Conceptual variables and quantum foundation

[Inge Helland]

Can one find a new foundation of quantum theory, a foundation which ultimately leads to the full theory, but at the same time a foundation which can be explained also to persons that never have been exposed to the ordinary Hilbert space machinery?

 

My answer is yes. I have tried to discuss my approach in a book and in several published papers. Now I have collected all the mathematical arguments in a single article: http://arxiv.org/abs/2305.06727. It might not be necessary to read this article in full details, however. I will explain my model and some of my main results below.

 

My basic notion is that of a variable. A variable can be a physical variable, a statistical parameter, a future data variable, a decision variable, or perhaps also other things. I divide the variables into accessible ones and inaccessible ones. Physical variables are accessible if we by some measurement can get as accurate values as we want to. In general, I only require that if theta is accessible and lambda is a function of theta, then lambda is also accessible.

 

In a measurement situation the notions accessible/ inaccessible may be connected to the mind of some observer/actor or to the joint minds of a communicating group of actors. All this agrees with Hervé Zwirn’s Conceptual Solipsism: Every description of the world must be relative to the mind of some observer. It is also in agreement with the interpretation of quantum mechanics due to Carlo Rovelly: Variables of different systems are relative to each other; one such system may be an observer (or a group of observers).

 

Some examples:

 

1) Spin of one particle. An observer A can have the choice between measuring the spin in the x direction or in the z direction. This gives two related accessible variables in the mind of A. An inaccessible variable is the unit spin vector phi. In the qubit case, the spin component in any direction a can be seen as a simple function of phi: sign(cos(a,phi)), taking the values -1 or +1. If phi is given a uniform distributiom on the unit sphere, the correct distribution of the component in the a direction results.

 

2) The EPR situation with Alice and Bob. For an independent observer Charlie, the unit spin components of both are inaccessible, say n_A and n_B. But it can be shown that the dot product of the two is accessible to Charlie: d =n_A . n_B. Specifically, one can show that Charlie is forced to be in an eigenstate for the operator corresponding to the variable d, which is the entangled singlet state corresponding to d=-3. It is easy to show that this implies that for Charlie and for the measured components in some fixed direction a, the component of Alice is opposite to the component of Bob. Note that Charlie can be any person. (Note: n_A . n_B=-3 for Charlie means that his spin components must satisfy n_A^x =-n_B^x, n_A^y=-n_B^y and n_A^z=-n_B^z. This has implications for the components in any direction a: n_A^a=-n_B^a.)

 

3) The Bell experiment situation. Look at the subsample of data where Alice measures her spin component in direction a and gets a response A, either -1 or +1, and where Bob measures in a direction b and gets a similar response B. Then A is accessible to Alice, but inaccessible to Bob. Similarly, B is accessible to Bob and inaccessible to Alice. For an independent observer Charlie, having all data, both A and B are accessible. But Charlie has his limitation as in 2) above, and this implies by Born's formula – anticipating this formula, for which a long series of arguments can be given - a fixed joint distribution of A and B. Again, Charlie can be any person. I have an article, published in Foundations of Physics, on what this limitation implies for him, using my point of view. That article unfortunately contains some smaller errors. The errors have now been corrected in a better and shorter article: http://arxiv.org/abs/2305.05299 . The conclusion is: In order to explain that the CHSH inequality can be violated in practice, we must assume that any observer is limited: In a fixed context and at some fixed time he is not able to keep as many variables in his mind as he may wish to. We are all limited in this sense.

 

4) The Monty Hall problem. An actor A opens a door, and gets a reward X. This reward is inaccessible to him before the door is opened, but accessible afterwards. His main problem is that he does not know anything about the state of the host and how he uses his knowledge. According to the Wikipedia article about Monty Hall there exists a quantum version. This has to do with the situation where A knows his X_1 after he has opened one door but does not know his X_2 after he has two choices, either keep his original choice or switch door. His inaccessible phi is the knowledge of the host.

 

5) A general decision problem with two alternatives. In the simplest case the actor A knows the consequences of both choices, they are accessible. But in more complicated cases, the consequences are inaccessible, and hence the consequence of his choice is inaccessible. Then an option can be to make a simpler sub-decision, where he knows the consequences. Maximal accessible decision variables seem to be of some interest here.

 

All these examples can, I think, be coupled to my approach towards QM. I will now sketch the basic elements of this approach.

 

My point of departure is a statement of Hervé Zwirn’s Convivial Solipsism, as noted before: Every description of the world must be relative to the mind of some observer. Different observers can communicate. A consequence of this is that physical variables also must be assumed to have some ‘existence’ in the mind of an observer. In the following I will take as a point of departure a concrete observer A. This will be assumed throughout the following arguments but note that A can be any person.

 

Postulate 1: Assume that A is in some (physical) context. Every (physical) variable in this context has a parallel existence in the mind of A.

 

The variables may be accessible or inaccessible to A. If theta is accessible,A will, in principle in some future be able to find as accurate value of theta as he likes. This is taken as a primitive notion. From a mathematical point of view, I only assume:

 

Postulate 2: If theta is accessible to A and lambda= f (theta) for some function f , then lambda is also accessible to A.

 

The crucial model assumption is now the following:

 

Postulate 3: In the given context there exists an inaccessible variable phi such that all the accessible ones can be seen as functions of phi.

 

In general, this postulate, taken together with some symmetry assumptions, has far-reaching consequences. And these symmetry assumptions will be shown to be satisfied in important cases, for instance when all accessible variables take a finite number of values.

 

Now I introduce a partial order among my variables: lambda is less than or equal to theta if lambda=f(theta) for some function f. If theta is accessible and lambda is less than or equal to theta, then I assume that lambda is accessible.

 

Postulate 4: There exist maximal accessible variables relative to this partial ordering. For every accessible variable lambda there exists a maximal accessible variable theta such that lambda is a function of theta.

 

This can be motivated by using Zorn’s lemma and Postulate 3, but such a motivation is not necessary if Postulate 4 is accepted. Physical examples of maximal accessible variables are the position or the momentum of some particle, or the spin component in some direction.

 

These 4 postulates are all that I assume. Through a long series of mathematical arguments, given in my article in arxiv 2305.0627 I can prove in the case of variables taking a finite number of values:

 

Theorem: Assume that there relative to the mind of an observer A in some given context among other variables exist two different maximal accessible variables, each taking n values. Then there exists a n-dimensional Hilbert space H describing the situation, and every accessible variable in this situation will have a unique self-adjoint operator in H associated with it.

 

This is my starting point for developing the quantum formalism from simple postulates. Using the same 4 postulates in the finite-dimensional case, further results can be proved, among other things:

 

- The eigenvalues of the operator associated with theta are the possible values of theta.

- The accessible variable theta is maximal if and only if all eigenvalues are simple.

- The eigenspaces of the operator associated with one of several variables, say theta. are in one-to-one correspondence with questions of the form ‘What is theta/ what will theta be if it is measured?’ together with sharp answers ‘theta=u’ for some u. In the maximal case this gives a simple interpretation of eigenvectors.

 

Note that my approach here is fully epistemic. It has to do with an agent seeking knowledge. In the finite-dimensional case we may concentrate on state vectors that are eigenvectors of some meaningful operator. If this operator is associated with a maximal accessible variable theta, then in general these state vectors have interpretations as questions-and-answers as above.

 

To show this requires some mathematics, given in the mentioned article, where also a further discussion is given. What is lacking here, are arguments for the Schrödinger equation and for the Born formula from simple assumptions. I refer to my Springer book for a detailed argument around  these topics, but the Born formula is discussed in the article.

Any comments to the approach above will be appreciated.

Inge

[David Marcus]

I don't know what you mean by "variable". The word is used informally in mathematics, but there are no variables in mathematics.

David

[Inge Svein Helland]

Dear David,

The word variable is used in physics and also extensively in statistics, where data are modeled as random variables. One can also think of parameters in statistics as variables: They vary over some parameter space. In my model a variable is anything that varies over a space.

Inge

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28. mai 2023 kl. 22:12 skrev David Marcus <david.ma...@gmail.com>:



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[Richard Gill]

When I learnt maths at university 50 years ago, there were variables. (And everything was actually a set). Maybe now that everyone talks category theory, variables don’t exist any more.

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[Richard Gill]

I think a better word would be “theoretical variable”

There is no need to attach it to some agent’s mind. It is of course relative to some picture of the world as consisting of various subsystems and to their descriptions relative to time and place and information

I know that Inge has a subjectivistic view akin to QBism (Quantum Buddhism!) and that he is influenced by Zwin’s notion of convivial solipsism. I also start with a personal standpoint of convivial solipsism, but by the time I am writing academic papers about quantum mechanics or working with experimentalists and analysing their data, I have moved on to accepting the fiction that there is a real world out there. 

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[Inge Svein Helland]

I agree that ‘theoretical variable’ is a good term.

Of course there is a real world out there. But When it comes to variables, they sometimes must be attached to the mind of an actor. In the Bell experiment Alice has her variables and Bob has his.

Inge

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29. mai 2023 kl. 08:41 skrev Richard Gill <gill...@gmail.com>:

 I think a better word would be “theoretical variable”

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[Mark Hadley]

Dear Inge,

I don't see why any variables must be assigned to the mind of an actor. 

EPR does not need people. It can just be machines recording results. Marks on a piece of paper or balls in different baskets. 

Cheers

Mark

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[Inge Svein Helland]

At some point of time some human may read the marks on the paper or count the number of balls in the basket. We need to think of  possible actor.

Inge

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29. mai 2023 kl. 11:27 skrev 'Mark Hadley' via Bell inequalities and quantum foundations <Bell_quantum...@googlegroups.com>:



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[Richard Gill]

I disagree that they *must* be attached to the mind of an actor. They *may* be attached to an agent, and the agent could be an AI.

I think that *persons* Alice and Bob are irrelevant to the Bell experiment. They are merely a literary device

[Inge Svein Helland]

The Bell experiment may be performed in practice. Then Alice and Bob are real persons, or rather, groups of communicating persons.

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29. mai 2023 kl. 12:04 skrev Richard Gill <gill...@gmail.com>:

 I disagree that they *must* be attached to the mind of an actor. They *may* be attached to an agent, and the agent could be an AI.

[Mark Hadley]

Or a single person.

Or an AI bot that announces the correlation

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[Inge Svein Helland]

If not ‘are’, may be seen as.

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29. mai 2023 kl. 12:27 skrev Inge Svein Helland <in...@math.uio.no>:

 The Bell experiment may be performed in practice. Then Alice and Bob are real persons, or rather, groups of communicating persons.

