# What if the Bohmian model turned out to be correct?

## Main Question or Discussion Point

I realise this is quite speculatory so feel free to move it somewhere more apt? But what implications would there be for science if the the Bohm interpretation proved to be the correct one (understand I am not favouring it I'm a Copenhagen man atm) But if it were proved that it was correct and that further the Universe only appeared probabilistic and was in fact deterministic what impact do you think this would have on the world of physics?

Just an Idle thought really. I want to understand the Bohm interpretation better so I Thought posing such a question would allow people to discuss it and it's positives and negatives.

Thanks. I suppose I could buy a book, but I'm a little short atm, so anyway, discus:

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In order to answer the question what would happen, if the Bohmian model turned out to be correct, we should first know that how precisely would it have turned out to be correct? What enabled scientists to verify it?

In order to answer the question what would happen, if the Bohmian model turned out to be correct, we should first know that how precisely would it have turned out to be correct? What enabled scientists to verify it?
Fuzziness is explained in classical terms, ie such niggles as the wave can be represented as deriving from a bohmian model, hidden variables becomes more valid for whatever reason.

And of course Quantum mechanics itself proved not to line up with an experiment, ie the theory itself was destroyed and Bohmian mechanics and thus it's interpretation became a fitter model.

I'm interested in any ideas of how these could be overcome, and any ideas why they would be unlikely to be overcome.

The only thing that any of these alternative interpretations have to offer, in my view, is the speculative possibility that a deeper understanding of how quantum events work might lead to a better ability to predict or, the ultimate achievement, influence them. One can easily imagine the practical applications of this ability, if it were ever achieved. But we are way, way, way off from that point. To me, it at least provides enough of an incentive to keep asking questions, but that's about it.

Demystifier
2018 Award
But if it were proved that it was correct and that further the Universe only appeared probabilistic and was in fact deterministic what impact do you think this would have on the world of physics?
I think such a discovery would be very promissing for potential applications. Physicists would start to think how to control the "hidden" variables, i.e., the initial positions of particles when the wave is not an eigenstate of the position operator. If this could be done, then EPR correlations could be really used for sending information instantaneously.

http://xxx.lanl.gov/abs/0705.3542
I have argued that validity of Bohmian mechanics could be used as a new argument for adopting string theory.

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Demystifier
2018 Award
In order to answer the question what would happen, if the Bohmian model turned out to be correct, we should first know that how precisely would it have turned out to be correct? What enabled scientists to verify it?
In
http://xxx.lanl.gov/abs/quant-ph/0406173 [Found.Phys.Lett. 18 (2005) 549]
I have explained how, in principle, a relativistic version of Bohmian mechanics could be experimentally verified.

Thanks very much for that link! Very interesting article. I will cite it to anyone who insists that the Bohmian interpretation or idea of particle trajectories are useless! :)

reilly
Bohm's interpretation has been around since 1952; more than 50 years. This is less time than between Maxwell's Equations (1861) and Einstein's Special Relativity (1905). During the 50+ years between 1952 and now, the lack of impact upon the physics community is stunning; few accept Bohm's approach. And, as I've repeatedly noted; no new physics has emerged from Bohm's approach to interpretation.

There's a certain irony, in addition to Bohm-Arhronov, Bohm did pioneering work in many-body physics, often with David Pines, on the electron gas, which helped point the way to the BCS theory of superconductivity. This work was right in the mainstream with use of the practical Copenhagen interpretation.

As time goes by, the odds diminish that Bohm's approach will be found to be valid. If it is, then the impact could be huge in ways that we cannot know at this time. And remember that any new approach must reproduce all the quantum physics that his been done over nearly a century. I very much doubt this will happen.

Nonetheless, Bohm will be remembered as one of the outstanding physicists of his generation. His text on qunatum theory is superb.
Regards,
Reilly Atkinson

reilly
I challenge Dr. Nikolic or anyone else to do some real problems in the Bohmian way:

1.Calculate the the LS and other relativistic corrections for hydrogen.

