Size of Electron
David Paterson
The classical radius of an electron is r = e^2/m*c^2.
I think that this definition comes from the formula for the cross
section of the electron photon interaction as the photon energy
tends to infinity.
However, I have heard electrons and other leptons referred to as
'point like particles' in discussions of electron nucleus interactions.
Which of these is correct?
Further, if an electron is a 'point like particle' - ie. a particle
of finite mass and negligible extent - then does an electron qualify
as a type of black hole?
David Paterson
CSIRO, Highett, Victoria
bbl...@eagle.wesleyan.edu
as both a particle and a wave?
The classical radius assumes a particle.
Electrons, acting as particles, have a negligible size compared to a nucleus
(thus point-like particles)
electrons do not have negligible extent, however, compared with their mass (not
high density). plus, some of its mass may be seen acting as a wave.
If black holes behaved as waves similarly, i'd be really scared.
Brian Blais @eagle.wesleyan.edu
Todd A. Brun
>How big is an electron?
>
>The classical radius of an electron is r = e^2/m*c^2.
>I think that this definition comes from the formula for the cross
>section of the electron photon interaction as the photon energy
>tends to infinity.
>
>However, I have heard electrons and other leptons referred to as
>'point like particles' in discussions of electron nucleus interactions.
>
>Which of these is correct?
>
characteristic length which can be calculated from the fundamental
constants e,m, and c. Figuring out such "length scales" is very common in
physics, since it lets one divide the units out and work in dimensionless
units, which is usually a little simpler than ferrying lots of constants
around.
The current standard model treats all the fundamental particles (leptons,
quarks, and gauge bosons) as pointlike. Some extensions to the model
(notably, string theory) postulate that the particles do have physical
extent, but that it is immeasurably small given the state of the art
(and for some time to come). These postulates are extremely helpful
in one way. Pointlike particles do indeed look quite a bit like black
holes (please, you cosmologists, don't all jump on me). That is the
main reason that there is no quantum theory of gravity; the gravitational
field becomes infinite as we integrate to zero radius; and unlike the
infinities that arise in Quantum Electrodynamics, these are "unrenormalizable"
(i.e., we can't divide them by some other infinite quantity to get a finite
number). Postulating finite extent (say, a tiny loop of string) gets
around this problem nicely, but runs into problems with Lorentz invariance.
>
>Further, if an electron is a 'point like particle' - ie. a particle
>of finite mass and negligible extent - then does an electron qualify
>as a type of black hole?
>
One interesting speculation stimulated by black hole decay is what happens
if there is a residual charge? Presumably, as long as there is charge,
it will (eventually) decay into a bunch of particles whose net charge sums
to the original black hole charge. A frequent handwaving sort of argument
in particle physics (not to imply that it is invalid, as it certainly is)
is that the reason the electron is stable is that it carries a charge, and
has no lighter particle to decay into. Protons are also stable, as far as
we know, but there is some theoretical reason to suspect that they may not
be (given a loooooooong half-life). So an electron (or positron) might
be seen as the final stage in a black hole's decay; a tiny singularity
whose charge prevents it from decaying further. (of course, a given black
hole would decay into lots and lots of different electrons, positrons, and
whatnot).
-- Todd
--------------------------------------------------------------------------
Department of Physics
California Institute of Technology
"Feezeeks? Ve don't need no lousy feezeeks!"
Department of Physics, California Institute of Technology
"Feezeeks? Ve don't need no lousy feezeeks!"
Michael J. Gourlay
] How big is an electron?
]
] The classical radius of an electron is r = e^2/m*c^2.
] However, I have heard electrons and other leptons referred to as
] 'point like particles' in discussions of electron nucleus interactions.
] Further, if an electron is a 'point like particle' - ie. a particle
] of finite mass and negligible extent - then does an electron qualify
I thought that it was settled by quantum physics: The electron has
both wave and particle properties. How can it even be said to have
a radius? When? When it isn't moving :) ? In orbit around a nucleus?
It's a cloud.
--
Michael J. Gourlay GT Box 35431
Georgia Institute of Technology, School of Physics, Atlanta Georgia, 30332
uucp: ...!{decvax,hplabs,ncar,purdue,rutgers}!gatech!prism!gt5431b
Internet: gt5...@prism.gatech.edu My opinions.
Jim Meritt
}dav...@dbrmelb.dbrhi.oz (David Paterson) writes:
}] How big is an electron?
}]
}] The classical radius of an electron is r = e^2/m*c^2.
}]
}] However, I have heard electrons and other leptons referred to as
}] 'point like particles' in discussions of electron nucleus interactions.
}]
}] Further, if an electron is a 'point like particle' - ie. a particle
}] of finite mass and negligible extent - then does an electron qualify
}] as a black hole?
}
} I thought that it was settled by quantum physics: The electron has
}both wave and particle properties. How can it even be said to have
}a radius? When? When it isn't moving :) ? In orbit around a nucleus?
}It's a cloud.
Why, when its still it's everywhere! :-)
"People think it must be fun to be a super genius, but they don't realize how
hard it is to put up with all the idiots in the world." - Calvin
............................................................................
UUCP:j...@aplvax.uucp BITNET:meritt%aplvm.BITNET INTERNET:j...@aplcen.apl.jhu.edu
Mikel Lechner
>One interesting speculation stimulated by black hole decay is what happens
>if there is a residual charge? Presumably, as long as there is charge,
>it will (eventually) decay into a bunch of particles whose net charge sums
>to the original black hole charge. A frequent handwaving sort of argument
What you leave unstated is that any net charge of a black hole
would intensify into a smaller region of space as it decays. For an
excess negative charge the intense negative electric field would increase
the probability that the negative member of particle/anti-particle pair
would be the one to escape. The effect would be a net negative charge
escaping from the back hole via Hawking's radiation.
--
Mikel Lechner UUCP: mi...@teraida.UUCP
Teradyne EDA, Inc.
Warren G. Anderson
>Further, if an electron is a 'point like particle' - ie. a particle
>of finite mass and negligible extent - then does an electron qualify
>as a type of black hole?
A quick back of the envelope calculation shows that the Schwarzchild
radius for an electron mass is ~10^-61 cm. Considering that the Planck
length, the smallest measurable distance, is ~10^-33 cm, it seems
rather meaningless to talk about black hole like properties of a
'point-like' electron. Note that a mass does not have to be localized
to a point to have an event horizon, it need simply have less spatial
extent than it's Schwarzchild radius. IMHO a quantum theory of gravity
will be needed before anyone can talk meaningfully about how a
point-like object of electron mass relates to black hole theory.