[Richard Gill]

The first sentence is true.

The second is an assertion which I think is your personal opinion. It is not my opinion.

Of course in QBism one is thinking of how an actor should update their opinion in order to optimally guide possible actions. It’s allowed to do that thought experiment.

[Inge Svein Helland]

An AI computed correlation has to be interpreted by some human(s).

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29. mai 2023 kl. 12:30 skrev Mark Hadley <sunshine...@googlemail.com>:



[Richard Gill]

Of course it’s allowed to think in that way.

I am allowed to ask you what your mathematics says independent of your preference to embed it in stories about actors or groups of communicating actors. I find the embedding very distracting. I also suspect it is creating unnecessary barriers for other people to find out what is the hard core maths that you have done.

[Richard Gill]

It does not have to be interpreted by any human. It can be destroyed in the coming nuclear annihilation of the human race before anybody looks at it. Not even visiting Martians may get to see it, later.

[Inge Svein Helland]

Dear Richard.

I am just curious: How can you motivate your opinion here, so that I eventually may update mine?

Inge

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29. mai 2023 kl. 12:32 skrev Richard Gill <gill...@gmail.com>:

 The first sentence is true.

[Richard Gill]

I think my opinion needs no motivation. You should explain why you think we do need to think of possible actors.

Look, if *you* are a pure solipsist then *you* must. But I think these different stances are just games. Or if you like: models. I play the game that there is an objective reality and there are objective probabilities. I think the definition of “science” is: let’s play that game together.

I adopt different positions at different hours of the day and in different contexts. Hedonist, solipsist, fighter for truth and justice. Sometimes I assume the role of a mathematician. Sometimes that of a child. And so on. In academic discourse I believe strongly in adopting the attitude that there is an external invective reality even if we cannot know it. I think physics makes that into an a priori assumption. Philosophy makes other assumptions. Politics makes yet other assumptions. Real life is complicated. Right now I’m spending 70% of my energy in trying to avert a miscarriage of justice in the UK, so I don’t have so much energy left for philosophical niceties. #lucyletby, in case anyone is interested. Off topic.

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On 29 May 2023, at 12:43, Inge Svein Helland <in...@math.uio.no> wrote:

 Dear Richard.

[Inge Svein Helland]

I showed your answer to my wife. We both have difficulties changing position the way you do.

I am convinced that there is a real world. This is not a game. That is why, when I have a model for the Bell experiment, I also need to think of the corresponding real experiment. With real people.

Inge

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29. mai 2023 kl. 14:08 skrev Richard Gill <gill...@gmail.com>:

 I think my opinion needs no motivation. You should explain why you think we do need to think of possible actors.

[Richard Gill]

I’m English (brought up in the Anglican Church, you know, the one founded by Henry 8 because the Pope asked more money than Henry cared to spend on it, in order to validate his divorce). Therefore more or less a catholic (We call it “the only true Catholic Church” in the official creed, and recite it very seriously every Sunday in Church). I can believe in several apparently contradictory things at the same time because language is ambiguous and imprecise and any statement in written language about the real world is only a model, really. It is almost always wrong but can be a good approximation to the truth and can therefore be useful nevertheless. I don’t lie. I just accept that it can be difficult to express the truth in a small number of words. 

True protestants (especially Calvinists) are stubborn believers in the written word. I think this is a bit naive (and such naivety has been the cause of many religious wars in the past).

I do often think of real experiments and I do often talk to real experimenters and try to help them analyse their data or improve their experimental technique. That’s not a game. As I said you are welcome to your point of view but I do not find your insistence on taking account of a real human Alice and Bob *necessary*. I repeat: I would prefer to see your mathematical findings shorn of this (to my mind) superfluous adornment. I know it has been part of your motivation in working out that maths. I have no objection to that, either. 

I think you would find it easier to get your work accepted if you took account of the difficulties which it gives to people like me.

[Inge Svein Helland]

OK, Richard, I will try. I will now spend the rest of the time before the Vaxjø meeting in revising my 42 page article, the background for my views.

Inge

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29. mai 2023 kl. 15:21 skrev Richard Gill <gill...@gmail.com>:

 I’m English (brought up in the Anglican Church, you know, the one founded by Henry 8 because the Pope asked more money than Henry cared to spend on it, in order to validate his divorce). Therefore more or less a catholic (We call it “the only true Catholic Church” in the official creed, and recite it very seriously every Sunday in Church). I can believe in several apparently contradictory things at the same time because language is ambiguous and imprecise and any statement in written language about the real world is only a model, really. It is almost always wrong but can be a good approximation to the truth and can therefore be useful nevertheless. I don’t lie. I just accept that it can be difficult to express the truth in a small number of words. 

To view this discussion on the web visit https://groups.google.com/d/msgid/Bell_quantum_foundations/C2C3ABA5-82FD-4297-8B88-757DA6FB2B9E%40gmail.com.

[Richard Gill]

David, maybe you are thinking of category theory? Bob Coecke is an exponent of using that and moreover coupling it to an expressive graphical notation for quantum mechanics

Not sure how useful that is for studying the possibility that classical physical models might be able to make the same empirical predictions a quantum mechanics apparently does allow.

On 28 May 2023, at 22:12, David Marcus <david.ma...@gmail.com> wrote:

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[David Marcus]

The word "variable" is used informally. Random variables are actually functions from a probability space to R. They are called "random variables" for historical reasons.

I'm not thinking of category theory.

David

[David Marcus]

Wikipedia isn't always a good source for understanding common math terms.

David

[David Marcus]

The laws of physics apply to the stuff people are made of just as they apply to other stuff. So, people shouldn't be in the laws.

David

[Richard Gill]

It’s a good source for finding out what people in general think. Which helps when you want to communicate with them.

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On 29 May 2023, at 17:28, David Marcus <david.ma...@gmail.com> wrote:



Wikipedia isn't always a good source for understanding common math terms.

David

On Sunday, May 28, 2023 at 10:56:44 PM UTC-4 Richard Gill wrote:

Variable (mathematics)

en.wikipedia.org

<wikipedia.png>

When I learnt maths at university 50 years ago, there were variables. (And everything was actually a set). Maybe now that everyone talks category theory, variables don’t exist any more.

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<wikipedia.png>

[Richard Gill]

That’s a noble aim, an ideal. Maybe however the best we can do is only to find out observer relative laws. 

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On 29 May 2023, at 17:35, David Marcus <david.ma...@gmail.com> wrote:



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[David Marcus]

Since we already have Quantum Mechanics theories without observers, the aim has been achieved.

David

[David Marcus]

The "variables" in high school algebra are names for numbers. "Variables" in Calculus were replaced by functions long ago. It is probably best to not use the word "variable" for a key element of your theory, since the word does not have a well-defined meaning. Or, you need to define it.

David

On Monday, May 29, 2023 at 1:48:44 PM UTC-4 Richard Gill wrote:

It’s a good source for finding out what people in general think. Which helps when you want to communicate with them.

Sent from my iPhone

On 29 May 2023, at 17:28, David Marcus wrote:



[Richard Gill]

I agree. And I think the word “conceptual variables” only makes things worse.

In classical physics the word is often used to stand for “functions on phase space” and phase space is the set of all possible values of all coordinates of particles’ locations and momenta. 

Inge seems to have classical variables in mind which of course need not have any QM parallel. In QM one does have “observables”. Inge assumes certain symmetries on various sets of values which classical  physical variables might have been imagined to possess. He associates a Hilbert space and hence quantum observables with this. He then also associates probability distributions with tide “observables”. Gleason’s theorem then forces them to obey the Born rule for some quantum state in that Hilbert space.

I don’t find all this helpful or illuminating. But if it is helpful and illuminating for a few other persons beyond Inge, that’s wonderful.

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On 1 Jun 2023, at 17:16, David Marcus <david.ma...@gmail.com> wrote:



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[Richard Gill]

Some people do not think that existing QM theories without observers are adequate. Do you support any particular one?

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On 1 Jun 2023, at 17:11, David Marcus <david.ma...@gmail.com> wrote:



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[David Marcus]

Bohmian Mechanics is a precise physical theory that agrees with experiment and is reasonable. Bohmian Mechanics can be made relativistic; see "Can Bohmian mechanics be made relativistic?", D. Dürr, S. Goldstein, T. Norsen, W. Struyve, and N. Zanghì, Proceedings of the Royal Society A 470, doi:10.1098/rspa.2013.0699(2013), http://math.rutgers.edu/~oldstein/papers/RBM.pdf .

The spontaneous collapse theories are ad hoc and have a weird ontology.

David

[Inge Svein Helland]

Dear Richard and David,

1) In order to partly try to satisfy you and perhaps others, I will from now on replace 'conceptual variables' with 'theoretical variables'.

2) These are not only limited to classical variables; an example may be spincomponents.

3) In my last paper I show that the symmetry conditions are satisfied in the finite-dimensional case.

4) I do not rely on the usual Gleason theorem, but a variant due to Paul Busch which also is valid in dimension 2, but requires other assumptions than noncontextuality.

But I know that there are other approaches to Born's rule.

5) As you say, I realize that I cannot convince you, but may be a few others might be interested.

6) To David: My approach to physics is as a statistician. Statisticians daily talk about random variables as models for future data, and sometimes also about parameters as variables. And why can't we also talk about physical variables?

7) My main message is some mathematical theorems. These stand firmly. But I am willing to discuss the interpretation of the theorems.

Inge

---

From: bell_quantum...@googlegroups.com <bell_quantum...@googlegroups.com> on behalf of Richard Gill <gill...@gmail.com>
Sent: 01 June 2023 17:58:04
To: David Marcus
Cc: Bell inequalities and quantum foundations
Subject: Re: [Bell_quantum_foundations] Re: Conceptual variables and quantum foundation

 

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[David Marcus]

Inge,

The phrase "random variable" has a well-defined meaning in probability: It
is a measurable function from a probability space to the reals (or to some
other suitable space). But, this doesn't mean that "variable" has a meaning
on its own. That is, we don't start with all variables and then consider
the random ones.

Statistics often uses probability models. So, we can have a probability
model for the outcome of an experiment. In Bayesian statistics, even the
parameters are modeled as random variables.

But, there are no "variables" in mathematics these days. So, if you want to
use the word "variable" (in a mathematical or physical context), you should
explain what you mean. It appears that by "physical variable", you mean a
property of an object.

David

[Inge Svein Helland]

David,

Mathematically seen, a random variable is a function on some probability space.

