potentials in relativity

preet0283

please elaborate ......" particle quantum mechanics is valid in the nonrelativistic regime by definition ...it refuses to obey relativity ...this is not bcoz we write non relativistic hamiltonians bt the concept of potentials is untenable in relativity ...since it assumes the transfer of information at an infinite speed"what do we mean when we say that the concept of potentials is untenable

Tom Mattson

Consider the hydrogen atom problem in QM, in which you put the Coulomb potential in the Schrodinger equation. Now ask yourself what happens if the proton is moved suddenly? According to QM the electron knows about this instantly, without any retardation. For this reason the true merger between quantum theory and SR is not relativistic quantum mechanics, but rather relativistic quantum field theory, which does not use potentials.

I wouldn't agree with the part of the statement that says, "this is not bcoz we write non relativistic hamiltonians", because that is clearly part of the problem. And not surprisingly, when the relativistic Hamiltonian is quantized, you end up with a theory that makes more accurate predictions.