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<p><font size="-1">Hi Chip, hi All,<br>
</font></p>
<p><font size="-1">the problem of the limitation of the internal
speed in the electron is not complicated. It is the cause if
relativistic dilation.</font></p>
<p><font size="-1">If an electron is a particle which is built by
something which permanently orbits at c, then in case of the
motion of the electron, this internal speed will continue to be
c with respect to the external frame. If now the electron moves
into an axial direction with respect to the orbit at speed v
then the circular motion will turn into a helical motion. If the
motion on the helix is still c then the period T of this motion
will be reduced to some T' as given by Pythagoras: T' = T *
sqrt(1/(1--v<sup>2</sup>/c<sup>2</sup>)), which by the way is
the Lorentz factor of SRT.</font></p>
<p><font size="-1">If the electron moves into an arbitrary direction
with respect to the orbit, then the calculation of more
complicated but has the same result. I can give it if there is a
demand.<br>
</font></p>
<p><font size="-1">To the radius of the electron itself (and I must
apologize that I did not fully follow the preceding discussion:</font></p>
<p><font size="-1">If the elementary charge e<sub>0</sub> in the
electron orbits at c then the magnetic moment of the electron is
classically µ = i*pi*R<sup>2</sup> where we insert for the
current i = e<sub>0</sub> * c/(2pi*R) . Then we get µ = c * e<sub>0</sub>*
R/2 . Now we can use the known value of the magnetic moment µ to
determine the radius R. The result of this is R = 3.86 * 10<sup>-13</sup>
m. <br>
</font></p>
<p><font size="-1">This result is in conflict with main stream as
the official physics says that the electron is point-like
(R<10<sup>-18 </sup>m). But it is in agreement with Erwin
Schrödinger. In his famous paper in which Schrödinger evaluated
the Dirac function, his result for the "size of the electron"
was "roughly about" R = 4 * 10<sup>-13</sup> m. Schrödinger came
to this result by pure QM considerations. And then he makes a
funny statement. He says in his paper: "We know that the
electron is point-like. So, there must be an error in my
calculation. But I cannot find this error". - I think that not
Schrödinger was in error but main stream is in error. And this
early result of Schrödinger confirms the classical calculation
which I have shown above.</font></p>
<p><font size="-1">Does this help the discussion?</font></p>
<p><font size="-1">Albrecht</font><br>
<br>
</p>
<div class="moz-cite-prefix">Am 09.01.2017 um 19:10 schrieb Chip
Akins:<br>
</div>
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<p class="MsoNormal"><span style="color:black">Hi All<o:p></o:p></span></p>
<p class="MsoNormal"><span style="color:black"><o:p> </o:p></span></p>
<p class="MsoNormal"><span style="color:black">For those of yoµu
who hold the hard line that nothing can move faster than c
(a common interpretation of SR) the following is a bit of
speculation.<o:p></o:p></span></p>
<p class="MsoNormal"><span style="color:black"><o:p> </o:p></span></p>
<p class="MsoNormal"><span style="color:black">If the energy
within the electron is all circulating at c, and the
electron is an extended particle, then the field lines might
look something like the following illustration
<o:p></o:p></span></p>
<p class="MsoNormal"><!--[if gte vml 1]><v:shapetype id="_x0000_t75" coordsize="21600,21600" o:spt="75" o:preferrelative="t" path="m@4@5l@4@11@9@11@9@5xe" filled="f" stroked="f">
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<v:imagedata src="mailbox:///C:/Users/AL/AppData/Roaming/Thunderbird/Profiles/lthhzma2.default/Mail/pop3.strato-7.de/Inbox?number=270185650&header=quotebody&part=1.1.2&filename=image001.png" o:title="" />
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v:shapes="Picture_x0020_1" height="166" hspace="12"
align="left" width="175"><!--[endif]--><span
style="color:black"><o:p></o:p></span></p>
<p class="MsoNormal"><span style="color:black"><o:p> </o:p></span></p>
<p class="MsoNormal"><span style="color:black"><o:p> </o:p></span></p>
<p class="MsoNormal"><span style="color:black"><o:p> </o:p></span></p>
<p class="MsoNormal"><span style="color:black"><o:p> </o:p></span></p>
<p class="MsoNormal"><span style="color:black"><o:p> </o:p></span></p>
<p class="MsoNormal"><span style="color:black"><o:p> </o:p></span></p>
<p class="MsoNormal"><span style="color:black"><o:p> </o:p></span></p>
<p class="MsoNormal"><span style="color:black"><o:p> </o:p></span></p>
