Are all elementary particles of the same type exactly the same?

Question

Are all elementary particles of the same type EXACTLY the same? Is there some variation in what an electron is, for example, or are they all the same?

@Christoph: So do you think there is no difference between electrons and positrons either? This is not an attempt at sarcasm: you made a good point, but I am not sure it does not prove more than it was intended to prove. — akhmeteli, Nov 30 '13 at 22:46
@akhmeteli: well, we do describe both particles and anti-particles with a single Dirac field; the idea of a single worline for all electrons is not really workable (despite conjectured proton decay involving positrons), but I like it nevertheless ;) — Christoph, Nov 30 '13 at 23:11
@Christoph: I agree, "we do describe both particles and anti-particles with a single Dirac field". However, the apparent conclusion seems to be: "electron is the same (or not the same) as positron to the same extent as two electrons with different spin projection on some axis." — akhmeteli, Nov 30 '13 at 23:28
@akhmeteli: in a way, yes: in the Dirac basis, the spinor components are related to the particle/anti-particle and spin up/spin down distinction; the gamma matrices are responsible for mixing them and can be decomposed as $\gamma^0=\sigma^0\otimes\begin{pmatrix}1&0\0&-1\end{pmatrix}$, $\gamma^k=\sigma^k\otimes\begin{pmatrix}0&1\-1&0\end{pmatrix}$; note that the second factor of $\gamma^0$ is diagonal, consistent with the idea that the particle/anti-particle distinction is related to projection onto the time axis — Christoph, Dec 01 '13 at 00:34

score 1 · Accepted Answer · answered Nov 30 '13 at 22:07

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This thread will inevitably descend into a semantic and/or philosophical discussion unless we have some at least somewhat precise notion of what it means for particles to be the "same".

In modern physics, elementary particles are fundamentally treated quantum-mechanically, and in quantum mechanics, they are modeled as being exactly the same in the following precise sense:

If a system consists of two or more elementary particles, then the state of the system only changes by a multiplicative constant (which happens to be $+1$ for bosons an $-1$ for fermions) when one permutes the labels of all of the particles. Now, it is also the case that in quantum mechanics, two states that differ by such a multiplicative constant are physically equivalent, so permuting the labels of all of the particles leads to a physically equivalent state of the system.

answered Nov 30 '13 at 22:07

joshphysics

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Nice one, as soon as I tried answering I wondered whether I'd opened a can of worms! – innisfree Nov 30 '13 at 22:10
@innisfree Yea I feel like this is one of those questions that could easily get out-of-hand. For example, akhmeteli's answer about electrons having different spin projections upon measurement is, of course, not false provided you interpret the term "same" in a particular way, but it kind of flies in the face of the way the terms "same" or "identical" are conventionally used in physics when referring to elementary particles. – joshphysics Nov 30 '13 at 22:13
With the slight caveat that it may depend on it's surroundings or energy. A lone neutron doesn't behave like one in an atom - although it does behave like any other lone neutron – Martin Beckett Nov 30 '13 at 23:10
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@Martin Beckett: I was under impression that neutron is not considered an elementary particle anymore. Am I wrong? – akhmeteli Nov 30 '13 at 23:30
@akhmeteli, correct, but it was the only common example I could think of. It doesn't change josh's answer – Martin Beckett Nov 30 '13 at 23:47
@joshphysics: Could you please give a reference to your definition (my concern is your definition does not contain the word "same" or "identical" related to a particle, rather than a state), or reformulate it in terms of creation/annihilation operators? – akhmeteli Dec 01 '13 at 00:30
@akhmeteli I don't know of a reference that explicitly says that identical particles are defined so as to satisfy the symmetrization postulate, but it is certainly a necessary condition for particles to be "identical," (see, for example, Cohen-Tannoudji's Quantum Mechanics p. 1368). In the language of QFT, all of this is formulated in terms of bosonic particles being quantized in terms of commutators of creation and annihilation operators and fermionic particles being quanized via anticommutators. Your point about quantum numbers is well-taken; I'm unsure any of this is more than semantics. – joshphysics Dec 01 '13 at 04:06
@akhmeteli It also occurs to me that perhaps a better term for, for example, electrons with different spin projections along a given axis would be "distinguishable." I don't think, for example, that most physicists would consider electrons at different spatial locations to be non-"identical," but I think they would call such photons distinguishable. Related: http://physics.stackexchange.com/questions/52086/what-are-the-differences-between-indistinguishable-and-identical – joshphysics Dec 01 '13 at 04:24
@joshphysics: "it is certainly a necessary condition for particles to be "identical,"" - that's what I suspected. I wonder if this "necessary" condition could be satisfied for electrons and positrons as well."I'm unsure any of this is more than semantics." I'm unsure your strong words "flies in the face of the way the terms "same" or "identical" are conventionally used in physics when referring to elementary particles" are more than semantics. – akhmeteli Dec 01 '13 at 05:44
@akhmeteli "flies in the face of" was inappropriate. Wording retracted. Sorry if you found it offensive. – joshphysics Dec 01 '13 at 06:46
@joshphysics: No offense taken. – akhmeteli Dec 01 '13 at 11:01

score 0 · Answer 2 · answered Nov 30 '13 at 21:57

All elementary particles of a particular type, e.g. all electrons, are excitations of the same quantum field, and are all identical and indistinguishable.

Because of the uncertainty principle, one cannot distinguish such particles by even their trajectories.

score 0 · Answer 3 · answered Nov 30 '13 at 21:57

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I'd say two electrons can differ, e.g., by their spin projection on some axis.

answered Nov 30 '13 at 21:57

akhmeteli

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Are all elementary particles of the same type exactly the same?

3 Answers3