Physical variables are properties of some object, but in my mathematical model I also see them as functions on some underlying space. More concretely, I assume mathematically that all accessible variables can be seen as functions of an underlying inaccessible variable phi. This is a strong assumption, but it turns out that from this simple assumption essential elements of quantum mechanics can be deduced.

The simple assumption can be motivated by a couple of physical examples.

So one has a choice. Either believe in a simple, but strong assumption. Or, alternatively take the whole Hilbert space apparatus as a point of departure.

Inge

---

From: bell_quantum...@googlegroups.com <bell_quantum...@googlegroups.com> on behalf of David Marcus <david.ma...@gmail.com>
Sent: 01 June 2023 21:55:39
To: Bell inequalities and quantum foundations

Subject: Re: [Bell_quantum_foundations] Re: Conceptual variables and quantum foundation

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[David Marcus]

Inge,

> Or, alternatively take the whole Hilbert space apparatus as a point of
> departure.

The Hilbert space stuff can be derived from Bohmian Mechanics.

David

[GeraldoAlexandreBarbosa]

Inge, 

Would you believe that your QM_Inge could derive any new result not able to be predicted by QM?

If yes, could you give an example?

If not, what is the purpose of QM_Inge?

Geraldo

On Mon, May 15, 2023, 03:15 Inge Helland <in...@math.uio.no> wrote:

Can one find a new foundation of quantum theory, a foundation which ultimately leads to the full theory, but at the same time a foundation which can be explained also to persons that never have been exposed to the ordinary Hilbert space machinery?

 

My answer is yes. I have tried to discuss my approach in a book and in several published papers. Now I have collected all the mathematical arguments in a single article: http://arxiv.org/abs/2305.06727. It might not be necessary to read this article in full details, however. I will explain my model and some of my main results below.

 

My basic notion is that of a variable. A variable can be a physical variable, a statistical parameter, a future data variable, a decision variable, or perhaps also other things. I divide the variables into accessible ones and inaccessible ones. Physical variables are accessible if we by some measurement can get as accurate values as we want to. In general, I only require that if theta is accessible and lambda is a function of theta, then lambda is also accessible.

 

In a measurement situation the notions accessible/ inaccessible may be connected to the mind of some observer/actor or to the joint minds of a communicating group of actors. All this agrees with Hervé Zwirn’s Conceptual Solipsism: Every description of the world must be relative to the mind of some observer. It is also in agreement with the interpretation of quantum mechanics due to Carlo Rovelly: Variables of different systems are relative to each other; one such system may be an observer (or a group of observers).

 

Some examples:

 

1) Spin of one particle. An observer A can have the choice between measuring the spin in the x direction or in the z direction. This gives two related accessible variables in the mind of A. An inaccessible variable is the unit spin vector phi. In the qubit case, the spin component in any direction a can be seen as a simple function of phi: sign(cos(a,phi)), taking the values -1 or +1. If phi is given a uniform distributiom on the unit sphere, the correct distribution of the component in the a direction results.

 

2) The EPR situation with Alice and Bob. For an independent observer Charlie, the unit spin components of both are inaccessible, say n_A and n_B. But it can be shown that the dot product of the two is accessible to Charlie: d =n_A . n_B. Specifically, one can show that Charlie is forced to be in an eigenstate for the operator corresponding to the variable d, which is the entangled singlet state corresponding to d=-3. It is easy to show that this implies that for Charlie and for the measured components in some fixed direction a, the component of Alice is opposite to the component of Bob. Note that Charlie can be any person. (Note: n_A . n_B=-3 for Charlie means that his spin components must satisfy n_A^x =-n_B^x, n_A^y=-n_B^y and n_A^z=-n_B^z. This has implications for the components in any direction a: n_A^a=-n_B^a.)

 

3) The Bell experiment situation. Look at the subsample of data where Alice measures her spin component in direction a and gets a response A, either -1 or +1, and where Bob measures in a direction b and gets a similar response B. Then A is accessible to Alice, but inaccessible to Bob. Similarly, B is accessible to Bob and inaccessible to Alice. For an independent observer Charlie, having all data, both A and B are accessible. But Charlie has his limitation as in 2) above, and this implies by Born's formula – anticipating this formula, for which a long series of arguments can be given - a fixed joint distribution of A and B. Again, Charlie can be any person. I have an article, published in Foundations of Physics, on what this limitation implies for him, using my point of view. That article unfortunately contains some smaller errors. The errors have now been corrected in a better and shorter article: http://arxiv.org/abs/2305.05299 . The conclusion is: In order to explain that the CHSH inequality can be violated in practice, we must assume that any observer is limited: In a fixed context and at some fixed time he is not able to keep as many variables in his mind as he may wish to. We are all limited in this sense.

 

4) The Monty Hall problem. An actor A opens a door, and gets a reward X. This reward is inaccessible to him before the door is opened, but accessible afterwards. His main problem is that he does not know anything about the state of the host and how he uses his knowledge. According to the Wikipedia article about Monty Hall there exists a quantum version. This has to do with the situation where A knows his X_1 after he has opened one door but does not know his X_2 after he has two choices, either keep his original choice or switch door. His inaccessible phi is the knowledge of the host.

 

5) A general decision problem with two alternatives. In the simplest case the actor A knows the consequences of both choices, they are accessible. But in more complicated cases, the consequences are inaccessible, and hence the consequence of his choice is inaccessible. Then an option can be to make a simpler sub-decision, where he knows the consequences. Maximal accessible decision variables seem to be of some interest here.

 

All these examples can, I think, be coupled to my approach towards QM. I will now sketch the basic elements of this approach.

 

My point of departure is a statement of Hervé Zwirn’s Convivial Solipsism, as noted before: Every description of the world must be relative to the mind of some observer. Different observers can communicate. A consequence of this is that physical variables also must be assumed to have some ‘existence’ in the mind of an observer. In the following I will take as a point of departure a concrete observer A. This will be assumed throughout the following arguments but note that A can be any person.

 

Postulate 1: Assume that A is in some (physical) context. Every (physical) variable in this context has a parallel existence in the mind of A.

 

The variables may be accessible or inaccessible to A. If theta is accessible,A will, in principle in some future be able to find as accurate value of theta as he likes. This is taken as a primitive notion. From a mathematical point of view, I only assume:

 

Postulate 2: If theta is accessible to A and lambda= f (theta) for some function f , then lambda is also accessible to A.

 

The crucial model assumption is now the following:

 

Postulate 3: In the given context there exists an inaccessible variable phi such that all the accessible ones can be seen as functions of phi.

 

In general, this postulate, taken together with some symmetry assumptions, has far-reaching consequences. And these symmetry assumptions will be shown to be satisfied in important cases, for instance when all accessible variables take a finite number of values.

 

Now I introduce a partial order among my variables: lambda is less than or equal to theta if lambda=f(theta) for some function f. If theta is accessible and lambda is less than or equal to theta, then I assume that lambda is accessible.

 

Postulate 4: There exist maximal accessible variables relative to this partial ordering. For every accessible variable lambda there exists a maximal accessible variable theta such that lambda is a function of theta.

 

This can be motivated by using Zorn’s lemma and Postulate 3, but such a motivation is not necessary if Postulate 4 is accepted. Physical examples of maximal accessible variables are the position or the momentum of some particle, or the spin component in some direction.

 

These 4 postulates are all that I assume. Through a long series of mathematical arguments, given in my article in arxiv 2305.0627 I can prove in the case of variables taking a finite number of values:

 

Theorem: Assume that there relative to the mind of an observer A in some given context among other variables exist two different maximal accessible variables, each taking n values. Then there exists a n-dimensional Hilbert space H describing the situation, and every accessible variable in this situation will have a unique self-adjoint operator in H associated with it.

 

This is my starting point for developing the quantum formalism from simple postulates. Using the same 4 postulates in the finite-dimensional case, further results can be proved, among other things:

 

- The eigenvalues of the operator associated with theta are the possible values of theta.

- The accessible variable theta is maximal if and only if all eigenvalues are simple.

- The eigenspaces of the operator associated with one of several variables, say theta. are in one-to-one correspondence with questions of the form ‘What is theta/ what will theta be if it is measured?’ together with sharp answers ‘theta=u’ for some u. In the maximal case this gives a simple interpretation of eigenvectors.

 

Note that my approach here is fully epistemic. It has to do with an agent seeking knowledge. In the finite-dimensional case we may concentrate on state vectors that are eigenvectors of some meaningful operator. If this operator is associated with a maximal accessible variable theta, then in general these state vectors have interpretations as questions-and-answers as above.

 

To show this requires some mathematics, given in the mentioned article, where also a further discussion is given. What is lacking here, are arguments for the Schrödinger equation and for the Born formula from simple assumptions. I refer to my Springer book for a detailed argument around  these topics, but the Born formula is discussed in the article.

Any comments to the approach above will be appreciated.

Inge

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[Inge Svein Helland]

David,

The Hilbert space stuff has also been derived from various assumptions by Lucien Hardy and others. I think that my postulates are fairly simple, and I also arrive at a specific interpretation, which the others do not do.

The derivation from Bohmian mechanics is unknown to me.

Inge

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From: bell_quantum...@googlegroups.com <bell_quantum...@googlegroups.com> on behalf of David Marcus <david.ma...@gmail.com>

Sent: 02 June 2023 18:23:33

To: Bell inequalities and quantum foundations
Subject: Re: [Bell_quantum_foundations] Re: Conceptual variables and quantum foundation

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[Inge Svein Helland]

Geraldo,

What is the purpose of trying to understand the world better?

Inge

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From: bell_quantum...@googlegroups.com <bell_quantum...@googlegroups.com> on behalf of GeraldoAlexandreBarbosa <geraldo...@gmail.com>
Sent: 02 June 2023 18:43:16
To: Inge Svein Helland
Cc: Bell inequalities and quantum foundations
Subject: Re: [Bell_quantum_foundations] Conceptual variables and quantum foundation

 

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[David Marcus]

> I think that my postulates are fairly simple, and I also arrive at a
> specific interpretation, which the others do not do.

What do you mean by "interpretation"? Are you proposing a theory that is
different from Bohmian mechanics and the spontaneous collapse theories? If
so, what ontology are you proposing?

> The derivation from Bohmian mechanics is unknown to me.

