Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

A Is entanglement based on first principles?

  1. Jul 20, 2016 #1
    Consider the original paper, ON THE EINSTEIN PODOLSKY ROSEN PARADOX by J. S. Bell from which the following quotes are taken:

    “Since the initial quantum mechanical wave function does not determine the result of an individual measurement, this predetermination implies the possibility of a more complete specification of the state.”

    In this quote we see that Bell refers to a wave function that is not the result of an individual measurement. However, the wave function was introduced specifically to describe individual measurements by Schroedinger. I have never seen a proof that allows this more loosely defined interpretation. Please correct me if I am wrong by supplying specific references. Bell continues,

    "Some might prefer a formulation in which the hidden variables fall into two sets, with A dependent on one and B on the other; this possibility is contained in the above, since λ stands for any number of variables and the dependences thereon of A and B are unrestricted. In a complete physical theory of the type envisaged by Einstein, the hidden variables would have dynamical significance and laws of motion; our λ can then be thought of as initial values of these variables at some suitable instant."

    This is wrong. Einstein never envisaged “a complete physical theory in which hidden variables would have dynamical significance”. He actually referred to quantum mechanics as a touchstone which would have to be derived if a more complete theory is proposed. In fact Bell correctly quotes Einstein as saying the following:

    "But on one supposition we should, in my opinion, absolutely hold fast: the real factual situation of the system S2 is independent of what is done with the system S1, which is spatially separated from the former."
    A. Einstein

    If we hold fast to the Schroedinger interpretation of a wave function then Einstein's quote merely refers to the actual measurements performed by Bob and Alice, not the questionable use of a wave function as referring to unobserved/unobservable systems, systems which come into existence in free space independently of the possibility of measurement. This is clearly a case of erecting a dummy Einstein and then defeating him. The actual mathematics of the EPR paper were given by Podolsky, not Einstein as stated in an earlier post on this forum by a philosophy major.
     
  2. jcsd
  3. Jul 20, 2016 #2
    The wave function (or more generally the quantum state) only predicts the probabilities of getting measurement outcomes, it does not predict individual measurement outcome. This is given by the Born rule and can be found in any textbook. Can you clarify what you mean by "the wave function was introduced specifically to describe individual measurements by Schroedinger"?

    I'm not sure what you mean by "a wave function that is not the result of an individual measurement." We can talk about a wave function after a measurement but a measurement result is a value, not a wave function.
     
  4. Jul 20, 2016 #3

    Paul Colby

    User Avatar
    Gold Member

    If QM is taken as first principles isn't the trivial answer to the question yes?
     
  5. Jul 20, 2016 #4

    bhobba

    Staff: Mentor

    Well things moved very quickly from when Schrodinger introduced the wave-function and what he envisioned it to be was quickly superseded by Diracs Transformation theory:
    http://www.lajpe.org/may08/09_Carlos_Madrid.pdf

    In fact Schrodinger goofed when he developed his equation - even though he got the right answer:
    https://arxiv.org/pdf/1204.0653.pdf

    Its the representation in the position basis of the quantum state. States, from the Born rule, most definitely do NOT determine the results of individual measurement. Einstein knew this championing the ensemble interpretation which is basically the Born rule taken to its logical conclusion.

    But to answer your question as detailed in the title entanglement most definitely comes from first principles - its the superposition principle applied to compound systems. That is if 2 systems can be in state |a> and |b> then system 1 in state |a> and system 2 in state |b> is written as |a>|b>. Similarly system 1 in state |b> and system 2 in state |a> is written as |b>|a>. But the principle of superposition says any linear combination such as 1/root(2) |a>|b> + 1/root(2) |b>|a> is also a possible state. Such states are peculiar to QM and are called entangled.

    Thanks
    Bill
     
    Last edited: Jul 20, 2016
  6. Jul 20, 2016 #5

    bhobba

    Staff: Mentor

    Of course.

    However I suspect the OP has something else in mind that perhaps needs further fleshing out.

    Thanks
    Bill
     
  7. Jul 20, 2016 #6
    Please strike the word individual except in the quote from Bell.
    I have to reflect a bit more before rephrasing my question.
     
  8. Jul 21, 2016 #7
    I'm not really sure what your question asks, but I assume from your earlier interest in the meaning of 'instantaneous' that you are looking for arguments that explain the effects of entangled states without the need to assume instantaneous communication, or alternatively to know exactly what instantaneous means in that context.

