Is Quantum Field Theory Redefining the Foundations of Quantum Mechanics?

[A. Neumaier]

If we restrict ourselves here to lattice regularization

This restriction is quite artificial. In particular, you cannot apply it to the standard model. Nobody working on the standard model is using this noncovariant regularization scheme. It is useful only in nonrelativistic QFT and partially in QCD. Even in QCD, there is lots of work done in covariant regularrizations.

many people abuse Occam's razor

... just like one can use an ordinary razor to murder someone ...

From what I've seen so far I wouldn't say there is something that sets BM apart as particularly unrealistic or unnecessarily convoluted

Well, from a mathematical point of view it is very unnatural and convoluted. It ditches not only relativity but also symplectic geometry (by dropping the symmetry between position and momentum) - both principles that lead to a huge amount of theoretical and practical insight into physics. If Bohmian mechanics were fundamental it would be surprising why these tools should have a place in the theory at all.

 

[Elias1960]

This restriction is quite artificial. In particular, you cannot apply it to the standard model. Nobody working on the standard model is using this noncovariant regularization scheme. It is useful only in nonrelativistic QFT and partially in QCD. Even in QCD, there is lots of work done in covariant regularrizations.

You cannot apply? Sorry, no, you can apply. There would be simply no point of doing it if all what you want is to shut up and calculate. Please, just accept that for doing different things different technical means are appropriate. If it is easier to compute integrals with dimensional regularization, fine, let's use dimensional regularization if we want to compute those integrals. But if we want to understand why all this can be done on a certain mathematically well-defined base, then the simplest choice if a lattice regularization on a large cube, which gives you a finite-dimensional theory.

And if all you want is to shut up and calculate, minimal QM is fine, and the measurement problem or Schroedinger's cat is simply irrelevant. If you, instead, want an interpretation which does not give rubbish if applied to Schroedinger's cat, then it is better to have a continuous trajectory $q(t)\in Q$. Given that the Schroedinger equation gives you a continuity equation for $|\psi(q)|^2$, this is not a problem at all. But with such a continuous trajectory you can describe the collapse by using the Schroedinger equation for the system and the measurement device, and then use the visible trajectory of the measurement device to compute the resulting effective wave function of the system.
$$\psi_{eff}(q_{sys}) = \psi_{full}(q_{sys}, q_{dev}(t)).$$

Well, from a mathematical point of view it is very unnatural and convoluted. It ditches not only relativity but also symplectic geometry (by dropping the symmetry between position and momentum) - both principles that lead to a huge amount of theoretical and practical insight into physics. If Bohmian mechanics were fundamental it would be surprising why these tools should have a place in the theory at all.

Very simple - once you can derive them starting from the theory, they have a place there. Mathematics is full of such surprises.

As someone who knows particle theory you should be aware how useful approximate symmetries are - even once they, as approximate symmetries, have no fundamental status at all, they can give as well huge amounts of theoretical and practical insights into physics, not? The question if some symmetry is useful has nothing to do with if it is fundamental or only emergent.