"Quantum Equilibrium and the Role of Operators as Observables in Quantum
Theory" by D. Dürr, S. Goldstein, and N. Zanghì, Journal of Statistical
Physics 116, 959-1055 (2004) http://math.rutgers.edu/~oldstein/papers/op.pdf

On Friday, June 2, 2023 at 1:35:09 PM UTC-4 Inge wrote:

David,

The Hilbert space stuff has also been derived from various assumptions by Lucien Hardy and others. I think that my postulates are fairly simple, and I also arrive at a specific interpretation, which the others do not do.

The derivation from Bohmian mechanics is unknown to me.

Inge

[Jan-Åke Larsson]

David,
Standard Bohmian mechanics is an addition on top of QM.

Dürr et al is an account on how to describe various things in (modern) QM from the point of view of Bohmian mechanics. As far as I remember, it is not a derivation of QM from Bohmian mechanics. I looked it up now, and sure enough, it starts

      

The paper starts with Hilbert space structure (here: the vector space that Ψ lives in), and certainly does not contain a derivation of Hilbert space structure.

Perhaps you mean a different paper? (Or can you be more specific on which derivation in the paper you mean?)

/Jan-Åke

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Department of Electrical Engineering SE-581 83 Linköping Phone: +46 (0)13-28 14 68 Mobile: +46 (0)13-28 14 68 Visiting address: Campus Valla, House B, Entr 27, 3A:512 Please visit us at www.liu.se

[Chantal Roth]

There is a simpler alternative, related to the Bohmian mechanics, that I think we should discuss more:

*Just* the (pilot) waves, without any extra "particles" - the wave itself is the "particle".

(Similar to the the quasi-particles of heat, phonons, which are also pure waves, the photons are also quasi-particles and are just composed of waves, nothing else).

See for instance the work of:

- Robert Close: https://www.classicalmatter.org/ (see also https://www.youtube.com/user/ClassicalMatter/videos)

- Marek Danielewski: Foundations of the Quaternion Quantum Mechanics (Video of talk https://elastic-universe.org/)

- Ilja Schmelzer: https://ilja-schmelzer.de/matter/

- Donald Chang: http://bochang.people.ust.hk/

- a summary I wrote a while ago: http://www.askingwhy.org/blog/first-puzzle-just-a-probability/puzzle-piece-2-whats-the-matter-with-matter/

Best wishes,

Chantal

To view this discussion on the web visit https://groups.google.com/d/msgid/Bell_quantum_foundations/907d89cb-a420-a194-0482-394be30a4ab2%40liu.se.

[GeraldoAlexandreBarbosa]

It is my feeling that "better" in this context, implies new insights, including predictions not made by QM - but for QM_Inge.

Geraldo A. Barbosa, PhD

KeyBITS Encryption Technologies LLC

https://www.keybits.tech/

1540 Moorings Drive #2B, Reston VA 20190

E-Mail: GeraldoABarbosa@keybits.tech 

Skype: geraldo.a.barbosa

Cellphone: 1-443-891-7138 (US)

[David Marcus]

Jan-Åke,

> Standard Bohmian mechanics is an addition on top of QM.

You'll have to say what you mean by "QM". If you have a particular physical theory in mind, what ontology are you using?

> The paper starts with Hilbert space structure (here: the vector space
> that Ψ lives in), and certainly does not contain a derivation of Hilbert
> space structure.

Yes, the solution to a PDE is a function in a Hilbert space. The paper shows how the connection between experiments and operators arises from the basic theory.

David

On Friday, June 2, 2023 at 4:43:02 PM UTC-4 Jan-Åke Larsson wrote:

    David,
    Standard Bohmian mechanics is an addition on top of QM.

    Dürr et al is an account on how to describe various things in (modern) QM from the point of view of Bohmian mechanics. As far as I remember, it is not a derivation of QM from Bohmian mechanics. I looked it up now, and sure enough, it starts

         

[David Marcus]

Chantal,

> There is a simpler alternative, related to the Bohmian mechanics, that I
> think we should discuss more: *Just* the (pilot) waves, without any extra
> "particles" - the wave itself is the "particle".

Solutions to the Schrödinger equation live in a high-dimensional space, not in the three-dimensional space that we live in. Also, the wave keeps spreading out, so you need to do something to make it stop doing that. So, you need something more in your theory than just the Schrödinger equation.

David

[Inge Svein Helland]

Geraldo,

If that can help, I have a very preliminary paper on possible links between my theory and special and general relativity. I do not in any way consider this as the final solution.

Inge

---

From: GeraldoAlexandreBarbosa <geraldo...@gmail.com>
Sent: 03 June 2023 00:06:05

[Inge Svein Helland]

Here is a brief statement on Bohmian mechanics in my language: The position of a particle at time t is accessible, but its path from time t to time t+s is inaccessible.

Inge

---

From: bell_quantum...@googlegroups.com <bell_quantum...@googlegroups.com> on behalf of David Marcus <david.ma...@gmail.com>

Sent: 03 June 2023 01:02:46

To: Bell inequalities and quantum foundations
Subject: Re: [Bell_quantum_foundations] Re: Conceptual variables and quantum foundation

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[Jan-Åke Larsson]

I have been completely clear:

Bohmian mechanics adds ontology to quantum mechanics.

That paper does not show how to "derive the Hilbert space stuff from Bohmian mechanics." It shows how to describe various advanced concepts in quantum mechanics from the point of view of Bohmian mechanics.

It uses the standard quantum-mechanical treatment and adds Bohmian ontology to the concepts.

(And as Bohmians typically do, they misinterpret contextuality and locality badly, but that is unfortunately very common.)

/JÅ

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[Chantal Roth]

David,

Yes - and the researchers listed below have all attempted to answer this :-).

I cannot possibly summarize it all in an email, so I would encourage you to read some of them.

The dimensions you brought up are just math, not physical dimensions.

A piece of the puzzle is that the space-time metric can be rewritten as space and density (Hagen Kleinert's World Crystal below).

This leads to the idea of spherical waves  (both transverse and longitudinal combined), waves in an elastic solid (see Robert Close below). Particles in that "model" are soliton waves.

For instance, you can rewrite Schrödinger's equations with quaternions in 3 dimensions (Marek's work below).

Robert Close has been able to derive the Dirac equation (and much more) with that (and also special relativity, which is an obvious/trivial consequence of any wave system).

I totally understand that you don't want to dig through all this material, it definitively took me a while :-), so if if you prefer an "easy" read, I summarized it to some extend here http://www.askingwhy.org/blog/first-puzzle-just-a-probability/puzzle-piece-2-whats-the-matter-with-matter/ (and on the other pages).

Hagen Kleinert: http://www.sbfisica.org.br/bjp/files/v35_359.pdf

Marek Danielewski: https://www.semanticscholar.org/paper/DEFECTS-AND-DIFFUSION-IN-THE-PLANCK-KLEINERT-THE-Danielewski/dea48df9be28f2e7afad832644febafd9f600cf9

https://arxiv.org/abs/0905.4479

I find this very cool: On the optical-mechanical analogy in general relativity: https://arxiv.org/abs/0905.4479

Specifically from Robert Close:

http://www.verumversa.com/Science/ClassicalWaveTheoryOfMatter.pdf 

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[Austin Fearnley]

Hi Chantal

I looked at your website, especially the two-slit diagram.  I also watched last year your video of the Duda online seminar of last November which included Robert Close.  Does your range of ways of obtaining slit effects include TSVF?

I have been interested in the TSVF pushed by Aharonov.  Unfortunately I find videos of his lectures difficult to follow because of accent.  

Aharonov et al claim in https://www.pnas.org/doi/10.1073/pnas.1704649114
Finally making sense of the double-slit experiment, 2017, in Figure 2, that you can get an interference pattern for the double slit experiment without relying on a particle also being a wave.  I do not understand it yet myself, which is why it may take me a year to write a paper on advanced and retarded waves.  My preon model has both advanced and retarded waves within every preon and hence also within every fundamental particle.  This means that in my own simulation of a Bell experiment one really has to say where the spin property is held within a particle.  That was over-complex for my paper on solving the Bell experiment, but it means that spin -0.5 is held in a retarded (forwards in time) preon within an electron.  And for a spin -1 photon, the spin is held in two advanced (backwards in time) preons.

Wave or particle?  My bottom turtle, somewhat below preons (which are fifth layer turtle), are waves or rather universes [I have a paper on this which I wrote into the FQXi essay competition a while back].  These are different kinds of universes than those in Many Worlds, which I do not like. Some preon theories use braids but I do not.  String theory/ special relativity/  allows high speed to compactify dimensions.  One FQXi irritating comment on my paper was that the universe is obviously not full of stringy threads: we do not see them. But ... the point about compactification is that the compactified dimensions have no lengths.  So a complete 4D compactification could be a point in our spacetime.  And our own 4D spacetime could be at a point in some other 4D universe.  Is a point a particle?  Is a universe a wave? And simultaneously both in different spacetime perspectives.  We can get information out of compactified dimensions but the information is very limited and quantised.

Austin

On Saturday, June 3, 2023 at 7:45:05 AM UTC+1 cr...@nobilitas.com wrote:

[GeraldoAlexandreBarbosa]

Inge,

I will wait for any explicit new application or insight. TKS for the offer.

Geraldo

[Алексей Никулов]

Dear David,

Solutions to the Schrödinger equation live in a high-dimensional

Hilbert space according to Born’s proposal to consider the Schrodinger
wave function as a description of the amplitude of the observation
probability. But solutions to the Schrödinger equation live in the
three-dimensional space that we live according to the Schrödinger wave
mechanics which describe a real density in the real three-dimensional
space rather than the knowledge of the observer about the probability
of different results of the upcoming observation.

The dimension of the Hilbert space depends on the number of particles
the knowledge about which the wave function describes. Schrodinger
understood that Born's proposal was a trick that was misleading. But
most people cannot understand for the present that the idea of a
quantum computer is a consequence of this trick. It is surprising that
the creators of a quantum computer cannot understand that the Hilbert
space describes the knowledge of the observer, while any real device,
including a quantum computer, must exist in a real three-dimensional
space.

I draw attention in the paper [1] on the example of the GHZ theorem
(proposed in 1989 by Daniel Greenberger, Michael Horne, and Anton
Zeilinger) that the rejection of realism by the creators of quantum
mechanics provoked the degradation of physical thinking. The mistakes
made in deducing the GHZ theorem and the idea of quantum computing
indicate that the rejection of realism led to the degradation of
physical thinking primarily because almost all scientists are naive
realists. Naive realists are sure that a high-dimensional Hilbert
space describes Nature rather than the knowledge of the observer.

