Electron built of what?
Jim Carr
loc...@best.com (Thomas N. Lockyer) writes:
>
> The models I have been working with do show a conjugate structure for
>the electron and positron.
They also show a size that is in huge disagreement with the data
for electron-electron and electron-positron scattering.
--
James A. Carr <j...@scri.fsu.edu> | "Whatever."
http://www.scri.fsu.edu/~jac/ |
Supercomputer Computations Res. Inst. | George Herbert Walker Bush
Florida State, Tallahassee FL 32306 |
Thomas Lockyer
Jim Carr (j...@ibms48.scri.fsu.edu) wrote:
: loc...@best.com (Thomas N. Lockyer) writes:
: >
: > The models I have been working with do show a conjugate structure for
: >the electron and positron.
: They also show a size that is in huge disagreement with the data
: for electron-electron and electron-positron scattering.
Jim: The models have the exact size of the *electron's* rationalized
Compton wavelength. Dirac had the point electron *zitterbewegung* over the
same rationalized electron Compton wavelength, to make his math work out,
so I am in good company.
: --
: James A. Carr <j...@scri.fsu.edu> | "Whatever."
: http://www.scri.fsu.edu/~jac/ |
: Supercomputer Computations Res. Inst. | George Herbert Walker Bush
: Florida State, Tallahassee FL 32306 |
--
Thomas N. Lockyer <loc...@svpal.org> | If you want to do the
1611 Fallen Leaf Lane | impossible, don't hire
Los Altos, CA USA 94024-6212 | an expert because he
Tel. (415)967-9550 | knows it can't be done!
|
| Henry Ford
Bernd Binder
Thomas Lockyer <loc...@svpal.svpal.org> wrote in article
<5islkb$h...@borg.svpal.org>...
> Jim Carr (j...@ibms48.scri.fsu.edu) wrote:
> : loc...@best.com (Thomas N. Lockyer) writes:
> : >
> : > The models I have been working with do show a conjugate structure for
> : >the electron and positron.
>
> : They also show a size that is in huge disagreement with the data
> : for electron-electron and electron-positron scattering.
>
> Jim: The models have the exact size of the *electron's* rationalized
> Compton wavelength. Dirac had the point electron *zitterbewegung* over
the
> same rationalized electron Compton wavelength, to make his math work out,
> so I am in good company.
>
Dear Sirs:
The Compton wavelength is a consequence of the rest mass and generally not
directly related to the size of a particle. Can somebody explain me please:
Why should the wavelength of e+/e- creation be related to the size of an
e+/e- ?
What is the big difference to the proton?
What's about the mass-energy density?
(The spatial variance of an object with any "~bewegung" is not the size of
an object. Sirs, you know what I mean)
Bernd Binder
Thomas Lockyer
Bernd Binder (b...@ipa.fhg.de) wrote:
: Thomas Lockyer <loc...@svpal.svpal.org> wrote in article
: <5islkb$h...@borg.svpal.org>...
: > Jim Carr (j...@ibms48.scri.fsu.edu) wrote:
: > : loc...@best.com (Thomas N. Lockyer) writes:
: > : >
: > : > The models I have been working with do show a conjugate structure for
: > : >the electron and positron.
: >
: > : They also show a size that is in huge disagreement with the data
: > : for electron-electron and electron-positron scattering.
: >
: > Jim: The models have the exact size of the *electron's* rationalized
: > Compton wavelength. Dirac had the point electron *zitterbewegung* over
: the
: > same rationalized electron Compton wavelength, to make his math work out,
: > so I am in good company.
: >
: Dear Sirs:
: The Compton wavelength is a consequence of the rest mass and generally not
: directly related to the size of a particle. Can somebody explain me please:
: Why should the wavelength of e+/e- creation be related to the size of an
: e+/e- ?
: What is the big difference to the proton?
The models I have been working with indicate that there is only one energy
where the photon can create basic particles, and that these are just the
electron, positron, electron type neutrino and muon type neutrino pair.
The model goes on the scale to the mass of both the proton and neutron
using the only basic particles that are available to make composites, the
electrons and neutrinos.
: What's about the mass-energy density?
Bernd: The models for the electron, that work successfully, are
described on: http://www.best.com/~lockyer/home3.htm If you take the
time to see those pages, you will find that the simple geometry supports
and relates *all* of the electron's fundamental physical constants.
Dirac had no model for the electron, so, to get a finite charge structure
from a *point* particle, he had to postulate that the electron trembled
about a region of space equal to lambda sub e bar, at the velocity of
light. Well, we know that this is can't be, because there is no mechanism
that dictates it to be so. He cheated so as to get the basis for a normal
magnetic moment that requires a current loop area.
