How can one electron be everywhere? If it is only at a certain position at a certain point in time then how can the electron get excited by photons?

Before you can answer this question, it is important to first ask: What exactly is an electron?

The Standard Model of particle Physics is a misleading term. This is the grandfather of all physics misnomers. It is, in fact, the Standard Model for quantum field physics. All fields are its fundamental objects. Consider the section of the Standard Model known as quantum electromagnetics (QED). This theory has two fundamental objects: the electromagnetic field, and the electron field. That’s it.

These fields are both functions of spacetime coordinates. One is a vector-valued, the other is spinor-valued. Except for very rare spots, these fields aren’t null anywhere. These fields are therefore present everywhere.

These fields are quantum fields and their interactions are subjected to certain rules. They interact in a way that exchanges energy and momentum. These units can also be counted using mathematical operators. These units of excitation are distinct. These units of excitation are our “particles”.

These units of excitations don’t necessarily need to be located in a particular place. These units of excitations are not miniature cannonballs. Imagine a bowl of water with tiny ripples. Then, shake the bowl. You will see more ripples. Can you point to a particular spot and say that this made the bowl ripple more? No.

Except in exceptional cases, the spatial distribution of excitations from the electromagnetic field and the electron field is not spatially restricted. They are everywhere. An excitation can have a defined position depending on how it is organized. For example, you could stick your finger in the bowl of water and create ripples. These excitations are distributed in space, which is their “natural” state.

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