B A question about Bell's Inequality and hidden variables

[PeterDonis]

Hypothetically speaking imagine...

You're getting sidetracked on mechanism again. But testing your mechanism is simple: just figure out whether the function $E(a, b) = F(A, B)$ that describes the results it produces can be factored the way I described in my last post, or not.

But when the particle was entangled, it lost it's probability and one of them always pointed up and one of them only pointed down, regardless of the angle it was tested on

You're not describing a particle that "lost its probability"--you're just describing the standard singlet state of two qubits, whose spins are guaranteed to always be opposite if they are both tested with the same angle. And yes, this state can (obviously) produce results that violate the Bell inequalities. Which means there is no way to write down a function that describes how the results depend on the measurement settings that will factorize in the way I described in my previous post.

So if I did the bell test with 3 randomly selected angles, it would still be a 50% chance of detection at each angle

A 50-50 chance for each one considered individually, yes. But you would always find that, if the angles selected were the same for both particles, their results would be opposite.

What you have not considered is what happens when the two angles are different. You will still get a 50-50 chance of each outcome for each particle considered individually, but now the correlation between the results for the two particles will be different--they won't always be opposite. But if you do a lot of trials at lots of different combinations of angles, you will find that the whole set of results is described by some function $E(a, b)$ that cannot be factorized in the way I described.

 

[DrChinese]

...the Bell theorem has many possible loopholes. The most serious of them is the fair sample loophole. ... As for today, numerical simulations may produce the nearest outcomes to QM while experiments are probably around 1 or 2% detection rate.

Loopholes are a topic for another thread.

But a number of Bell tests have been done without detection issues requiring the fair sampling assumption. Here's a great one:

Experimental loophole-free violation of a Bell inequality using entangled electron spins separated by 1.3 km
https://arxiv.org/abs/1508.05949

 

[Leo1233783]

But a number of Bell tests have been done without detection issues requiring the fair sampling assumption.

I aim to work on experimental raw data. Possibly with external referees like this one : Significant-loophole-free test of Bell's theorem with entangled photons and many others. We are talking of sciences. Experiments must be rigorous and reproducible. It is the basis of any scientific education.

I have myself no opinion. I fluctuate between interpretations 3 times in the same hour.
I tried to compress the post. If you need details on anything above , please ask.

 

[rede96]

Heuristically, it goes like this: we have some probability, correlation...

Thank you for explaining that in more detail.

So, whatever is causing the thingie we're interested in, it cannot break down into something that only depends on the settings at A, and something that only depends on the settings at B

So if I've understood all this correctly, then what this is telling me is that there is no information a particle could carry that would lead to a violation of bell's inequality because any information it held would just lead to a different outcome at A and at B independently. But no combination of the settings at A and the settings at B could lead to violation of Bell's inequality due to the way the probabilities factorise.

Therefore what is causing the thingie we are interested in can only happen after the measurement. And we can separate A and B far enough so that no information could pass between them in the time taken to measure them both respectively. Hence non locality.

Is that correct?

And yes, this state can (obviously) produce results that violate the Bell inequalities. Which means there is no way to write down a function that describes how the results depend on the measurement settings that will factorize in the way I described in my previous post.

So here's the crux of my confusion. In my hypothesis, assuming a bell test had not been done, then the probabilities we assume for the bell test would be exactly the same as the probabilities that are used. As the individual particles act in exactly the same way as electrons for example. Also, whenever we measure the entangled states at the same angles we always see anti correlation. Which again is what we see with electrons. EDIT: Hence why we'd assume the same probabilities.

It would only be when we ran the bell test that we would discover that the probabilities wouldn't factorise to be dependant on just the settings at A and the setting at B. BUT we would still have violation of Bell's inequality that could be explained classically.

So back to the real world, when we do get a violation of Bell's inequality how we do we know that there is not something weird going on with entanglement that means maybe the probabilities we assume for entangled states being measured at different angles, are not correct? As in my imagined scenario.

EDIT: In other words how do we know that entangled particles aren't just correlated within a certain range of angles relative the north / south poles of the magnetic field but then setting of angle dependant at angles outside of that range? If that makes sense?

 

[DrChinese]

1. BUT we would still have violation of Bell's inequality that could be explained classically.

2. So back to the real world, when we do get a violation of Bell's inequality how we do we know that there is not something weird going on with entanglement that means maybe the probabilities we assume for entangled states being measured at different angles, are not correct? As in my imagined scenario.

EDIT: In other words how do we know that entangled particles aren't just correlated within a certain range of angles relative the north / south poles of the magnetic field but then setting of angle dependant at angles outside of that range? If that makes sense?

1. There are NO classical datasets that reproduce the quantum expectation values. As I have mentioned, you can hand pick them, and it still won't work. Just try.