The structure of the model, described on the web pages,
results from the calculus of related rates and the balancing of the
electric and magnetic forces, during photoproduction, that dictate the
electron size of exactly lambda sub e bar.
: (The spatial variance of an object with any "~bewegung" is not the size of
: an object. Sirs, you know what I mean)
Exactly, from Dirac to Feynman they had no structural model for the
electron. So, Dirac had to invent *zitterbewegung* for the electron, and
Feynman had to invent *going backwards in time* to make positrons. Both
postulates are niave and have no basis in reality.
: Bernd Binder
Regards: Tom: http://www.best.com/~lockyer
Jim Carr
Jim Carr (j...@ibms48.scri.fsu.edu) wrote:
|
| loc...@best.com (Thomas N. Lockyer) writes:
| >
| > The models I have been working with do show a conjugate structure for
| >the electron and positron.
|
| They also show a size that is in huge disagreement with the data
| for electron-electron and electron-positron scattering.
loc...@svpal.svpal.org (Thomas Lockyer) writes:
>
>Jim: The models have the exact size of the *electron's* rationalized
>Compton wavelength.
I know. That is why your models are wrong.
The data for electron-electron and electron-positron scattering
clearly show that the electron is much smaller than that.
>Dirac had the point electron *zitterbewegung* over the
>same rationalized electron Compton wavelength, to make his math work out,
>so I am in good company.
You are seriously confused about what Dirac did, and the predictions
that QED makes for electron-electron scattering -- predictions that
were recently verified at very high momentum transfer.
Thomas N. Lockyer
In article <5iqurk$p...@news.fsu.edu> j...@ibms48.scri.fsu.edu (Jim Carr) writes:
>From: j...@ibms48.scri.fsu.edu (Jim Carr)
>Subject: Re: Electron built of what?
>Date: 13 Apr 1997 15:41:40 GMT
>loc...@best.com (Thomas N. Lockyer) writes:
>>
>> The models I have been working with do show a conjugate structure for
>>the electron and positron.
> They also show a size that is in huge disagreement with the data
> for electron-electron and electron-positron scattering.
Jim: The models have the exact size of the *electron's* rationalized Compton
wavelength. Dirac had a point particle electron *zitterbewegung* over a
region of the size of the electron's rationalized Compton wavelength, just to
make the math lead to a finite charge structure and a normal magnetic moment.
So the models do directly what Dirac had to crackpot.
>--
> James A. Carr <j...@scri.fsu.edu> | "Whatever."
> http://www.scri.fsu.edu/~jac/ |
> Supercomputer Computations Res. Inst. | George Herbert Walker Bush
> Florida State, Tallahassee FL 32306 |
Regards: Tom: http://ww.best.com/~lockyer/home3.htm
ThomasL283
There seem to be some question about the *size* of the electron model not
being correct. Well the electron model I have been working with, is
correct, by definition, because the model supports *all* of the electron's
numbers. Dirac got the same numbers by doing some funny postulating. Let
me quote a discussion of Dirac particles by Yu. A. Alexandrov in his book
"Fundamental Properties of the Neutron" page 168, quote:
"A qualitative picture is as follows: a free Dirac particle does not move
along a straight line, but 奏rembles' or 租ances' (zitterbewegung) at the
velocity of light about a point moving uniformly at the speed of travel of
the particle. This dancing motion covers a region of the size of (h
bar/mc), where m is the mass of the particle. In the case of the electron
with a charge e the trajectory of this motion is a small current-carrying
loop, and in the presence of an external magnetic field the electron
behaves as if it has a magnetic moment (e h bar/2mc). Moreover, effects
should be expected associated with the fact that the motion of a charge
will not be that of a point- like particle, but like a charge distributed
over some finite volume. This effect causes an additional shift in the S
levels of a hydrogen atom and is described in the Dirac theory by the term
introduced by Darwin. The trembling of a point- like electron therefore
leads to apparent finite charge structure and a normal magnetic moment."
Unquote:
My comment, the (h bar/mc) of Dirac's dancing motion, is the
rationalized Compton wavelength of the electron, same size as the electron
model on the web page;
http://www.best.com/~lockyer/home3.htm
If any of you think the mass of the electron can dance at the velocity of
light, I've got a nice bridge in Brooklyn I will sell you.
regards: Tom: http://www.best.com/~lockyer
Todd K. Pedlar
ThomasL283 wrote:
> There seem to be some question about the *size* of the electron
> model not being correct. Well the electron model I have been working
> with, is correct, by definition, because the model supports *all* of
> the electron's numbers.
