size of the electron: current views?
Antoni S. Gozdz 21131
related questions:
1. what is the _current_ upper bound (experimental or theoretical) on the
size of the electron at rest, and who did the work?
2. are there _any_ solid experimental indications that it has a finite size?
(I know it appears to have no structure).
"Pointlike" will not pass; you can't have a cake and eat it, too ;-).
Tony
---------------------
Tony Gozdz
to...@nyquist.bellcore.com
Stanley J. Sramek
> 1. what is the _current_ upper bound (experimental or theoretical) on the
> size of the electron at rest, and who did the work?
>
> 2. are there _any_ solid experimental indications that it has a finite size?
> (I know it appears to have no structure).
>
> "Pointlike" will not pass; you can't have a cake and eat it, too ;-).
Here is a philosophical view of this question. If the electron has no
structure, then it has no size. When we speak of an object having "size"
what we mean is "the average maximum distance between any two of its
constituent sub-particles." For example, the diameter of a golf ball is
the average maximum distance between any two of its atoms. The diameter of
a hydrogen atom is the average distance between its proton and electron.
Since the electron, as far as is presently known, has no constituent
sub-particles, then the concept of "size" is meaningless for it.
Disclaimer: I am not, and have never been, a particle physicist.
Therefore, I may not know what I am talking about.
************************************************************************
* Stanley J. Sramek My posted statements *
* Texaco Inc. do not reflect the *
* Houston, Texas, U.S.A. views of my employer. *
************************************************************************
SCOTT I CHASE
>Having been mildly flamed in a different group, let me pose two
>related questions:
>
>1. what is the _current_ upper bound (experimental or theoretical) on the
> size of the electron at rest, and who did the work?
The full answer to this question is nontrivial. By direct experiment
using 100 GeV beams of electrons, we know that the electron has no
detectable structure. That energy corresponds to a wavelength of
roughly 10^-6 m * (100 *10^9)^-1 = 10-15 m. That a probe with wavelength
10^-15 m (1 fermi) detects no deviations from point-like behavior gives
you a direct upper limit.
However, you can do more than an order of magnitude better (to an energy
scale of several TeV) by indirect methods. The idea is that any finite-sized
electron must be composite. The subcomponents inside must be bound together
by some new very strong confining force. Two electrons will have residual
contact (four fermion) interactions based upon exchange of the gauge particles
of that new interaction among the electron's subcomponents, the absence of
which can be used to set a fairly general, though somewhat model dependent,
energy scale for the substructure. So far, we have never seen evidence
of such contact interactions, and to the best our knowledge the electron
is both pointlike and fundamental.
>2. are there _any_ solid experimental indications that it has a finite size?
> (I know it appears to have no structure).
None whatsoever. Yet.
-Scott
--------------------
Scott I. Chase "It is not a simple life to be a single cell,
SIC...@CSA2.LBL.GOV although I have no right to say so, having
been a single cell so long ago myself that I
have no memory at all of that stage of my
life." - Lewis Thomas
Matt McIrvin
>The full answer to this question is nontrivial. By direct experiment
>using 100 GeV beams of electrons, we know that the electron has no
>detectable structure. That energy corresponds to a wavelength of
>roughly 10^-6 m * (100 *10^9)^-1 = 10-15 m. That a probe with wavelength
>10^-15 m (1 fermi) detects no deviations from point-like behavior gives
>you a direct upper limit.
This doesn't sound right to me; doesn't 1 fermi correspond to about
200 MeV? I think you mean 10^-17 m (I'd say 2 x 10^-18 m, but that's
the same order of magnitude).
Thus the electron is known to be much smaller than a proton, which
is about a fermi big, by this method.
>However, you can do more than an order of magnitude better (to an energy
>scale of several TeV) by indirect methods.
That would correspond to an electron size of less than about 10^-20 m,
or about ten... um... you need to use one of those funky new SI
prefixes. Ten zeptometers, or something.
This is pretty impressive. The "classical radius" that shows up in
some early-20th-century theories is about one twenty-thousandth of the
Bohr radius, which is about half an angstrom; so the "classical radius
of the electron" would be a couple of fermis. (This was the radius
you got from the assumption that all the mass of the electron came
from electric field energy-- maybe there was something in there too
about the stresses required to hold the thing together against Coulomb
repulsion. It's 1/137 of the electron Compton wavelength, which
is 1/137 of the Bohr radius.) We've obviously gone far beyond that.
--
Matt 01234567 <-- The original Indent-o-Meter
McIrvin ^ Someday, tab damage will light our homes!
Hiroshi
>
>Here is a philosophical view of this question. If the electron has no
>structure, then it has no size. When we speak of an object having "size"
What about the pure mathematical "black hole"?
It must have no structure, however from far place, it looks
as if it has a radious.