You are right when you write: “Also, the wave keeps spreading out, so

you need to do something to make it stop doing that. So, you need

something more in your theory than just the Schrödinger equation”.
Bohmian's mechanics is also a trick that is misleading. This trick
misled first of all Bell.

[1] Alexey Nikulov, Physical Thinking and the GHZ Theorem. Found.
Phys. 53, 51 (2023). DOI: https://doi.org/10.1007/s10701-023-00693-y ,
available at https://www.researchgate.net/publication/370581308_Physical_Thinking_and_the_GHZ_Theorem?_sg%5B0%5D=OsFaLd7du-PZqqQ5-RhvheXmPzJmgLt6ibhHus-Pgu7yzmPEdYubmSTNP-2koT9z65pACcqagXBba94CZh128Vo-fBTacGqUVWGGeTvK.Ro2l_BRd5STQj28W7s_llx5g1jkMqIF1x2iasiE6ZBucdJUUE1k4UDDIf2aXSi2jU65z2MxFhr5jBj97JV0ciQ
.

With best wishes,

Alexey


сб, 3 июн. 2023 г. в 02:02, David Marcus <david.ma...@gmail.com>:

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[Mark Hadley]

There is no trick.

QM allows us to calculate the probabilistic results of experiments. 

It uses a high dimensional parameter space, that is not unusual for any probability function. 

It's predictions are correct. Including predicted results for quantum computing. 

You are confusing the correctness of QM with the inadequacy of extra assumptions that some people add. You should question these spurious assumptions. 

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[Inge Svein Helland]

Geraldo,

The paper that I sent you, was meant to imply a new application/insight: My approach appears to imply a possiblity for a new attack on the link between quantum mechanics and relativity. This is an area where there are many open problems. I do not say that I am able to solve all these, only that my way of thinking may be can contribute something here.

Inge

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Sent: 03 June 2023 11:11:06

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[Chantal Roth]

Hi Austin,

The double slit experiments in that model is almost boringly simple :-).

You can essentially do this in a bathtub :-).

The elastic solid model is really super trivial in its basic assumptions.

Just regular old fashioned 3 spatial dimensions, time (separate dimension) and density (of space or the "fabric of space" or whatever you want to call it).

The change in density leads to gravity (via trivial refraction, just like in optics).

Particles/antiparticles are waves / anti waves.

The dirac spinors are transverse rotations in 3D space (each pauli matrix is a rotation/twist around an axis...)(the "belt" trick" - so you can do a continuous "rotation" in 3D space via a 3D spinor and not disrupt the elastic solid space grid...).

Special relativity (I have a page on that) is so trivial, you can explain it to a kindergardener in that model.

What I like about this is the total simplicity. No "epicycles" :-).

Obvoiusly I am overyl simplifying things in this email, so I would recommmend to read the actual papers on this (there are multiple on each topic..), but all in all, it seems to me at least that the puzzle pieces fit together into a coherent picture. Plus it requires no (weird) extra dimensions, no multiple universes, no retrocausality etc :-).  The only (IMHO) slightly weird thing is that the universe is some kind of 3D elastic "jello" (with varying density) :-). (Kind of funny though). All in all, it seems less weird to me than all the other options :-).

I know it is very hard to consider alternative ideas...

What could help is to pretend this is some SF story, where we "build" a universe out of an elastic solid (jiggling) jello, with varying density (considering the work I mentioned from the authors below), and see what comes out of it, to observe what is similar to "our" universe what is potentially missing. Sounds like fun to me at least :-). (Jello Universe :-).

I am quite sure you will see that it covers a wide range of topics (yes, some are missing, and those require more research. That doesn't meant it is wrong, it only means we have to spend more time to think about it :-)).

Best wishes,

Chantal

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[David Marcus]

Austin,

> Wave or particle?

As Bell pointed out, it seems obvious that there are particles guided by waves.

David

[David Marcus]

Inge,

> Here is a brief statement on Bohmian mechanics in my language: The
> position of a particle at time t is accessible, but its path from time t
> to time t+s is inaccessible.

The theory tells us what is happening. The theory tells us what the world
is doing and what happens when we do an experiment. Experiments are just
things that happen in the world, so the physical laws apply to them just as
they apply to everything else.

David

[David Marcus]

Jan-Åke,

> Bohmian mechanics adds ontology to quantum mechanics.

Indeed. If there is no ontology, it isn't really a physical theory. With no
ontology, where are the chairs and tables (not to mention the electrons and
atoms)?

If you don't like the onotology of particles that move, what ontology do
you suggest?

David

[David Marcus]

Chantal,

> Yes - and the researchers listed below have all attempted to answer this

Are you proposing a research project or a complete theory? If the latter,
what are the formulas? Apparently, your theory does not include the
standard Schrödinger equation.

David

[Jan-Åke Larsson]

Marcus,
That is why most people either don't like QM, or simply misunderstand it.
Or, add their own ontology and then criticize the result.

The only "ontology" in QM are preparation and measurement devices, their inputs and outcomes, and transformations that you can perform. (The quantum "state", "system", or "particle" does not have ontological status in QM.)

I should point out that I'm not particularly happy with this either, but that is not what we are discussing here.

The fifteen interpretations of QM (I've lost count) attempts to add ontology in different ways, none are really satisfactory. Bohmian mechanics isn't quite an interpretation since it adds something to the theory but still, in my view it misses the mark, but I'm always prepared to learn something new.

My question here is: Do you, or do you not, have a pointer to a paper where they derive the Hilbert space structure from Bohmian mechanics? This would mean they start from something else and perform the derivation (Dürr et al do not).

/Jan-Åke

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[Austin Fearnley]

Hi Chantal

The two-slit experiment may be boringly simple using waves, so can I forget it?  No. I think it was Mark who stressed that a model has to explain everything, so I need to explain both the Bell experiment and the two-slit experiment using retrocausality.

Aharanov's use of TSVF seems to me to be a link between retrocausality (with which I explain the Bell experiment) and the two-slit experiment which he claims to reproduce in his paper https://www.pnas.org/doi/10.1073/pnas.1704649114 .

How does the jello model explain the Bell experiment results?  Is that using the pilot wave model?  I have not seen a detailed solution of the Bell experiment using pilot waves.  Does it use weird jello?   such as superfluid jello :)  Maybe you have a simple paragraph (as I know you like deep understanding) detailing the pilot wave solution of Bell.  It seems to me to be just as unappealing as superdeterminism. Retrocausality is in some way IMO connected with superdeterminism, but I have not seen a satisfactory (IMO) solution using superdeterminism. Do not like superdeterminism.

I know you are interested in Malus.  A normal description of a Bell experiment starts at origin/source and ends at A and B simultaneously.  Malus alone cannot explain this Bell experiment result.  But using retrocausality, half of the data starts at A (first measurement) goes on to O (where entanglement is originated) and ends at B (second measurement).  Measurement A acts as the polarisation creator.  Measurement B acts like a Malus measurement as the particles inputted to B are polarised, unlike in a normal Bell exeriment explanation where they are randomy polarised.  So here Malus does explain the Bell result.

Austin

[David Marcus]

Alexey,

> But solutions to the Schrödinger equation live in the three-dimensional
> space that we live according to the Schrödinger wave mechanics which
> describe a real density in the real three-dimensional space rather than
> the knowledge of the observer about the probability of different results
> of the upcoming observation.

The solutions of the Schrödinger equation are in a high-dimensional space.
The domain of the function is the number of particles plus 1 (for time).
Maybe you are referring to using the solution to determine the matter
density in space. This can be done. See

"Many-Worlds and Schrödinger's First Quantum Theory" by
V. Allori, S. Goldstein, R. Tumulka, and N. Zanghì,
British Journal for the Philosophy of Science 62(1): 1-27 (2011),
http://math.rutgers.edu/~oldstein/papers/mwasfqtFINAL.pdf

If you subscribe to this theory, the world is rather different than we
teach people in school: Rather than the world being made up of atoms and
electrons, matter is continuous in space.

David

[David Marcus]

Jan-Åke,

> The only "ontology" in QM are preparation and measurement devices, their
> inputs and outcomes, and transformations that you can perform. (The
> quantum "state", "system", or "particle" does not have ontological status
> in QM.)

The word "mechanics" is there because the theory is supposed to explain how matter (such as electraons, chairs, tables) move. If you throw out the matter, you've basically given up the game.

If there is no ontology, then you can't discuss locality. Locality refers to what happens to the stuff.

> My question here is: Do you, or do you not, have a pointer to a paper
> where they derive the Hilbert space structure from Bohmian mechanics?
> This would mean they start from something else and perform the derivation
> (Dürr et al do not).

You appear to be using the word "Hilbert space structure" in a way that I'm not familiar with. Is the writing down of a differential equation already "Hilbert space structure" for you? Classical Mechanics includes differential equations in its basic formulas.

David

[Jan-Åke Larsson]

Marcus,

I've a feeling you are only at the beginning of your journey.

On 2023-06-03 16:08, David Marcus wrote:

Jan-Åke,

> The only "ontology" in QM are preparation and measurement devices, their
> inputs and outcomes, and transformations that you can perform. (The
> quantum "state", "system", or "particle" does not have ontological status
> in QM.)

The word "mechanics" is there because the theory is supposed to explain how matter (such as electraons, chairs, tables) move. If you throw out the matter, you've basically given up the game.

Quantum "mechanics" isn't a mechanical theory. At best, you could call it quantum "kinematics" but you might hesitate there too.

If there is no ontology, then you can't discuss locality. Locality refers to what happens to the stuff.

Exactly. Which is why Bell needs two assumptions: locality and realism. Without one, you cannot argue for (or against) the other. Some people here prefer different words like "local determinism", but I agree with you Marcus, Locality refers to what happens to stuff. (I would say more here but that would move us away from the present subject.)

> My question here is: Do you, or do you not, have a pointer to a paper
> where they derive the Hilbert space structure from Bohmian mechanics?
> This would mean they start from something else and perform the derivation
> (Dürr et al do not).

You appear to be using the word "Hilbert space structure" in a way that I'm not familiar with. Is the writing down of a differential equation already "Hilbert space structure" for you? Classical Mechanics includes differential equations in its basic formulas.

Yes, but classical mechanics postulates "stuff" as you put it and uses differential equations to describe what happens to stuff.

Quantum mechanics postulates differential equations and uses those to predict probabilities of outcomes. It doesn't actually postulate "stuff" or "describe" anything (there is no "mechanics")

I and Inge were hoping you had found someone that could derive QM from postulating what happens to "stuff" and use differential equations to describe it. But apparently not.