"All" of its "numbers"? Perhaps you can direct me to the place on
the model that predicts a small electron radius for the purposes of
calculating scattering phenomena? The compton wavelength for the
electron is neatly tucked into your model (by hand, I might add) but
there are more "numbers" for the electron than simply the compton
wavelength.
It seems also that your cubic model leaves something out. While
the straight edge has a length of lambda-bar, or the compton wavelength
over 2pi, the diagonal has a length therefore of sqrt(2)*lambda-bar.
Where does this fit in to the physical world? It should have some
physical meaning, too.
Todd
------------------------------------------------------------------
Todd K. Pedlar - Northwestern Univ., Nucl. & Particle Physics
FNAL E835 Homepage: http://numep1.phys.nwu.edu/tkp.html
------------------------------------------------------------------
Phone: (847) 491-8630 (630) 840-8048 Fax: (847) 491-8627
------------------------------------------------------------------
" semper ubi sub ubi " Anon., 15th c.
------------------------------------------------------------------
Thomas Lockyer
Todd K. Pedlar (to...@numep0.phys.nwu.edu) wrote:
: ThomasL283 wrote:
:
: > There seem to be some question about the *size* of the electron
: > model not being correct. Well the electron model I have been working
: > with, is correct, by definition, because the model supports *all* of
: > the electron's numbers.
: "All" of its "numbers"? Perhaps you can direct me to the place on
: the model that predicts a small electron radius for the purposes of
: calculating scattering phenomena? The compton wavelength for the
: electron is neatly tucked into your model (by hand, I might add) but
: there are more "numbers" for the electron than simply the compton
: wavelength.
Todd: The model gives the value for the spin angular momentum from
it's mass radius of 1/2 lambda bar. And the model gives the Bohr magneton
from the charge radius of sqrt 2 times the mass radius and the fact that
there are two current loop areas (the front and back cube faces). And the
model shows the mechanism that makes the electron spin from a chance
arrangement of the vectors going in the same direction in the front and
back cube faces.
: It seems also that your cubic model leaves something out. While
: the straight edge has a length of lambda-bar, or the compton wavelength
: over 2pi, the diagonal has a length therefore of sqrt(2)*lambda-bar.
: Where does this fit in to the physical world? It should have some
: physical meaning, too.
Yes, if you will notice, this charge radius of sqrt(2) x lambda bar/2
derives the Bohr magneton from the two current loops. Print out the web
pages and you can then follow the math. What I like about this model is
it gives a simple structure that relates *all* of the electron's
fundamental physical constants in one neat package, with nothing left
over.
:
: Todd
: ------------------------------------------------------------------
: Todd K. Pedlar - Northwestern Univ., Nucl. & Particle Physics
: FNAL E835 Homepage: http://numep1.phys.nwu.edu/tkp.html
: ------------------------------------------------------------------
: Phone: (847) 491-8630 (630) 840-8048 Fax: (847) 491-8627
: ------------------------------------------------------------------
: " semper ubi sub ubi " Anon., 15th c.
: ------------------------------------------------------------------
Regards: Tom: http://www.best.com/~lockyer/home3.htm
Matt McIrvin
In article <5itbot$j...@news.fsu.edu>, j...@ibms48.scri.fsu.edu (Jim Carr) wrote:
> loc...@svpal.svpal.org (Thomas Lockyer) writes:
> >Dirac had the point electron *zitterbewegung* over the
> >same rationalized electron Compton wavelength, to make his math work out,
> >so I am in good company.
>
> You are seriously confused about what Dirac did, and the predictions
> that QED makes for electron-electron scattering -- predictions that
> were recently verified at very high momentum transfer.
Well, if one does a Foldy-Wouthuysen transformation on QED, the electron
*does* end up with an effective charge radius on the order of the Compton
wavelength. This is often explained as equivalent, semiclassically, to the
zitterbewegung in the Dirac theory. It does not contradict the high
momentum scattering results, because the agreement found is with a Dirac
point particle, and the Dirac theory is equivalent to the Foldy-Wouthuysen
transformed version.
But this, as far as I can tell, has nothing to do with Lockyer's model.
Thorsten Ohl
thoma...@aol.com (ThomasL283) writes:
> Well the electron model I have been working with, is
> correct, by definition, [...]
^^^^^^^^^^^^^^^^^^^^^^
ROTFL!
He hath spoken. Though shallst not question His correctness ...
