3 ms·
The paper goes astray in my view right at the start, when it points out that time is a parameter in the Schrodinger equation, not an operator, so that equation
by pdonis 4y ago
The paper goes astray in my view right at the start, when it points out that time is a parameter in the Schrodinger equation, not an operator, so that equation gives no way to uniquely derive a probability distribution for measurement results as a function of time--but then fails to note the solution to that problem, which is to not use the Schrodinger equation in the first place. The correct framework in which to treat time on the same footing as other observables is relativistic quantum field theory. That is never even mentioned in this paper.
(To be fair, I have never seen any discussion or comparison of QM interpretations that uses QFT as its framework; they all use non-relativistic QM, even though we know that's just an approximation. But it's still an issue even if it's an extremely common one.)
- d_tr 4y agoI do not know QFT or String Theory and I have a question. Can these other equations be derived from the Schrödinger equation using a suitable Hamiltonian? And do you mean that you need time to be in the Hamiltonian as an observable to satisfy Lorentz invariance?
- pdonis 4y ago> Can these other equations be derived from the Schrödinger equation using a suitable Hamiltonian? No, it's the other way around: given a quantum field theory, under certain conditions (the main one I'm aware of is choosing a particular frame and taking the non-relativistic limit), you can derive a Schrodinger equation. > And do you mean that you need time to be in the Hamiltonian as an observable to satisfy Lorentz invariance? I mean that a fully relativistically correct treatment needs to treat time and space on the same footing. In quantum field theory that is usually done by making the quantum fields local operators, i.e., a quantum field is a mapping of points in spacetime to operators. In the simplest case, a free scalar field, these are the creation and annihilation operators of an infinite set of harmonic oscillators.