Graduate Bohr's solution to the EPR paradox

[N88]

The definition of CLR is not the question. QM, Bell, etc don't have any material quibble with the definition itself. Any more than QM or Bell has anything to say about the definitions of fairies and centaurs. It is the substance of what's defined that is at issue. That is ruled out by Bell's Theorem.

Commonsense local realism (CLR) is the union of Einstein's local-causality (no causal influence propagates superluminally because no speed can exceed light-speed under relativity) and Bohr's physical-realism (some physical properties change interactively because Planck's quantum of action is not zero).

So, please, would you mind pointing to the terms that represent (to your mind) the fairies and centaurs here?

I take it that you are familiar with Bell's final views re his famous theorem? Like: ".. all this action at a distance business will pass. If we're lucky it will be to some big new development like the theory of relativity. Maybe someone will just point out that we were being rather silly, with no big new development. But anyway, I believe the questions will be resolved," based on Bell near the end of his life (1990:9) http://www.quantumphil.org./Bell-indeterminism-and-nonlocality.pdf

 

[Zafa Pi]

all this action at a distance business will pass. If we're lucky it will be to some big new development like the theory of relativity.

Perhaps so. See post #9 in https://www.physicsforums.com/threads/er-epr.917145/#post-5783494

 

[bhobba]

I have seen many comments that say QM requires a new or different kind of probability theory. This is not true and perhaps not what they mean.

Generalized probability models is a totally respectable area of mathematics eg:
http://philsci-archive.pitt.edu/12905/1/paper.pdf

QM is not the same as ordinary probability theory eg the pure states can continuously go from one state to another - ordinary probability theory can't do that. See for example:
https://arxiv.org/pdf/quant-ph/0101012.pdf

Thanks
Bill

 

[bhobba]

Probability theory is simply logic - the logic of plausible reasoning. Read Jaynes about this. There is only one logic. It makes no sense to generalize logic.

Ordinary probability theory is the Kolmogorov Axioms - not logic. What Jeans or anyone else wants to read into it beyond that is their business. Most of the time applied mathematicians use the frequentest view based on the strong law of large numbers - but not always eg Bayesian statistics often uses the Jeans interpretation (eg Bayesian) and sometimes the decision theory interpretation is even used eg credibility theory. Its freely chosen to make understanding the math as intuitive as possible. As John Baez correctly says much of QM 'arguments' is simply arguments about the meaning of probability in another stetting:
http://math.ucr.edu/home/baez/bayes.html

And indeed even ordinary logic can be generalised. That too is an approach to QM - see for example:
https://www.amazon.com/dp/0387493859/?tag=pfamazon01-20

However we are entering areas other sections of this forum are better suited to discuss eg Set Theory, Logic, Probability, Statistics.

Thanks
Bill

 

[bhobba]

Maybe someone will just point out that we were being rather silly, with no big new development. But anyway, I believe the questions will be resolved," based on Bell near the end of his life (1990:9) http://www.quantumphil.org./Bell-indeterminism-and-nonlocality.pdf

Here are the facts:

1. Bell is simply a correlation - that's it - that's all.
2. It has statistical properties different to correlations found in ordinary life.
3. Want it to be like ordinary life - then you need FTL influences of some sort.
4. Once you get into that you are into the territory of things being non local.
5. In QFT locality is defined by the so called cluster decomposition property:
https://www.physicsforums.com/threads/cluster-decomposition-in-qft.547574/
6. Note - correlations are specifically excluded hence Bell is of zero concern for locality in QM.

If you want to read more into it than the above - go ahead - many do. But please realize that's all you are doing - it changes nothing about what really is going on which basically is - we have a different kind of correlation in QM than classically. This is hardly surprising since its a different kind of probability model. And correlations are specifically excluded from locality in our most fundamental theory - QFT. The simplest view is just accept you have a different kind of correlation. Since locality in QFT excludes correlations there is no need to even worry about it as far as locality is concerned.

Thanks
Bill

 

[Zafa Pi]

Generalized probability models is a totally respectable area of mathematics eg:
http://philsci-archive.pitt.edu/12905/1/paper.pdf

The 1st quote by Feynman in the introduction is exactly what I'm talking about. How one calculates probabilities doesn't impact probability theory.
The behavior of probability amplitudes is no generalization of standard probability theory. If I defined a probability matrix as one whose entries are non-negative and add to 1 and then develop a theory about them and notice that the theory doesn't satisfy the axioms of probability theory, so what.