> "A qualitative picture is as follows: [zitterbewegung]
^^^^^^^^^^^
It's a _qualitative_ description of the Darwin term, which is used in
undergraduate texts for a semiclassical explanation. If you
understand Quantum Mechanics, you don't need this explanation, because
you know that the Dirac equation is the only first order equation
compatible with spin 1/2 representations of the Lorentz group.
In a sense, the Dirac equation is ``true by definition''. NB:
you still have to check that its predictions are compatible with
experiment, i.e. that teh electron behaves like an irreducible spin
1/2 representation of the Lorentz group.
ceterum censeo: what is _your_ prediction for the Bhabha scattering
cross section?
--
Thorsten Ohl, Physics Department, TH Darmstadt --- PGP: AF 38 FF CE 03 8A 2E A7
http://crunch.ikp.physik.th-darmstadt.de/~ohl/ -------- 8F 2A C1 86 8C 06 32 6B
Thomas N. Lockyer
In article <uezpuzo...@crunch.ikp.physik.th-darmstadt.de> Thorsten Ohl <o...@crunch.ikp.physik.th-darmstadt.de> writes:
>From: Thorsten Ohl <o...@crunch.ikp.physik.th-darmstadt.de>
>Subject: Re: Electron built of what?
>thoma...@aol.com (ThomasL283) writes:
>> Well the electron model I have been working with, is
>> correct, by definition, [...]
> ^^^^^^^^^^^^^^^^^^^^^^
> ROTFL!
>He hath spoken. Though shallst not question His correctness ...
Thorsten, we *define* the electron by it's mass, charge, spin angular momentum
and magnetic moment. Those numbers are supported by the electron model I
have been working with, and that's what was meant by *correct by definition*.
>> "A qualitative picture is as follows: [zitterbewegung]
> ^^^^^^^^^^^
>It's a _qualitative_ description of the Darwin term, which is used in
>undergraduate texts for a semiclassical explanation. If you
>understand Quantum Mechanics, you don't need this explanation, because
>you know that the Dirac equation is the only first order equation
>compatible with spin 1/2 representations of the Lorentz group.
>In a sense, the Dirac equation is ``true by definition''. NB:
>you still have to check that its predictions are compatible with
>experiment, i.e. that teh electron behaves like an irreducible spin
>1/2 representation of the Lorentz group.
>ceterum censeo: what is _your_ prediction for the Bhabha scattering
>cross section?
Why would I want to do that? There are too many variables. But, if you are
meaning the *point* particle aspect being verified by Bhabha scattering then
this also might be reconciled by the model. The model is spinning at exactly
(c) so that by relativity, it should appear *optically* as a point particle.
Think of looking down on a disk spinning at (c), it should appear, from our
stationary frame, as a point.
>--
>Thorsten Ohl, Physics Department, TH Darmstadt --- PGP: AF 38 FF CE 03 8A 2E A7
>http://crunch.ikp.physik.th-darmstadt.de/~ohl/ -------- 8F 2A C1 86 8C 06 32 6B
Regards: Tom://www.best.com/~lockyer/home3.htm
Jim Carr
thoma...@aol.com (ThomasL283) writes:
>
> ... Dirac got the same numbers by doing some funny postulating.
This might explain Thomas' view of how theories are derived.
> ... Yu. A. Alexandrov in his book
>"Fundamental Properties of the Neutron" page 168, quote:
>
>"A qualitative picture is as follows:
^^^^^^^^^^^^^^^^^^^
You should not rely on a qualitative description for quantitative
results such as the prediction of Dirac's theory and QED (which
are not the same thing) for the electron form factor.
--
James A. Carr <j...@scri.fsu.edu> | "What are those, Daddy?"
http://www.scri.fsu.edu/~jac/ | Young girl at Smithsonian
Supercomputer Computations Res. Inst. | exhibit of objects and letters
Florida State, Tallahassee FL 32306 | left at the Vietnam Memorial.
sing...@teleport.com
:| They also show a size that is in huge disagreement with the data
:| for electron-electron and electron-positron scattering.
:
:loc...@svpal.svpal.org (Thomas Lockyer) writes:
:>
:>Jim: The models have the exact size of the *electron's* rationalized
:>Compton wavelength.
:
: I know. That is why your models are wrong.
:
: The data for electron-electron and electron-positron scattering
: clearly show that the electron is much smaller than that.
Jim, correct me please but it seems that you are invoking a 'size' for an
electron when QM actually posits nonzero probability of aspects of the
electron even light years away from what might be called the 'center' of
the particle. To establish that an electron is any 'size' at all implies
a geometry associated with it, wouldn't you agree? Why is it that the
geometry is not immediately evident to you? I mean one easily can
understand that a sphere would be inappropriate just because it doesn't
provide all the geometry necessary to express all the physical attributes
of an electron. The correct geometry is evident to me but I'm confident
that it is not evident at all to you or you would never have let the
conversation progress in the direction it has.
