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Dear Bob, I found your paper ‘Bohmiann mechanics and consistent histories’ fascinating. Before reading this paper I always missed the point(s) concerning your interpretation (even though I apparently downloaded your preprint 10 years ago…). Now it seems that things a getting more clear for me.
If I follow the reasoning of your paper CH (consistent history) paths have only an approximate meaning since projectors should not be too precise if we dont want to disturb the wave packets too much. For Bohmian mechanics of course the precision is instead infinite since the theory defines a dynamical trajectory for a point like object. In your CH model you can not preserve interference and path(s) at the same time since your precision is limited by the law of measurements (for example in the region J of the figure 1 we have fringes). Bohmian mechanics can explain both path and interference in one model and in the region J the particle must bounce in order to explain fringes and nodes. There is no contradiction between both models if we compare them ONLY with observables i.e. detectors outputs limited by the Heisenberg principle and the law of entanglement. Now, for me the question is the following : Are you ready to accept an approximate precision in the definition of an ontology? This is clearly not the case for Bohmian but it seems to be clearly the case in your CH interpretation.
Of course, I agree with you that Bohmian mechanics will contain a metaphysical part leading to surrealistic behavior but this will never contradict facts and even explain them (this is the aim of an ontological model after all). This is the price you have to pay in the Bohmian universe and I agree with you: it is fundamental to accept that limitation. Your model instead, is the best that we can keep by sticking to the strict laws of observables (with the Wigner correlation formula P(1–>2)=tr(P2P1rhoP1P2) etc..). The price you have to pay is that you definition is coarse grained and that the more precise you could define a path the more invasive you will be. Still my question ‘are you ready to accept such an imprecise ontology?’ remains. For me there is no contradictions as far as you accept to consider these paths as detector paths like in a bubble chamber or in the experiments used by Serge Haroche with Rydberg atoms. If instead you want to define path with an infinite precision and go back to an ontology without approximation a la Newton or Einstein I am afraid that you should use instead something like the de Broglie Bohm dynamics. Of course, I want to point out, that I have a very deep respect for both ways of looking at the problem and since I am mainly an experimentalist working with photon detectors and correlators I am very sensitive to your approach which is pragmatic and still keep a track of ontology (unlike the too positivist Bohrian do). Still I am convinced that the aim of physics is to describe the universe as it is not only as we see it (with imprecise eyes). By doing that I am necessarily weakening the correspondance between facts and theory which was admitted to be one to one in the Newton time (at least in theory of course: Newton or Laplace were not idiots and understood very well the diffference between dreams and real experiments with unperfect data and apparata). This is a philosophical aspect I found fascinating something like the end of Popper.
I would be very interested to know your point of view on my short analysis.
I will go through the phys Today debate and to the comments by Basil during this day if I can find the time.
With best regards
PS: I added a paper I wrote where my view was balanced between Bohr and Bohm (actually I prefer de Broglie 🙂 )
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