Gerard 't Hooft's "Fast Vacuum Fluctuations"

[Quanundrum]

Gerard 't Hooft has been a renegade in Quantum Foundations for quite some time, insisting that there is natural order underlying the Quantum Mechanical mysteries. Essentially a local, deterministic hidden variable perspective.

He has recently posted a new paper on arXiv where he lays out his conclusions, on his website he says

Progress in my personal research on the origin of quantum mechanics as a doctrine for describing atoms, molecules, sub-atomic particles and more. Aim: write models that reproduce quantum behavior such that they can run on a classical computer. Question: how can one mimic quantum interference effects in a classical computer? Thought to be impossible, but the mechanism described in my latest paper works! For me, quantum mechanics is no mystery anymore. All one has to understand is:
The Emergence of Quantum Mechanics from Fast Vacuum Fluctuations

I'm intrigued to hear opinions on this. Despite initial skepticism, and not being a fan of appealing to authority, I do think it's worth consideration.

 

[Paul Colby]

Is it fair to ask what,

$p_i = -i\frac{\partial }{\partial x_i}=\frac{2\pi n_i}{L_i}$

means? He’s equating a partial differential operator to a rational number. This means nothing as far as I can see.

 

[PeterDonis]

Is it fair to ask what,

$p_i = -i\frac{\partial }{\partial x_i}=\frac{2\pi n_i}{L_i}$

means? He’s equating a partial differential operator to a rational number. This means nothing as far as I can see.

More precisely, a rational number times $\pi$.

What he is doing in that particular case is replacing an operator (in this case, the momentum operator) by its eigenvalues when applied to a spectrum of eigenstates. This is a perfectly OK thing to do and is common in QM; he probably didn't think it was necessary to mention it because the intended audience of his paper is people for whom it is already common knowledge.

 

[Sunil]

I'm not completely sure what the point of this paper is.

That a classical Hamiltonian system can be embedded into a Hilbert space so that the Hamiltonian evolution generates an unitary transformation is known from Koopman 1931. In this paper, the Hilbert space is simply the $\mathcal{L}^2$ on the phase space, as defined by the invariant $dp\land dq$ measure, and the evolution is simply the one generated by the Hamiltonian evolution.

That Hilbert space is much greater than that of the quantum theory we would get by canonical quantization, essentially the one of two particles where the commuting operators $\hat{p}=\hat{p}_1+\hat{p}_2$ and $\hat{q}=\hat{q}_1-\hat{q}_2$ are measured, a standard approximate common measurement of position and momentum of the first particle if the second particle is in the ground state so that $\hat{p}_2,\hat{q}_2\approx 0$. If this second particle is in a harmonic oscillator ground state, the corresponding subspace is also known as the holomorphic representation, because the wave functions are holomorph functions modulo a normalization factor $\psi(p,q) = \psi(z,\bar{z}) = f(z)e^{-\frac12 z\bar{z}}$ or so (out of memory).

This seems to be a similar construction. The high energy of the high frequency degrees of freedom are then used to get rid of the additional degrees of freedom.

Ref:
Koopman B.O. (1931). Hamiltonian Systems and Transformations in Hilbert Space. Proceedings of the National Academy of Sciences 17 (5), 315-318.

 

[Paul Colby]

he probably didn't think it was necessary to mention it because the intended audience of his paper is people for whom it is already common knowledge.

Very likely the case.

So, why isn’t this just a hidden variable scheme?

 

[PeterDonis]

why isn’t this just a hidden variable scheme?

I haven't fully digested the paper yet, so I can't say what, if any, difference there is between his model and, say, the type of local hidden variable model that was described in Bell's papers on Bells Theorem, and which are ruled out by that theorem. As I understand it, the model in this paper is claimed to make the same predictions as QM, which would mean it cannot be the same type of local hidden variable model as Bell's paper rules out. But by the same token, the paper claims that the model does not have "non-locality"; I'm not sure at this point what that means exactly.

 

[Paul Colby]

which would mean it cannot be the same type of local hidden variable model as Bell's paper rules out

I would think any referee would require the author to address this question explicitly even if the result replicates QM behavior.

 

[PeterDonis]

I would think any referee would require the author to address this question explicitly even if the result replicates QM behavior.

If the result does replicate QM predictions, then it is a well established mathematical theorem that it cannot be a local hidden variable model in the sense that Bell defined that term, so it would be superfluous for the referee to request an explicit statement to that effect. Scientific papers are not required to restate things that are common knowledge to experts in the field.

 

[Paul Colby]

Scientific papers are not required to restate things that are common knowledge to experts in the field.

If it were that common in this case I would hope someone would have addressed my question.

 

[PeterDonis]

If it were that common in this case I would hope someone would have addressed my question.

If you agree that the results in the paper replicate the QM predictions, then there would be no need for any explicit statement in the paper that the model is not a local hidden variable model, since that will be obvious to any expert in the field, even if it's not obvious to you.

If you do not agree that the results in the paper replicate the QM predictions, then it seems to me that your questions should be focused on that point, since it is a disagreement with an explicit claim of the paper, rather than on whether or not the paper's model is a local hidden variable model.

 

[Paul Colby]

I'm taking the more common third option which is to just ignore the paper and move on. Thanks for your time.

 

[Paul Colby]

Evidently 't Hooft disputes Bell as a limitation in this paper. Maybe I can ignore this one as well

https://arxiv.org/abs/quant-ph/0701097

 

[eloheim]

Anyone interested enough to not ignore this paper, by any chance? I'm not familiar with anything quite like it, although to me it feels like a kind of cellular automaton pilot wave theory. Does anyone see how it manages quantum strength correlations without non-locality?

 

[PeterDonis]

Anyone interested enough to not ignore this paper, by any chance?

I don't think it's a matter of lack of interest, as much as the fact that the paper does not give much detail on the proposed model, so it's hard to know exactly what is being proposed or whether the details justify the general claims that t'Hooft is making.

 

[Paul Colby]

There does seem to be a real lack of discussion on a topic people in this forum would normally be all over. The notoriety of the author is no assurance in itself the papers claims are valid. If there are details missing because they are obvious to experts, discussing these here would be of benefit.

 

[A. Neumaier]

There does seem to be a real lack of discussion on a topic people in this forum would normally be all over.

The approach looks to me like a dead end, not worth discussion.

 

[Paul Colby]

The approach looks to me like a dead end, not worth discussion.

I don’t dispute this. In your opinion, what was the cause of death.

 

[A. Neumaier]

In your opinion, what was the cause of death.

Too messy to convince other people to work on it, or even discuss it in detail. Good foundations must be clear and elegant.

 

[Quanundrum]

The approach looks to me like a dead end, not worth discussion.

Would you like to elucidate as to why you consider it to be a dead-end? Again, I am not trying to appeal to authority here, but at the very least, a man of Gerard 't Hooft's stature declaring that he - after decades in the field - is now content with quantum mechanics, ought to be worthy of a discussion. I am not convinced of his 'fast vacuum fluctuation' solution, but it is interesting that he's able to identify an actual model of quantum mechanics that is both local and deterministic without violating Bell's Inequalities. That alone is more interesting than 99% of papers published/pre-printed on arXiv every year IMO

 

[A. Neumaier]

Would you like to elucidate as to why you consider it to be a dead-end?

See post #18. I will not waste my time discussing details.

 

[Paul Colby]

Well, for me the nail in the coffin is the magic step used to select slow states. Why, for example, are only 2 states out of the continuum observable? I can’t follow the hand waving well enough.