Bernd Binder
sing...@teleport.com wrote:
>
> In article <5itbot$j...@news.fsu.edu>, j...@ibms48.scri.fsu.edu (Jim Carr) wrote:
>
> :| They also show a size that is in huge disagreement with the data
> :| for electron-electron and electron-positron scattering.
> :
> :loc...@svpal.svpal.org (Thomas Lockyer) writes:
> :>
> :>Jim: The models have the exact size of the *electron's* rationalized
> :>Compton wavelength.
> :
> : I know. That is why your models are wrong.
> :
> : The data for electron-electron and electron-positron scattering
> : clearly show that the electron is much smaller than that.
>
> electron even light years away from what might be called the 'center' of
> the particle. To establish that an electron is any 'size' at all implies
> a geometry associated with it, wouldn't you agree? Why is it that the
> geometry is not immediately evident to you?
Dear Sirs:
Is a 'size' necessary to express all the physical
attributes of an electron?
Again: please don't confuse spatial distribution
(resulting in an effective radius) and geometry!
(Anomalous g-factor experts where are you?)
Bernd Binder
Jim Carr
j...@ibms48.scri.fsu.edu (Jim Carr) wrote:
:
:| They also show a size that is in huge disagreement with the data
:| for electron-electron and electron-positron scattering.
:
:loc...@svpal.svpal.org (Thomas Lockyer) writes:
:>
:>Jim: The models have the exact size of the *electron's* rationalized
:>Compton wavelength.
:
: I know. That is why your models are wrong.
:
: The data for electron-electron and electron-positron scattering
: clearly show that the electron is much smaller than that.
sing...@teleport.com writes:
>
>Jim, correct me please but it seems that you are invoking a 'size' for an
>electron when QM actually posits nonzero probability of aspects of the
>electron even light years away from what might be called the 'center' of
>the particle.
Lockyer postulates a size.
The way in which this is looked for in experimental data is to
calculate the angular distribution expected for the scattering
of point charged particles from one another and compare this to
the data. For electron scattering, this works out so you can
just divide the two of them and get a "form factor" that is a
function of momentum transfer -- and just the bessel transform
of the radial charge distribution. A size (rms radius) shows
up as the slope near the origin. [This description is in the
language of a non-relativistic reduction that we use in nuclear
physics, and which you can use to make contact with Hofstadter's
experiments, for example. A schematic description is in an Ann.
Rev. article of ours while details can be found in many places.]
If there is no structure, you get just 1, indicating a delta
function in coordinate space.
For the electron, one must be more careful since the scattering
theory itself has some interesting features. Recent experiments
have seen inside the screening effect of the vacuum polarization
charges, for example. But in the range Lockyer has in his model,
you would see deviations long *long* before then.
>To establish that an electron is any 'size' at all implies
>a geometry associated with it, wouldn't you agree?
Whatever you choose to model will show up in scattering observables.
>I mean one easily can
>understand that a sphere would be inappropriate just because it doesn't
>provide all the geometry necessary to express all the physical attributes
>of an electron.
It is easiest if you express the possible function in terms of a
multipole decomposition that isolates the possible angular dependence
(expanded in Y_J's) times simple functions that can themselves be
defined in terms of a model independent expansion or calculated
from a model.
rsansbury
>
> It is easiest if you express the possible function in terms of a
> multipole decomposition that isolates the possible angular dependence
> (expanded in Y_J's) times simple functions that can themselves be
> defined in terms of a model independent expansion or calculated
> from a model.
>
thing,the electron changes in size ad shape depending on temperature and
surrounding electric and magnetic fields. Let me explain by quoting the
best book on the subject "Another consideration is that charge
polarization inside electrons and nuclei has been shown not to exist
after their spin, that is their magnetic aspect, has been allowed
for;.but of course if we interpret spin as charge polarization then this
difficulty vanishes. (see The electric dipole moment of the cesium
atom,a new upper limit to the electric dipole moment.Weiskopf , M.C.,
Carrico, Gould ,Lipworth and Stein, Physical Review Letters
1968,vol21,p1645). We will show later that spin can be so interpreted and
that the concept of spin is an unnecessary circumlocution to avoid
directly stating the existence of a mass orbiting a central point in any
circle on an imaginary sphere of radius about 10^-15 meters moving as a
spinning surface would have to move at velocities in excess of the speed
of light.
