Dalo

Non-locality

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22 minutes ago, uncool said:

To clarify a little bit: in the proof of Bell's no-go theorem, the following assumption is made:

 

A classical (local hidden variable) theory is required to measure the expectation value of a random variable X according to [math]\int X(\lambda) p(\lambda) d \lambda[/math], according to some (hidden) probability measure p. On the other hand, a quantum theory is required to measure the expectation value of a random variable X according to [math]\int \langle \phi | X | \phi\rangle[/math], according to Bohr's rules. The theorem is then that there is a limit to the outcomes from any classical theory that doesn't appear for a quantum theory, as defined there, and therefore (since our experiments match Bohr's rules) that a quantum theory is necessary (or rather, a classical theory is insufficient).

 

You seem to be asking for a justification for the assumption - why should a classical theory require such an integral - and seem to think you have something that runs counter to that. Correct?

I have made it perfectly clear from the start, and if you want I will produce quotes from this thread, that I am not analyzing the mathematical structure of Bell's theorem, or that of von Neumann's argumentation.

In fact, I emphatically declared that the problem of hidden variables cannot be solved by mathematical means. The fact alone that there are at least two theories, von Neumann's and Bell's, with completely different conclusions, makes my position at least plausible.

My claim is that the whole concepts of local and non-local are wrong in the context of the experiment described by Maudlin. I am not ready yet to widen the claim to the whole domain of entanglement situations considered by quantum theory. I lack the expertise to analyze in sufficient details every example. The drawing I presented above does show that it does not really matter which property or which particle is considered. But it is a general argument which I would find very difficult to defend in all cases.

So, no, I am not pretending anything special about Bell's Theorem, except that I reject it in this special case, as well as von Neumann's. Whether one or the other can be proven mathematically to be correct in other situations is beyond anything I could claim.

 

Edited by Dalo

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What, exactly, do you mean by "reject [Bell's theorem]"? Do you accept that the theorem - the mathematical theorem - has been proven?

 

I was guessing that you were doubting the relationship between the mathematics and the physics, because if you accept both the mathematics and the relationship between the mathematics and the physics, then the only consistent possibility is to accept the physics. 

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1 minute ago, uncool said:

What, exactly, do you mean by "reject [Bell's theorem]"? Do you accept that the theorem - the mathematical theorem - has been proven?

 

I was guessing that you were doubting the relationship between the mathematics and the physics, because if you accept both the mathematics and the relationship between the mathematics and the physics, then the only consistent possibility is to accept the physics. 

No, I do not think that Bell's Theorem has been proven in this special case. If I did, I would not advance my claim. Is that clear enough for you?

And I certainly do not doubt the relationship between Physics and Mathematics. Not believing that Bell's theorem is necessarily valid is not rejecting all mathematics.

Edited by Dalo

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Just now, Dalo said:

No, I do not think that Bell'sTheorem has been proven in this special case. If I did, I would not advance my claim. Is that clear enough for you?

That's not how theorems work. If there is a special case where the theorem doesn't work, then it's not a theorem (assuming the consistency of mathematics as a whole).

There are two possibilities. Either 1) you doubt the proof of the theorem, or 2) you doubt that the hypotheses of the theorem apply. Do you know which one?

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6 minutes ago, uncool said:

That's not how theorems work. If there is a special case where the theorem doesn't work, then it's not a theorem (assuming the consistency of mathematics as a whole).

There are two possibilities. Either 1) you doubt the proof of the theorem, or 2) you doubt that the hypotheses of the theorem apply. Do you know which one?

It is the assumption that both systems (photon + filter) are different, and that we still get the famous (empirical, therefore undeniable) statistical regularities. I say that they are not different according to the assumptions that:

1) both photons have the same polarization,

2) both filters are identical.

If you accept those assumptions, they show according to me that both systems are equal and that it is therefore not surprising that they react in a predictable way, conform the known statistical regularities. That makes the distinction between local and non-local, and the necessity to appeal to hidden variables, both meaningless.

