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I am thinking about this from quite some time but could not come up with any satisfactory explanation. In a nutshell, how would one explain the pseudo forces felt by non-inertial observers given that the fundamental laws of physics are quantum mechanical?

Since in quantum mechanics one always talks about potentials instead of forces, I cannot think of anything that I can relate to the acceleration. In other words, given an electron for example, can we say that in the frame of an electron there is exists a pseudo force? I think no because of couple of reasons. First, it doesn't have a precise position to attach a reference frame to and second, even if we could do that, there is no way we would be able to talk about its acceleration because it doesn't exist in quantum mechanics. Which should also generalize to any macroscopic object that is simply made up of trillion quantum particles. Thus, I see no reason for pseudo force to exist for any observer in the first place! I am extremely confused about this. Any ideas?

Peaceful
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In classical Lagrangian mechanics for a single particle moving in a non-inertial reference frame, pseudoforces can be described in terms of so-called generalized potentials. There is a Lagrangian $$L(t,{\bf x}, \dot{\bf x}) =m \dot{\bf x}^2/2 + {\bf A}(t, {\bf x}) \cdot \dot{\bf x} + u(t,{\bf x})$$ where $A$ an $u$ are respectively a vector field and a scalar field constructed out of the known motion of the reference frame with respect a given inertial reference frame. Euler-Lagrange equations produce the usual law of motion including centrifugal, Coriolis force, and so on if you want to describe the dynamics of the particle in Newtonian fashion. However this approach only relies upon the Lagrangian/Hamiltonian framework.

N.B.: The case of the electromagnetic interaction is treated exactly with the same formalism and, up to factors including the value of the charge, ${\bf A}$ and $u$ are the given vector and scalar potentials.

The afore-mentioned Lagrangian defines a corresponding Hamiltonian via the standard Legendre transformation. $$H(t,{\bf x}, {\bf p}) = \frac{({\bf p}-{\bf A}(t,{\bf x}))^2}{2m} - u(t,{\bf x}) $$ Replacing canonical coordinates for the corresponding operators, you have the quantum Hamiltonian operator.

I do not understand well your objection about a reference frame at rest with the electron. Such a concept is not necessary in this picture. It is only necessary to know the motion of your reference frame with respect to an inertial reference frame. If you accept that, in some sense, the electromagnetic force acts on electrons, I cannot see a deep reason to reject the action of pseudoforces.

Valter Moretti
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