    The problem was addressed by Bell, and (in effect) he shows that if our rules for the resolution of entangled states are correct, then when resolution is forced on two widely separated particles, the outcome at each particle is dependent on the outcome at the other. In particular, he shows how one can design an experiment to confirm that dependence. That is not quite what Bell says, but it follows from what he said.

    The experiment has been done a number of times, but the outcome is in effect a sampling exercise, so the sample, the number of entangled pairs studied, must be large enough to make the probability of a false result small. In brief, the experiment sends entangled particles to two widely separated locations, and varies the state (meaning the orientation of the detectors) at one or both locations. The aim is to show that changing the state at one location A affects the outcome at the second location B, even when the change at A takes place outside the past light cone of the outcome at B. In other words, if information about the change of state travels from A to B and arrives at B in time to affect the outcome, it travels faster than light.

    The experiment has been done a number of times in a number of ways, I believe, but can't quote the papers. There do seem to be a few people who claim that the experiments are not conclusive. The experimental result relies on (in effect) performing a series of similar experiments, each of which gives a result which quantum theory predicts (say) to have a 60% chance of one outcome (0, say) and 40% chance of the other (1, say). The total experiment relies on running so long a series that we can be sure that the probability of outcome is indeed 60/40, and the chance of a misleading result is vanishingly small. However, it is the nature of the experiment that not all of the individual results are recorded. Those who claim the experiments are not conclusive point out that if the failure of an individual result is somehow correlated with the outcome, then the logic underlying use of a long series of individual results is flawed. If a 1 outcome is more likely to be missed than a 0 outcome, then we will see more 0's but not because that outcome is more probable. I don't find the argument appealing, but I am just an amateur.

    There is another more interesting experiment that as far as I know has not been attempted: perhaps it is still impractical. It relates to your earlier question about what 'instantaneous' means. If information about the change at A reaches B at faster than the speed of light, how much faster? If there is an answer to that, say at twice the speed of light, then we should still be able to find how fast by making the change of state later and the separation greater until we eventually manage to generate outcomes that do not obey the expected quantum law.

    This is an experiment that we expect to fail, rather like the Michelson Morley experiment to find a variation in the speed of light. If against all our expectations we did find there was a window in which the quantum law did not apply, we would have narrowed down what we mean by 'instantaneous'.
     
  9. Jul 21, 2016 #8

    Paul Colby

    User Avatar
    Gold Member

    In the classical example of two gyroscopes the correlation is instantaneous and no one is shocked and surprised because there is no interaction involved. Both gyroscopes have a preexisting classical value prior to measurement. In the quantum case there is no contribution to the system hamiltonian or interaction term connecting the measurements, so no interaction occurs. However, like all quantum measurements, classical values are replaced by quantum operators, state vectors and an elaborate song and dance. Like all measurements in QM there is a strong dependance on the choice of the measurement device so there are no preexisting QM ones ever. So, the correlation is instantaneous and there is no interaction term. This is very likely a fundamental aspect of nature just like the speed of light being a universal constant.
     
  10. Jul 21, 2016 #9

    bhobba

    Staff: Mentor

    Exactly.

    Its just a correlation with different statistical properties than classical correlations.

    People make too big a deal out of it IMHO.

    Its caused by the fact in QM things do not necessarily have values independent of measurement - if it does or doesn't is very interpretation dependent. The twist is if you insist it has values even when not measured then non local influences are required. but only if you insist.

    Thanks
    Bill
     
    Last edited: Jul 22, 2016
  11. Jul 22, 2016 #10
    That's partly why I started the other thread on delayed choice (apart from some misunderstanding on the nature of light, which was kindly corrected). Quantum effects collapse the whole system regardless of spacelike separation, but not at a 'speed', since the effect happens even regardless of event order. bhobba has made his thoughts on this very clear, and Dr Chinese was kind enough to (re)link a couple of papers and quote which are quite relevant. I will take the liberty of requoting here:

    http://arxiv.org/abs/quant-ph/0201134
    You can entangle particles AFTER they are detected, see page 5 for a discussion.

    http://arxiv.org/abs/1209.4191
    You can entangle photons that never co-existed, and therefore never interacted.
    "The role of the timing and order of quantum measurements is not just a fundamental question of quantum mechanics, but also a puzzling one. Any part of a quantum system that has finished evolving, can be measured immediately or saved for later, without affecting the final results, regardless of the continued evolution of the rest of the system. In addition, the non-locality of quantum mechanics, as manifested by entanglement, does not apply only to particles with spatial separation, but also with temporal separation. Here we demonstrate these principles by generating and fully characterizing an entangled pair of photons that never coexisted. Using entanglement swapping between two temporally separated photon pairs we entangle one photon from the first pair with another photon from the second pair. The first photon was detected even before the other was created. The observed quantum correlations manifest the non-locality of quantum mechanics in spacetime."

