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An electron has a mass of $9.10938291(40) \times 10^{−31} kg$. It also has a volume of $0 m^3$. This would imply it has infinite density. Shouldn't that make it collapse into a black hole? Why doesn't it?

Christopher King
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  • Point particles can be described by delta functions.for example see this, http://math.mit.edu/classes/18.013A/HTML/chapter28/section03.html – Paul Jul 13 '15 at 02:49
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    Possible duplicates: http://physics.stackexchange.com/q/75911/2451 , http://physics.stackexchange.com/q/165823/2451 and links therein. – Qmechanic Jul 13 '15 at 07:08
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    Out of curiosity, would you care to share the reference that says electron has "volume of 0m^3"? It looks extremely suspicious. Usually different materials say that it can be treated like a point-charge (I don't think I have seen point-mass version anywhere.) I don't think they say, they are point particles. This has some implication, notably, you usually can simplify electron to a point given that you look from far enough that this makes sense. – luk32 Jul 13 '15 at 10:19
  • At the same time, an electron has zero mass and a wavelength of 1.23nm. This would imply it has zero density. Shouldn't that make a Crooks Tube not work? – OrangeDog Jul 13 '15 at 12:40
  • @luk32: it's probably better to say that there is no observation that shows any structure to an electron, and all observations are consistent with models that treat the electron as a point particle. – Zo the Relativist Jul 13 '15 at 13:47

2 Answers2

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The angular momentum and charge of an electron are both large enough that a black hole would not form. If you believe classical general relativity all the way down to the scale of an electron (and you really shouldn't), then the electron will form a naked singularity.

More exactly, for the case of a spinning body, the horizon is at the zero of

$$r^{2} - 2Mr + a^{2}$$

Where $a$ is the angular momentum divided by the mass (in $G = c = 1$ units), and $M$ is the black hole's mass. If you put in the numbers for the electron, this equation has no real zeroes. Adding charge to the picture will only make the matter worse.

Zo the Relativist
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  • It's not immediately obvious that electrons being singularities conflicts with current observations. – OrangeDog Jul 13 '15 at 12:31
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    @OrangeDog: sure. But certainly, when you start talking about general relativistic effects of electrons, then you start getting into a full theory of quantum gravity, and you should stop believing in raw general relativity. – Zo the Relativist Jul 13 '15 at 13:46
  • Also, naked singularities break most of the assumptions made about how realistic models of general relativity work. – Zo the Relativist Aug 02 '15 at 19:35
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Why don't electrons collapse into black holes?

Because the electron isn't a point-particle. Its field is what it is. It isn't some speck that has a field, it is that field. There's energy in that field, that energy has a mass-equivalence, and it doesn't have a zero volume. Also note that we can diffract electrons. And that the Einstein-de Haas effect demonstrates that "spin angular momentum is indeed of the same nature as the angular momentum of rotating bodies as conceived in classical mechanics". And that in atomic orbitals electrons "exist as standing waves". I could go on. There's ample evidence for the wave nature of matter. There's no evidence for the point-particle nature of matter. Some will dispute this and point to scattering experiments, but there's a wrong inference at work there. It's like hanging out of helicopter probing a whirlpool with a bargepole, then declaring that because you can't feel the billiard ball that's causing this, it must be really really small.

All in all I'm afraid the people who tell you the electron is a point-particle are promoting a myth that was borne from mathematical simplification. It's quantum field theory, not quantum point particle theory. IMHO pictures like this which say the electron is less than 10-18 m in size are misleading and irresponsible, and shouldn't even be shown to schoolchildren.

John Duffield
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