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As far as I understand, electrons are infinitely stable since they are the least massive particle with non-zero electric charge. However, when accelerated to high-energies, the energy (or mass) of the electrons increases. Does this mean that at sufficient energies it is possible for these electrons to decay (e.g. into a muon, muon antineutrino, and electron neutrino) without scattering off any other particles?

dmckee --- ex-moderator kitten
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DaYu1729
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    Short answer: no. There's nothing for an electron to decay into without violating the conservation of charge, invariant mass or lepton number. – dukwon Dec 07 '15 at 21:35
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    The energy of the electrons increases. The mass of the electrons does not. – AccidentalFourierTransform Dec 07 '15 at 21:40
  • @AccidentalFourierTransform - Right. In some books I've read that the mass increases as $\gamma m_0$, but I also prefer to not think of it that way (hence the quotes). In any case, the point is, there should be enough energy in the electron to decay into another more massive particle. – DaYu1729 Dec 07 '15 at 21:44
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    no matter how fast an electron is moving: in its reference frame it is still, and its energy is $mc^2\sim .511\ \mathrm{MeV}$. In that frame it cannot decay, so neither can it in any other frame. – AccidentalFourierTransform Dec 07 '15 at 21:49
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    The notion of "relativistic mass" has become controversial. Many authors (myself among them) discourage it; in part because it generates exactly the kind of question you just asked. The answer to your questions is "Obviously no" (for the reason that AccidentalFourierTransform gives), but the language of relativistic mass makes it seem to the beginner like a reasonable question. – dmckee --- ex-moderator kitten Dec 07 '15 at 22:02
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    @dmckee: "has become? Einstein warned about avoiding the concept of increasing mass back in 1948!*. – Gert Dec 07 '15 at 22:20
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    @Gert The real pushback against it (an active and public effort to get people to stop putting it in books) got underway in with the 1987 and 1989 papers of Okun. Nor should the idea of been squashed early on: turning problems around, finding new notations and new ways of talking about thinks has been a fruitful source of progress in science. It's just that we've reached the point where covariant formulations are clearly better than ones that are not. And there are still dissenters which is what makes the word "controversial" apropos: people argue about it. – dmckee --- ex-moderator kitten Dec 07 '15 at 22:55
  • Related: http://physics.stackexchange.com/questions/180698/will-1-gram-of-matter-moving-at-relativistic-speeds-completely-annihilate-a-larg http://physics.stackexchange.com/questions/128938/why-is-binding-energy-delta-mc2 and probably a few others. – dmckee --- ex-moderator kitten Dec 07 '15 at 23:00

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Particle interactions, including decays, must always satisfy energy and momentum conservation in all reference frames. This means that high-energy electrons in an accelerator don't count; to the other electrons traveling down the accelerator with them, everyone is relatively at rest.

An interesting counterexample involves a hard-to-escape reference frame.

rob
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