QM is not the same as ordinary probability theory eg the pure states can continuously go from one state to another - ordinary probability theory can't do that. See for example:
https://arxiv.org/pdf/quant-ph/0101012.pdf

Wiener processes do that and are part of standard probability theory.

 

[bhobba]

Wiener processes do that and are part of standard probability theory.

You need to read the literature. The above is wrong BTW, being based on standard probability theory you can't continuously go from one pure state to another.

First - what - generally is the definition of a mixed state? What is a pure state? Then once you understand that what are they in ordinary probability theory and QM?

BTW I have given a lot of links where you can look up the answer eg
https://arxiv.org/pdf/1402.6562.pdf

Thanks
Bill

 

[Zafa Pi]

You need to read the literature.

All of it? You're a tough task master.

First - what - generally is the definition of a mixed state? Then once you understand that what are they in ordinary probability theory and QM?

Nielsen & Chuang pp 100 - 111, I've read it and understood it. If you tell me to read Ballentine, I'll tell you no thanks. I've even seen you answer a B level question that way.

 

[Zafa Pi]

1. Bell is simply a correlation - that's it - that's all.

General Relativity is simply a modification of Newton's theory - that's it - that's all.

 

[bhobba]

General Relativity is simply a modification of Newton's theory - that's it - that's all.

Not quite - its based on entirely different idea - no prior geometry. Newtonian gravitation is based on the idea of forces. Correlations are the same thing in QM or ordinary probability theory.

Thanks
Bill

 

[Zafa Pi]

Not quite - its based on entirely different idea - no prior geometry. Newtonian gravitation is based on the idea of forces. Correlations are the same thing in QM or ordinary probability theory.

Thanks
Bill

That's what a modification does. Your notion of modification is too restrictive. But I think my point was lost.

 

[bhobba]

All of it? You're a tough task master.

OK then - just read section 3 on examples in the paper I linked to. Its only a few pages.

The state space of QM and ordinary probability theory are entirely different. In ordinary probability theory the outcomes are your pure states and are perfectly distinguishable from each other. A mixture is simply the convex sum of pure states and the weight of that mixture gives the probability of getting a particular pure state. Each outcome is different and you can't continuously go from one to the other through other pure states - they are all distinguishable.

In QM the pure states are not distinguishable and there is a continuous transformation going from any pure state to another via other pure states. A mixture is exactly the same - the convex sum of any pure state. Mixtures and pure states form the state space of QM. Again a mixture gives the probability of getting that pure state.

Thanks
Bill

 

[bhobba]

That's what a modification does. Your notion of modification is too restrictive. But I think my point was lost.

Your not kidding its lost. A correlation is the same - geometry and forces - different concepts - with due respect to Symplectic geometry.

Thanks
Bill

 

[Zafa Pi]

OK then - just read section 3 on examples in the paper I linked to. Its only a few pages.

No, you read Feynman's short paragraph in the opening of the introduction.

The state space of QM and ordinary probability theory are entirely different.

Probability theory doesn't have a state space. That classical theory can theoretically distinguish different states and QM can't is no reflection on probability theory.

It seems we are getting into a pissing match and not making any headway on convincing the other of our own position. Hence I would like to give up.

 

[bhobba]

Probability theory doesn't have a state space.

I just don't know what to say. It does and is defined in the paper I linked to.

I know you are a retired professor of probability so this has me flummoxed.

That being the case let's go over to Set Theory, Logic, Probability, Statistics and discuss it with people at your level . I will do the initial post.

Thanks
Bill

 

[Denis]

The above is wrong BTW, being based on standard probability theory you can't continuously go from one pure state to another.
First - what - generally is the definition of a mixed state? What is a pure state? Then once you understand that what are they in ordinary probability theory and QM?

Take the state space of some classical probability theory, mixed as well as pure states. It is a convex space. Then, take some convex subspace out of it. This subspace are, say, all those states you can prepare with the given devices. Does this restriction to some subset of producible states change probability theory? Invalidate any of the axioms used by Jaynes?

