# Why are all particles of the same type identical?

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## Main Question or Discussion Point

Why all particles of same type identical? All electrons are identical to each other, all protons are identical..etc. It is as if they are copy pasted from each other!

For me this is one of the biggest mysteries ever, why we don't detect more massive or less massive electrons?

Is it related to the accuracy of our measurements devices? As an analogy If we zoom in at sand then we will see some small sand grains and some big sand grains, but if we zoom out it will appear to us that all sand grains are same size,

Are there any theories explaining this? (Please don't bring up philosophical ideas like there is only 1 electron in the universe that is travelling back and forth in time)

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mfb
Mentor
Is it related to the accuracy of our measurements devices? As an analogy If we zoom in at sand then we will see some small sand grains and some big sand grains, but if we zoom out it will appear to us that all sand grains are same size,
No. If the particles would not be exactly identical they wouldn't follow the Bose-Einstein or Fermi-Dirac statistics, and we know they do.
Why all particles of same type identical?
That is what "type" means! If they wouldn't be identical they would be different particle types.
So your question is basically "why is there such a limited set of particles". Well: We don't know, but it is certainly easier than a huge or even infinite number of them. I'm not aware of models that would allow an infinite number of particle types.

phinds
Gold Member
2019 Award
Why all particles of same type identical?
Physics is not good at answering, and really doesn't even try to answer, "why" questions. Physics tries to describe what is and use that to predict what might happen next. The problem with "why" questions is that they always lead to just MORE "why" questions. If electrons were different from each other in some way (skipping for the moment mfb's valid point) then the next question would be "why those particular differences", or "why don't they ever exceed <some characteristic>", or "why don't they ever get green?" or "why ...

haushofer
I always thought quantum field theory answers this question nicely: particles are excitations of the very same underlying quantum field. But maybe that's too simplistic.

hilbert2
Gold Member
Of course you could say that electron and positron are two forms of the same particle, with different electric charge, and the same for muon and antimuon, but it would just be a matter of terminology with no effect on the actual theory.

Staff Emeritus
2019 Award
"Why all particles of same type identical?"

Isn't this a tautology? If they weren't identical, wouldn't they be of different types?

"Why all particles of same type identical?"

Isn't this a tautology? If they weren't identical, wouldn't they be of different types?
Not neccessarly new types, what I meant is why they dont come with slight differences, for example like electrons with slightly different mass, but still in range of electron's mass.

I always thought quantum field theory answers this question nicely: particles are excitations of the very same underlying quantum field. But maybe that's too simplistic.
But this will lead to same question, why the field excitations are identical?

hilbert2
Gold Member
But this will lead to same question, why the field excitations are identical?
Actually, the electron and positron are excitations of the same field, but are still classified as different particles.

atyy
But this will lead to same question, why the field excitations are identical?
Quantum particles can be identical in more ways than classical particles because they do not have trajectories (within the quantum formalism). Identical classical particles still have different trajectories, whereas identical quantum particles do not have different trajectories.

This quantum notion of identical particles is built into the formalism by specifying a symmetry or anti-symmetry of the quantum wave function. In field theory, the identical nature of the excitations is specified by the commutation relations of operators that create the excitations.

vanhees71
Gold Member
2019 Award
I always thought quantum field theory answers this question nicely: particles are excitations of the very same underlying quantum field. But maybe that's too simplistic.
No, it's not too simplistic. I'd however not call it "excitations" but more precisely one-particle Fock states. One should note that in relativistic physics the notion of particles make only sense in terms of (asymptotically) free one-particle Fock states.

vanhees71
Now, why are they described by the "same field"? That has to do with the fact that today the only successful description of relativistic QT is within local microcausal QFTs. To get a local field operator for free particles, you have to use two irreducible representations of the Poincare group with the same Casimir-operator values ($m^2=p_{\mu} p^{\mu}$ and the spin $S$). For this there are two distinct representations, namely the ones with $p^0=\sqrt{m^2+\vec{p}^2}$ and $p^0=-\sqrt{m^2+\vec{p}^2}$. To construct local quantum fields (i.e., fields transforming like classical fields under a representation of the proper orthochronous Lorentz group) you need to orthogonally add both representations.