Bohmian mechanics starts from QM, so postulates differential equations, derives solutions AND THEN proceeds to add particles to the solutions, and from then on uses classical mechanics. (Meaning there is "mechanics" in Bohmian mechanics.) But BEWARE, it starts from QM. So the "stuff" gets placed (randomly initially) according to QM predictions. One big question is why the initial particle distribution in Bohmian mechanics is the square of the wave function.

You may want to read up on that. (I can't give good pointers because this was a while back.)

Best
Jan-Åke

David

On Saturday, June 3, 2023 at 9:46:27 AM UTC-4 Jan-Åke Larsson wrote:

Marcus,
That is why most people either don't like QM, or simply misunderstand it.
Or, add their own ontology and then criticize the result.

The only "ontology" in QM are preparation and measurement devices, their inputs and outcomes, and transformations that you can perform. (The quantum "state", "system", or "particle" does not have ontological status in QM.)

I should point out that I'm not particularly happy with this either, but that is not what we are discussing here.

The fifteen interpretations of QM (I've lost count) attempts to add ontology in different ways, none are really satisfactory. Bohmian mechanics isn't quite an interpretation since it adds something to the theory but still, in my view it misses the mark, but I'm always prepared to learn something new.

My question here is: Do you, or do you not, have a pointer to a paper where they derive the Hilbert space structure from Bohmian mechanics? This would mean they start from something else and perform the derivation (Dürr et al do not).

/Jan-Åke

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[Chantal Roth]

David,

The math is the same. It is just a different interpretation.

I would suggest to read some of the links below, as the Schrödinger equation is explained:

http://www.verumversa.com/Science/ClassicalWaveTheoryOfMatter.pdf

and also in Marek's work (links are below).

By the way, this is what Schrödinger himself said about the Born interpretation:

He himself thought the waves were real waves...

What we observe as material bodies and forces are nothing but shapes and variations in the structure of space…..Let me say at the outset, that in this discourse, I am opposing not a few special statements of quantum physics held today (1950s), I am opposing as it were the whole of it, I am opposing its basic views that have been shaped 25 years ago, when Max Born put forward his probability interpretation, which was accepted by almost everybody. I don’t like it, and I’m sorry I ever had anything to do with it. ( The Interpretation of Quantum Physics.)

http://www.askingwhy.org/blog/speeches-of-einstein-and-schrodinger/the-meaning-of-wave-mechanics-schrodinger/

Best wishes,

Chantal

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[Chantal Roth]

Hi Austin,

Yes, the Bell experiments are a puzzle - I don't have a good answer (I am not sure anyone does :-).

My *guess* is that at least a part of it (not all) is due to the Malus law.

But it is not enough.. so I am not sure if the "remainder" can be explained due to experimental errors or similar, or if there is indeed something else "magical" needed. I assume time will tell :-).

Given that this is literally the *only* experiment I know of that cannot be explained yet, I am hopeful that there will be a reasonable solution at some point.

I am not a fan of superdeterminism either or any other such "explanation".

Best wishes,

Chantal

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[David Marcus]

Jan-Åke,

> Yes, but classical mechanics postulates "stuff" as you put it and uses
> differential equations to describe what happens to stuff.

Indeed. And, Bohmian Mechanics does the same.

If your theory does not have stuff in it, then why not?

David

On Saturday, June 3, 2023 at 10:33:41 AM UTC-4 Jan-Åke Larsson wrote:

Marcus,

I've a feeling you are only at the beginning of your journey.

[Jan-Åke Larsson]

It isn't my theory.

(I'd express Bohr's view using your words as: There isn't any stuff to describe. You can only ever talk about predictions of measurement outcomes. Quantum mechanics predicts probabilities of measurement outcomes. Nothing more, nothing less.)

As for me, I'm working on different things, more Bohm-like. I think there IS some explaining to do. Hence my interest in your claim. But that is a different story.

/Jan-Åke

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[David Marcus]

Jan-Åke,

> (I'd express Bohr's view using your words as: ...

Bohr was wrong. We can see there is stuff all around us. We have good reason for believing there really are electrons and atoms.

Bell said it best:

"Is it not clear from the smallness of the scintillation on the screen that we have to do with a particle? And is it not clear, from the diffraction and interference patterns, that the motion of the particle is directed by a wave? De Broglie showed in detail how the motion of a particle, passing through just one of two holes in screen, could be influenced by waves propagating through both holes. And so influenced that the particle does not go where the waves cancel out, but is attracted to where they cooperate. This idea seems to me so natural and simple, to resolve the wave-particle dilemma in such a clear and ordinary way, that it is a great mystery to me that it was so generally ignored."

For more on Bohr, see

"The Sokal Hoax: At Whom Are We Laughing?" by Mara Beller, Physics Today, September 1998, https://bohmian-mechanics.net/sokalhoax.html

David

[Jan-Åke Larsson]

Say that I agree with you. Then we'd need something that does *not* start with QM itself. You were saying there was such a thing. So I was interested in your claim, but there was nothing in that paper to that effect.

Have a good weekend
/Jan-Åke

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[David Marcus]

Jan-Åke.

> Then we'd need something that does *not* start with QM itself. You were

> saying there was such a thing

You appear to have thought that I said that I could derive the Schrödinger equation from something else. I don't think I said that, but I'm sorry if I wasn't clear. What I meant was that we can derive the use of Hilbert space operators to calculate the results of experiments from the differential equations that say how particles move.

David

[Austin Fearnley]

Hi Chantal

Thanks, that was useful.  I did not want to waste further efforts on retrocausality if Bohm pilot waves were a better explanation. So I can forget pilot waves, for now.

IMO retrocausality is my complete answer though maybe it needs a better title than retrocausality. 

Your quote from Schrodinger says that " ...material bodies and forces are nothing but shapes and variations in the structure of space..."

I agree.  In my preon model, particles are made of compactified spacetimes ..but not shapes or knots of our own spacetime.  There are five other compactified 4D spacetimes which interplay to form particles.  One could call them red, green, blue, spin and weak isospin 4D spacetimes.  And one gets quantised information from them.   But if retrocausality is a hard sell then 24D is an even harder sell!  :)

Austin

[Jan-Åke Larsson]

No, you can adapt the quantum-mechanical use of Hilbert space operators so it fits in the ontology of Bohmian mechanics.

/Jan-Åke

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[David Marcus]

Jan-Åke,

> No, you can adapt the quantum-mechanical use of Hilbert space operators
> so it fits in the ontology of Bohmian mechanics.

I'm not sure what you are saying, so I'll just quote what Dürr, Goldstein, Zanghì wrote:

"Bohmian mechanics is arguably the most naively obvious embedding imaginable of Schrödinger's equation into a completely coherent physical theory. It describes a world in which particles move in a highly non-Newtonian sort of way, one which may at first appear to have little to do with the spectrum of predictions of quantum mechanics. It turns out, however, that as a consequence of the defining dynamical equations of Bohmian mechanics, when a system has wave function psi its configuration is typically random, with probability density rho given by |psi|^2, the quantum equilibrium distribution. It also turns out that the entire quantum formalism, operators as observables and all the rest, naturally emerges in Bohmian mechanics from the analysis of 'measurements'. This analysis reveals the status of operators as observables in the description of quantum phenomena, and facilitates a clear view of the range of applicability of the usual quantum mechanical formulas."

For details, see their paper.

David

[Jan-Åke Larsson]

Perhaps you do not understand the difference. They do not claim to derive QM from Bohmian mechanics. They claim the QM formalism can be recast using the ontology of Bohmian mechanics.

All the best
Jan-Åke

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[David Marcus]

Jan-Åke,

I confess that I don't know what you mean by "QM". Do you mean the Schrödinger equation? The measurement postulates? Bohr's claims about reality or the lack thereof? All of these?

David

[Jan-Åke Larsson]

Marcus,

What I mean is the formal machinery that lets you predict the probabilities for measurement outcomes that you use the mathematics of quantum mechanics to calculate. Sometimes called "the bare theory". I suppose for you that would mean the Schrödinger equation, projective measurements, and Born's rule. You do not need the projection postulate or Bohrs claims. Just the mathematical machinery.

You explicitly said (and I quote): "The Hilbert space stuff can be derived from Bohmian Mechanics." which means to both Inge and me that you claim that this mathematical machinery can be derived from Bohmian mechanics. Inge then said "The derivation from Bohmian mechanics is unknown to me" to which your response was referring to Dürr et al's paper. Which contains no such derivation.

To me "the Hilbert space stuff" includes Schrödinger's equation, measurement operators, mixed states, POVMs, Born's rule, partial traces, transformations, quantum computer gates, entanglement, uncertainty, and so on, but not really the projection postulate which to me is just a notational simplification since you could avoid that altogether and just use a final measurement for the whole state.

You have to realize I teach quantum algorithms and quantum information theory where we use pretty advanced "Hilbert space stuff" without needing Bohr's claims or for that matter Bohmian mechanics, and I also just finished a two-semester PhD level course on quantum foundations, covering everything from Planck to the latest Bell inequality tests. (I've spent 25 years in this field and have published over 80 papers with over 4500 citations so I do have some experience.)

/Jan-Åke

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[Алексей Никулов]

Dear David,

You fairly remarke “If there is no ontology, then you can't discuss
locality. Locality refers to what happens to the stuff” clarifies the
essence of the misconception of those believers in quantum mechanics
(including the Nobel prize winners of the last year) who refute local
realism with the help of experimental results. The ridiculous notion
of ‘local realism’ appeared only because the EPR used the requirement
of locality to refute quantum mechanics, and not its principle that
operators acting on different particles commute.

But I cannot agree with you that Bohmian Mechanics can describe what
happens to stuff. Bohmian Mechanics cannot do without collapse, for
example, when describing the interference experiment on two slits.
Bohmian Mechanics does not use the collapse of the wave function, but
it should use the collapse of the quantum potential. No collapse of
stuff or of a real field is thinkable. Only our knowledge can collapse
at observation.

The authors of the article [1] that you specified wrote in the
abstract: “Schrodinger’s first proposal for the interpretation of
quantum mechanics was based on a postulate relating the wave function
on configuration space to charge density in physical space”. When I
wrote that solutions to the Schrödinger equation live in the

three-dimensional space that we live according to the Schrödinger wave

mechanics, I meant exactly what the authors [1] wrote: the Schrödinger
wave mechanics describes charge density in physical space. Schrodinger
recognized his wave mechanics as an untenable theory and was
considering Born's proposal as a trick. This trick has misled several
generations of physicists, provoked many interpretations and the idea
of quantum computing.

