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Do Bell and PBR together point toward nonlocal reality?

  1. Jun 4, 2013 #1


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    The Bell theorem (and its variations) suggests that either locality or reality is wrong.
    The PBR (Pusey-Barrett-Rudolph) theorem (and its variations) suggests that quantum state is real (ontologic).

    So what do they tell us together? Do they suggest that eventually it is only locality which is wrong? Do they suggest that the right interpretation of quantum mechanics should be formulated in terms of nonlocal reality?

    Or perhaps "reality" in Bell theorem has nothing to do with "reality" in PBR theorem?
  2. jcsd
  3. Jun 4, 2013 #2


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    I think it is the last one.
  4. Jun 4, 2013 #3


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    In the EPR special case in which the element of reality criterion is met (wavefunction is 100% certain to give an expected result), then the 2 definitions of reality are the same. But the EPR case falls apart after that, when the element of reality is no longer 100% certain. PBR accounts for that case because it says the wave function and therefore its related probability is not an EPR element of reality but is consistent with the predictions of QM.

    If Bell says (either one or both of) locality and realism are incompatible with QM, then I read PBR as saying EPR realism is incompatible with QM. I know many don't read it that way, but you ask what they imply. So for the Bohmian, I say you should now reject both locality AND realism. That probably isn't much of a stretch for you. :smile:
  5. Jun 4, 2013 #4
    For the Bohmian, above theorems are very comfortable. Because in Bohmian theory, the wave function is (together with the configuration) part of the reality. dBB is nonlocal (thus, compatible with Bell) and the wave function is real (thus, compatible with PBR).

    And, of course, dBB is a realistic interpretation, so, realism is fine, no reason to reject it.
  6. Jun 4, 2013 #5
    As DrChinese explains, it seems that the PBR theorem is basically another nail in the coffin of local realistic theories: PBR gives us good reason why we shouldn't buy into a view--the epistemic view of quantum states--that would undermine Bell's theorem.
    That's an interesting way to put it. I would imagine that it could be possible for quantum mechanics to be correct but actually epistemic, and that the uncertainty in predictions is a relic of our ignorance of the system's actual state (a point in classical phase space), but PBR stands as reason to believe that QM isn't actually epistemic.
    Last edited: Jun 4, 2013
  7. Jun 5, 2013 #6
    I thought that PBR + Bell have no bearing on the realism/non-realism issue. It only bears on the debate between the different "realistic" interpretations; that is, if one holds the position that there's something "out" there that ψ represents (realism) then ψ must be ontic and not epistemic. So non-realist interpretations like Copenhagen/Bohr's are not affected. Scott Aronson argues that other post-QM scenarios (Penrose) are also not affected. He writes:
    QUANTUM MECHANICS-Get real: Do quantum states offer a faithful representation of reality or merely encode the partial knowledge of the experimenter? A new theorem illustrates how the latter can lead to a contradiction with quantum mechanics.

    Personally, the anti-realist stance makes no sense to me at all, whether the local or the non-local variety. I mean if there are no ontic issues, what's the difference if something is local vs non-local? I've never been able to understand this.
  8. Jun 5, 2013 #7
    That's a silly thing to say. Henry Stapp has written whole books on how wavefunction collapse could be a fundamental part of physics.
  9. Jun 5, 2013 #8
    Well, the extent to which we can develop a rational posture about some kind of non-local reality depends on the logical consistency of the actual non-local models of reality that we have available to us. I've been trying to develop a reasonable model for such a reality in this thread. The actual development of the model starts at this post. My reasoning starts with the assumption that "non-localism implies universalism". Using this assumption, I am attempting to develop a picture of universally defined elemental harmonic oscillators that can be trivially added together in order to realize a constantly evolving composite universal waveform. No probability fields are involved; only pure mechanism.

    All thoughtful criticisms of this Bohm-like model of the universe are highly welcome!
  10. Jun 5, 2013 #9
    The PBR theorem is totally overrated. There is a version of Bohmian mechanics due to Maxim Raykin (it's on arxiv) which doesn't use wavefunctions at all. The Bohmian trajectories are still there, but they come from a different equation of motion. This escapes PBR because of a PBR assumption about ontic overlap of epistemic states - the assumption that there must be ontic states which are covered by more than one epistemic state (wavefunction state). This is not true of Bohmian mechanics, it's not true of Raykin's theory, and the widespread belief that "PBR proved that the wavefunction must be real" is just wrong, because it misses the essential role played by the overlap assumption.
  11. Jun 6, 2013 #10


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    I think you are right. The existence of some reality (lambda) is an ASSUMPTION of the PBR theorem. What the theorem shows is that IF some lamda exists, THEN wave function can be determined uniquely from that lambda.