Edited by Dalo

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6 minutes ago, Dalo said:

It is the assumption that both systems (photon + filter) are different, and that we still get the famous (empirical, therefore undeniable) statistical regularities. I say that are not different according to the assumptions that:

1) both photons have the same polarization,

2) both filters are identical.

If you accept those assumptions show that both systems are equal and that it is therefore not surprising that they react in a predictable way, conform the known statistical regularities. That makes the distinction between local and non-local, and the necessity to appeal to hidden variables, both meaningless.

So to be clear: do you accept the mathematical proof of Bell's theorem? Your problem is with the assumptions of the theorem, not with the proof itself?

Edited by uncool

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Just now, uncool said:

So to be clear: do you accept the mathematical proof of Bell's theorem? Your problem is with the assumptions of the theorem, not with the proof itself?

I reject Bell's Theorem for as far as it concerns the example I have analyzed and the claim I have presented. 

As I have just told you a couple of posts ago, I am not analyzing the mathematical structure of Bell's Theorem, but expressing an opinion, a judgment, on its implications. And that is, whether it be an assumption or a conclusion, the idea that both systems are different and in need of hidden variables, be they local or non-local, for their explanation.

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8 minutes ago, Dalo said:

I reject Bell's Theorem for as far as it concerns the example I have analyzed and the claim I have presented. 

As I have just told you a couple of posts ago, I am not analyzing the mathematical structure of Bell's Theorem, but expressing an opinion, a judgment, on its implications. And that is, whether it be an assumption or a conclusion, the idea that both systems are different and in need of hidden variables, be they local or non-local, for their explanation.

I am not asking you to analyze its mathematical structure. I am asking you only whether you accept the mathematical proof in it. Either the proof is valid, or it is not; whether that proof is being applied to a specific example or not is irrelevant. So I ask you again: do you accept that the proof is valid?

 

Edit: As a note, you are free to have an answer along the lines of "I don't know whether the proof is valid; I think there is a problem with the conclusion for this example, and I don't know whether that problem appears in the assumptions or in the proof."  

Edited by uncool

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9 minutes ago, uncool said:

I am not asking you to analyze its mathematical structure. I am asking you only whether you accept the mathematical proof in it. Either the proof is valid, or it is not; whether that proof is being applied to a specific example or not is irrelevant. So I ask you again: do you accept that the proof is valid? 

One could also say that the example I have presented does not fall under the cases treated by the theorem. Take your pick. I have no desire to attack or defend Bell's theorem because it would mean analyzing it mathematically, which I cannot do. I react to its general meaning and assumptions. Feel free to draw your own conclusions whether my position is justified or not.

You seem to think that if a mathematical argumentation is mathematically or logically valid then it has to be true, and that is a very wrong assumption. That is why there is such a thing as pure mathematics. The validity of a mathematical theorem does not say anything about its empirical usefulness or even its general truth. It only shows that correct conclusions have been logically deduced from the initial assumptions, and that the calculations are correct. That does not mean that the assumptions are necessarily true.

And that is the whole point. Bell did not show that von Neumann could not calculate or could not think logically. He doubted his (von Neumann's) initial assumptions and presented his own.

The matter therefore is a matter which assumptions you start with, and that is not a mathematical decision.

Edited by Dalo

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11 minutes ago, Dalo said:

One could also say that the example I have presented does not fall under the cases treated by the theorem. Take your pick. I have no desire to attack or defend Bell's theorem because it would mean analyzing it mathematically, which I cannot do. I react to its general meaning and assumptions. Feel free to draw your own conclusions whether my position is justified or not.

You seem to think that if a mathematical argumentation is mathematically or logically valid then it has to be true, and that is a very wrong assumption. That is why there is such a thing as pure mathematics. The validity of a mathematical theorem does not say anything about its empirical usefulness or even its general truth.

I never said that it did. In fact, that was the point of one of the first questions I asked you. 