     
  12. Jul 22, 2016 #11

    Nugatory

    User Avatar

    Staff: Mentor

    The lower bound is at least 10,000 times the speed of light: http://arxiv.org/abs/1303.0614
     
  13. Jul 22, 2016 #12

    bhobba

    Staff: Mentor

    Of course one can try to measure any actual speed and if it is finite that would be very very interesting.

    That said its the exact quantum analogue of putting red and green slips in envelopes. Open one and you immediately know the other but there is nothing involving any kind of communication going on - all you have done is correlate the slips.

    As Einstein said 'God is subtle, but He is not malicious'. Don't try and over complicate it. As I said previously IMHO far too mush 'guff' is written about something that really isn't all that hard.

    Thanks
    Bill
     
  14. Jul 22, 2016 #13
    Don't delayed-choice experiments render this moot? Or do they still potentially suffer from the freedom-of-choice loophole?
     
  15. Jul 22, 2016 #14
    Those statements here seem to be inconsistent (are the red and green slips inside the envelopes not red and green??) and in striking disagreement with Bell!
    As a reminder, he argued in his "Bertlmann's socks" article (and essentially that argument is called "Bell's theorem"):

    "Dr. Bertlmann likes to wear two socks of different colours. Which colour he will have on a given foot on a given day is quite unpredictable. But when you see [..] that the first sock is pink you can be already sure that the second sock will not be pink. Observation of the first, and experience of Bertlmann, gives immediate information about the second. There is no accounting for tastes, but apart from that there is no mystery here. And is not the EPR business just the same ?"

    [after arguing that it's quite different:] "Phenomena of this kind made physicists despair of finding any consistent space-time picture of what goes on the atomic and subatomic scale."
    "It is as if we had come to deny the reality of Bertlmann's socks, or at least of their colours, when not looked at."

    "Could it be that the first observation somehow fixes what was unfixed [..], not only for the near particle but also for the remote one? For EPR that would be an unthinkable "spooky action at a distance". To avoid such action at a distance they have to attribute, to the space-time regions in question, real properties in advance of observation, correlated properties, which predetermine the outcomes of these particular observations."
    "It is important to note that to the limited degree to which determinism plays a role in the EPR argument, it is not assumed but inferred. What is held sacred is the principle of "local causality" - or "no action at a distance."

    "If we do not accept the intervention on one side as a causal influence on the other, we seem obliged to admit that the results on both sides are determined in advance anyway, independently of the intervention on the other side, by signals from the source and by the local magnet setting. But this has implications for non-parallel settings which conflict with those of quantum mechanics. So we cannot dismiss intervention on one side as a causal influence on the other."

    In other words: according to Bell, "denying the reality of the sock's colours when not looked at", can not explain the correlations as long as we adhere to Einstein-local causality. Which makes me wonder, how can either having no values when not measured, or having predetermined values before measurement, explain the correlations according to you?
     
  16. Jul 22, 2016 #15
    Sorry for the long delay, but writing about physics is a very difficult process. I have posted on this forum prematurely in the past and paid for it.
    I joined the thread after it had changed from instantaneous to Bell's theorem. I am not interested in arguments about whether Bell's theorem is correct in its mathematical content. I had never completely understood it in physical terms until Dr. Chinese explained it very simply in terms of Bob and Alice detecting the polarization of the photons. That's when I could finally interpret it my own way.

    My purpose in participating in this forum is not to convince anyone that I am right. Quantum mechanics is not going to change. I would like to be able to express my ideas rationally without trivial errors, and my participation here helps me to do that. My initial assumption is that qm is not wrong, but incomplete. I know that I am wrong within the context of accepted theory. If that offends to the point you can't respond in a reasonable way then don't.

