How I Stopped Worrying and Learned to Love Orthodox Quantum Mechanics - Comments

[Demystifier]

What is your opinion of the hydrodynamic formulation?

I think it cannot explain why the unique measuremenet outcomes appear. For instance, in the two-slit experiment with a single photon, why do we detect photon at a single position only?

 

[vanhees71]

I am not an expert for applications of BM as a computational tool, but I think the Wyatt's book is the best.

In which sense is BM a "computational tool"? It only adds the trajectories a posteriori when the wave function is calculated from "conventional QT". I always considered BM as just an alternative deterministic non-local interpretation of non-relativistic QT but not that one can establish some practical calculational tools using it.

 

[Demystifier]

In which sense is BM a "computational tool"? It only adds the trajectories a posteriori when the wave function is calculated from "conventional QT".

There is a way to compute trajectories first and then to infer the wave function from it. See e.g. https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.82.5190

 

[martinbn]

My recent paper "Bohmian mechanics for instrumentalists" linked in my signature below is a sort of an elaborated version of the insight at the beginning of this thread.

My problem with your signature is that it seems that there is quite a bit of wishful thinking motivated only by the desire that BM is the true description of the world.

 

[Demystifier]

My problem with your signature is that it seems that there is quite a bit of wishful thinking motivated only by the desire that BM is the true description of the world.

You may call it wishful thinking, I call it physical hypothesis motivated by physical intuition based on BM. In a sense, any scientific hypothesis can be thought of as wishful thinking, but it doesn't make the hypothesis less scientific. The 19th century hypothesis that matter is made of atoms was also an example of "wishful thinking".

“The reasonable man adapts himself to the world: the unreasonable one persists in trying to adapt the world to himself. Therefore all progress depends on the unreasonable man.”
― George Bernard Shaw

 

[martinbn]

Not sure if Shaw meant physics, I suspect that by the world he probably meant society.

You may call it wishful thinking, I call it physical hypothesis motivated by physical intuition based on BM. In a sense, any scientific hypothesis can be thought of as wishful thinking, but it doesn't make the hypothesis less scientific. The 19th century hypothesis that matter is made of atoms was also an example of "wishful thinking".

The way your proposal looks to me, in line of your example, is as someone proposing that atoms don't exist and it only appears that way. And he suggests that based on his favorite model.

 

[Auto-Didact]

I think it cannot explain why the unique measuremenet outcomes appear. For instance, in the two-slit experiment with a single photon, why do we detect photon at a single position only?

The mathematical reason for unique measurement outcomes in single particle wavefunctions is due to the non-local nature of the system i.e. the presence of some cohomology element $\eta$: for any sufficiently small open subregion $G'$ of a region $G$, the cohomology element $\eta$ vanishes when restricted down to $G'$. See this thread for elaboration and/or further discussion.

In either case, the hydrodynamic formulation doesn't specifically set out to answer such a question in the first place, even though it might be able to if one would select the correct nonlinear PDE to generalize towards which naturally contains such non-local properties.

Excuse me, I should have clarified earlier; I meant what is your opinion on the mathematical physics (as explained here) of the hydrodynamic formulation of QM? Do you view such mathematical work as pure baseless numerology? I get the feeling many theoretical physicists do.

For more background, here is a recent survey article by fluid dynamicist John Bush (MIT, Applied Math), primarily described in section 4 and 5 (feel free to skip section 1-3, if you are already familiar with it and/or like me not necessarily so much interested in experimental analogues): Pilot Wave Hydrodynamics.

 

[Auto-Didact]

My problem with your signature is that it seems that there is quite a bit of wishful thinking motivated only by the desire that BM is the true description of the world.

"The supreme task of the physicist is to arrive at those universal elementary laws from which the cosmos can be built up by pure deduction. There is no logical path to these laws; only intuition, resting on sympathetic understanding of experience, can reach them. In this methodological uncertainty, one might suppose that there were any number of possible systems of theoretical physics all equally well justified; and this opinion is no doubt correct, theoretically. But the development of physics has shown that at any given moment, out of all conceivable constructions, a single one has always proved itself decidedly superior to all the rest."
- Einstein

You may call it wishful thinking, I call it physical hypothesis motivated by physical intuition based on BM. In a sense, any scientific hypothesis can be thought of as wishful thinking, but it doesn't make the hypothesis less scientific. The 19th century hypothesis that matter is made of atoms was also an example of "wishful thinking".

“The reasonable man adapts himself to the world: the unreasonable one persists in trying to adapt the world to himself. Therefore all progress depends on the unreasonable man.”
― George Bernard Shaw

"Long may Louis de Broglie continue to inspire those who suspect that what is proved by impossibility proofs is lack of imagination."
- John Stewart Bell

Not sure if Shaw meant physics, I suspect that by the world he probably meant society.

The way your proposal looks to me, in line of your example, is as someone proposing that atoms don't exist and it only appears that way. And he suggests that based on his favorite model.

"One should not reproach the theorist who undertakes such a task by calling him a fantast; instead, one must allow him his fantasizing, since for him there is no other way to his goal whatsoever. Indeed, it is no planless fantasizing, but rather a search for the logically simplest possibilities and their consequences."
- Einstein