    But it's also interesting to see how others think of it.
  12. Jun 6, 2013 #11


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    I don't think that this theory escapes PBR. True, the wave function psi(x,t) is not a part of its formulation. But the theory is formulated in terms of another function p(x,t), which is essentially a logarithm of psi(x,t). Thus, the reality of p is equivalent to the reality of psi.

    Or perhaps your point is that psi is not real in Bohmian mechanics? If that is the case, then I have to say that most Bohmians (including myself) disagree.
  13. Jun 6, 2013 #12


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    Well the original PBR paper was pretty clear:

    'The argument depends on few assumptions. One is that a system has a real physical state - not necessarily completely described by quantum theory, but objective and independent of the observer. This assumption only needs to hold for systems that are isolated, and not entangled with other systems. Nonetheless, this assumption, or some part of it, would be denied by instrumentalist approaches to quantum theory, wherein the quantum state is merely a calculational tool for making predictions concerning macroscopic measurement outcomes.'

    My interpretation - the Ensemble Interpretation - for example evades it. Copenhagen may or may not depending on precisely what variant you adhere to - but I think the most common one is, while it considers the wavefunction completely describes a quantum system, it is nothing more than a theoretical concept.

    Schlosshauer and Fine did an interesting analysis that showed for every interpretation where the theorem applies one exists where it doesn't and conversely (at least that's my reading anyway):

    My view is just like when QM was first developed and the Copenhagen interpretation put forward we didn't know much about decoherence which has shed a lot of light of foundational issues there is a lot more to be worked out before its fully understood - and there will probably be a few surprises. Of course I have zero idea what they will be.

    Last edited: Jun 6, 2013
  14. Jun 6, 2013 #13


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    One issue is the words "realism" (in the EPR sense) and "reality" (in the PBR sense). Though the words have the same root, these are 2 different ideas. With EPR realism, there is physical reality to all particle observables at all times. This is a non-contextual viewpoint, because reality is independent of the observer.

    With PBR, the wave function itself is considered to be its own reality (although particle observables are not mapped to definite values more than the HUP would support). In this sense, there is still observer dependence ie there IS contextuality.

    So I personally see Bohmian class theories as contextual. In my mind, they would need to be contextual in order to escape PBR. Because PBR excludes theories in which there is EPR realism, even as it embraces wave function reality. Not everyone reads PBR quite as I do, but the flip side is that PBR implies that QM IS a complete description of reality. I am sure a lot of folks feel the same.
  15. Jun 6, 2013 #14
    There is no problem with the difference, the relevant notion of realims is that of PBR. The realism of all particle variables all the time is not a definition of realism, but a consequence of realism combined with Einstein causality and the 100% correlations. So it makes no sense to put this into the definition of realism.

    dBB theory is contextual, there was never any doubt about this AFAIK. But to name it "observer dependence" is dangerous, it may be misleading because it suggests some relevance of consciousness. What is measured is the result of an interaction between the "measured object" and the "measurement device", which depends on the state of above, so to name this "measurement" is already misleading.

    From point of view of dBB theory the wave function and the configuration really exist. So dBB is very comfortable with PBR. But, of course, for dBB the wave function alone is not complete. Thus, it cannot follow from PBR that the wave function alone is complete.
  16. Jun 6, 2013 #15


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    Can you elaborate on this? What's the connection with locality?
  17. Jun 6, 2013 #16
    If Yakir Aharonov's time symmetric interpretation of quantum mechanics is applied, a form of locality can be preserved.
  18. Jun 7, 2013 #17


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    One should distinguish interaction locality (there is no interaction at a distance) from ontological locality (the reality is well defined at a local point in spacetime). Any interpretation which claims that wave function is real is ontologically NON-local, even if it is local in the interaction sense (like many-worlds and time-symmetric interpretation).

