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[ QUOTE ] The Brans-Dicke theory was abandonned, for empirical equivalency was just that (no one cared to fund further research). [/ QUOTE ] I think Bohmian mechanics has suffered or is suffering a similar fate, though I'm not certain about it. If so, it's a shame, since Bohm's interpretation really is fascinating. Thanks for the examples. [/ QUOTE ] Or possibly because it has serious conceptual flaws. However, Bohm's rewriting of Schrödinger's equation in terms of variables that seem interpretable in classical terms does not come without a cost. The most obvious is increased complexity: Schrödinger's equation is rather simple, not to mention linear, whereas the modified Hamilton-Jacobi equation is somewhat complicated, and highly nonlinear -- and still requires the continuity equation for its closure. The quantum potential itself is neither simple nor natural. Even to Bohm it has seemed "rather strange and arbitrary" (Bohm 1980, p. 80). And it is not very satisfying to think of the quantum revolution as amounting to the insight that nature is classical after all, except that there is in nature what appears to be a rather ad hoc additional force term, the one arising from the quantum potential. The artificiality suggested by the quantum potential is the price one pays if one insists on casting a highly nonclassical theory into a classical mold. Moreover, the connection between classical mechanics and Bohmian mechanics that is suggested by the quantum potential is rather misleading. Bohmian mechanics is not simply classical mechanics with an additional force term. In Bohmian mechanics the velocities are not independent of positions, as they are classically, but are constrained by the guiding equation. In classical Hamilton-Jacobi theory we also have this equation for the velocity, but there the Hamilton-Jacobi function S can be entirely eliminated and the description in terms of S simplified and reduced to a finite-dimensional description, with basic variables the positions and the (unconstrained) momenta of all the particles, given by Hamilton's or Newton's equations. It can be argued that the most serious flaw in the quantum potential formulation of Bohmian mechanics is that it gives a completely false impression of the lengths to which we must go in order to convert orthodox quantum theory into something more rational. The quantum potential suggests, and indeed it has often been stated, that in order to transform Schrödinger's equation into a theory that can, in what are often called "realistic" terms, account for quantum phenomena, many of which are dramatically nonlocal, we must add to the theory a complicated quantum potential of a grossly nonlocal character. It should be clear that such sentiments are inappropriate, since the quantum potential need not be mentioned in the formulation of Bohmian mechanics and in any case is merely a reflection of the wave function, which Bohmian mechanics does not add to but shares with orthodox quantum theory. quoted from a google search. First link. Greg |
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