A high-dimensional Hilbert can describe the knowledge of the observer
according to Born's proposal and real many-worlds according to
Everett’s many-worlds view of quantum theory. It is important to know
that Everett proposed the many-worlds interpretation of quantum
mechanics in order to eliminate psychology from physical theory. A
real device can be made on the basis of a description of a reality but
not of the knowledge of the observer. I agree with David Deutsch that
a quantum computer can be real only in the reality of Many Universes.
But unlike Deutsch, I cannot believe in the existence of many
universes, each of which has its own frog as a photon detector and its
own David Deutsch.

I think that the publication [1] is one of the many hopeless attempts
to save quantum mechanics from the absurd. It is time for the authors
of such attempts to understand that Nature can be incognizable for our
reason.

[1] V. Allori, S. Goldstein, R. Tumulka, and N. Zanghì, "Many-Worlds
and Schrödinger's First Quantum Theory" British Journal for the
Philosophy of Science 62(1): 1-27 (2011).

With best wishes,
Alexey

вс, 4 июн. 2023 г. в 00:08, David Marcus <david.ma...@gmail.com>:

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[David Marcus]

Chantal,

> The math is the same.

The same as what? I looked at your webpage. Are you suggesting waves as the ontology? If so, you need to give actual equationis.

David

[Chantal Roth]

David,

I would recomment to read the work of the authors, since they wrote it pretty well I think, instead of me speding all the time to rewrite it, so I would encourage you to either read those (or what the videos I provided if you prefer youtube :-).

I am just tried to summarize it on my blog. 

By the math is the same I mean: the same SR and GR, same Schrödinger/Dirac, same EM etc.

It is mainly ontology - but of course, if an ether model is proposed, there is additional math since it would be more fundamental and QM/SR/GR etc are emergent from that. *That* math is of course partially new, and the authors I think are doing a good job to explain it.

Best wishes,

Chantal

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[David Marcus]

Alexey,

> Bohmian Mechanics cannot do without collapse, for example, when
> describing the interference experiment on two slits.

There is no collapse of the wave in Bohmian Mechanics. The Schrödinger equation is true at all times.

You can solve the differential equations of the theory and reproduce the interference pattern of two-slit experiment. You can see pictures of the solutions in many places. People didn't just make up these pictures; they are calculated from the differential equations.

It is a mystery to me how you could write what you wrote. Maybe you are using a different definition of "Bohmian Mechanics".

David

[David Marcus]

Chantal,

> By the math is the same I mean: the same SR and GR, same
> Schrödinger/Dirac, same EM etc. It is mainly ontology

You need to give formulas for the ontology. I looked at the links you gave, but I don't see anything suitable.

David

[David Marcus]

Jan-Åke,

> To me "the Hilbert space stuff" includes Schrödinger's equation,
> measurement operators, mixed states, POVMs, Born's rule, partial traces,
> transformations, quantum computer gates, entanglement, uncertainty, and
> so on

Maybe we are using different definitions of "Bohmian Mechanics". Using my definition (and the one in the paper), the only item on your list that is in the postulates of the theory is the Schrödinger equation. The rest are in there, but as theorems.

David

[Chantal Roth]

David,

The model we've been discussing proposes an ontological interpretation where there exists a "real" quantum field or "ether" (bad word), from which particles and other phenomena emerge as wave-like excitations. In this framework, standard formulas like the Schrödinger or Dirac equations, as well as Special and General Relativity, retain their usual forms. However, their interpretation changes: they are seen as describing waves in this underlying ether, rather than fundamental aspects of reality in themselves.

This interpretation introduces a new layer of underlying physics to the traditional quantum model, which obviously comes with its own math. Robert Close has worked on modelling these as torsion waves in an elastic solid (I would encourage you to read his work: http://www.verumversa.com/Science/ClassicalWaveTheoryOfMatter.pdf. You can't possibly have read al l his in such a short time :-). (He is also on the forum and might be willing to answer questions. I cannot possibly do this in an email and do it justice), and Marek Danielewski has attempted to describe such waves using Cauchy's elasticity equations (https://www.mdpi.com/1099-4300/22/12/1424 and several previous papers, here is the video https://www.youtube.com/watch?v=QXDUItMVE4U). These could be considered as some of the "ontological formulas" of this model. Yes there are some differences among these, but the basic idea is the same among them.

Regarding your question about experimental distinguishability, it could potentially be challenging, as this interpretation fundamentally produces the same observable effects as current interpretations. However, there could be subtle differences in extreme conditions or at high precision, and future experiments could potentially be designed to test these differences. Any ideas are welcome!

The main point of this is that there is no "magic", it is *simple*.

All the stuff that most people find weird (like SR, GR, matter/anti-matter etc) are (almost) trivial, and to me that is worth a lot, even if everything else stays the same. Occam's razor :-). (*)

Here are more links (not sure if all still work): https://elastic-universe.org/links/

Best wishes,

Chantal

PS (*) All except Bell, that is. No good explanation other than it is either experimental or somehow due to some non-local effect of the ether/waves.. time will tell I hope.

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[Алексей Никулов]

Dear David,

The problem is not with solving differential equations in theory, but
with an experiment, so far a thought experiment. Imagine that behind
the two slits is a Wilson cloud chamber. Do you really believe that
the observed trajectories will correspond to the motion of particles
in the Bohm quantum potential?

With best wishes,
Alexey

вс, 4 июн. 2023 г. в 17:36, David Marcus <david.ma...@gmail.com>:

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[David Marcus]

Chantal,

> ... In this framework, ... This interpretation ...

So, you don't actually have a theory. Just a research project.

David

[David Marcus]

Alexey,

> Imagine that behind the two slits is a Wilson cloud chamber. Do you
> really believe that the observed trajectories will correspond to the
> motion of particles in the Bohm quantum potential?

I'm not an experimentalist, but I believe the stuff in the cloud chamber will affect the trajectories of the electrons and ruin the interference pattern.

The theory predicts the interference pattern, and we can observe the latter. So, I "really believe" the theory.

The following article reports experimental evidence that photons follow Bohmian trajectories. See Figure 3:

Observing the Average Trajectories of Single Photons in a Two-Slit Interferometer
Sacha Kocsis et al.
Science 332, 1170 (2011);
DOI: 10.1126/science.1202218
http://science.sciencemag.org/content/332/6034/1170

David

On Sunday, June 4, 2023 at 2:04:08 PM UTC-4 Alexey wrote:

Dear David,

[Chantal Roth]

I am not sure how this is supposed to help with our discussion.

If you are interested in any constructive discourse, I would highly recommend to actually read the work of these authors.

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[Jan-Åke Larsson]

(shaking head)

Bohmian mechanics uses "the Hilbert space stuff" as a basis. It starts from quantum mechanics.

I repeat: It starts from quantum mechanics. The Hilbert space is already there.

Theorems you can derive from the properties of the Hilbert space (as present in the postulates of quantum mechanics), are also possible to derive in Bohmian mechanics, since it uses quantum mechanics as a basis for everything. What you need to check is that the ontology of Bohmian mechanics (which is the thing you add to quantum mechanics) also gives a consistent picture of the properties you talk about in the theorems.

Dürr et al are checking that the (full, extensive) machinery of quantum mechanics is consistent with Bohmian ontology. They don't derive anything.

I do respect their efforts, I like the paper. But it is not that they derive anything from specifically Bohmian postulates. They just check that the more recent tools we use in QM do not contradict Bohmian ontology.

/Jan-Åke

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[David Marcus]

Jan-Åke,

> since it uses quantum mechanics as a basis for everything

I asked you what exactly in "quantum mechanics" you meant by this. You told me. I pointed out that most of the items you listed were not in the postulates of Bohmian Mechanics. You then repeated your assertion that they are.

I'm sorry, but I don't understand what you are saying. You seem to be saying that if we can derive something from a theory, then the something is already there. I suppose that is true in some sense. But ever since Euclid, we've realized that there is a difference between theorems and axioms.

Bell's book, second edition, page 160: "More importantly, in my opinion, the subjectivity of the orthodox version, the necessary reference to the 'observer', could be eliminated." Bell is pointing out that Bohmian Mechanics does not include things in its postulates that are in standard Quantum Mechanics.

David

[Jan-Åke Larsson]

David,

I told you what is in the postulates of quantum mechanics. I quote: "I suppose for you that would mean the Schrödinger equation, projective measurements, and Born's rule." This includes postulating a Hilbert space.

The other things I listed are consequences (of the QM postulates). Like you say, theorems that are consequences of the axioms. Sometimes complicated consequences.

The observer is not in any postulate in quantum mechanics, seen as a theory that makes predictions of measurement outcomes. You are talking about an interpretation of quantum mechanics, an interpretation that contains observers, an interpretation that I do not use at any point. I specifically did not add "observer" in my list. You are mixing too many things.

Dürr et al do not derive anything from "Bohmian mechanics postulates" whatever that might mean. They do not "derive Hilbert space stuff". They check that the theorems of quantum mechanics do not contradict Bohmian ontology.

/Jan-Åke

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[Алексей Никулов]

Dear David,

You wrote that you “believe the stuff in the cloud chamber will affect
the trajectories of the electrons and ruin the interference pattern”.
Quantum mechanics has always been for most scientists a religion they
believe in rather than a scientific theory they understand. I wrote
already that I admire the genial prophecy of Einstein, who wrote to
Schrodinger in 1928: "The soothing philosophy—or religion?—of
Heisenberg-Bohr is so cleverly concocted that for the present it
offers the believers a soft resting pillow from which they are not
easily chased away. Let us therefore let them rest….This religion does
damned little for me".

You believe in one of the confessions of the quantum religion. If
Bohmian Mechanics were for you not one of confessions of the quantum
religion that you believe in, but a scientific theory that you
understand, you would not been believing, but would have to explain
how the stuff in the cloud chamber will affect the trajectories of the
electrons and ruin the interference pattern. This process is real
because the observer's consciousness does not participate in it.
Therefore, it must be described within the framework of a physical
theory. I wrote already that Schrodinger and few other critics
understood that quantum mechanics is a trick rather than a physical
theory. The trick is obvious: quantum mechanics describes the
observed, but does not describe the process of observation.

