Is the Concept of Potentials Incompatible with 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

 

[quantumdude]

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.

 

[denian]

in relativity?"

When we say that the concept of potentials is untenable in relativity, we are referring to the fundamental principles of relativity, which state that the laws of physics should be the same for all observers regardless of their relative motion. In other words, the concept of potentials, which are used to describe the forces acting on particles, assumes that information can be transferred instantaneously, which goes against the principles of relativity.

In classical mechanics, potentials are used to describe the forces acting on particles, such as gravitational or electric forces. However, in relativity, the concept of potentials breaks down because it implies that information can be transferred at an infinite speed. This goes against the fundamental principle of relativity, which states that the speed of light is the maximum speed at which information can be transferred.

Additionally, in relativity, the concept of potentials is replaced by the concept of fields. Fields are used to describe the interactions between particles, and they do not rely on the assumption of instantaneous information transfer. This allows for a consistent and unified description of the laws of physics in all reference frames.

In summary, the concept of potentials is untenable in relativity because it violates the fundamental principles of relativity and is replaced by the concept of fields, which provides a more consistent and unified description of the laws of physics in all reference frames.