The electron is a particle. The mass of the electron is $9.10938215(45)\times 10^{−31}\, {\rm kg}$.
But why is the mass exactly what it is?
What in physics defines the mass of a elementary particle?
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$\begingroup$ Could you be more explicit about what you want to know? In physics mass is defined as a fundamental parameter of our theories and its value is determined by measurement so that the theories give correct predictions for other events. Do you want to know more about the way it is measured or about the role it plays in our theories? $\endgroup$– MarekCommented Mar 7, 2011 at 8:44
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$\begingroup$ I want to know more about invariant mass of elementary particles. So how we can predict/calcolate (not measureing) the mass of particle. $\endgroup$– GJ.Commented Mar 7, 2011 at 9:42
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$\begingroup$ Are you asking about the ratios of the masses of the particle? Surely the number that represents the mass of a particle depends on the chosen units. $\endgroup$– MBNCommented Mar 7, 2011 at 15:21
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$\begingroup$ @MBN: Certainly I'm asking about mass ratios. $\endgroup$– GJ.Commented Mar 7, 2011 at 15:39
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2 Answers
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Dear GJ, the mass of every electron is exactly the same - as long as our experiments and theories may say - and the same value of mass manifests itself
in the energy/mass conservation law;
in the source of the gravitational field that the object containing massive particles such as the electron produces;
in the resistance towards acceleration that the massive objects have.
All those versions of the "mass" are the same quantity.
In our modern theories of the world, the mass of the electron is the coefficient of a "mass term" in the Lagrangian or Hamiltonian, $-m\bar\psi\psi$, that is almost fundamental and can't have any deeper explanation.
Well, almost. In fact, in the "electroweak theory" - unifying all electromagnetic phenomena (including light) with the weak nuclear interactions (notorious as the origin of the beta-decay) - the mass of electrons (and other particles) arises from the interactions with the Higgs field. So the actual term is actually $$-y h \bar\psi\psi$$ where $\psi$ is the Dirac field for the electron. Here, $h$ is the Higgs field which takes the nonzero value of $h=v$ in the vacuum - the spontaneous symmetry breaking (Higgs mechanism). This value of $v$, about $247$ GeV, is universal for all particles. However, the difficult information about the electron mass is moved to the parameter $y$, the so-called Yukawa coupling, which is dimensionless (no units) and whose value is much smaller than one.
When the Universe is described by string theory, the value of the Yukawa coupling $y$ and the Higgs value in the vacuum, $v$, can be in principle calculated from first principles (in the natural units, e.g. the Planck units, not in kilograms - the unit of "kilogram" was a randomly chosen social convention that the farmers chose to sell vegetables, without any justification why it's not e.g. $1.3$ times different).
However, there are many (but discretely) possible Universes according to string theory and we can't say which one is right, so in practice, we can't calculate the value of the electron mass from purely theoretical considerations. So far, we need to measure it to know the value. Chances are that the situation won't change for quite some time.
answered Mar 7, 2011 at 8:44
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$\begingroup$ It is curious that every electrically charged elementary particle also has mass (obviously, a charged particle without mass would cause problems), but we attribute this mass to the interaction with the Higgs field. Has anyone proposed an idea why charged particles interact with the Higgs field and acquire mass (thus saving the absurdity of a massless charged particle)? $\endgroup$– DaviusCommented Jul 13, 2023 at 22:18
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$\begingroup$ Because both the scalar fields and their cubic interactions are possible and consistent and everything that is not forbidden is mandatory with a nonzero coefficient. Also, the only theory that goes deeper than quantum field theory, namely string theory, generally derives these fields and interactions in most vacua. $\endgroup$ Commented Jul 15, 2023 at 2:52
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Right now, the elementary particle masses simply have to be measured. We don't have any explanation for why the masses have the particular values they do.
One of the major goals of unified theories (string theory and the like) is to be able to derive the elementary particle masses, or at least derive the ratios between the masses of different particles. But we're a long way off from doing so.
