Is the quantum wave function a real object or a mathematical tool?

[Demystifier]

Most think that QFT in the non-relativistic limit reduces to ordinary QM. A careful analysis in the paper I posted shows the limit is not ordinary QM.

The non-relativistic limit of relativistic QFT is non-relativistic QFT. Non-relativistic QFT, also known as "second quantization", is widely used in condensed matter physics. In general, states in non-relativistic QFT do not have a definite number of particles. However, when non-relativistic QFT is applied to states with a definite number of particles, the resulting theory is equivalent to non-relativistic QM.

The Padmanabhan's point is that the NR limit of (relativistic) QFT is not merely NRQM of particles, but NRQM of particles and antiparticles. While this is correct, I find it a bit trivial. For instance, it means that the NR limit of QFT based on the Dirac equation is not merely NRQM of electrons, but NRQM of electrons and positrons. True, but so what? It doesn't make the usual NRQM of electrons wrong, it only means that a similar theory can also be applied to positrons. As long as we study processes in which the number of electrons and positrons does not change, there is no much difference between NRQM and NR limit of relativistic QFT. Of course, when we study processes in which the number of particles and/or antiparticles changes, then we must take into account the full relativistic QFT, nobody denies that.

So loosely speaking, it is still true that NR limit of relativistic QFT is NRQM, with the only caveat that the latter describes particles and antiparticles.

 

[bhobba]

He also points out that you get two Schrodinger's equations (one for the particle, and another for the antiparticle) in the Heisenberg picture, but not operating on the quantum state, but on the quantum field.

Thanks
Bill

 

[Demystifier]

He also points out that you get two Schrodinger's equations (one for the particle, and another for the antiparticle) in the Heisenberg picture, but not operating on the quantum state, but on the quantum field.

Yes, but it can also be transformed to the Schrodinger picture, and obtain two Schrodinger's equations for the quantum states.

 

[Matterwave]

How can it real if it doest exist?

Yes, it is an open question if quantum fields are real or not. I, along with Art Hobson think they are real.

However as a mentor I w.ould suggest a new thread.

I agree it is a fine point but for foundational issues it pays to be carefull.

Thanks
Bill

So, for example, the MWI might (would? I'm not a MWI guy lol, let's ask Sean Carrol) say that "the only real thing is the global wave function" -- you will be pedantic here and demand that they mean the wave function in QFT and not NRQM? I think that's fine but it's just being a bit pedantic.

And I don't know if the paper you quoted made much difference here. At best NRQM was an approximation anyways. Whether you *need* two copies of it to make the approximation precise doesn't really change how you go about ontology imo.

I'm ok if we split the thread, or if you'd like to stop the discussion here for being philosophy and not physics. I realize we are getting into the weeds and it's mostly philosophical weeds... (At least my position).