# Logical/mathematical proof for the identity of electron

Gold Member
Premise 1: Physics don't believe in sense "organs" of the human "robot" (more commonly said "common sense deceives us").

Premise 2: Physics believes in logic or mathematics.
Background thrust: Quantum mechanics.

Premise 3: Everything which "revolves" around the nucleus might not have identical properties. There might be some property of particles (revolving around the nucleus) which are not the same, because of our sense not detecting it. Then, we might say the particles to be identical only w.r.t our senses, but that is not the spirit of our physics, it must be proved logically. Or else we might define particles of such and such properties to be such and such, but that doesn't define them to be entirely identical.

So, are particles revolving around the nucleus identical in all properties in reality? Or is there any logical or mathematical proof to show that the particles are all identical?

The same argument can be applied to all the particles which we call identical.

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Delta2
Homework Helper
Gold Member
if you asking if all electrons (or all protons or all neutrons) in the universe are identical then yes they are but this is taken as an axiom, cannot be proved (well at least i vent seen a proof based on other axioms).

anorlunda
Staff Emeritus
Physics uses the clever trick called commutation to address thst subject. Take two particles close to each other, Then swap their positions (interchange them.). How does the mathematics change after the swap? There are two answers, +1 and -1. For bosons, there is no change, +1. For fermions, the swapped pair is -1 times the original (the sign flips).

Given those two answers, it pretty much excludes the possibility that the two particles have "identities" that can be distinguished.

In still other words, if AB and BA are indistinguishable, then A and B don't have individually distinguishable properties.

DrClaude
Mentor
The shell structure of atoms is only possible because electrons obey the Pauli exclusion principle, which is based on the Pauli principle anorlunda mentioned, which can only be true if electrons are indistinguishable. Similarly, when you do statistical physics, you don't get the same answer whether particles are distinguishable or not, and it turns out that the correct answer (the one corresponding to experimental observation) is the one where identical quantum particles are indistinguishable.

The fact that all electrons are exactly alike even prompted Feynman to come up with a theory where there was actually a single electron in the universe, and that it was coming back through time and reappeared at a given instant as a second electron, went back through time again and reappeared as a third electron, and so on. This was based on his observation that the positron, the anti-particle of the electron, looks like an electron traveling backwards in time. This is all a bit tongue in cheek, and we know today the fundamental reason why are electrons are the same: they correspond to the same excitation of a field (see Quantum Fields Theory).

DrewD and mfb