    There is also a third notion of locality - signal locality (inability to send superluminal signals controlled by humans), which is obeyed by all interpretations of QM.
  19. Jun 7, 2013 #18

    Again please visualize two particles that are quantum entangled moving apart in opposite directions. At a space-like distance from their common origin, Alice measures the spin of one of the particles and finds that the spin is in the up direction. In traveling from the point of origin to Alice, we may understand the particle's wave function to have, in a probabilistic sense, taken all possible paths and to possess all possible states consistent with the initial boundary condition of the system at the origin. With TSQM we must now visualize a time-reversed wave function which proceeds backwards in time from the occurrence of Alice's experiment to the time and point of origin for Alice's particle. This backward in time wave function would also, in a probabilistic sense, take all possible paths and possess all possible states consistent with three constraints: (i) the time evolution of the wave function is backward in time; (ii) the time-reversed wave function is bounded by the initial state of the system at the origin and (iii) the time-reversed wave function is also bounded by the particle location and spin information arising from Alice's experiment. It should be noted at this point that due to conservation of momentum the direction of spin manifest in Alice's time-reversed wave function will be opposite to the spin direction that Alice measured; and identical to the spin Bob will find when his measurement occurs. In any event, Alice's time-reversed wave function may be understood to carry the spin information arising from Alice's experiment to the time and location of origin for the entangled particles. Here, the information contained in Alice's time reversed wave function may be understood to "bounce" forward in time in a state that is entangled with Bob's particle. Please note that weak measurements of Bob's and Alice's particles immediately prior to the occurrence of their respective ideal measurements will show that each particle has remained entangled with the other.

    My conclusion from the foregoing is that TSQM reintroduces a classic-like causality, and locality, to quantum mechanics that I believe has very broad implications. This interpretation based on time reversal is far from original. As early as in 1983 Costa de Beauregard gave a formulation of the EPR setting that allowed a time-reversed EPR.

    J. W. Moffat in his paper “Quantum Measurements, Nonlocality and the Arrow of Time” (See: http://arxiv.org/pdf/gr-qc/9710019) proposes an absorber wave function reduction process to resolve the EPR paradox that is based on the retarded (forward-in-time) and advanced (backward-in-time) waves that John Cramer proposed in his transactional interpretation of QM.

    The TSQM approach, which I favor, is presented in a paper by Yakir Aharonov and Jeff Tollaksen titled New Insights on Time-Symmetry in Quantum Mechanics (see http://arxiv.org/PS_cache/arxiv/pdf/0706/0706.1232v1.pdf

    Additionally, Dr. Henry Stapp in a private communication I catalyzed has stated:

    “If one considers an EPR-Bohm-Bell correlation experiment, then during some interval in Process Time the initial (singlet) state of the two particles will be created.
    Over an interval in Process Time this singlet state will grow out in an expanding V-shaped region of spacetime, toward the two far-apart detection regions. At some Process Time a detection will occur. At that moment in Process Time the state of the universe in the space-time past of the associated space-like surface will suddenly change, relative to what it was at the earlier moments in Process Time. In the V-shaped region of spacetime the state will suddenly jump from a singlet state of the two diverging particles to a state in which, for example, one particle is polarized in one specific direction, specified by the orientation of the device in one of the two regions, and the particle traveling along the other wing of the V is polarized in the opposite direction. The correlation between the parts in the two wings will be fixed instantly (in Process Time) over the entire V-shaped region in spacetime. The effective transfer of information about the choice of polarization direction, which choice was seemingly made by the agent/observer in one region, is made via the V-shaped region that extends backward in time: the [apparent] faster-than-light transfer of information is made by an effective transfer first backward in time to the region where the two particle interacted (or originated), and then forward along the other wing of the V.”
  20. Jun 7, 2013 #19
    ¿ What is realism

    ¿What does mean realism in QM. ¿ And ontology
  21. Jun 8, 2013 #20
    Yakir Aharonov's time symmetric interpretation of quantum mechanics offer a way to explain the EPR paradox and preserve the local realism that Einstein was seeking.
  22. Jun 9, 2013 #21
    Realism taken alone means that there is some reality. This is the type of reality used by PBR as well as by Bell. Some [itex]\lambda\in\Lambda[/itex]. The choice of λ has to be made by particular physical theories.

    Now we start with the observation of 100% correlations of values measured far away, and the criterion of reality
    Then we measure it at A, and assume that the measurement in A does not disturb the system at B, then we can predict the result of the same measurement at B, thus, it has to be an element of reality. But we need this additional assumption, which is a consequence of Einstein causality.
  23. Jun 9, 2013 #22
    Time-symmetric interpretations, with causal influences into the past, are interpretations for those who like science fiction and mystics. There is not a single bit of empirical evidence in favour of causal influences from future into the past.

