Union of Classical and Quantum

[Rade]

In reading D. Bohm "Quantum Theory" (1979), on p. 625 he makes the statement..."without appeal to a classical level, quantum theory would have no meaning". And then ..."quantum theory presupposes the classical level and the general correctness of classical concepts in describing this level "[e.g., the classical level--added for clarity]

If I read Bohm correctly, he seems to suggest that reality must always be dialectic union of the mathematics of the classical and quantum--that is, there does not exist a "classical reality" or a "quantum reality", only a reality that is a union of the classical and quantum.

Since Bohm's book is now > 35 years old, are his statements concerning relationship of classical to quantum held in 2005 to be valid ? Or, has new information since 1979 shown Bohm to be incorrect. Clearly, Bohm understood quantum mechanics, thus I cannot believe that what he said above was not true as of 1979. Thanks for any clarification that can be provided.

 

[reilly]

These days we can, I think, be a bit less dogmatic. Many of concepts we use in physics were developed before the advent of QM -- energy, motion, momentum, charge, mass, and so on. We do not have much choice but to use them, as most have yet to be replaced, and we tend to think in classical terms -- if nothing else, we are captives of our language. Reality? Who knows? It's an old, old word, and an old, old concept.
Rgards,
Reilly Atkinson

 

[dextercioby]

It's actually 26 years old. :P One of the fundamental observables in a quantum theory is the SPIN (of a particle or of a classical/quantum field) which doesn't have a classical analogue.

Daniel.

 

[reilly]

dextercioby - What's actually 26 years old?

I certainly did not mean to imply that there are not concepts peculiar to QM. But isn't interesting that we use a classically based word, spin, to describe a QM concept. Indeed we are captives of our language.
Regards,
Reilly Atkinson

 

[DrChinese]

It's actually 26 years old. :P

My copy is a lot older - I believe it originally came out in the early 50's.

I would not agree with Bohm's statement in a literal way. A useful theory (one that works) does not need to be reconciled with other theories. There are historical issues that come into play here, and his statement could better be seen in that light.

 

[metacristi]

My copy is a lot older - I believe it originally came out in the early 50's.

I would not agree with Bohm's statement in a literal way. A useful theory (one that works) does not need to be reconciled with other theories. There are historical issues that come into play here, and his statement could better be seen in that light.

Yes as far as I know the first edition of that book appeared in 1951 (that is before his famous article of 1952, the basis of [the] bohmian interpretation of QM) and treats only the Copenhagen interpretation, Bohr's version. Since Bohr held that no direct access at the quantum level is ever possible (only indirect one), taking also in account his positivistic leanings, those quotes do make sense, to some extent at least (in this view only the interpretations using a part of the classical concepts could be justified as being meaningful and at least approximately true).

Bohr strong operationalism is evident in this passage (1949): '‘However far the phenomena transcend the scope of classical physical explanation, the account of all evidence must be expressed in classical terms. (. . . ) The argument is simply that by the word experiment we refer to a situation where we can tell others what we have done and what we have learned and that, therefore, the account of the experimental arrangements and of the results of the observations must be expressed in unambiguous language with suitable application of the terminology of classical physics.’

Nowadays the positivist approach has lost much of its appeal, 'deeper' languages are perfectly accepted in describing the results of experiments; all theories using a language very far from the classical language are acceptable, as much as they accommodate well observed facts (all we need additionally are some auxiliary assumptions which to 'bridge' the languages used at the different levels - it is a well known fact now that such 'bridging principles' are absolutely necessary to account, as an example, for the emergent phenomena such as 'solidity', 'wetness', 'colour' characteristic to the macro world).

 

[reilly]

I first enountered Bohm's QM text in 1958, when I was an undergraduate grappling with QM, which then seemed very strange and very abstract, and very different from classical physics. My professors were all solidly grounded in classial physics and, in a sense, tried to ground and explain QM in terms of classical concepts -- hence we spent quite a lot of time on the WKB approach, and also on the Hamilton Jacobi approach, contact transformations, Poisson Brackets and such -- showing close connections with QM and it's wave theory of matter. Hence my emphasis on the constraints of classical concepts and language. Almost 50 years later, the physics community has become far more comfortable with QM, and with QFT, than was the case when I was a student. I suspect that the classical connections are studied less thoroughly now.

Still, I suspect that deep down, we all have a problem with wave particle duality -- how can particles diffract. We know they do, but it's, in my view, passing strange. Classical alternating current is certainly wave-like, but, unless I'm mistaken, AC does not suffer diffraction in the classical realm.

In his QM text's section on QM and Classical Concepts(Chap 23) , Bohm asserts that the classical approach says the world can by analysed into distinct elements, that the state of each element can be described by dynamical variables capable of highly precise specifications, and that everything is controlled by causal laws. I'm not so sure, mainly because of the self energy problems of classical E&M. the distinction beteen a particle and it's fields, seen clearly in Poynting's Thrm, is less than precise.

If you look for it, you can always find trouble most anyplace. Nature seems to delight in throwing lot's of curveballs.

Regards,
Reilly Atkinson

 

[straycat]

One of the fundamental observables in a quantum theory is the SPIN (of a particle or of a classical/quantum field) which doesn't have a classical analogue.

Daniel.

This is true. However, I think it is interesting to take a look at the "box within a box" model of a spinor in MTW [1], which shows a classical object with the transformation properties of a spinor. Mark Hadley has used this as inspiration to come up with a "classical" model [2] of the electron that possesses spin. Is his model correct? Who knows. But it is at least interesting as a thought exercise to show that it may be *possible* to model spin using purely classical notions!

David

[1] Misner, Thorne, Wheeler. Gravitation - see figure 41.6, p 1149, in the section on spinors (sec 41.5).

[2] M. J. HADLEY, Spin half in classical general relativity, Class.Quant.Grav., 17 (2000), pp. 4187–4194.