Travis Norsen

Submitted to “Quantum Nonlocality and Reality – 50 Years of Bell’s theorem”

J.S. Bell’s remarkable 1964 theorem showed that any theory sharing the empirical predictions of orthodox quantum mechanics would have to exhibit a surprising — and, from the point of view of relativity theory, very troubling — kind of non-locality. Unfortunately, even still on this 50th anniversary, many commentators and textbook authors continue to misrepresent Bell’s theorem. In particular, one continues to hear the claim that Bell’s result leaves open the option of concluding *either* non-locality *or* the failure of some un-orthodox “hidden variable” (or “determinism” or “realism”) premise. This mistaken claim is often based on a failure to appreciate the role of the earlier 1935 argument of Einstein, Podolsky, and Rosen in Bell’s reasoning. After briefly reviewing this situation, I turn to two alternative versions of quantum theory — the “many worlds” theory of Everett and the Quantum Bayesian interpretation of Fuchs, Schack, Caves, and Mermin — which purport to provide actual counterexamples to Bell’s claim that non-locality is required to account for the empirically-verified quantum predictions. After analyzing each theory’s grounds for claiming to explain the EPR-Bell correlations locally, however, one can see that (despite a number of fundamental differences) the two theories share a common for-all-practical-purposes (FAPP) solipsistic character. This dramatically undermines such theories’ claims to provide a local explanation of the correlations and thus, by concretizing the ridiculous philosophical lengths to which one must go to elude Bell’s own conclusion, reinforces the assertion that non-locality really is required to coherently explain the empirical data.

Dear Travis,

in Your paper You write at page 2 “The important thing was instead that the only way to explain the perfect correlations locally is to attribute outcome-determining properties to the individual particles”. This may be called simply as a pre-determination.

I think that this statement is not correct.

I have recently written a paper(http://vixra.org/pdf/1502.0088v1.pdf) in which I have presented the local explanation of EPR correlations without the necessity of the pre-determination.

In fact, the modified QM (http://vixra.org/pdf/1503.0109v1.pdf) is the local theory having the same empirical predictions as the standard QM.

I understand what is the source of this discrepancy. This is the anti-von Neumann axiom which is the basis of the modified QM.

Jiri Soucek

I’m highly skeptical of your claim, Jiri. Can you summarize in a couple of sentences how this local explanation works, to motivate me to look at the paper(s)?

Dear Trevis,

I have reconsidered my last reply and I have found that my objection was only partly true – I am sorry. As a result I found that inside the standard QM (with the von Neumann axiom) your argumentation is OK (i.e. the pre-determination must exist), while in the context of the modified QM (with the anti-von Neumann axiom) your argumentation is not correct (i.e. the pre-determination need not exist).

As a consequence, in the modified QM there exists the local explanation of EPR correlations and in the standard QM such an explanation does not exists. This is an important difference between these two theories and I hope I will be able to

clarify this point better in the future.

In fact, You have considered the problem in the context of the standard QM.

Your Jiri Soucek

I still don’t understand. My statement wasn’t “in the context of standard QM” but was instead intended as completely theory-neutral. I think the only way to explain the perfect EPR correlations in a locally causal way, is with pre-determined values. If you think that’s wrong (and have some concrete example of a theory which serves as a counterexample) I’d be interested to hear about it. But you’ll have to give me some kind of advertisement/motivation, because the argument for my claim is so clear and simple that I basically regard it is impossible that it could be wrong.

Dear Trevis,

I have finally found the simpler formulation of this local explanation of EPR.

Let us consider systems S and R which are in the standard singlet state and the measuring systems A at the area of Alice and B at the area of Bob.

The measuring system A has the basis |A+>, |A-> where these two states are individual states and let us assume that in the standard (von Neumann) measurement the state |A+> is linked to the state |Sphi+> of the measured system S and the state |A-> is linked to the state |Sphi->. The system S has individual states |S+>, |S-> and states |Sphi+>, |Sphi-> are not individual states but collective states, i.e. states of ensembles. The same for Bob, i.e. |B+>, |B->, |Rphi+>, |Rphi-> and Bob`s measurement links |B+> with |Rphi+> and |B-> with |Rphi->.

I shall describe at first the situation in terms of ensembles. The state of an ensemble is homogeneous if all systems in this ensemble are in the same individual state (e.g. an ensemble of A`s can be in the homogeneous state |A+> in which each individual system is in the individual state |A+>).

