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Sam_Goldberg

- 46

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Before responding to my post, please note that I am only familiar with the mathematics of nonrelativistic quantum mechanics, and don't know any quantum field theory. All I have is this vague idea that quantum field theory is the union of special relativity and quantum mechanics, where the number of particles is not definite and both electrons and photons are described as excitations of a quantum field. The dynamics of the electrons and photons are, apparently, lorentz invariant.

Anyway, my question is this: there seem to be certain elements in nonrelativistic quantum mechanics that I can't see how to make lorentz invariant. No matter what interpretation one uses, it seems as if we have an irreparable violation of lorentz invariance. Take the Copenhagen interpretation, with its wavefunction collapse. The process of wavefunction collapse blatantly violates lorentz invariance, and I do not see how one could suitably modify it in such a way that it becomes lorentz invariant. Have they have figured out how to extended wavefunction collapse to quantum field theory such that it is lorentz invariant?

Even if one uses an interpreation without wavefunction collapse I don't see how one could still have lorentz invariance due to the nonlocality of quantum mechanics (EPR experiment). For example, in Bohmian mechanics, a many particle system is guided by the wavefunction. Since the wavefunction lives in configuration space, the guiding equation for the particles is nonlocal and in violation of lorentz invariance.

I am only familiar with the Copenhagen and Bohm interpretations, and I don't see how either can be extended to obtain lorentz invariance. Maybe quantum field theory does this, and I am simply not aware of it. Or it might be that there is an interpretation of quantum mechanics that is readily extendable to ensure lorentz invariance. To be honest, I am doubtful that a different interpretation of quantum mechanics will really make a difference. I have only heard of the many worlds interpretation and have not studied it in detail, but it seems that the branching of a universe into many other universes is also in violation of lorentz invariance (just like wavefunction collapse), and it does not seem easy to fix it. So I'm really stuck.

Or perhaps quantum field theory isn't lorentz invariant?