No. This is simply an example of a "generalization" which is none.

Then, you should not mingle mathematics with the interpretation of logic and probability theory. Logic defines some laws of thinking, of rigorous reasoning, probability theory in the Jaynes interpretation too. This does not mean that the same mathematical rules can have some other applications. Say, the rules of logic may be used to describe, in some approximation, the behavior of certain semiconductor configurations if they are used in certain circumstances. In this application, the rules of logic are not used as rules of thinking, but describe approximately some physics. So, no problem arises if it appears that some of the rules of "logic" appear to fail sometimes - simply the device is inappropriate as a computer chip to implement logic. The rules of thinking are, instead, not changed at all.

Similarly, for the logical rules of plausible reasoning there may be other applications, say, in some approximate statistics of large numbers of repetitions of some experiments. Again, while these other applications of the same mathematics may fail, and possibly require generalizations to describe these experiments differently, it does not mean that the rules of plausible reasoning have become invalid and have to be changed to describe these experiments.

Confusing the laws of logical reasoning, inclusive plausible reasoning, with applications of the same mathematics in other applications, which can possibly fail and be generalized, would be fatal, because the result would be not only confusion ("quantum logic") but also the use of wrong ("generalized") rules for logical reasoning.

 

[ueit]

Let me get this straight. You are saying that given the setup I described in post #56 what Alice does in her experiment can affect Bob's results in his experiment, under the assumption of classical EM theory. That doesn't violate locality for classical theory?

The setup is irrelevant. No matter how you arrange the experimental components, their internal particles (field sources) will always be in interaction via the electric and magnetic fields produced by them. Their motion will be correlated. Locality does require a limited speed for physical interactions but does not preclude distant systems to become correlated at light-speed. The electrons and nuclei that make up Bob, Alice and Eve have been interacting via electric and magnetic fields long before the experiment began so your initial state in the experiment is not one in which those persons are isolated. So, according to classical EM, during the experiment you evolve deterministically a state in which Alice, Bob and Eve are already correlated.

Andrei

 

[Denis]

This is simply fatalistic big conspiracy. Everything is predefined by the initial conditions from big bang time, even this text written now is already predefined. Science would be, in such a world, simply some ritual without meaning, but we, of course, follow this ritual because this is predefined too.

 

[bhobba]

No. This is simply an example of a "generalization" which is none.

Of course its a generalisation. Thats the whole point. You reinterpret probability theory in a state space formalism.

In general you are given some space. Elements (also called states) that are not the convex sum of other elements are called pure. All elements are pure or mixed. The mixed states have a simple interpretation - the weight in the of the convex sum of pure states is interpreted as the probability of the pure state in that sum. Such formulations are called generalized probability theories/models. Its easy to put standard probability theory in such a formulation - in fact its the simplest generalized probability theory. QM can be put in such a form - in fact its the next most simple one after ordinary quantum theory:
https://arxiv.org/abs/quant-ph/0101012

I post the above a lot but it can be explained quite simply - QM is simply the next most complex generalized probability model after normal probability theory. The difference is the continuity assumption - QM has continuous transformations through other pure states - you can't do that with ordinary probability theory. Everything else is the same.

Its not hard - but in this thread some don't seem to get it - don't know why.

Anyway I can't explain it any simpler/better so its the last I will say on it.

Thanks
Bill

 

[ueit]

This is simply fatalistic big conspiracy. Everything is predefined by the initial conditions from big bang time, even this text written now is already predefined. Science would be, in such a world, simply some ritual without meaning, but we, of course, follow this ritual because this is predefined too.

According to classical physics it is true that everything is determined. How is this a surprise? However, the normal understanding of the word "conspiracy" requires more than determinism. It requires some sort of intelligent agent that arranges the initial state with some purpose in mind (like you writing a text). Classical physics does not imply the existence of such an agent therefore your complain is unjustified.

The discussion was about the possibility of isolated systems. If the systems interact continuously just like in the case of charged particles in electromagnetism or massive particles in general relativity they cannot be isolated. That's all.

Also, the idea that correlations can only appear after starting the experiment is absurd. If you look at the sky you don't see stars moving randomly, waiting for you to decide to start the experiment so that they can start interacting. You see order, and that order is a result of local interaction between the objects in the past. Exactly the same reasoning applies to electrons and nuclei, only it's much harder to observe them.

