Trying to Understand Bell's reasoning

[DrChinese]

I hope that works out for you.

Don't go away mad.

I really wasn't trying to insult you. We all write funny stuff from time to time. As you say, there are plenty of my posts that sound like I am smoking something. (Of course, who knows...?)

 

[ThomasT]

Don't go away mad.

I really wasn't trying to insult you. We all write funny stuff from time to time. As you say, there are plenty of my posts that sound like I am smoking something. (Of course, who knows...?)

What would give you the impression that I was mad, or going away? I don't always take the time to put smileys. (I'm smiling right now, can you tell?)

We agree that BIs are violated. We agree, I think, on the meaning of hidden variable (per EPR elements of reality). What remains is to hash out the reason(s) for BI violations and GHZ inconsistencies, etc. I'm saying that this can be understood via the application of logic.

As for explaining the correlations in, say, optical Bell experiments, well, that's an optics, not a logic, problem.

The logic problem can be absolutely solved. The optics problem is a bit stickier, but the correlations are not mysterious, and don't need nonlocality, from an optics point of view.

The solutions to both the logic and the optics problems hinge on the idea (and application) of global or joint parameters.

No need for nonlocality. (It's a silly idea anyway. Don't you think?)


As for this thread, I think the OP's point has been made. QED

This deals with one part of the logic problem.

 

[Boy@n]

Thomas, so what's your logical explanation for quantum entanglement? You see it just as a result of false tests or as real natural phenomenon?

If real, and if I let my imagination free, how crazy would be the idea that by separating quantum entangled particles we create a quantum wormhole and thus changing state of one would affect the other at the same time?

 

[Boy@n]

Seems 'my' idea is not new, see: http://iopscience.iop.org/0295-5075/78/3/30005

 

[JesseM]

Sorry I missed this post earlier Thomas:

Based on H, which includes all values for |a-b|, the angular difference between the polarizer settings

H is intended to encompass local physical facts in the past light cone of both the measurements and the experimenter's choices about what measurement settings to use. So, H doesn't include the specific detector settings.

and all values for |L_a - L_b|, the emission-produced angular difference between the optical vectors of the disturbances incident on the polarizer settings, a and b

Can you explain what you mean by "optical vectors of the disturbances", and how they are supposed to interact with the detector setting to determine the outcome of each measurement? You never replied to this post where I suggested one possible interpretation of what you might mean, and why this interpretation wouldn't be able to explain the statistics predicted by QM:

can you explain the nature of the local hidden variables, and how they interact with the angle of the polarizer to give the probabilities of different outcomes? For example, maybe you're suggesting that each particle has an identical hidden variable giving the angle v of its polarization vector, and that to determine the probability a particle is detected we just take the angle of the polarizer it goes through (a or b) and the angle of the particle's polarization vector (which has the same value v for both particles) and calculate cos² of the angle between them (i.e. cos²(a-v) for the first particle going through polarizer a, and cos²(b-v) for the second particle going through polarizer b). If so, this would not give a coincidence rate of cos²(a-b), as you can see if you set a=b while making v different from a and b; in that case cos²(a-v)=cos²(b-v)=some number between 0 and 1, so there is some nonzero probability the two particles will give opposite results, despite the fact that cos²(a-b)=1 (this is basically the same argument I was making in the first paragraph of post 81, except I forgot to take cosine squared rather than just the cosine of the angles).

respectively, then when, eg., |a-b| = 0 and |L_a - L_b| = 0, then P(B|AH) /= P(B|H).

Why do you say that? Again, your model isn't clear.

In this case, we can, with certainty, say that if A = 1, then B = 1, and if A = 0, then B = 0. So, our knowledge of the result at A can alter our estimate of the probability of B without implying FTL information transmission.

