I’ve read a number of ‘physics for morons’-type books that make statements such as “the electron is point-like” or “the electron has no extension in space”. If this were literally true, if it truly was the case that an electron has a radius of zero, wouldn’t it then be the case that the electron’s mass would be spread over a vanishingly small volume? Would that not make electrons into little black holes?
I guess the same type of argument could be used with respect to the electron’s charge, no? Is this what “renormalization” addresses?
I’ve always had the same impression, that the electron is thought to have no volume.
According to this page, the radius is known to be less than 10[sup]-18[/sup]m, and the radius could very well be zero.
I’m no physicist (I’m sure one will be along shortly), but I wouldn’t expect that this is really comparable to black holes, since the physics at this scale are so different from typical “black hole scale”.
I looked over a bunch of web pages and the answer seems to be–no one knows. One page, in fact, lists 6 different values between 3.96 x 10[sup]-13[/sup] m and 1 x 10[sup]-18[/sup] m.
Part of the problem is quantum mechanics. Under classical physics, the radius is 2.817940285 x 10[sup]-15[/sup] m.
Under quantum mechanics, the radius ® can be calculated (where the particle is at complete rest) as: r=(1 ± i)*R/2 where R is the calculated event horizon for the electrons rest mass and i is the square root of negitive 1.
If I calculated the Schwarzschild radius for an electron correctly it’s 1.37 x 10[sup]-60[/sup] m. The effective radius for a non moving electron is somewhere between it and the classical physics number. No one really seems to think it’s zero except the pages put up primarily for laymen. but when dealing with quantum mechanics, wave mechanics and the uncertainy priciple, it gets complicated. As Heisenberg pointed out, you just can’t picture subatomic particles as little balls. The radius of an electron is an equation more than a real distance. And that equation includes (in this case) the square root of negative one.
I’ve always thought we should consider electrons (and other sub-atomic particles) as incompressible point-masses - I guess that’s the naive pre-QM view.
A related question: what do we know about the radii of other particles compared to the radius of an electron? E.g. quarks (smaller?), protons (always drawn as larger spheres in text books), photons…? Are these just taboo questions that particle phycisists have abandoned as impossible to know? Is the Planck length a lower limit for the radius of any particle?
What would we mean by “radius” of an electron? The radius of the smallest possible spherical volume that an electron can occupy? We’re not talking about particles anymore once we get down to single electrons, so I just wonder what exactly we’re referring to as the “radius.”
First off, we can’t, of course, define a hard radius for an electron any more than we can for an atom or a nucleus or any other really really small thing. Hence, what is typically done is to use a size scale where the thing will typically be.
For example, it’s not really correct to talk about the size of a hydrogen atom being one Bohr radius (in principle, the electron associated with the nucleus could be, oh, 4000 miles away), but the probability is highest that the electron WILL be at about a Bohr radius, so we go ahead and call a Bohr radius the size of a hydrogen atom.
In a similar way, one can’t give a hard number for the size of a proton, but from experiments, a soft number would be on the order of 10[sup]-15[/sup] meters or so.
As far as I know, quarks, electrons, photons, and the like (what we’d call fundamental particles) are all essentially point particles. This should be distinguished from composite particles (protons, neutrons, various mesons and baryons), which do have some size, albeit a really small one.
It’d be great if we could say that electrons are miniature black holes-- There’d be all sorts of interesting theoretical consequences. Unfortunately, though, we can’t reliably say anything about gravity on a quantum scale, so as of yet, we basically have no clue.
If I ever come up with a theory of quantum gravity, I’ll let you know.
The classical electron radius is a fairly meaningless number which is the radius of a uniformly charged sphere with charge equal to the electron charge and classical electrostatic energy equal to the electron’s rest energy. It doesn’t have much meaning because it assumes that the electron is a classical object, which it clearly is not.
The statement that an electron is pointlike or has zero radius is an empirical statement based on scattering experiments (like those done in colliders). When high-energy particles are scattered off of (e.g.) protons, the results seem to show internal substructure: The proton, at small enough length scales, does not behave like a featureless ball of charge; instead, it’s “made out of quarks.” No such effect has been seen for electrons, as far as I know.