2. Obviously, you can run a correlation test on entangled pairs at any 2 desired angles and verify that the quantum predictions are correct. What angles do you think the quantum predictions (cos^2 of theta) are not correct? It should be obvious that this has been tested up one side and down the other. There may have been tens of thousands of Bell tests run by now supporting the predicted quantum correlations.

Everything operates well in line with the predictions of QM. And those are clearly incompatible with local realism. Spin and polarization testing is but one area that this manifests itself. Probably over a thousand DIFFERENT tests of local realism (being falsified) as well. There have been no published reports I am aware of that indicate a FAILURE to falsify local realism - which would be big news itself if it could be replicated.

 

[rede96]

1. There are NO classical datasets that reproduce the quantum expectation values. As I have mentioned, you can hand pick them, and it still won't work. Just try.

Well, for what it's worth I can artificially create a data set that reproduces the quantum expectation values based on classical thinking. I just make some wild assumptions about how entangled particles work.

In essence I randomly generate an angle theta to represent the angle of the component of spin (Z direction) for both entangled particles. Then each detector selects one of three agreed angles randomly (as per normal bell test.) Then if theta is within a certain (small) range of the detector angle then it's detection is always up. So I can ensure particles measured at the same angle are always correlated. There is another range of angles where detection is probabilistic, so I get a certain amount of matches just by chance at different angles. Then there is another range where if the angle of the component of spin of particle falls outside of that range relative to the detector then because of some imagined property of the spin states, one particle will always be attracted to the north pole of the magnetic field and one to the south pole. Hence artificially reducing the number of matches.

By messing around with the probabilities and range I can artificially create the right number of matches and still have both particles exactly correlated when measured at the same angle. Like I said not sure what it means, but I can do it that way.

 

[PeterDonis]

Is that correct?

It's too vague to be either correct or incorrect. What is "information"? What does it mean for a particle to "carry" information?

You need to stop thinking in vague ordinary language terms. Bell formulated his theorem using math for a reason.

In my hypothesis, assuming a bell test had not been done, then the probabilities we assume for the bell test would be exactly the same as the probabilities that are used.

What does this even mean?

It would only be when we ran the bell test that we would discover that the probabilities wouldn't factorise to be dependant on just the settings at A and the setting at B. BUT we would still have violation of Bell's inequality that could be explained classically.

What does "classically" mean? If you are referring to the hypothetical model of yours that you keep talking about, it's too vague for me to tell whether "classically" is an appropriate adjective to describe it.

when we do get a violation of Bell's inequality how we do we know that there is not something weird going on with entanglement that means maybe the probabilities we assume for entangled states being measured at different angles, are not correct?

We don't have to assume any probabilities in order to measure violations of the Bell inequalities. We measure the probabilities. We don't assume them.

You seem to have things backwards. We don't assume something about the probabilities, and then try to decide whether violations of the Bell inequalities are consistent with our assumptions. The reasoning goes like this:

When we do experiments, we find that if we take the correlations between the results of measurements on pairs of spacelike separated particles, which have been prepared in a particular way (the way that quantum mechanics calls "entangled"), those correlations violate the Bell inequalities.

Bell's Theorem says that, if the correlations violate the Bell inequalities, then no function that factorizes in the way I described can produce those correlations. (The theorem is usually stated in the contrapositive form to this, but logically the two versions are equivalent, and the version I've just stated is more relevant to this discussion.)

Therefore, whatever-it-is that is producing the correlations cannot be described by a function that factorizes in the way I described.

The reasoning above assumes nothing about the probabilities; those are measured. It assumes nothing about the "state" of the particles, or about whatever "mechanism" might or might not be at work behind the scenes to produce the observed results. The preparation process that makes the particles is an objective process, which can be replicated without making any assumptions about what it is doing other than what is directly observed. So are the measurement processes.

What you appear to be trying to do is to construct some mechanism that will produce correlations that violate the Bell inequalities, but which somehow isn't "nonlocal", by whatever vague definition of that term you are using. But, as I said above, Bell formulated his theorem using math for a reason. "Nonlocal" is a vague ordinary language term. But whether or not the function that describes the correlations factorizes is a precise mathematical question that has a precise mathematical answer.

for what it's worth I can artificially create a data set that reproduces the quantum expectation values based on classical thinking.

"Classical thinking" is a vague ordinary language term. To put it bluntly, say this statement of yours quoted just above is correct. Who cares?

What you cannot do is create a data set that reproduces the experimentally measured results (which are consistent with the QM prediction), and describe it using a function that factorizes in the way I described. It's mathematically impossible: that's what Bell proved. And with that, this discussion has gone around in circles long enough. Thread closed.