A further advantage of regarding spin as electrostatic dipoles is that
the evidence, from the emission spectra of ammonia, for nuclear
quadropoles as part of the nuclear force of N14 in addition to the point
charge or Coloumb force can be more systematically represented as the
uninterrupted Taylor expansion of the potential of an unknown
distribution of charge inside the nucleus up to the third terms (see
Coles and Good in the Physical Review of 1946). That is we do not have to
throw out the dipole term in the Taylor expansion.
Quantum theory offers no explanation of the lack of radiation from the
ground state orbits of atoms or the quasi stable excited orbits,
transitions between which produce the familiar radiation of atomic
emission spectra. The proposed premise as will be discussed later in
connection with Maxwell's theory requires some freedom in the movement of
free electrons in antennas and loosely bound electrical charge in
molecules whose oscillation produces and comprises the receiving of, the
radiation of light; such freedom does not occur with completely bound
electrons except in the transitional states involved in the emission of
spectra. Also completely bound orbital electrons in randomly oriented
orbits can exert constantly changing electrostatic forces that half of
the time increase and half of the time oppose the similar motions of
adjacent orbitals so that there is no radiation loss.
Another implication of the proposed premise is that the apparent
increase in the mass of a particle with its velocity is due to an
inelastic decrease in the rate of increased charge polarization and so
magnetic responsiveness of the moving particle as the elastic limit-the
velocity of light- is approached. This is shown to be a an equally valid
interpretation of Kaufmann's demonstration in 1903 of the effect of a
crossed electric field and magnetic field at right angles to one another
on beta electrons ejected from a radium nucleus at velocities near the
speed of light. The faster of the already fast electrons should have been
more deflected by the magnetic field than they were. That they were not
can be ascribed to an increase in the inertial mass of the beta electrons
to infinity or to a decrease in its rate of increase in responsiveness to
a magnetic field as its finite limit of elasticity is approached. If the
latter interpretation is assumed, the corallary of course is that the
conservation of matter principle Lavosier used so successfully in a. 1770
to infer the chemical combinations of the elements need not be revised
into a conservation or transformation principle of mass-energy. Such an
ambiguous principle extant in 1770 might have prevented Lavosier's
discoveries."
and
"Suppose for example that a sustained voltage difference producing a
current also acts on a mass m* of charge q inside the nucleus or
electron with a force qE and that this force is directed from left to
right along a horizontal X axis on the counter-clockwise orbiting
particle m* for a time 10^-14sec = t* between thermal collisions as
described above. What is the net force F acting on q that can produce the
desired ellipse?
The general equation for the velocity, v, of a particle of mass, m,
subject to an inverse square force kR^-2 at some particular point in its
path at a distance, R, from the source of the inverse square force and at
an angle a* from a specified line is (mR^2)(v^2/kR) =1+e*cosa* where e*
denotes the eccentricity of the particles path. For the electrostatic
force, in newtons, between two electrons of charge e, in coulombs,
k=(9)(10^9)(e^2) while for the gravitational force in Newtons between two
masses m and M in kilograms k=(6.67)(10^-11)Mm Thus in the electrostatic
case v^2= (9)(10^9)(e^2)(1+e*)/mR where m here denotes the electron mass.
This equation is derived in some form in most mechanics texts; see for
example, Dynamics, by W.E. Williams, Van Nostrand 1975 p41.
We must take into account the central force projected on the X axis
which acts half of the time in the same direction, half the time in the
opposite direction as the exterior force; thus:(qEą(9)(10^9)(q^2) /R^2) =
F= (10^-19)(E) ą (9)(10^(9-38+30+15x)). We assume at room temperature R
is the classical electron radius R= (9)(10^9)e^2/mc^2 = (2.82)10^-15
meters that is F=qEą(c^2)(x) approximately; here we are denoting the
mass of the electron by m and the much smaller mass of a charged particle
inside the electron or the nucleus by m*; hence the velocity of light, c,
can be regarded also as a measure of the elasticity of charge
polarization within electrons and nuclei. Ft*/2m* = v1-v = v0(1+e*)^1/2
- v0 which equals v0e*/2 according to the binomial approximation.
