Reply To: God knows where all the particles are!

Robert Griffiths

Dear Travis,

Early in this thread you made reference to your contribution to Healey’s “Comments on Bohmian mechanics”. I took a look at it, and maybe these remarks should go there, but they also seem to fit very well in this discussion.

I once heard the story, no doubt apocryphal, that when one of Wigner’s students would go to him claiming some new and profound result about Hilbert space, the master would reply: What does it say in the case of 2 x 2 matrices? In somewhat the same spirit I suggest that before claiming that Bohm’s interpretation allows us to understand tables and chairs and planets, we first try it out in a very simple case: the motion of one particle. Does it give us the right answer?

Not every reader of this column will be familiar with the claims of Englert et al. that Bohmian trajectories are “surrealistic”. Perhaps the best reference is not their original paper (see the bibliography in [3]), but instead one by Dewdney, Hardy, and Squires [1], three physicists who at least at that time, were very sympathetic to the Bohmian perspective. (If my memory does not fail me, Dewdney was a student of Hiley, who was Bohm’s close associate.) What they showed was that a Bohmian particle can in certain circumstances trigger a detector (containing its own Bohmian particle interpreted in proper Bohmian fashion) while coming no place near it. The fundamental idea is the same as what you find in Vaidman’s “Counterfactual communication protocol” in this forum: an empty wave can do various things even when the corresponding particle is far away. And given the nonlocality that Bohmian experts readily admit is present in the theory, that should come as no surprise.

But for experimental physicists a theory like this is, indeed, a nasty surprise, for they design their experiments and interpret the results assuming that interactions are local. (As my authority on this matter may be questioned, let me say that as an undergraduate many years ago I myself carried out an experiment of this sort, and in more recent years have attended talks by competent experimentalists in which it was clear that they interpreted their experiments in this way.) Indeed, justifying the experimentalists’ perspective that the observed outcomes (‘pointer positions’) reveal properties of the (microscopic) measured system before it interacted with their apparatus, is what I call the ‘second measurement problem’, and I am about to claim in print [2] that Bohmian mechanics does not provide an adequate solution: it sometimes gives the right answer, and sometimes the wrong answer. This is a serious issue if one wants to claim that Bohmian mechanics is in agreement with experiment.

In the Dewdney et al situation [1] the consistent histories (CH) approach [3] gives an answer in agreement with the way an experimentalist would view the situation; i.e., it solves the second measurement problem discussed in [2]. And since CH provides an explanation, via quasiclassical frameworks (Gell-Mann and Hartle), of how classical physics as a good approximation to quantum physics under the proper circumstances, it is as good as anything else in on offer when it comes to a quantum understanding of chairs and tables and planets. So why should I believe your claim that the Bohmian approach is giving the right answer for 10^23 particles when it gives the wrong answer for 1 or 2?

Bob Griffiths

[1] C. Dewdney, L. Hardy, E. J. Squires, “How late measurements of quantum trajectories can fool a detector”, Phys. Lett. A 184, pp. 6-11.

[2] R. B. Griffiths, “Consistent Quantum Measurements”, arXiv:1501.04813; it should appear before too long in Studies in the History and Philosophy of Modern Physics.

[3] R. B. Griffiths, “Bohmian mechanics and consistent histories”, Phys. Lett. A 261, pp. 227-234. arXiv:quant-ph/9902059.

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