Why not say a scalar potential as a function representing the matter itself? [duplicate]

Question

[Question] Why not say a scalar potential as a function representing the matter itself?

At first glance, this idea seems to make the duality, which is the biggest difficulty in understanding quantum phenomena, understandable. For example, suppose that a center of the electric scalar potential is a portion called an electron, and a portion around the center is also interpreted as an actually-existing portion, which is responsible for a wavy property of the electron. In this case, it seems easier to understand that a single electron interferes with itself.

Of course, I thinks that, due to other problems I hadn't thought of, these ideas are not being adopted in physics.

I'd appreciate it if someone could tell me what makes it impossible to say that scalar potentials represent matter itself or that the matter is something permeating the entire space.

Answer 1

It is a very wrong picture, that the particles are points.

The current view of physics: particles are excitations of fields. A field is a set of numbers (scalars) or vectors or tensors defined at each point in space(time).

You could imagine fields the following way: Temperature has a single value given to every point in the room, so it's a number (scalar) field. 8f every point would have an associated velocity too, it would have direction, thus it would be a vector field. If they would have a couple of properties related to each other defined for every single point in space it would be a tensor field.

The lowest energy of the field is called vacuum, and if you disturb it by giving energy to it, you create particles in the form of wave packets. Thus is defined by quantum field theory and particle wave duality.

The standard model of particle physics contains scalar and vector particles which are fermions, bosons, which refer to their statistical properties.

Spacetime itself is a tensor, at every point of spacetime you can associate a quantity called metric tensor, which defines gravity.

As you can see the picture is way more complicated.

String theory is a hypothesis and most likely doesn't have much to do with real physics, although the study towards it gave to physics a lot of mathematical tools.