The length scale probed by a scattering experiment is inversely proportional to the energy of the particles, so the electron is only known to be smaller than we can currently measure. This is still much larger than the radius of a black hole with the mass of an electron (assuming that the classical formula R = GM/c[sup]2[/sup] works in this case, which is doubtful).
I vaguely recall discussions about some property of an electron- either the “dipole moment” or the “magnetic moment” or something like that- which would in some sense mean that the electron was not a dimensionless point. That no value for this quantity had yet been found but that measurements had ruled out any value above a certain limit. Anyone know what I’m referring to?
Well, it certainly can’t be the magnetic moment because electrons have a non-zero magnetic moment already. I expect what you’re thinking of must be an electric dipole moment, which would indicate that whatever “shape” the electron actually “is” (when discussing an object so small, talking about shape is fairly meaningless, but let’s just pretend), it’s not spherical and hence not a point. I can’t think of anyone off the top of my head who claims that electrons have non-zero dipoles, and I would strongly suspect that any results seen in experiments to determine the electron’s dipole moment would give a null result (that is, the experiment would be consistent with zero), although as there is bound to be some uncertainty it could probably never be ruled out electrons actually have some tiny but non-zero electric dipole moment.
I guess at least some of the (apparent) confusion has to do with the use of a classical paradigm to describe what is clearly non-classical. As a number of you have said, it’s not even self-evident how the radius of an electron should be defined, or even probed. And, even if we could define or probe it, we’d probably need to use an as-yet-to-be-formulated theory of quantum gravity to understand it.*
[sup][sub]*so, Chronos, keep us posted on how your quantum gravity work is coming along.[/sub][/sup]
In its usual laconic manner, the Particle Data Table’s take on the electron dipole moment is that “A nonzero value is forbidden by both T invariance and P invariance.” The quoted best estimate for the experimental value (I’m using the 1994 edition) is -0.3 plus/minus 0.8 times 10 to the minus 26 e cm. In other words, zero.
The 2000 edition has it pushed down to (0.18 ± 0.16)*10[sup]-26[/sup]e cm. The thing is, theoretically, we’re almost certain that that number is zero, but the experimentalists like to test just to make sure. It’s not a bad practice, actually: A few years ago, most theorists were almost certain that the neutrino was massless, but now the experimentalists are showing some pretty good evidence that they do have mass.
In general, it’s almost never possible to prove that something’s exactly zero, just to show that it’s really, really small. A theorist will then come along and say “Oh, come on! You just can’t have something that’s that small, if it’s not exactly zero!”, and then proceed to plug zeros into his equations, but the experimentalists are harder to convince.
Chronos - is the same thing true for the singularity of a black hole? i.e., we know it’s “small”, but hesitate to say it’s zero since we don’t like dimensionless objects in physics? (who was it that said that a black hole is where the universe divided by zero? )
Not really, since we’ve been discussing the extent to which one can establish whether a quantity can be measured to be zero. Black hole singularities aren’t accessable to our experimental measurements, so that issue is moot. (And note that Chronos was talking about quantities which theorists believe are zero, not things which theorists suspect can’t be dimensionless.) Furthermore, in the black hole context a singularity is pretty much pointlike by definition.
However, there is a parallel with electrons in that if they are points, then there’s a singularity involved - but in the electric field rather than the gravitational field. Peoples’ dislike of black hole singularities thus also applies to the idea of point electrons. In both cases, I’d suggest that the dislike is less to do with singularities per se, than the fact that these are cases where you’re forced into thinking about electric or gravitational fields of unlimited strength. And we don’t have confidence that current theories apply in precisely these circumstances.
There are also arguments suggesting that the universe has to have a minimum length - if that’s so, then pointlike things become impossible. This is however a bit more speculative than the argument that singularities in current theories are places where we can’t have confidence that those theories apply.
