between one-particle states in spatially separated regions and, once more, the consistent, albeit non-local, description is obtained by tracing over the appropriate multi-particle state when working with a fixed number of particles and using a field theoretic description for an indefinite number of particles.

(In a discussion forum one isn't addressing any particular person, but the discussion itself, hence the use of impersonal pronouns instead of personal pronouns.)