DrChinese
Science Advisor
Gold Member
- 7,190
- 1,009
Congrats to stevendaryl on hitting 2000 posts!
This is a contradiction.When drawing conclusions from this most important and profound theorem, I wonder if somebody has interpreted its proof of the falseness of local realism as implicitly referring to elementary particles as realistic objects.
No, those are not the only possibilities. Bell showed that the predictions of QM cannot be reproduced by a certain type of theory--a local hidden-variables model. QM is not such a theory. So there is no contradiction between Bell's theorem and QM.This is a contradiction.
If Bell proved formally - mathematically some limit exists, then there is no possibility to go over these limit.
Simply: there are only two mutually exclusive possibilities:
1. Bell proof is wrong - a mistake
2. QM is a wrong model, because predicts impossible correlations, what proved Bell.
The logic makes no compromises!
Thanks. Wow. That sounds like a lot, but I see it's nothing compared to your record.Congrats to stevendaryl on hitting 2000 posts!
In mathematics there is no alternative worlds, especially: one with the parameters, and other without.No, those are not the only possibilities. Bell showed that the predictions of QM cannot be reproduced by a certain type of theory--a local hidden-variables model. QM is not such a theory. So there is no contradiction between Bell's theorem and QM.
Bell has also proven an inequality, but not unconditionally. Instead, it requires some assumptions and if a theory (like QM) violates these assumptions, then it needn't satisfy the inequality. There is no mathematical contradiction.In mathematics there is no alternative worlds, especially: one with the parameters, and other without.
Everything that has been proven there is certain, indisputable, there is no alternative.
For example: |a+b| <= |a| + |b|, for any real number a, b.
This has been proven, it's true - unconditionally.
Bell proved an implication, a statement of the form:In mathematics there is no alternative worlds, especially: one with the parameters, and other without.
Everything that has been proven there is certain, indisputable, there is no alternative.
For example: |a+b| <= |a| + |b|, for any real number a, b.
This has been proven, it's true - unconditionally.
You never find the: a,b which breaks this inequality, because these don't exist.
If you now create a theory which anyway breaks this inequality, then the theory will be false.
Unfortunately, the Bell's inequality is an example of this type certainty - mathematical tautology.Bell has also proven an inequality, but not unconditionally. Instead, it requires some assumptions and if a theory (like QM) violates these assumptions, then it needn't satisfy the inequality. There is no mathematical contradiction.
If it was as you say, there would be no discussion of non-classical correlations, entanglement of particles, and so on.Bell proved an implication, a statement of the form:
"If X is true, then Y is true."
He did not prove "Y is true."
If X is false, then Y might be false.
A lot of mathematical theorems (I would say the vast majority of them) have the form of an implication: If [itex]x[/itex], [itex]y[/itex] and [itex]z[/itex] are integers, and each is greater than 0, then [itex]x^3 + y^3 \neq z^3[/itex]. The theorem isn't true without the condition. For example, [itex]x=0[/itex], [itex]y=0[/itex], [itex]z=0[/itex] is a counter example.
You will find that it is impossible to break the inequality if you assume that the result of the measurement at a detector can be written as a function of the state of the particle that hits that detector and the state of the detector. That's what Bell's theorem says.Write the inequality, and try to break it;
you'll find that this is impossible - absolutely.
You will find a copy of Bell's paper presenting his theorem here: http://www.drchinese.com/David/Bell_Compact.pdfIn the mathematical theorems there are no particles, so there is no question of any particle parameters.
Why do you say that? Bell proved that for every theory of a certain type, (local realistic), his inequality holds. QM violates his inequality. Therefore, QM is NOT a theory of that type. There is no contradiction. Neither Bell nor QM is wrong.If it was as you say, there would be no discussion of non-classical correlations, entanglement of particles, and so on.
Let's go through what Bell proved. Part of it is a mathematical theorem. It's just a fact, and I don't think there is any dispute about it. The second part is the application of this fact to physics. That is NOT pure mathematics. You can't apply mathematics to physics without making assumptions, and if you prove that something is impossible, you really have only proved that, under those assumptions, it is impossible.In the mathematical theorems there are no particles, so there is no question of any particle parameters.
You just have three (or four) series of numbers with values from the set {1, -1}.
You calculate these correlations by well-known formulas, and check the inequality.
Your mission is to show the series, which break the inequality. That's all.
