Reply To: God knows where all the particles are!

Aurelien Drezet

Dear Reinhard, I was not apparently allowed by my computer to write you a comment directly (probably the bohmian demon in my Windowsystem). I Copy and paste a reply in the Max section on Bohmian concerning the value of Bohmian mechanics for physics: I changed a bit the structure.

First of all, BM offers a much better perspective than Copenhagen concerning describing what is reality. More precisely, if you focus your attention on the empirical contents of Bohm’s theory and say that it looks like the view of a god (: ‘only god knows where the particle is ‘ ) then you could conclude that BM is indeed metaphysical. However, I ask now what do you exactly mean by empirical contents? I think that when you try to answer a question like this one you should be quite prudent and modest. Like Heisenberg discussing with Einstein we should never forget: Theories always come before the experiments (I am both a theoretician and an experimentalist and I accept that very well). Now, BM is a theory it has a clear dynamical framework and it reproduces all data (at least in the non relativistic domain). What you want more?
Like you we could say that the paths predicted by BM are surrealistic (actually it was Scully after Heisenberg who used this language but it fits here as well) and not observable. Well, that’s a bit provocative but this is not true. Trajectories given by BM agree with facts and can be tested in that reduced sense (Weak measurements or Protective measurements even allow more see below). Indeed, BM will predicts the good probability which are associated with the trajectories and there is nowhere contradiction between BM and QM (by the way what is QM without a clear ontonlogy a set of rules for technicians ?). Of course, you can not measure a path like you could do it in classical mechanics because Heisenberg principle prohibits that but this is the price to pay here: If you want to reproduce QM predictions you must accept this limitation. You must abandon some aspects of Classical mechanics. If you reject that: no chance for you to explain QM. Heisenberg refused even to listen Bohm for that reason : BM for him was classical physics so it should be wrong. But Heisenberg was mistaken : We dont try to save the classical realm but its goal which is to give an interpretation of the world independently of the observer.
I want to say a bit more about that: If you anyway reject Bohm or Stochastic QM à la Nelson what should you propose instead? If you go back to Copenhagen then you are only hiding yourself under the quantum carpet since you dont have a definition of what is the reality anymore: you need an observer but you cant define it precisely. Do you need a PhD, like Bell suggested provocatively, an environment, an infinite number of Wigner’s friends (with cats)? This is wavy and the choice of Bohm is not. If you want to observe a path anyway I suggest to use protective measurements [Aharonov Vaidman, Phys Lett. A 178, 38 (1993).]. Indeed, the protective measurement protocol can be used to ‘detect’ the particle at points that the Bohmian particle never comes near. This is because the wave function is an active element in BM. This allows to record a velocity without disturbing the position. There is no paradox because you didn’t use a ‘destructive’ von Neumann protocol for velocity. You are still free to define the position of the particle after that so you will get both the velocity and the position. This is not yet a path but you are getting closer from it. Clearly, Of course the Bohmian program has some limitations. If you remember Popper and his falsificationism you realize that BM is not completely testable (This is necessary, I repeat it, for reproducing QM). This is a problem I agree but nowhere It has been written that Popper was right for ever. Additionally, the sciences do it in the same way like BM and nobody seems to be offended by that. Consider cosmology and Black holes ? Would you say that these objects are not for science? what about quarks if we can not separate them ? These theoretical objects have some consequences which can be tested but we can not observe all and some part will stay for ever may be outside the experimental deomain. Anyway, I agree with you on a another point BM is not unfortunately unique. I don’t speak here about Nelson theory which is no yet in the maturity of BM (despite years of efforts) but more about the problem of relativistic BM. Since for BM we need a privileged observable (like position in the non relativistic theory) we should define the same for quantum field and an univocal answer is not yet existing. Personally, I believe that BM is only a temporary expedient. One day we will get a much better theory which will explain why particles have such and such properties like mass and charge. BM is the best candidate for helping us if we can give a better foundation to the theory. Still, I think that Bohr view on reality is a dead end since it will only offer you the sleeping property of opium and will not allow you to, may be, discover something new (or not).

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