2. Work out the temporal interference pattern of the neutral K meson system;

3. Work out the radiative corrections to coincidence detection high energy electron-proton scattering.

4. Calculate the electron's magnetic moment to 13 decimal places.

5.With all spin and isospin factors in a relativistic format, show that the so-called 3-3 resonance exists in pion-nucleon scattering, with the partial wave approach, and estimate the mass of the resonance.

6. (Too much scattering?) Do superconductivity.

With the exception of number 4 and 6 these are all relatively straightforward to formulate with conventional field theory. The magnetic moment problem is very difficult, but it can be and has been done. And 2-6 have been done during the last 50 years; number 1 was done in the 1930s.

These will provide a very minimal test of the Bohm approach to do real physics.

Regards,
Reilly Atkinson

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Well, it only took a couple hundred years for Newton's corpuscular theory of light to catch on. :) Give Bohm's interpretation some time.

I challenge Dr. Nikolic or anyone else to do some real problems in the Bohmian way: [...]
I challenge Reilly to derive classical mechanics, namely the equation F=ma, from standard quantum mechanics.

I challenge Reilly to derive classical mechanics, namely the equation F=ma, from standard quantum mechanics.
$$i\hbar\partial_t \Psi(t,x) = \Big(-\frac{\hbar^2}{2m}\nabla^2 + U(x)\Big)\Psi(t,x)$$

$$\implies\quad \int d^3x\; \Psi^*(t,x)\Big(-\nabla U(x)\Big)\Psi(t,x) = \partial_t \int d^3x\; \Psi^*(t,x)\Big(-i\hbar\nabla\Big)\Psi(t,x)$$

$$\implies\quad F = ma$$

Details are left as an exercise.

Since the Schrodinger equation already assumes the momentum-energy relations of classical mechanics, it would be pretty hard to derive classical mechanics from the Schrodinger Equation in a non-tautological way.

$$i\hbar\partial_t \Psi(t,x) = ...$$
Details are left as an exercise.
Jostpuur, I think you mean that the Ehrenfest theorem solves the problem to derive classical mechanics from standard quantum mechanics. Indeed from that theorem one obtains that

$$\frac{d}{dt}\langle p \rangle = - \langle \nabla V \rangle,$$

where $$\langle \cdot \rangle$$ is the mean value of the quantum operator. Thus, at the macroscopic level a localized wave packet can be associated with a trajectory evolving approximately according to the Newton's law. However it is well-known that, under measurement-like interactions, the wave function spreads over regions which are no longer localized, neither from a macroscopic point of view. In this case it is no longer possible to associate a trajectory to the wave function, and the problen to recover classical mechanics from standard quantum mechanics remains, in my opinion, open.

ZapperZ
Staff Emeritus
2018 Award
Jostpuur, I think you mean that the Ehrenfest theorem solves the problem to derive classical mechanics from standard quantum mechanics. Indeed from that theorem one obtains that

$$\frac{d}{dt}\langle p \rangle = - \langle \nabla V \rangle,$$

where $$\langle \cdot \rangle$$ is the mean value of the quantum operator. Thus, at the macroscopic level a localized wave packet can be associated with a trajectory evolving approximately according to the Newton's law. However it is well-known that, under measurement-like interactions, the wave function spreads over regions which are no longer localized, neither from a macroscopic point of view. In this case it is no longer possible to associate a trajectory to the wave function, and the problen to recover classical mechanics from standard quantum mechanics remains, in my opinion, open.
But isn't that the whole point of QM, that classical mechanics is only a "special case"?

Furthermore, your challenge to Reilly isn't exactly the same as his challenge for Bohm model. His challenge does not ask one to go from quantum to classical. His challenge for those who claim that Bohm model is a "better" interpretation of quantum phenomena, then the proof is in the pudding, i.e. one should use Bohm's formulation and derive those phenomena.

I think that's a fair request. We often tout Lagrangian/Hamiltonian mechanics to be better than straightforward Newtonian mechanics when solving certain problems. We can't just say that and hope to get away with it. Rather, we show it in painstaking details. I don't see this as being any different.

Zz.

But isn't that the whole point of QM, that classical mechanics is only a "special case"?