    We have, of course, very strong evidence against Einstein causality. It is not possible to give any realistic interpretation of violations of Bell's inequality compatible with Einstein causality. So it has to be given up. But that means we have to go back to classical causality, and there is no reason to go into the direction of sci-fi mystics of causal influences into the past.
    Last edited: Jun 9, 2013
  24. Jun 9, 2013 #23
    No so.
    Introduction to Time Symmetric Quantum Mechanics (TSQM)

    Nearly all physical processes at the microscopic level are time symmetric, such that that the theoretical statements that describe them remain true if the direction of time is reversed. (See http://en.wikipedia.org/wiki/Arrow_of_time) It is the second law of thermodynamics and our experience that conventionally limits classical mechanics and the equations of Maxwell, Schrödinger and Heisenberg to a “forward in time” direction. Accordingly, any quantum system is normally described in terms of the quantum state(s) of the system’s initial condition(s) and the subsequent evolution of the initial state(s) in a “forward in time’ direction. However, in time-symmetric quantum mechanics (TSQM), quantum systems must be described both in terms of forward-in time evolution of the systems’ initial boundary states, but also in terms of some future-defined boundary conditions that evolve backward in time.

    A more detailed description of TSQM

    (For readers seeking an in dept introduction to TSQM, a multitude of relevant papers can be found on Google Scholar. Also, Jeff Tollaksen's (who previously taught at George Mason) in a paper titled “Novel relationships between superoscillations, weak values, and modular variables” (http://iopscience.iop.org/1742-6596/70/1/012016) wrote the following:

    "The 'time-asymmetry' attributed to the standard formulation of Quantum Mechanics (QM) was inherited from a reasonable tendency learned from Classical Mechanics (CM) to predict the future based on initial conditions: once the equations of motion are fixed in CM, then the initial and final conditions are not independent, only one can be fixed arbitrarily. In contrast, as a result of the uncertainty principle, the relationship between initial and final conditions within QM can be one-to-many: two 'identical' particles with identical environments can subsequently exhibit different properties under identical measurements. These subsequent identical measurements provide fundamentally new information about the system which could not in principle be obtained from the initial conditions. QM’s 'time-asymmetry' is the assumption that measurements only have consequences after they are performed, i.e. towards the future. Nevertheless, a positive spin was placed on QM’s non-trivial relationship between initial and final conditions by ABL [named after the physicists Yakir Aharonov, Peter Bergmann, and Joel Lebowitz] who showed that the new information obtained from measurements was also relevant for the past of every quantum-system and not just the future. This inspired ABL to re-formulate QM in terms of Pre-and-Post-Selected-ensembles. The traditional paradigm for ensembles is to simply prepare systems in a particular state and thereafter subject them to a variety of experiments. These are 'pre-selected-only-ensembles.' For pre-and-post-selected-ensembles, we add one more step, a subsequent measurement or post-selection. By collecting only a subset of the outcomes for this later measurement, we see that the “pre-selected-only-ensemble” can be divided into sub-ensembles according to the results of this subsequent 'post-selection-measurement.' Because pre-and-post-selected-ensembles are the most refined quantum ensemble, they are of fundamental importance and subsequently led to the two-vector or Time-Symmetric reformulation of Quantum Mechanics (TSQM) [4, 5]. TSQM provides a complete description of a quantum-system at a given moment by using two-wavefunctions, one evolving from the past towards the future (the one utilized in the standard paradigm) and a second one, evolving from the future towards the past. While TSQM is a new conceptual point-of-view that has predicted novel, verified effects which seem impossible according to standard QM, TSQM is in fact a re-formulation of QM. Therefore, experiments cannot prove TSQM over QM (or vice-versa). The motivation to pursue such re-formulations, then, depends on their usefulness."
  25. Jun 9, 2013 #24
    TSQM's Experimental Verifications

    There is now third party research that quantitatively confirmed predicted outcomes which were unique to the TSQM formulation of quantum mechanics. As these outcomes cannot be explained by the traditional formulations of quantum mechanics, I believe that paradigm shifting evidence of “Quantum Miracles” is both beginning to emerge from independent research groups and is beginning to be recognized in the popular media (See Discovery Magazine http://discovermagazine.com/2010/apr/01-back-from-the-future/article_view?b_start:int=0&-C

    It must be emphasized that unique predictions of TSQM have been experimentally confirmed. These experimental verifications of TSQM are occurring in the context of "weak measurement" theory and research that itself involves both intriguing explanatory and ontological implications. As examples, please consider the following:
    "Experimental joint weak measurement on a photon pair as a probe of Hardy's Paradox" http://arxiv.org/pdf/0810.4229
    "Direct observation of Hardy's paradox by joint weak measurement with an entangled photon pair" http://arxiv.org/pdf/0811.1625
    "Quantum interference experiments, modular variables and weak measurements" http://arxiv.org/pdf/0910.4227
    "Postselected weak measurement beyond the weak value" http://arxiv.org/pdf/0909.2206
    "Complete characterization of post-selected quantum statistics using weak measurement tomography" http://arxiv.org/pdf/0907.0533
    and dozens more.
  26. Jun 9, 2013 #25

    At this point, you are probably wondering if TSQM is real or merely a mathematical-construct of dubious relevance to reality. Although numerous proofs are proffered in the above-cited papers, the following was presented in the Quantum Paradox class I attended and, to me, was particularly convincing. It also illustrates a phenomena that I will be mentioning in other notes.