 

[zonde]

I post the above a lot but it can be explained quite simply - QM is simply the next most complex generalized probability model after normal probability theory. The difference is the continuity assumption - QM has continuous transformations through other pure states - you can't do that with ordinary probability theory. Everything else is the same.

Its not hard - but in this thread some don't seem to get it - don't know why.

Probability theory is math theory. QM is physics theory. It does not make sense to compare the two theories.

 

[zonde]

So, according to classical EM, during the experiment you evolve deterministically a state in which Alice, Bob and Eve are already correlated.

The only problem is that according to classical EM any correlation between Alice, Bob and Eve is so weak that there is no way it can produce very strong correlations observed in experiments.

 

[Zafa Pi]

I just don't know what to say. It does and is defined in the paper I linked to.

I know you are a retired professor of probability so this has me flummoxed.

That being the case let's go over to Set Theory, Logic, Probability, Statistics and discuss it with people at your level . I will do the initial post.

Thanks
Bill

As the response to your post in the probability forum has vindicated my position I will make an attempt to deflummox the situation. I will do this by providing a concrete example that is as simple as I can make it and yet be sufficiently robust to deal with the nuances under discussion. I think this technique would help resolve many of the debates that occur here.

The example is simple random walk on the integers. The state space for this dynamical system (denoted by RW) is the integers, the transitions occur at the discrete times given by the non-negative integers. If we are in state n at time t, then at time t+1 we will be in either state n-1 or n+1 with prob ½ each. The model RW is called a stochastic process because the transitions involve the use of random variables (rv's). In this case the rv's are iid copies of ±1 with prob ½ each, often called a "fair coin".

RW is most emphatically not probability theory (PT), nor an extension or generalization of PT. The same goes for QM. I think this is the source of confusion. RW does indeed have a state space, PT does not. (IMO the most elegant presentation of PT can be found in the first few pages of Ed Nelson's "Radical Elementary Probability Theory")

However, questions about RW, such as, what is the prob that if we are in state n, then at some future time we will come to be in state n again?, can be answered employing PT. In this case the answer is 1, and RW is said to be recurrent. If, however, we changed our rv to +1 with prob ⅔ and -1 with prob ⅓ then we have a new model RW* where the return prob and other probs are very different. This is what Feynman was referring to in the link you provided in post #63.

As the state space of RW becomes more refined and the transition times become shorter in the right proportion the limit becomes Brownian motion on the line, a continuous stochastic process.

 

[Zafa Pi]

According to classical physics it is true that everything is determined.

I think your position in this post is referred to as superdeterminism. That is not the prevailing view of CT, rather it is local determinism. And in that context my set up with Alice and Bob is ok.

 

[ueit]

The only problem is that according to classical EM any correlation between Alice, Bob and Eve is so weak that there is no way it can produce very strong correlations observed in experiments.

What is your evidence supporting this statement?

 

[ueit]

I think your position in this post is referred to as superdeterminism. That is not the prevailing view of CT, rather it is local determinism. And in that context my set up with Alice and Bob is ok.

This is false. Classical determinism implies that any state follows uniquely from a past state. Classical EM is like that. This is not a controversial position at all.

 

[stevendaryl]

RW is most emphatically not probability theory (PT), nor an extension or generalization of PT.

I don't think anybody is talking about random walks as a generalization of probability theory, nor Schrodinger's equation as a generalization of probability theory. They're talking about the rules for combining probabilities. And that can very well be described as a kind of probability theory.

 

[Zafa Pi]

I don't think anybody is talking about random walks as a generalization of probability theory, nor Schrodinger's equation as a generalization of probability theory. They're talking about the rules for combining probabilities. And that can very well be described as a kind of probability theory.

But they do talk about QM being a generalization of probability. I was merely simplifying the point.

 

[Zafa Pi]

This is false. Classical determinism implies that any state follows uniquely from a past state. Classical EM is like that. This is not a controversial position at all.

Thus all states follow from the state of the big bang, right?

 

[stevendaryl]

But they do talk about QM being a generalization of probability. I was merely simplifying the point.

Well, that's a mistake. It's an application of a generalization.