Note v0^2/R = (9)(10^9)(2.56)(10^-38)/(R^2)(m*) for a circular orbit
so v0=(2.9)(10^-7)/m*^1/2 where m* must be very small. For example
suppose E=(4.5)(10^-3)V/meter so that the velocity of the electron,
v=(2.46)10^-4 meters/sec and that r= 10^-1 meters so that
rv/c*=(2.46/3)10^(-1-4-8) meters =(e*/(1-e*))R; then e*=.99. Since qE is
10^-19-3 Newtons about compared to a centripetal force of
(9)(10^9)(q^2)/(R^2) =10^2 newtons, the force F needed to cause an
elliptical distortion of the circular orbit is only strong enough half
of the time between thermal collisions when it is not opposed by the
central force. During half of this time i.e a quarter of the time the
exterior force acts to slow down the orbiting mass, m*, and a quarter of
the time it acts to speed up m*. Such a combination of forces acting
continuously over time is clearly equivalent to another single force
acting at a single instant tangential to the orbiting mass. The effect
of such equivalent forces is to produce an elliptical distortion of the
circular orbit of eccentricity e* such that the major axis of the
produced ellipse is perpendicular to a specific tangential force. That is
eEt/m*= e*v0/2 approximately. The reason for "approximately" is that we
know that the combination of decreases and increases in v0 that leads to
the elliptical distortion due to E is equal to the ellipticity produced
by a continual increase in v0 due to approximately the same value of E.
In the above example, the ellipticity is .99 and so eEt/m* = .99v0/2
=(.99/2)(2.9)(10^-7/(m*^1/2); eEt*=(1.602)(10^-19)(4.5)(10^-3)(10^-14) =
(7.2)(10-36). Hence (7.2)(10-36) = (.5)(2.9)(10^-7)(m*^1/2) which
implies that approximately m*=[(4.8)10^-29]^2=(10^-56.4) kg., v0 = 10^22
meters/sec; the escape velocity kinetic energy is .7(10^-12) Joules or
7MeV according to various texts e.g. Richtmyer "the threshold for pair
formation is E*=2mc^2 =1.022 MeV [where E* denotes the total energy, m,
denotes the rest mass of an electron and c, the speed of light]". Hence
pair production provides independent support for this model if we allow
such enormous speeds are possible.(note if rv/c=10^-11 then e*=10^-4 and
so E* must have become large enough to compensate for the reduction in
t*, the time between collisions. The time between collisions associated
with the dipole parameter e*=.99 has determined the estimate of m*
There are problems with this analysis. One, we have accepted a
10^-14 sec. interval between collisions of free electrons and lattice
ions. The force of these thermal collisions -according to kinetic theory
(3/2)kT=1/2 mv^2 where k= 1.38(10^-23 ) Joules per degree Kelvin -
produces velocities of 10^5 meters/sec for free electrons (and smaller
recoil velocities for the heavier lattice ions.), an order of magnitude
less than the outer orbital electron velocities of atoms and so forces
that are much greater than the drift velocity forces. Hence they should
produce greater ellipsoids which results in what we have assumed to be a
sphere of radius equal to the classical electron radius. ( Acording to
Sommerfeld's modification of the kinetic theory applied to nearly free
electrons in a conductor, the force of thermal collisions produces
velocities of 10^6 meters per second)
Hence the radius of the electron in the context of lower
temperatures and lower thermal velocities should be much smaller and our
assumption of the radius of a sphere might be modified to be of a
classical electron elliptical semimajor axis of 10^-15 m.. for free
electrons between thermal collisions at room temperature and less at
lower temperatures. However since the average thermal velocity is zero
so is the average thermal dipole. So in this sense the average ellipsoid
is a sphere of radius 10^-15 meters.
Another problem is the enormous speeds assumed. As stated above a
reinterpretation of the Kaufmann experiment suggests that mass does not
increase to infinity as the speed of light is approached. Rather there is
a decreasing rate of responsiveness of a rapidly moving charged mass to a
magnetic field and then at the speed of light an expulsion of the even
smaller charged mass orbiting inside the rapidly moving charged mass.
The elliptical distortion of this orbit is the cause of the
responsiveness of the larger charged mass to a magnetic field. Unless
the expelled smaller charged mass is captured by an oppositely charged
particle it could travel the length of the 28 known galaxies a distance
of 2.5 million light years since one light year is 9.4698 times
10^15meters and since there are 3.1536 times 10^7 seconds in a year.
The occurrence of such trajectories imply that there has occured the
splitting of an electron, a positron or an electron-sized neutral
particle inside an atomic nucleus. Note pair production as well as beta
emission seems always to occur in the vicinity of an atomic nucleus"
Ralph Sansbury
Jim Carr
| It is easiest if you express the possible function in terms of a
| multipole decomposition that isolates the possible angular dependence
| (expanded in Y_J's) times simple functions that can themselves be
| defined in terms of a model independent expansion or calculated
| from a model.
rsansbury <r...@concentric.net> writes:
>
> Scattering experiments and multipole assumptions are inadequate; For one
>thing,the electron changes in size ad shape depending on temperature and
>surrounding electric and magnetic fields.