Furthermore, your challenge to Reilly isn't exactly the same as his challenge for Bohm model. His challenge does not ask one to go from quantum to classical. His challenge for those who claim that Bohm model is a "better" interpretation of quantum phenomena, then the proof is in the pudding, i.e. one should use Bohm's formulation and derive those phenomena.

I think that's a fair request. We often tout Lagrangian/Hamiltonian mechanics to be better than straightforward Newtonian mechanics when solving certain problems. We can't just say that and hope to get away with it. Rather, we show it in painstaking details. I don't see this as being any different.

Zz.
I think physicists can aspire to find a theory which explains in a unified, reasonably simple and compehensible way both quantum and the classical phenomena. I think Bohmian mechanics does not provide a better interpretation of quantum phenomena, but at least provides (or tries to provide) this unified explanation. This is surely not the case, for instance, of the Copenhagen interpretation ...

ZapperZ
Staff Emeritus
2018 Award
I think physicists can aspire to find a theory which explains in a unified, reasonably simple and compehensible way both quantum and the classical phenomena. I think Bohmian mechanics does not provide a better interpretation of quantum phenomena, but at least provides (or tries to provide) this unified explanation. This is surely not the case, for instance, of the Copenhagen interpretation ...
I'm not sure to what extent it can unify, when it hasn't managed to derive just those within the quantum phenomena. That's a tall order to aspire - unification - when it hasn't shown any success yet within the realm that it should work.

Zz.

I think physicists can aspire to find a theory which explains in a unified, reasonably simple and compehensible way both quantum and the classical phenomena. I think Bohmian mechanics does not provide a better interpretation of quantum phenomena, but at least provides (or tries to provide) this unified explanation. This is surely not the case, for instance, of the Copenhagen interpretation ...
I agree with the sentiment, certainly. The Copenhagen "interpretation", of course, doesn't even try to do this. But Reilly does have a good point too that the fact that Bohmian mechanics hasn't been able to provide anything new in so long is decent evidence that it might not be such a good candidate for a unification theory. Something more radical is probably going to be necessary.

Hans de Vries
Gold Member
I challenge Reilly to derive classical mechanics, namely the equation F=ma, from standard quantum mechanics.

Presuming Special Relatively, the only assumption one has to make is E=hf to equate
the principle-of-least-action of Classical Mechanics to the principle-of-least-phase
of Quantum Mechanics to the principle-of-least-proper-time of Special Relativity.

This is the Heart and Soul of Physics.

Regards, Hans

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Presuming Special Relativity - but doesn't Special Relativity presume a great deal of classical mechanics itself, namely the conservation laws and energy-momentum relations?

no new physics has emerged from Bohm's approach to interpretation.
No offence, but you seemed to agree that the Bell's inequalities, inspired by the Bohmian interpretation, qualify as new physics, so maybe your statement is too categorical?

I challenge Dr. Nikolic or anyone else to do some real problems in the Bohmian way:

1.Calculate the the LS and other relativistic corrections for hydrogen.

2. Work out the temporal interference pattern of the neutral K meson system;

3. Work out the radiative corrections to coincidence detection high energy electron-proton scattering.

4. Calculate the electron's magnetic moment to 13 decimal places.

5.With all spin and isospin factors in a relativistic format, show that the so-called 3-3 resonance exists in pion-nucleon scattering, with the partial wave approach, and estimate the mass of the resonance.

6. (Too much scattering?) Do superconductivity.

With the exception of number 4 and 6 these are all relatively straightforward to formulate with conventional field theory. The magnetic moment problem is very difficult, but it can be and has been done. And 2-6 have been done during the last 50 years; number 1 was done in the 1930s.

These will provide a very minimal test of the Bohm approach to do real physics.

Regards,
Reilly Atkinson
Non-relativistic Bohmian interpretation predicts the same probabilities as the standard quantum mechanics. So, whether one is a fan of this interpretation or not, there is no need to solve any non-relativistic problems "the Bohm's way". If something is easier to do in the Heisenberg's picture, that does not mean that the Schroedinger's picture is worse, or vice versa.
There is no generally recognized relativistic Bohmian quantum theory, as far as I know, so it's difficult to offer "Bohmian" solutions of relativistic problems. Certainly, this is a drawback of the interpretation. Its strong point is that it exists at all, proving that quantum mechanics is not necessarily indeterministic. That's what Bell highly appreciated.
You offered your "very minimal test", but somebody may disagree. Indeed, many problems, where quantum effects are not important, can be solved (exactly or approximately) in classical mechanics, but cannot, or are very difficult to solve in quantum mechanics. Does it mean that quantum mechanics is worse than classical mechanics?