11 minutes ago, Dalo said:

It only shows that correct conclusions have been logically deduced from the initial assumptions, and that the calculations are correct. That does not mean that the assumptions are necessarily true.

And that is the whole point. Bell did not show that von Neumann could not calculate or could not think logically. He doubted his initial assumptions and presented his own.

The matter therefore is a matter which assumptions you start with, and that is not a mathematical decision.

Then we have gotten exactly to the point of the question I asked you. You seem to agree (or at least, are refusing to dispute) the mathematical correctness of the theorem - but instead, whether the mathematical assumptions of the theorem match physical reality (or alternatively, what is meant by a "classical (local) theory"). Which is exactly what I asked with my integral question.

Edited by uncool

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13 minutes ago, uncool said:

I never said that it did. In fact, that was the point of one of the first questions I asked you. 

Then we have gotten exactly to the point of the question I asked you. You seem to agree (or at least, are refusing to dispute) the mathematical correctness of the theorem - but instead, whether the mathematical assumptions of the theorem match physical reality (or alternatively, what is meant by a "classical (local) theory"). Which is exactly what I asked with my integral question.

Glad this point has been taken care of.

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Then we are back to where I started. Namely: 

You seem to be asking for a justification for the assumption - why, philosophically, should a classical theory require such a mathematical description - and seem to think you have something that runs counter to that. Correct?

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Just now, uncool said:

Then we are back to where I started. Namely: 

You seem to be asking for a justification for the assumption - why, philosophically, should a classical theory require such a mathematical description - and seem to think you have something that runs counter to that. Correct?

wrong. I have no such general claims. I am, once again, limiting myself to the very direct question whether the example given by Maudlin of the entanglement of photons is correct. My answer in short is negative.

 

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6 minutes ago, Dalo said:

wrong. I have no such general claims. I am, once again, limiting myself to the very direct question whether the example given by Maudlin of the entanglement of photons is correct. My answer in short is negative.

 

I see no general claims in that question. "something that runs counter to that" could mean a counterexample. To be more explicit: you seem to be saying that you think your example fails to be described mathematically by the systems described in Bell's theorem. Correct?

Edited by uncool

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Just now, uncool said:

I see no general claims in that question. "something that runs counter to that" could mean a counterexample.

I think it would be easier if you presented your own opinions. Second guessing mine is not helping any of us.

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Just now, Dalo said:

I think it would be easier if you presented your own opinions. Second guessing mine is not helping any of us.

I strongly disagree; this is an attempt at precision, something that you - of all people here - should welcome. It is an attempt to get at the heart of what you think the problem is - the precise place where you think philosophy and the current descriptions of quantum theory (including entanglement) disagree. 

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Just now, uncool said:

I strongly disagree; this is an attempt at precision, something that you - of all people here - should welcome. It is an attempt to get at the heart of what you think the problem is - the precise place where you think philosophy and the current descriptions of quantum theory (including entanglement) disagree. 

Disagree you may, but that does not change the fact that I have not confronted in this thread the issues you mention. They are certainly fundamental and my own claim has certainly consequences. But that is not the subject of this thread, even if those issues are strongly related to it.

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7 minutes ago, Dalo said:

Second guessing mine is not helping any of us.

Uncool is not second guessing yours; rather trying to get you to clarify your position. But, as always, you refuse to do this because ... well, because of course you do.

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Just now, Dalo said:

Disagree you may, but that does not change the fact that I have not confronted in this thread the issues you mention. They are certainly fundamental and my own claim has certainly consequences. But that is not the subject of this thread, even if those issues are strongly related to it.

It seems to me that you have not because you have not followed your own argument to its natural conclusion. Your argument seems to be entirely related to rejecting the conclusion of Bell's theorem to your experiment; if you accept the mathematical validity of Bell's theorem, then you must reject the application of the assumptions of Bell's theorem to your experiment.