Hiroshi Murakami
John W. Cobb
There are two different issues here. One is: is there a fundamental
length associated with a quantity using its properties and fundamental
constants? The second is what is the characteristic size of the "form-factor"
that must be used when doing calculations (especially effective
quantum field calculations).
For the first question, I can take the mass of the object, the
Gravitational constant and the speed of light and combine them
together dimensionally to get a distance, called the "Scwarzschild
Radius", G*m/(c*c) = 6.75E-56 cm (for an electron). Also, I can take
the charge of the electron, its mass, and the speed of light and also
get a length, called the "classical electron radius" or the "Thomson
radius", e*e/(m*c*c) = 2.82E-13 cm (for an electron). Physically, the
Scwarzschild radius is that radius at which an orbiting object would
have to have a velocity "on the scale of" the speed of light in order to
have stable rotation (where "on the scale of" is used so that constants
like 2 and pi are not used in the legnth definition). The Thomson radius
is "on the order of" the radius at which a metal sphere with a charge of
the electron would be if the energy contained in its electric field
equaled the mass of the electron. So the Scwarzschild radius tells you
something about the strength of the electron couplings to gravitational
forces while the Thomson radius tells you something about the strength
of the electron couplings to electromagnetic forces.
Now the second question asks what is the "extent" of the electron. This
can be a tricky question. For instance, in a hydrogen atom, one commonly
says that the electron's radius is the Bohr radius (about 0.5 Angstroms).
What this means is that there is a high probability that the electron
will be found within a sphere with a Bohr radius centered around the
hydrogen nucleas (a proton). What determines this size is the uncertainty
principle. The electron would like to be right on top of the proton, but
it would take too much energy to constrain it to such a small volume, so
it expands to a larger volume to decrease its average kinetic energy
expectation. But this radius is not really intrinsic to the electron.
Rather it is a consequence of the dance that the electron does with the
nucleus and the restrictions of the uncertainty principle. For instance,
if the nucleus had twice as much charge, and there was still just one
orbiting electron, then its radius would be smaller (i.e. hydrogen-like
helium).
By other tokens you can ask "what is the typical extent" of the electron
wavefunction in other situations. For isntance, in a metal like copper,
each conduction electron is distributed over a much larger volume than the cube
of the Bohr radius, because the regular metallic lattice allows a
delocalization of the electron over distances much longer than the
atomic separation. Likewise, in superconductors, the electrons can "acquire"
a size that is even macroscopic, and of course the "electron plane wave"
used so often in theoretical calculations has exact momentum, so its
extent is infinite. This is not just a theoretical construct. There is no
fundamental restriction on realizing this situation, only prgamatic issues
about actually building the device. That is, and electron plane wave is
possible in the way that a particle with exact position and momentum is not.
I want to empahsize again, however, that the "sizes" or "extents" that I
am speaking of in these last 2 paragraphs concerns the size of a sphere that
the electron would have a high probability of being found in.
However, when you look at these "sizes of the electron" you find that
it is determined not just by the electron, but also by the physical
context in which it is found. A deeper question to ask is what is the
intrinsic size of the electron, but what is meant by intrinsic size?
For an electron I don't know. The electron is fundamental, to the best
of my knowledge. As a Gedanken, imagine I have a "machine" that can measure
the position of a particle in a box. Suppose this machine has a dial for
accuracy (i.e. accurate to 1 cm, 1 micron, 1 nanometer, etc). Now put one
electon in the machine and measure its position. My machine will measure
that the electron is located in just 1 position, no matter how small I
set the size dial. Note: I am not violating the uncertainty principle here
becuase after each measurement, the act of measuring will "kick" the electron
into a new position, and as I set the size dial ever smaller, the kick
gets ever harder, but there is no reason I cannot, in principle, create
such a machine (position is an observable).
The behavior of the electron in this measuring machine can be contrasted
with that of say a proton, where when I set my dial to some small size
(on the order of a Fermi or less), I find that the proton seems to be
at more than one point. This is because the proton is not a "fundamental"
particle, but is composed of quarks. So when you squint small enough, what
looked like a point, now looks like a ball, and when you squint further,
you see that the ball is composed (metaphorically) of 3 smaller balls that
are held together by strings. Thus you can say that the proton does have
an intrinsic size and it is the radius of this composite ball.
However, with the electron, no matter how much we squint, we never
see the point start to look like a ball. It is always a point (as
far as we know). In this sense the electron is said to be pointlike
or fundamental, or to have no intrinsic size.
Let me again re-iterate. There are 2 size issues here. The first is the
size over which the wavefunction is spread, the second is the size
of the object when the position of the wavefunction is measured
(wavefunction collapse). At collapse, the electron appears to collapse
to a point.
Now if you are interested in a physics problem which length should you use?
Well, this depends on your problem. For instance, the size of the wavefunction
is what is important in determining whether you sit on your chair or
fall through it.
