Bohr's solution to the EPR paradox

[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.

 

[OCR]

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

Maybe... right ? [COLOR=#black]..[/COLOR] [COLOR=#black].[/COLOR]

 

[Zafa Pi]

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

In spite of that not being the prevailing view, and not treated in the vast majority of texts, I see your point.

 

[Zafa Pi]

Maybe... right ? [COLOR=#black]..[/COLOR] [COLOR=#black].[/COLOR]

The big bang knew you would say that.

 

[OCR]

The big bang knew you would say that.

I know...[COLOR=#black]..[/COLOR]

 

[ueit]

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

Yes, that is a direct implication (of course under the assumption that classical physics, say EM + GR are a fundamental, correct description of nature). Classical physics is also reversible so you could calculate the state at the big bang from the present one, if the required data would be available.

 

[Zafa Pi]

Your answer to

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

was

Yes, that is a direct implication (of course under the assumption that classical physics, say EM + GR are a fundamental, correct description of nature). Classical physics is also reversible so you could calculate the state at the big bang from the present one, if the required data would be available.

but earlier when I said

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.

you said

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.

Now I refer you to https://www.physicsforums.com/threa...minism-and-bells-theorem.914439/#post-5761059
Then why all the controversy?

 

[OCR]

BTW... you are welcome !

Thanks for the question mark?

 

[ueit]

Your answer to
was
but earlier when I said
you said

Now I refer you to https://www.physicsforums.com/threa...minism-and-bells-theorem.914439/#post-5761059
Then why all the controversy?

Look, do you deny that determinism implies that the present state follows uniquely from the past state? If so, please define what you mean by determinism, and state clearly if you think that in classical EM the state at a certain time is or it is not determined by the past state of the system.

As long as I didn't make use of any assumption other than the properties of classical EM I feel no need to go into the subject of superdeterminism. We can if you want, but at this point is not necessary.

 

[Zafa Pi]

Look, do you deny that determinism implies that the present state follows uniquely from the past state?

Look, all I was doing was pointing out there was controversy that you were denying. I'm merely a simple mathematician that believes in the axiom of choice. IMO determinism is an idea about reality (yuck) that's not even wrong.

 

[ueit]

Look, all I was doing was pointing out there was controversy that you were denying. I'm merely a simple mathematician that believes in the axiom of choice. IMO determinism is an idea about reality (yuck) that's not even wrong.

This is what determinism is, according to Laplace:

https://en.wikipedia.org/wiki/Laplace's_demon

"We may regard the present state of the universe as the effect of its past and the cause of its future. An intellect which at a certain moment would know all forces that set nature in motion, and all positions of all items of which nature is composed, if this intellect were also vast enough to submit these data to analysis, it would embrace in a single formula the movements of the greatest bodies of the universe and those of the tiniest atom; for such an intellect nothing would be uncertain and the future just like the past would be present before its eyes."

Classical electrodynamics is such a theory. Both the concept of determinism and the formulation of classical electrodynamics predate Bell's theorem and his invented word "superdeterminism" so your attempt to change the subject in that direction makes little sense.

"Free choice" is not an axiom of classical electromagnetism so I find it irrelevant to this discussion. In fact I doubt there is any place for this concept in any physical theory, quantum mechanics included.

The fact that you believe that determinism is wrong is again irrelevant. I'm not arguing here that it is true (although I do believe so). What I am trying to argue is that in classical electromagnetism you cannot have isolated systems in the way you want. So, can you please make a clear statement about your opinion on this? Can you provide an example of physical system that is described by classical electrodynamics and yet can be shown to consist of two subsystems that are isolated in the way you envision?

 

[PeterDonis]

Thread closed for moderation.

Edit by @DrClaude: this thread was going nowhere and will stay closed.