    The following Quantum Box experiment provides one "proof" (there are many others) that TSQM is “real”. Before I go on to describe the experiment, you may wish to review an early description of the experiment. (See: http://arxiv.org/abs/quant-ph/0310091v1)

    Now, please visualize a set of nine boxes arranged in a three by three matrix with the columns labeled from left to right: Box A, B, and C; and rows labeled from bottom to top: time t, t+1 and t+2. A particle entering the system at the bottom (e.g. at time t) is understood to have a one-third probability of being in Box A, B, or C at all levels, t, t+1 and t+2. I understand that these probabilities were confirmed through ideal (von Neumann) measurements taken at each level. (We will defer the question: “what causes the wave function to “collapse” into one box and not in another” to my discussion of the Anthropic Principle.) In any event, these confirming measurements were not part of the experiment that I am about to describe.

    In the experiment that was reported in the lecture I attended, a very large ensemble of particles was introduced into the experiment and, although ideal measurements were taken at time t+2 for Boxes A, B, and C, only the experimental data for those particles found Box A (the post-selection sub-ensemble) were retained for further consideration. The theory behind the experiment is, to my understanding, that the ideal measurement of the sub-ensemble of particles found in Box A at t+2 constitutes a boundary condition, which through the propagation of a time-reversed wave, constrains the potential locations and states of the particle to that subset of positions and states that remain possible given both the t (starting) boundary condition and t+2 (ending) boundary condition. Mathematically, the theory generates for the selected sub-ensemble a probability of “1” that the particle at time t+1 will be found in Box A and also generates a probability of “1” that the particle at time t+1 will be found Box B. This means that if an ideal measurements had been conducted at time t+1 and Box A or Box B were, metaphorically speaking, opened, the particle would always be found inside the selected Box with absolute certainty. While this verification cannot be actually performed using ideal measurements, the prediction can be experimentally confirmed using weak measurements where the selected sub-ensemble includes a large number of particles. (Information on weak measurements may be found in the papers listed above.) The resulting interference pattern that Dr. Tollaksen presented arose from these weak measurements and was proffered as proof that TSQM is not just a mathematical model (with explanatory value) but also reflects an underlying reality (that I will explore in other papers).

    Noting that the probability of finding the particle in Box A and Box B at t+1 were both “1”, you may be wondering about Box C. Here, the mathematics predicts something that seemed astounding. Where the subject particles are electrons, TSQM predicts a particle with all of the attributes of a positron – but with a fundamental difference. The particle predicted for Box C must have a negative mass. (Although not discussed by Drs. Aharonov or Tollaksen, it appears that this finding would be necessary under a reasonable extension of the conservation of lepton law.) In any event, this outcome was mathematically demonstrated by Dr. Tollaksen and implicitly confirmed in the Physics Applications class that I later completed where it was shown that the time-reversed evolution of a matter wave was impossible where a positive mass was involved. Additionally, Dr. Tollaksen indicated that experimental verifications of these negative mass particles had been obtained.

    Subsequent to my preparation of the above lecture notes, a description of the experiment was published. Here is what Yakir Aharonov, Sandu Popescu, and Jeff Tollaksen had to say:

    "What about box 3? There are, altogether, only N particles. But we already know from the pre- and postselections that there are N particles in box 1 and also N particles in box 2. So we are forced to predict that the third box contains −N particles, a negative occupancy! ... The probe that measures the gravitational field of box 3, instead of being attracted to the box, is in fact repelled by it. The paradoxical result is, of course, just a quantum fluctuation, a measurement error, but an error that happens with virtual certainty. And the effect is not restricted to the gravitational field. Any interaction (for example, electric or magnetic) sensitive to the number of particles will be as if there are −N in box 3, so long as the coupling is small enough to be nondisturbing." Source: A time-symmetric formulation of quantum mechanics, Physics Today, November 2010, Pages30-31
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