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There is a related question at What defines the mass of elementary particle? but my question is more fundamental.

Why do we treat particle masses as exact values? If a particle is indeed an excitation/resonance of a field, then like any excitation/resonance, should that resonance not have a finite "width"?

There does appear to be evidence of some spatial variation in the fine-structure constant within the universe (e.g., arXiv eprint 1008.3907).

I ask because it is not clear to me whether we defined the mass to be exact, a priori, or if we assume as much because variation would be difficult to handle, or if our measurements are not accurate enough to resolve any variation about some mean mass for any given particle.

Is there a fundamental reason why we treat, say, all electrons as having the same mass? I recall the assumption that electrons are identical particles and I understand that measurements support this, but can any of our observations actually test for variation in mass between any two electrons?

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    $\begingroup$ It is fairly easy to test for variation in mass between two electrons (or protons, or ...). None has been seen. $\endgroup$
    – Jon Custer
    Commented May 5, 2017 at 14:02
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    $\begingroup$ Concerning the paper link. A useful thing to do with a paper of that age on a topic of great interest is follow up with more recent articles that cite it. Just using the arXiv's internal citation tracking for the paper I find this recent meta analysis which includes the work of link to and cast doubt on the idea (or at least forces us to defer judgement) using a more complete data set. $\endgroup$
    – dmckee --- ex-moderator kitten
    Commented May 5, 2017 at 16:50
  • $\begingroup$ @dmckee - Ah, so there is recent evidence that this work is no longer supported? Shoot, I thought it was an interesting observation but I suppose I should have been more careful in my reading. $\endgroup$
    – honeste_vivere
    Commented May 5, 2017 at 17:05
  • $\begingroup$ The meta analysis I pointed to doesn't close the idea out as a possibility, but it finds that results of varied studies are less than uniform and that the overall significance is much lower than the value quoted in the paper you linked. It also says that there is a purposes built observational search on right now, so there may be news on that front in the next couple of years. $\endgroup$
    – dmckee --- ex-moderator kitten
    Commented May 5, 2017 at 17:42
  • $\begingroup$ If we didn't have identical particles pauli exclusion everything asteroid-size and above would collapse and black holes do not make good scientists. $\endgroup$
    – Kevin Kostlan
    Commented Sep 27, 2017 at 16:35

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