The point I am trying to make is about the failure of the freedom assumption, not about locality. The theory is local, OK. Once you know the local field (which would be rather difficult, as it would require infinite resolution and accuracy) you can ignore distant sources, OK. So what?That's true. Everything can affect everything else. But the point of a local theory is that everything that's relevant about distant particles and fields is already captured in the values of local fields and the positions/momenta of local particles. So the evolution equations don't need to take into account anything other than local conditions.
This is in contrast to a nonlocal theory, where the evolution equations must potentially take into account everything.
The experiments must provide these lists, and this is just the raw data, measured during experiment on both sides.QM, and in particular, the EPR experiment, does not provide us with such a set of 4 lists of numbers. That's because in a twin-pair experiment, the experimenters (call them Alice and Bob) must make a choice: For each run [itex]i[/itex] of the experiment, Alice must decide whether to measure [itex]A_i[/itex], or to measure [itex]A'_i[/itex]. She can't measure both. Similarly, Bob must decide whether to measure [itex]B_i[/itex] or [itex]B'_i[/itex]. He can't measure both.
In that case you lose completely the context of these Bell-type inequalities.So an EPR experiment, you don't get 4 lists of numbers, each of which is either -1 or +1. You get 4 values, 2 of which are +1 or -1, and 2 of which are ?, meaning unmeasured.
To such, let say: a free-version of the problem, applies quite different inequality,If you assume that there really are 4 numbers for each [itex]i[/itex], and that those 4 numbers are either +1 or -1, but we just don't know what two of them are, that leads to a contradiction. But QM doesn't say that there are 4 numbers associated with each run. It only says there are two numbers, the numbers actually measured by Alice and Bob. To assume that there are 4 numbers goes beyond QM to some "hidden variables theory" that is supposed to explain QM. Bell proved that there is no such hidden variables theory. There is no way to replace the ? by +1 or -1 everywhere so that the statistics for unmeasured values obey the predictions of QM.
QM shows nothing special in this area. We know very well the formal mathematical truths are universal, unbreakable, indestructible.So QM, together with Bell's theorem, shows us that quantum measurements are not simply a matter of measuring a variable that had a pre-existing value whether you measured it or not. What is it, if not that? Well, that's the big question.
The experimental tests are not verifying the correctness of the mathematical theorem - we know that it's correct (unless there's an error in the proof and no one has found one in the past century, so that's not a serious possibility).The experimental tests/verification of the mathematical theorems are completely pointless.
I don't know what represent the A, B.The theorem is stated in the form (I've already posted a link to Bell's original paper, and for this discussion we probably need to focus on that) "If A then B", and therefore "If not B then not A". That's the theorem, and no one is arguing about it.
The purposes of the experiments is to discover whether B is false; if it is then the mathematical logic of the theorem "if not B then not A" tells us that A is false.
The "failure of freedom assumption" means that Alice and Bob's choice of measurement settings are not free. In that view, those too is a function of the parameters you claim are somehow tied up in the other parameters you are mentioning. But that cannot be! There is no known influence of those parameters on the human brain!! (Except of course in superdeterminism.) And if you care to postulate some connection, it can be ("easily") falsified.The point I am trying to make is about the failure of the freedom assumption, not about locality. ...
Have you read the paper yet? (I'll repeat the link so people who new to this thread won't have to dig back through it to find it: http://www.drchinese.com/David/Bell_Compact.pdf)I don't know what represent the A, B.
The EPR-tests were designed to verify some inequalities, never the whole reality, nor the basics of math.
OK. This is a formal proof of the inequality.Have you read the paper yet? (I'll repeat the link so people who new to this thread won't have to dig back through it to find it: http://www.drchinese.com/David/Bell_Compact.pdf)
When I say that the theorem is of the form If A then B, A represents the "vital assumption" stated after equation 1 in the paper, and formalized in the integral in equation 2; and B represents the inequality.
It can be violated by a theory in which ##P(\vec a,\vec b)## isn't of the form as given by equation (2). This is the case for QM.OK. This is a formal proof of the inequality.
So, it's true - it can't be violated in any way.
No, it is a formal proof that if a certain precondition holds, then the inequality cannot be violated in any way.OK. This is a formal proof of the inequality.
So, it's true - it can't be violated in any way.
I think you are confused about this topic. You seem to be expressing a view that is at odds with what everyone else has said about Bell's inequality. As I said recently in a different thread, the fact that something is an establishment view doesn't make it right, but it makes Physics Forums the wrong place for you to be arguing about it.The experiments must provide these lists, and this is just the raw data, measured during experiment on both sides.
...
QM shows nothing special in this area. We know very well the formal mathematical truths are universal, unbreakable, indestructible.
The experimental tests/verification of the mathematical theorems are completely pointless.