When you write that you believe, you are admitting that Bohmian
Mechanics is also a trick. This trick played a crucial role in the
appearance of Bell's inequalities, as Bell believed that this trick
could describe realistically paradoxical quantum phenomena. Because of
this belief, Bell did not notice that only Bohm's quantum mechanics,
but not orthodox quantum mechanics, can predict the EPR correlation
and violation of Bell's inequalities, see [1]. I demonstrate in [1] on
the example of the GHZ theorem that the belief in the quantum religion
results in the degradation of physical thinking.

Numerous interpretations and different, often opposite understandings
indicate that quantum mechanics is a religion, not a scientific
theory. Different interpretations of quantum mechanics are different
confessions of a religion. Different faiths in religions such as
Christianity are justified by the fact that the subject of Christian
faith is not accessible to understanding for our reason. Quantum
mechanics, like any theory, is created by our (humans) reason. Any
scientific theory should be understood unambiguously and should not
have interpretations. Quantum religion, which has interpretations and
is understood in different ways, is idolatry, since the theory is
created by our reason.

[1] Alexey Nikulov, Physical Thinking and the GHZ Theorem. Found.
Phys. 53, 51 (2023). DOI: https://doi.org/10.1007/s10701-023-00693-y

With best wishes,
Alexey

вс, 4 июн. 2023 г. в 23:30, David Marcus <david.ma...@gmail.com>:

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[David Marcus]

Alexey,

I'm sorry, but I don't understand what you wrote.

David

[David Marcus]

Jan-Åke,

> I suppose for you that would mean the Schrödinger equation, projective
> measurements, and Born's rule.

We disagree as to what the postulates of Bohmian Mechanics are. I don't understand why this is. Here is a succinct description of Bohmian Mechanics:

   https://sites.math.rutgers.edu/~oldstein/papers/qts/node4.html

The postulates of the theory are in the second paragraph. As it says, there are just the two equations.

You say that you like the paper

   "Quantum Equilibrium and the Role of Operators as Observables in Quantum Theory"
   by D. Dürr, S. Goldstein, N. Zanghì
   http://math.rutgers.edu/~oldstein/papers/op.pdf

But, you think the abstract that the authors wrote is wrong, i.e., does not summarize the paper correctly. I suggest people read the paper and see for themselves whether the abstract is correct. I will leave it at that.

David

[Chantal Roth]

It is essentially "Quantum Religion" vs "Science".

Science should not have "interpretations".

Do we have "interpretations" of how DNA is transcribed?

Or for how to build a computer chip?

There it would seem absolutely crazy to do that.

I agree with Alexey, QM feels more like a religion right now - where you have groups of people who "belief" one thing versus another, and usually people are quite opposed to any other thinking.

The "Copenhagen " folks - the "Orthodox Church".
The "Many worlds" believers - the "Reformist movement"

The "Bohmian" theorists - the "Revivalist group"

The "Waves in Ether" clan - the "Pantheists" 

 :-)

Cheers,

Chantal

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[Jan-Åke Larsson]

David,

On 2023-06-05 00:09, David Marcus wrote:

Jan-Åke,

> I suppose for you that would mean the Schrödinger equation, projective
> measurements, and Born's rule.

We disagree as to what the postulates of Bohmian Mechanics are. I don't understand why this is. Here is a succinct description of Bohmian Mechanics:

   https://sites.math.rutgers.edu/~oldstein/papers/qts/node4.html

The postulates of the theory are in the second paragraph. As it says, there are just the two equations.

I quote: "Bohmian mechanics (or the de Broglie-Bohm theory) is the minimal completion of Schrödinger's equation", meaning that it starts with Schrödinger's equation. Meaning that it needs the Hilbert space of solutions from the very start. It also needs Born's rule for the initial distribution of particles.

I don't see how you can think anything else than what is literally there.

You say that you like the paper

   "Quantum Equilibrium and the Role of Operators as Observables in Quantum Theory"
   by D. Dürr, S. Goldstein, N. Zanghì
   http://math.rutgers.edu/~oldstein/papers/op.pdf

But, you think the abstract that the authors wrote is wrong, i.e., does not summarize the paper correctly. I suggest people read the paper and see for themselves whether the abstract is correct. I will leave it at that.

I don't know if I think it is wrong. Somewhat overstated maybe.

In Bohmian mechanics one adds ontology: "Bohmian mechanics (or the de Broglie-Bohm theory) is the minimal completion of Schrödinger's equation", but the Hilbert space machinery is always there. Of course the Hilbert space machinery gives you the same things as it would without the ontology. You just take your advanced concept, translate it into Hilbert space statements, add your Bohmian ontology and voila: The thing  'Naturally emerges in Bohmian mechanics from the analysis of "measurements"'.

This is how it must be, otherwise Bohmian mechanics would be inconsistent.


Best
Jan-Åke

David

On Sunday, June 4, 2023 at 4:46:12 PM UTC-4 Jan-Åke Larsson wrote:

David,

I told you what is in the postulates of quantum mechanics. I quote: "I suppose for you that would mean the Schrödinger equation, projective measurements, and Born's rule." This includes postulating a Hilbert space.

The other things I listed are consequences (of the QM postulates). Like you say, theorems that are consequences of the axioms. Sometimes complicated consequences.

The observer is not in any postulate in quantum mechanics, seen as a theory that makes predictions of measurement outcomes. You are talking about an interpretation of quantum mechanics, an interpretation that contains observers, an interpretation that I do not use at any point. I specifically did not add "observer" in my list. You are mixing too many things.

Dürr et al do not derive anything from "Bohmian mechanics postulates" whatever that might mean. They do not "derive Hilbert space stuff". They check that the theorems of quantum mechanics do not contradict Bohmian ontology.

/Jan-Åke

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[Richard Gill]

I disagree. We have maths. The maths works, it describes accurately what we see in experiments. It describes what we see in new experiments which nobody thought of doing before.

In order to communicate the maths we need pictures and words. Some people cling to the pictures and words which seemed to be working well up to the end of the 19th century. I’m convinced that QM reality demands that we reappraise the traditional pictures and words. Bell inaugurated the field of “experimental metaphysics”. It is more alive than ever and the religious wars are getting more and more virulent. 

This Google group has been created to provide a level playing field where this war may be fought in a dignified, respectful, civilized, ritualized manner.

I’m for the QBism (quantum Buddhism). Experimental data is real. Tables and chairs are real. The rest is imagination. I think Belavkin’s “eventum mechanics” is the way to resolve the apparent paradoxes of conventional (Copenhagen) QM. I think it admits that irreducible randomness is a basic and fundamental element of the physical universe. We are evolutionarily unable to accept that. Aristotle was wrong: not everything has a cause. Our belief in that is a prejudice. It worked well for a few million years but now we can see it is not universally true.

Richard

Sent from my iPad

On 5 Jun 2023, at 09:56, Chantal Roth <cr...@nobilitas.com> wrote:



It is essentially "Quantum Religion" vs "Science".

Science should not have "interpretations".

Do we have "interpretations" of how DNA is transcribed?

Or for how to build a computer chip?

There it would seem absolutely crazy to do that.

I agree with Alexey, QM feels more like a religion right now - where you have groups of people who "belief" one thing versus another, and usually people are quite opposed to any other thinking.

The "Copenhagen " folks - the "Orthodox Church".
The "Many worlds" believers - the "Reformist movement"

The "Bohmian" theorists - the "Revivalist group"

The "Waves in Ether" clan - the "Pantheists" 

 :-)

Cheers,

Chantal

On Sun, Jun 4, 2023, at 11:37 PM, David Marcus wrote:

Alexey,

I'm sorry, but I don't understand what you wrote.

David

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[ben smith]

Chantal, Richard and all

Another group: crackpots -  Puritans

Belief that you have been chosen by God and are one of the Elect who will join with God in the afterlife.  So your idea is endorsed on high simply because you are special.

Following back along my paternal family tree I hit a roadblock at 1580s.  There are three possible nth great grandfathers, so one could say that these three (Peter, George, Thomas) are entangled? (Could I make a qutrit here?)  I feel sure it is one of them (only one of them is really in Monty Hall’s prize box)  but working out which one is right is similar QM but only because it deals with probabilities.

Peter left a Will in 1616 declaring that he aspired to be one of the Elect. Likewise his widow in her Will of 1634.   George was likely to be an attorney.  His son definitely was.  George was near Halton Castle in 1570s which is where Queen Elizabeth had rounded up local catholics after the Pope’s papal Bull.  Was George an Anglican and prosecuting catholics at Halton, or was he catholic and being prosecuted himself.  :)

Austin

On 5 Jun 2023, at 08:56, Chantal Roth <cr...@nobilitas.com> wrote:



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[Richard Gill]

Dear Chantal

The problem with the people who operate in this world which you mention - a local realistic world - is that its denizens are, on the whole, sorely ignorant of Bell’s theorem. Of course they have heard of it. They think it is irrelevant but their reasoning (if any) is very clearly *wrong*. And having bought in (in a big way) to an underlying theory of waves in an ether, they are demotivated from finding out what Bell’s reasoning has to say about the adequacy of their theory.

Also, they feel supported by 50 years of hiding behind the loopholes. And so many of such classical thinkers are still talking about the defects of Weihs 1998 experiment. It’s interesting (both psychologically and mathematically), but I feel there are a lot of dinosaurs out there in this field which you support so strongly.

Richard 

Sent from my iPad

On 4 Jun 2023, at 19:26, Chantal Roth <cr...@nobilitas.com> wrote:



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[Chantal Roth]

Richard,

To me Bell is one of many puzzle pieces only, and the experiments are not *that* overwhelming (yet?).

The whole picture of all pieces has to fit together and make sense.

These include SR, GR, QM, and questions like: why is there a speed of light, what is space, why should there be "paradoxes" (as in SR), what is the reason for SR, GR etc, what is the structure of matter, why is there matter/antimatter etc etc (gazillion more). 

Whatever interpratation one picks, ideally all puzzle pieces have to fit and ideally *make sense*. It should also use the fewest assumptions and parameters (Occams Razor).  Any interprtation that has "paradoxes" IMHO is flawed by design (a paradox is indicative of a flaw). 

That local realistic interpreation to me seems to fit most of those pieces *so far* - except Bell. All the other interpretations have other drawbacks (other pieces that don't fit, paradoxes, don't really explain anything etc) that appear a lot worse to me. That is probably a personal choice.

I hope time will tell :-).

(Once I retire or win the lottery, I will dedicate my time to this kind of research, but until then unfortunately, I have to spend most of my time working :-/)

By the way, I have no problem being proven wrong - I have had many "beliefs" that turned out to be completely wrong multiple times, so I think I can deal with it if this happens :-).

Cheers,

Chantal

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