    To analyze entanglement from first principles we have to go back to the beginnings of qm. Dirac's transformation theory treats emission and absorption as symmetric processes. This evolved from an earlier paper by Dirac, The emission and absorption of radiation which stated the same idea. It is accurate for all formulations of qm because non-relativistic theory is about changes in energy. If we look at characteristics of field we see evidence that these processes are not symmetric. Wave mechanics is based on energy absorption and can be shown to be equivalent to matrix mechanics, derived from emission processes, because it can be used to calculate the diagonal matrix elements. However, the reverse is not true. Matrix elements are derived using Fourier analysis and include transition probabilities giving the intensity of the spectral lines which cannot be derived using the Schroedinger equations. So quantum mechanical properties of field are not symmetric if we look at the emission and absorption of radiation.

    In my mind the question of whether entanglement is based on first principles boils down to whether the use of a wave function to describe the photons is legitimate. Ignoring for now the legitimacy of describing two spatially separate physical entities with a single function, which I also question, look at the symmetries involved. The photons are created by an emission process and detected by absorption. They are symmetric processes so long as we look at the energies involved, but Bell is basing his arguments on properties of the photon fields, their polarization, whose symmetry with respect to emission and absorption has not been demonstrated by anyone as far as I know. If they are not symmetric then Dirac did not take them into consideration in his transformation theory and I question whether they can be legitimately described within the context of transformation theory.
     
  17. Jul 22, 2016 #16

    bhobba

    Staff: Mentor

    There is no inconsistency or disagreement with bell.

    I will state it again.

    Both the red and green slips and bell type correlations are simply that - correlations. The difference is the red and green slips remain red and green at all times, for bell type correlations that may or may not be the case depending on QM interpretation. They have different statistical properties - that's all - but does not change the fact they are still just correlations. If you want it to be like red and green slips then you must have non local interactions. That's all there is to it.

    But people for some reason make more out of it.

    Thanks
    Bill
     
  18. Jul 22, 2016 #17

    bhobba

    Staff: Mentor

    That's false. Each can be derived from the other. It simply in the Schrodinger picture operators remain fixed but the state changes, whereas in the Heisenberg picture the state is fixed but the operators changes.

    I gave a reference where Schrodinger got his equation from - its was basically a crock and had errors - it was from the Hamilton-Jacobi equation and nothing to do with energy absorption - to the best of my knowledge anyway.

    In modern times it comes from symmetry considerations but that is a whole new thread.

    Can I ask where you are getting this from?

    Thanks
    Bill
     
    Last edited: Jul 22, 2016
  19. Jul 22, 2016 #18

    bhobba

    Staff: Mentor

    Well photons do not have a wave-function but that is itself a whole new thread and can be avoided by considering electrons in bell type experiments.

    I gave the general definition/explanation of entanglement. Its simply applying the principle of superposition to compound systems.

    Its very intuitive, but strictly speaking it is in fact an axiom of QM ie the tensor product of individual systems vector spaces is the space of the combined systems:
    http://www-bcf.usc.edu/~tbrun/Course/lecture04.pdf

    Thanks
    Bill
     
  20. Jul 22, 2016 #19

    Zafa Pi

    User Avatar
    Gold Member

    Indeed you have stated it again and again. We will never know how Einstein would have reacted to Bell's observations, but given the degree to which Einstein was wedded to determinism it is reasonable to assume that he may have accepted Bell's Inequality and not the QM predicted correlations. Einstein was no slouch and that alone makes it a big deal. (it would be fantastic to know how he would have reacted to the confirming tests of QM) Everybody prior to 1900 would have accepted Bell's Inequality if told Alice and Bob couldn't communicate (locality). There are those that think Bell should have received a Nobel prize. I personally find it weird and beautiful. It is a big deal, and perhaps you understand it so well that you're jaded.
     
  21. Jul 22, 2016 #20
    It's also been argued that if the effects observed in Bell-type experiments propagate at any finite speed, then non-locality could be exploited for superluminal communication (e.g. 'can't stay hidden'):
    Quantum non-locality based on finite-speed causal influences leads to superluminal signalling
    http://www.nature.com/nphys/journal/vaop/ncurrent/full/nphys2460.html

    Quantum correlations in Newtonian space and time: arbitrarily fast communication or nonlocality
    http://lanl.arxiv.org/pdf/1210.7308.pdf
     
    Last edited by a moderator: May 8, 2017
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook




Similar Discussions: Is entanglement based on first principles?
Loading...