ZapperZ
Staff Emeritus
2018 Award
Non-relativistic Bohmian interpretation predicts the same probabilities as the standard quantum mechanics. So, whether one is a fan of this interpretation or not, there is no need to solve any non-relativistic problems "the Bohm's way". If something is easier to do in the Heisenberg's picture, that does not mean that the Schroedinger's picture is worse, or vice versa.
There is no generally recognized relativistic Bohmian quantum theory, as far as I know, so it's difficult to offer "Bohmian" solutions of relativistic problems. Certainly, this is a drawback of the interpretation. Its strong point is that it exists at all, proving that quantum mechanics is not necessarily indeterministic. That's what Bell highly appreciated.
You offered your "very minimal test", but somebody may disagree. Indeed, many problems, where quantum effects are not important, can be solved (exactly or approximately) in classical mechanics, but cannot, or are very difficult to solve in quantum mechanics. Does it mean that quantum mechanics is worse than classical mechanics?
But to carry your analogy further, there are problems that are easier to deal with in the Schrodinger picture, and then there are problems that are easier to handle in the Heisenberg picture. That's why we are taught both so that we can switch back and forth. Are there any such examples we can attribute to the Bohm picture? If there is, then it will illustrate very clearly the usefulness of Bohmian QM.

The same can be said of your analogy of classical and quantum mechanics. There are definitely situations when one is more appropriate to be used versus the other. In what type of problems would an analogous situation arises between CI and Bohm?

Zz.

Presuming Special Relatively, the only assumption one has to make is E=hf to equate
the principle-of-least-action of Classical Mechanics to the principle-of-least-phase
of Quantum Mechanics to the principle-of-least-proper-time of Special Relativity.

This is the Heart and Soul of Physics.

Regards, Hans
I would add phase (Lorentz) invariance; what do you think?

But to carry your analogy further, there are problems that are easier to deal with in the Schrodinger picture, and then there are problems that are easier to handle in the Heisenberg picture. That's why we are taught both so that we can switch back and forth. Are there any such examples we can attribute to the Bohm picture? If there is, then it will illustrate very clearly the usefulness of Bohmian QM.

The same can be said of your analogy of classical and quantum mechanics. There are definitely situations when one is more appropriate to be used versus the other. In what type of problems would an analogous situation arises between CI and Bohm?

Zz.
Somebody (I don't remember who it was) proposed to use the Bohm's approach as a purely calculational method for numerical solution of the Schroedinger equation. Whether this has any advantages for some problems, I don't know, but it seems possible. But , as I said, this may be much less important than the fact that the mere existence of the Bohmian interpretation proves that quantum mechanics is not necessarily indeterministic. Thus, this interpretation has great conceptual significance for any physicist, whether he/she loves or hates determinism. What may be even more important, it has great conceptual significance for any layman, as (in)determinism of the nature is an extremely important and intriguing philosophical issue, relevant for everyone. So, for example, however deeply we may hate determinism, we cannot just shut up a deterministically minded philosopher, telling him that his beliefs contradict firmly established results of quantum physics. If you wish, the Bohmian interpretation has also significance similar to that of a no-go theorem. A no-go theorem is, by definition, extremely non-constructive, but it saves us efforts, as we are not trying to do something that just cannot be done. For example, von Neumann's theorem proving impossibility of hidden variables is mathematically impeccable, but the existence of the Bohmian interpretation demonstrates that the assumptions of the theorem may be unreasonably strong.
Summarizing, I am not sure the fate of any interpretation hinges on the results of some "pissing contest" ("and how can you derive the Klein-Nishina formula in your interpretation?")
As for my opinion, the Bohmian interpretation is not very appealing, but, no offence, CI looks much worse:-)