In what way would a multipole expansion fail to characterize the
result of scattering within such a model? Indeed, what it would
provide is a specific temperature and field-dependent strucutre
function for each multipole. All the multipole expansion assumes
is that angular momentum is conserved. You are even free to insert
your own favorite interaction when calculating the cross section,
before comparing it to the Mott cross section.
> Let me explain by quoting the
>best book on the subject
Your book?
> "Another consideration is that charge
>polarization inside electrons and nuclei has been shown not to exist
>after their spin, that is their magnetic aspect, has been allowed
>for;.but of course if we interpret spin as charge polarization then this
>difficulty vanishes. (see The electric dipole moment of the cesium
>atom,a new upper limit to the electric dipole moment.Weiskopf , M.C.,
>Carrico, Gould ,Lipworth and Stein, Physical Review Letters
>1968,vol21,p1645).
Is that quote from Weiskopf or you? You use the citation as if it
indicates the Weiskopf et al established that one can interpret
spin as charge polarization but I doubt he would confuse magnetic
and electric dipole effects.
In contradiction to your assertion, by the way, I see that your
discussion makes explicit and repeated use of multipoles:
> A further advantage of regarding spin as electrostatic dipoles is that
^^^^^^^
>the evidence, from the emission spectra of ammonia, for nuclear
>quadropoles as part of the nuclear force of N14 in addition to the point
^^^^^^^^^^^
>charge or Coloumb force can be more systematically represented as the
>uninterrupted Taylor expansion of the potential of an unknown ...
^^^^^^^^^
In what way does your use of mulitipole expansions show they
are inadequate, as you claim above? I also saw no indication in
the omitted text of any proposed alternative to scattering or
other observations of an atom as a test of your model, or any
model for that matter.
rsansbury
j...@ibms46.scri.fsu.edu (Jim Carr) wrote:
>
>
> Is that quote from Weiskopf or you? You use the citation as if it
> indicates the Weiskopf et al established that one can interpret
> spin as charge polarization but I doubt he would confuse magnetic
> and electric dipole effects.
>
only after allowing that spin exists. The idea here is that spin is an
awkward approximation of electrostatic dipole.
> In contradiction to your assertion, by the way, I see that your
> discussion makes explicit and repeated use of multipoles:
>
Yes but not in the standard meaning which excludes, mistakenly the
dipole term in the multipole expansion as explained in the paragraph you
quote elliptically
>> A further advantage of regarding spin as electrostatic dipoles is
that
> ^^^^^^^
>>the evidence, from the emission spectra of ammonia, for nuclear
>>quadropoles as part of the nuclear force of N14 in addition to the point
> ^^^^^^^^^^^
>>charge or Coloumb force can be more systematically represented as the
>>uninterrupted Taylor expansion of the potential of an unknown ...
> ^^^^^^^^^
>
>
Ralph Sansbury
Jim Carr
j...@ibms46.scri.fsu.edu (Jim Carr) wrote:
|
| Is that quote from Weiskopf or you? You use the citation as if it
| indicates the Weiskopf et al established that one can interpret
| spin as charge polarization but I doubt he would confuse magnetic
| and electric dipole effects.
rsansbury <r...@concentric.net> writes:
>
> No Weiskopf says that there is no electrostatic dipole but implicitly
>only after allowing that spin exists. The idea here is that spin is an
>awkward approximation of electrostatic dipole.
OK. Just want to be clear on that.
| In contradiction to your assertion, by the way, I see that your
| discussion makes explicit and repeated use of multipoles:
> Yes but not in the standard meaning which excludes, mistakenly the
>dipole term in the multipole expansion as explained in the paragraph you
>quote elliptically
Then I think you do not know what the standard meaning is. Any
multipole expansion is silent on the physics other than the
assumption about the rotational properties of space.
Weiskopf did not *omit* the dipole term, he showed it was small.
His was not the last work on the subject if the PDG tables are
any indication of the state of the field -- which they are.
You job is to show that you can explain the data as well, and
your data set includes a number of polarization observables that
complicate your quest.
To repeat the annotated elliptic quote (I like that):
| > ... or Coloumb force can be more systematically represented as the
| >uninterrupted Taylor expansion of the potential of an unknown ...
| ^^^^^^^^^
This is not quite what a multipole expansion is, because you do not
treat the angle dependence with the Y.Y terms, but that is the idea.
The coefficients are unknowns that you fit to the data. The only
biases are in the data and the termination of the L series, both
of which are usually tested.