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

1. Mar 19, 2008

### Schrodinger's Dog

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:

Last edited: Mar 19, 2008
2. Mar 19, 2008

### jostpuur

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?

3. Mar 19, 2008

### Schrodinger's Dog

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.

4. Mar 19, 2008

### peter0302

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.

5. Mar 19, 2008

### Demystifier

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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6. Mar 19, 2008

### Demystifier

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.

7. Mar 19, 2008

### peter0302

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! :)

8. Mar 19, 2008

### 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

9. Mar 19, 2008

### 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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10. Mar 19, 2008

### peter0302

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

11. Mar 19, 2008

### bg032

I challenge Reilly to derive classical mechanics, namely the equation F=ma, from standard quantum mechanics.

12. Mar 19, 2008

### jostpuur

$$i\hbar\partial_t \Psi(t,x) = \Big(-\frac{\hbar^2}{2m}\nabla^2 + U(x)\Big)\Psi(t,x)$$

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

$$\implies\quad F = ma$$

Details are left as an exercise.

13. Mar 19, 2008

### peter0302

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.

14. Mar 19, 2008

### bg032

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.

15. Mar 19, 2008

### ZapperZ

Staff Emeritus
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.

16. Mar 19, 2008

### bg032

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 ...

17. Mar 19, 2008

### ZapperZ

Staff Emeritus
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.

18. Mar 19, 2008

### peter0302

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.

19. Mar 19, 2008

### Hans de Vries

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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20. Mar 19, 2008

### peter0302

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