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22 minutes ago, Strange said:

Uncool is not second guessing yours; rather trying to get you to clarify your position. But, as always, you refuse to do this because ... well, because of course you do.

Then you are both putting the cart before the horse. In the thread Why I am a determinist, I briefly engaged these issues.

In this thread I  want to build a case for them. It is evident that I am no fan of Bohr's interpretation of quantum physics. But a philosophical opinion as this is nothing new. The EPR paper heralded it, and there are hundreds of publications that defend it. What could my own reiteration mean in such a context?

I think that my contribution would be much more meaningful if I proved such a thing as the claim I have presented here. That is why I refuse to be sidetracked towards a general abstract discussion.

17 minutes ago, uncool said:

It seems to me that you have not because you have not followed your own argument to its natural conclusion. Your argument seems to be entirely related to rejecting the conclusion of Bell's theorem to your experiment; if you accept the mathematical validity of Bell's theorem, then you must reject the application of the assumptions of Bell's theorem to your experiment.

That is a very interesting claim. I hope you will flesh it out.

17 minutes ago, uncool said:

then you must reject the application of the assumptions of Bell's theorem to your experiment.

I don't understand how this can be a critique. Have I not said the same clearly enough just a few posts ago to you specifically?

1 hour ago, Dalo said:

I reject Bell's Theorem for as far as it concerns the example I have analyzed and the claim I have presented.

 

2 hours ago, Dalo said:

I am not ready yet to widen the claim to the whole domain of entanglement situations considered by quantum theory. I lack the expertise to analyze in sufficient details every example. The drawing I presented above does show that it does not really matter which property or which particle is considered. But it is a general argument which I would find very difficult to defend in all cases.

People who would agree with me and at the same time have the necessary expertise would have a much easier time applying my analysis to other examples.

Edited by Dalo

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16 minutes ago, Dalo said:

Have I not said the same clearly enough just a few posts ago to you specifically?

No, you hadn't, because there is a difference between rejecting the theorem and rejecting the application of its assumptions. I do not mean it as a critique. I mean it as an attempt to make your position clearer. Now that it is clear you reject the application of the assumptions of Bell's theorem - namely, the integrals - your position is far clearer.

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Just now, uncool said:

No, you hadn't, because there is a difference between rejecting the theorem and rejecting the application of its assumptions. I do not mean it as a critique. I mean it as an attempt to make your position clearer. Now that it is clear you reject the application of the assumptions of Bell's theorem - namely, the integrals - your position is far clearer.

All I understood is "your position is far clearer". :)

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1 minute ago, Dalo said:

All I understood is "your position is far clearer". :)

I wouldn't be happy yet.

 

Here's the thing: your rejection of those assumptions is precisely where a mathematical understanding of the physics comes in. Understanding the difference between those two integrals is precisely where you must learn the mathematics behind both classical and quantum mechanics.

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4 minutes ago, uncool said:

Here's the thing: your rejection of those assumptions is precisely where a mathematical understanding of the physics comes in. Understanding the difference between those two integrals is precisely where you must learn the mathematics behind both classical and quantum mechanics.

I do not agree. This is a "technicist" or "scientist" (from scientism)  view that is a very subtle way of denying opponents any legitimacy unless they agree with the mathematical or interpretational premises. It is a circular argument with absolutely no value at all.

Keep your convictions of superiority if you will, I refuse to acknowledge it. And this refusal is not a rejection of science but of a certain toxic and elitist view of science.

Edited by Dalo

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1 minute ago, Dalo said:

I do not agree. This is a "technicist" or "scientist" (from scientism)  view that is a very subtle way of denying opponents any legitimacy unless they agree with the mathematical or interpretaional premises. It is a circular argument with absolutely no value at all.

Keep your convictions of superiority if you will, I refuse to acknowledge it. And this refusal is not a rejection of science but of a certain toxic and elitist view of science.

It is not that you must agree with the premises. It is that you must understand them in the first place. It is that if you wish to reject what experts are saying, you need to know what they are saying in the first place.

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