Some advantages of Bohmian mechanics

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    Roderich Tumulka

    A big advantage of Bohmian mechanics is its clarity. It has simple, clear statements about what exists in the world (wave function and particles), and how that evolves with time. Everything else is a matter of analysis of the theory. In particular, one can analyze measurement situations (which are dealt with by axiom, not by analysis, in standard quantum mechanics), and one can derive what observers in a universe governed by Bohmian mechanics—observers made out of Bohmian particles—will see (it turns out that they observe outcomes in agreement with the usual predictive rules of quantum mechanics).

    Let me contrast Bohmian mechanics (BM) with orthodox quantum mechanics (OQM).

    In OQM one insists on misleading terminology: for example, one says “particle” but does not mean a material point with a trajectory; one says “measurement” but does not mean the discovery of a value that was defined already before the experiment; one says “quantity” but means an operator. In BM, there is no need for misleading terminology.

    In OQM, one believes that reality itself is paradoxical, although we cannot see the inconsistencies due to the uncertainty relations. I find this belief indigestible. BM has no need for it.

    In OQM, one usually needs to “interpret” the results of any computation. In BM, this is unnecessary because the theory itself is clear enough.

    It is hard to formulate OQM while it is easy to formulate BM. In two ways. First, it is hard to give a reasonably precise and reasonably general formulation of the measurement postulate if you want avoid idealization. The statement of the postulate becomes very complicated if you want to state which operator to use for a given experiment, if experiments are not instantaneous, if the time and duration of the experiment can be random, etc.. BM, in contrast, can be formulated by stating the equation of motion; the formulation of measurement rules is equally complicated as in OQM, but such rules are not part of the fundamental formulation of the theory. Second, while BM can be stated in a few postulates, OQM is associated with philosophical ideas that cannot be summarized in a few basic postulates, including the idea of complementarity, that of splitting the world into two realms (classical and quantum), and that reality is somehow made of operators.

    It never gets clear how OQM answers the quantum measurement problem. I have heard people say that you cannot know the wave function of the apparatus (because it has >10^23 variables), or that you cannot solve the Schrodinger equation for >10^23 variables, or that it is too hard to carry out an experiment proving the existence of both contributions in the wave function of Schrodinger’s cat, but none of these makes the problem go away. In BM, it is clear that the measurement problem is absent because there are further variables besides the wave function.

    Bohmian mechanics is a satisfactory theory of quantum mechanics, whereas orthodox quantum mechanics leaves much to be desired.

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