# Why do electrons repel?

To answer this question one must look deeply within physics. Quantum mechanics doesn’t answer the question. However, Quantum field theory does, and it does so in a delicate interplay between Quantum Physics and Relativity.

The attraction and repelling effects of exchange particles are due to their spin .

Let’s first look at the problem from a classical perspective. If we have two charged particles, then the attraction/ repulsion is encoded classically within the potential. This goes like:

V(r)~+-q1q2r,

First, we need to understand why these terms exist. The charges exist because the force between two particles is dependent on their strength. The nature of the forces makes it inversely square. This is why the inverse distance exists.

What is the Inverse Square of Nature’s Force?

Surprisingly, the Inverse square nature force has nothing to do Electromagnetism. It is actually linked to the number dimensions of space that we live in, .

This boils down to +-

Get in front of your potential. We would have q1q2>0 The force will be repulsive if the particle distance is increased. This is because the overall potential energy of the system is decreased and it tends to have lower total energy. For the opposite, however, it is true. q1q2<0

The force is attractive. This can all be seen when you plot the distance vs. the potential.

Let’s now move onto Quantum field theory. Within the QFT framework one studies what is known as the Moller scattering [1]. This is an electron-electron scattered pictorially as

what is happening here is the time axis is pointing upwards, two electrons come in they interact via the exchange of a photon (spin-1) and they move away.

This is what happens when the momentum of the “photons” is transferred in such a manner that they repel one another. If one is brave enough (Refer Chapter 3 and 6) [2]), you can show that such interaction is possible in the classical limit exactly as we have previously written. This resolves the +- crucial issue.

sign in the potential which we argued is responsible for the repulsion/attraction.

It is very complex, and one must do a lot of research to make such computations.

Let me end by sharing a lovely illustration that is somewhat inaccurate, but still conveys the main idea. This is the main idea:

it is the exchange of these “photons” that is responsible for attraction/repulsion.

Imagine you and your friend are riding skateboards and throwing things at each other. Depending on the object/how much you throw, you will either feel attraction or repellence.

This then explains why like charges repel and unlike charges attract.

Classic gravitational theory has positive charges, making the potential attractive. If you have a spin-2 particle, QFT can be used to determine if it has an attractive force. This is the gravitational force via exchange of a postulated particle called the “Graviton”.

Edit: I have forgotten to mention that the QFT in a Nutshell textbook by Anthony Zee, which explains the phenomena better than any other section, is a beautiful and elegant approach to the subject.

Footnotes