Finally, let me add that the effective "measuring machines" that have
been built, have a limited dial. They cannot go to arbitrarily small
sizes, but only down to about 2E-17 cm. So if the electron is in fact a
ball (or non-fundamental) whose radius is much smaller, then we cannot
know it at this time. The "effective measuring machines" that are used
are particle accelerators like the Tevatron, SLAC, CERN, SSC (RIP). They
are usually "rated" in terms of the energy of their colliding particles.
This energy can be equated to an equivalent distance by another
dimensional analysis game. Let L = hbar * c / E be the length. Thus
1 TeV (1e12 electron volts) will "probe" a distance of 2E-17 cm. This
forumla essentially says that if you have an ultre-relativistic particle,
it momentum is ~ E/c. And using the uncertainty relation delta-x * Delta P
~ hbar, you can define "an order of magnitude" estimate of the length
scale that is being probed. As you can see, the higher the energy, the
smaller the length scale. This is why particle physicists want to build
bigger and bigger accelerators to get higher energies to probe shorter scales.
-john .w cobb
--
---------------------------------------------------------------
John W. Cobb My posts don't reflect the views of my employer
Because my posts are usually opaque.
---------------------------------------------------------------
SCOTT I CHASE
>sic...@csa5.lbl.gov (SCOTT I CHASE) writes:
>
>>The full answer to this question is nontrivial. By direct experiment
>>using 100 GeV beams of electrons, we know that the electron has no
>>detectable structure. That energy corresponds to a wavelength of
>>roughly 10^-6 m * (100 *10^9)^-1 = 10-15 m. That a probe with wavelength
>>10^-15 m (1 fermi) detects no deviations from point-like behavior gives
>>you a direct upper limit.
>
>This doesn't sound right to me; doesn't 1 fermi correspond to about
>200 MeV? I think you mean 10^-17 m (I'd say 2 x 10^-18 m, but that's
>the same order of magnitude).
Oops. It was a simple multiplication error. As you can see from my
numbers above, you should get
10^-6 m * (100*10^9)^-1 = 10^-17 m.
You might even notice that you can detect structure long before the
scatterer is one full wavelength, and correct by another factor of
2*pi to get your 2 x 10^-18 m.
To be truthful, I knew that 1 fermi sounded much too big, but after thinking
about it for a while, I decided that I had to trust my calculation rather
than my intuition. Bad choice.
Anyway, to complete my argument, when you use indirect methods to
set a structure scale limit of 1.5 TeV, that then would correspond to
about 10^-19 m, or 10^-4 proton diameters.
-Scott
--------------------
Scott I. Chase Mutationem motas proportionalem
SIC...@CSA2.LBL.GOV esse vi motrici impressae.
Hoyt A. Stearns jr.
>Having been mildly flamed in a different group, let me pose two
>related questions:
>
>1. what is the _current_ upper bound (experimental or theoretical) on the
> size of the electron at rest, and who did the work?
>
>2. are there _any_ solid experimental indications that it has a finite size?
> (I know it appears to have no structure).
>
According to Ronald W. Satz in his paper "Theory of Electrons and Currents",
Reciprocity, Vol. XIII, No. 1, Autumn 1983,
"...The Reciprocal System is much more specific on the details of electron
attributes that conventional theory... The electron is a spherical particle
resulting from the rotation of a single photon. The frequency of the photon
is 2R = 6.576115 E15 cycles/second. The rotational speeds in revolutions per
second around the three axes are r/pi , 2R/pi , 4R/pi or
1.0466212 E15 rev/sec. , 2.0932424 E15 rev/sec , 4.1864848 E15 rev/sec.
The electron may be charged or uncharged. If charged, the electron has an
added rotational vibratory motion of R/2pi = 5.233106 E14 cycles/sec.
<The neutrino-like uncharged electron is almost unobservable.>
The diameter d of the electron is one natural space unit, reduced by the
appropriate inter-regional ratio (142.22 here). Thus,
d = 4.55884 E-8 m /142.22 = 3.2054 A.
--
Hoyt A. Stearns jr.|ho...@isus.stat.| International Society of Unified Science|
4131 E. Cannon Dr. | .com OR | Advancing Dewey B. Larson's Reciprocal |
Phoenix, AZ. 85028 |enuucp.asu.edu!| System- a unified physical theory. |
voice 602 996-1717 |stat.com!wierius!isus!hoyt OR ho...@isus.tnet.com_________|
SCOTT I CHASE
>
>The diameter d of the electron is one natural space unit, reduced by the
>appropriate inter-regional ratio (142.22 here). Thus,
>
>d = 4.55884 E-8 m /142.22 = 3.2054 A.
I suppose that you discount the experimental evidence which clearly show
that the electron has a radius at least 8-10 orders of magnitude smaller
than this prediction?
-Scott
-------------------- i hate you, you hate me
Scott I. Chase let's all go and kill barney
SIC...@CSA2.LBL.GOV and a shot rang out and barney hit the floor,
no more purple dinosaur.