Sure, but that's not a probability conditioned on H. If H includes everything in the past light cone of the measurements, it already includes information about everything that happened to the particle prior to measurement, including the hidden variables (like your 'optical vectors') that were given to the particles by the source. So though the result at A can alter your estimate of the probability of B if the source assigned both of them correlated hidden variables, if you already know everything in the past light cone of the measurement of B, then you already know whatever hidden variables were assigned to B by the source, so the result of A tells you nothing further about the probability of B in a local hidden variables model, i.e. P(B|H) = P(B|AH).

 

[JesseM]

This isn't yet clear to me. If we assume a relationship between the polarizer-incident disturbances due to a local common origin (say, emission by the same atom), then doesn't the experimental situation allow that both Alice and Bob know at the outset (ie., the experimental preparation is in the past light cones of both observers) that if A=1 then B=1 and if A=0 then B=0 (and if A=1 then B=0, and vice versa) for certain settings without implying FTL transmission?

Yes, but that just shows that P(AB) is different from P(A)*P(B), or that P(B|A) is different from P(B). If L represents everything that happened in the past light cone of the measurement B, then L will already include whatever hidden variables were assigned to the B-particle by the source, so if you know L then learning A will tell you nothing new about the hidden variables assigned to B by the source, which is why P(B|L) = P(B|LA).

I agree that if P(B|L) /= P(B|AL) then P(A|L) /= P(A|BL), but doesn't the correctness of both of those expressions follow from the contingencies for certain settings which follow from the experimental preparation which is in the past light cones of both A and B?

No, see above. Again, you seem not to understand that Bell's argument was explicitly based on considering the possibility that the correlations between A and B might be explained by common hidden properties assigned to the two particles by the source.

In another reply to billschnieder you stated:

Consider the possibility that you may not actually understand everything about this issue, and therefore there may be points that you are missing. The alternative, I suppose, is that you have no doubt that you already know everything there is to know about the issue, and are already totally confident that your argument is correct and that Bell was wrong to write that equation ...

Yes, and people who are challenging thoroughly mainstream claims, and believing they have noticed some obvious flaw that thousands of very intelligent physicists have been missing for decades, have a special responsibility to consider the possibility that they may not understand everything (if they have a reasonable amount of intellectual humility).

Is it possible that the equation is wrong for the experimental situation, but that Bell was, in a most important sense, correct to write it that way vis EPR? Haven't hidden variables historically (vis EPR) been taken to refer to underlying parameters that would affect the prediction of individual results? If so, then wouldn't a formulation of the joint situation in terms of that variable have to take the form of Bell's ansatz? If so, then Bell's ansatz is, in that sense, correct. However, what if the underlying parameter that's being jointly measured isn't the underlying parameter that determines individual results?

Bell's ansatz applies to all possible underlying parameters that qualify as "local hidden variables" (i.e. variables associated with a particular position such as the position of the particle, and variables whose value can only be causally influenced by events in their past light cone at any given moment).

For example, if it's the relationship between the optical vectors of disturbances emitted during the same atomic transition, and not the optical vectors themselves, that's being jointly measured, then wouldn't that require a different formulation for the joint situation?

See my question in the previous post about what you mean by "optical vectors". Are the optical vectors supposed to be local hidden variables?

Do the assumptions that (1) this relationship is created during the common origin of the disturbances via emission by the same atom, and that (2) it therefore exists prior to measurement by the crossed polarizers, and that (3) counter-propagating disturbances are identically polarized (though the polarization vector of any given pair is random and indeterminable), contradict the qm treatment of this situation? If not, then might the foregoing be taken as an understanding of violations of BIs due to nonseparability of the joint entangled state?

Again, I need clarification about whether "polarization vectors" are supposed to be local hidden variables, and if so how they are supposed to interact with polarizers to produce measurement outcomes. If they are local hidden variables, then Bell's theorem does apply to them, and the statistics that would result from these polarization vectors would obey the Bell inequalites. But the Bell inequalites are violated in QM (and experimentally), so the theory won't work.