Let us assume that Alice has made her measurement and that she has found the system A in the individual state |A+>. In terms of ensembles this means that Alice should consider the new ensemble (subensemble) such that in this subensemble the system A is in the state |A+>. The ensemble of whole systems A+S+R+B will then be in the state |A+> x |Sphi+> x |Rphi-> x |B-> since there are correlations between A and S, S and R, R and B.

Let us now consider the individual run of the experiment, say the first run. This individual experiment must be considered as an element of the ensemble of experiments. This is the consequence of the “Principle of virtual ensemble” which is the hidden assumption of any probability theory: every event can be considred as a member of an ensemble of events (i.e. probability can be associated only with an ensemble, not with the individual system).

Bob`s ensemble will be in the homogeneous state |B-> and thus in the first run Bob obtains that his system B is in the individual state |B->. The point is that after the Alice`s measurement systems A and B are in the homogeneous states |A+> and |B->, while the states of systems S and R are in non-homogeneous states |Sphi+> and |Rphi->.

The main fact: states of systems A and B are correlated individually while states of systems S and R are correlated collectively, i.e. as ensembles.

There is no correlation between individual states of S and R in the subensemble. I.e. there is no individual pre-determination. Thus the “nonlocal” correlation between A and B is mediated by the correlation between ensembles of S`s and R`s but ensembles are generally nonlocal objects.

Thus the information of the result of Alice`s measurement is transfered to Bob through the virtual ensemble of whole systems. The content of this information is expressed in the fact that Alice`s system A is a member of the subensemble. This information need not be transfered to Bob since the unique important information for Bob is the fact that his system B is in this subensemble, but this is the consequence of the fact that both Alice and Bob are considering the first run of the experiment.

Simply speaking the point is in the fact that systems S and R are correlated (after Alice has made her measurement) only collectively, not individually.

From the anti-von Neumann axiom (each two different individual states must be orthogonal) follows simply why Bell inequalities cannot be derived. The derivation is based on the considerations containing individual systems. Each derivation must consider at least two different bases. But there is in disposition only one base containing individual states. Thus in the modified QM there are no Bell inequalities and nonlocality of the modified QM cannot be deduced.

In fact, I have no general proof of the locality of the modified QM, I can only assert that standard proofs of the nonlocality cannot be applied.

Jiri Soucek

I can’t follow your argument. You say that “there is no correlation between individual states of S and R in the subensemble.” But it is an empirical fact (or, if you prefer, a prediction of QM) that the outcomes of measurements will be perfectly (anti-) correlated. How does your model account for this empirical fact? It seems that if, as you say, there are no correlations built into the state assignments for the individual pairs, then your theory will have to predict less-than-perfect (anti-) correlations of measurement results … unless, of course, the model involves some nonlocal mechanism whereby the state of the distant particle “snaps into line” when the nearby measurement is made. That’s just exactly the dilemma posed by EPR, i.e., the argument that local determinism is the only way to account for the EPR correlations locally: either Bob’s particle was “programmed” to yield a certain result all along, or it only acquired this program as a result of the measurement performed by Alice. Pre-determination, or non-locality.

Dear Travis,

You write “But it is an empirical fact (or, if you prefer, a prediction of QM) that the outcomes of measurements will be perfectly (anti-) correlated”.

This perfect correlation is between states of measuring systems A and B (these are outcomes of the measuremeents) but not between states of measured systems S and R.

In modified QM in the measurement there is a link between the individual state of A and the collective state of S.

There is a pre-detetrmionation for S and R but only collective since states |Sphi+> and |Rphi-> (and also the original singlet state) are not individual states.

Perhaps the right name for my explanation is the collective pre-determination – there is an information written into states of S and R but this is the collective information, not the individual information.

This collective pre-determination of S and T cannot be transformed into the individual pre-determination since these states are not individual. In standard QM this can be transformed since each pure state is individual.

The modified QM is neither psi-ontic (like standard QM) nor psi-epistemic (like operational or statistical QM) but psi-hybrid – some pure states are individual (ontic), but other pure states are collective (epistemic). Outcome states of measuring systems are always individual.

In fact, I agree with You that there is necessary some pre-determination, but it could be only collective, not individual. But in deriving Bell inequalities the individual pre-determination is necessary.

Thanks You for your remarks, they are inspiring for me.

Jiri Soucek

Dear Travis,

I have written a letter, in which I have given the new local explanation of EPR correlations. I hope now this explantion is clear and indubitable.

It can be found at

http://vixra.org/pdf/1508.0147v1.pdf

Your Jiri Soucek