<p class="MsoNormal"><span style="color:black"><o:p> </o:p></span></p>
<p class="MsoNormal"><span style="color:black">At any rate, the
field lines would spiral outward from the center, moving at
c at all points.<o:p></o:p></span></p>
<p class="MsoNormal"><span style="color:black"><o:p> </o:p></span></p>
<p class="MsoNormal"><span style="color:black">This structure
would not exhibit a specific frequency, or a finite set of
frequencies, but would contain any frequency one might
choose. So unless we can conceive of some mechanism which
would only make certain frequencies visible, or some
boundary conditions which would constrain the energy to a
specific radius. Then this approach is not useful in
discovering the electrons mysteries.<o:p></o:p></span></p>
<p class="MsoNormal"><span style="color:black"><o:p> </o:p></span></p>
<p class="MsoNormal"><span style="color:black">In fact, if a
photon, or an EM wave if you prefer, can have a spin of
hbar, and has a momentum of <i>p=E/c</i>, then the radius
of action of this wave is <i>r = hbar/momentum</i>. Such a
wave then must have a transverse displacement velocity of at
least 3.489 times <i>c</i> in order for the wave to exist
in this form. Also, the internal wavefront must be moving at
the <i>sqrt(2) c. </i>So I think it must be that some
things simply move faster than <i>c </i>as John Stewart
Bell suggested. A more Lorentzian form of relativity.<o:p></o:p></span></p>
<p class="MsoNormal"><span style="color:black"><o:p> </o:p></span></p>
<p class="MsoNormal"><span style="color:black">Chip<o:p></o:p></span></p>
<p class="MsoNormal"><span style="color:black"><o:p> </o:p></span></p>
<div>
<div style="border:none;border-top:solid #E1E1E1
1.0pt;padding:3.0pt 0in 0in 0in">
<p class="MsoNormal"><b><span
style="font-size:11.0pt;font-family:"Calibri",sans-serif">From:</span></b><span
style="font-size:11.0pt;font-family:"Calibri",sans-serif">
General
[<a class="moz-txt-link-freetext" href="mailto:general-bounces+chipakins=gmail.com@lists.natureoflightandparticles.org">mailto:general-bounces+chipakins=gmail.com@lists.natureoflightandparticles.org</a>]
<b>On Behalf Of </b>Dr Grahame Blackwell<br>
<b>Sent:</b> Sunday, January 08, 2017 4:10 PM<br>
<b>To:</b> Nature of Light and Particles - General
Discussion
<a class="moz-txt-link-rfc2396E" href="mailto:general@lists.natureoflightandparticles.org"><general@lists.natureoflightandparticles.org></a><br>
<b>Subject:</b> Re: [General] On particle radius<o:p></o:p></span></p>
</div>
</div>
<p class="MsoNormal"><o:p> </o:p></p>
<div>
<p class="MsoNormal"><span
style="font-size:10.0pt;font-family:"Arial",sans-serif;color:navy">Hi
Chip,</span><o:p></o:p></p>
</div>
<div>
<p class="MsoNormal"> <o:p></o:p></p>
</div>
<div>
<p class="MsoNormal"><span
style="font-size:10.0pt;font-family:"Arial",sans-serif;color:navy">Many
thanks indeed for your succinct and well-presented case
('succinct' is clearly a useful word in this discussion -
as well as a good strategy!).</span><o:p></o:p></p>
</div>
<div>
<p class="MsoNormal"><span
style="font-size:10.0pt;font-family:"Arial",sans-serif;color:navy">I
need to go through this carefully and thoroughly and see
how it relates to my own understanding of the situation.
As we're all agreed, we all have things to learn from each
other and (here I DO agree with Vivian's metaphor) each
have some aspect of the elephant (in the room?) to
contribute. I'm really looking forward to considering
what you've said below and hopefully assimilating it into
a fuller understanding on my own part of the issues that
need to be taken into consideration.</span><o:p></o:p></p>
</div>
<div>
<p class="MsoNormal"> <o:p></o:p></p>
</div>
<div>
<p class="MsoNormal"><span
style="font-size:10.0pt;font-family:"Arial",sans-serif;color:navy">I'll
come back to you when I've processed it thoroughly (may
take a few days) and have some thoughts to offer.</span><o:p></o:p></p>
</div>
<div>
<p class="MsoNormal"> <o:p></o:p></p>
</div>
<div>
<p class="MsoNormal"><span
style="font-size:10.0pt;font-family:"Arial",sans-serif;color:navy">Thanks
again,</span><o:p></o:p></p>
</div>
<div>
<p class="MsoNormal"><span
style="font-size:10.0pt;font-family:"Arial",sans-serif;color:navy">Grahame</span><o:p></o:p></p>
</div>
<blockquote style="border:none;border-left:solid navy
1.5pt;padding:0in 0in 0in
4.0pt;margin-left:3.75pt;margin-top:5.0pt;margin-right:0in;margin-bottom:5.0pt">
<div>
<p class="MsoNormal"><span
style="font-size:10.0pt;font-family:"Arial",sans-serif">-----
Original Message ----- <o:p></o:p></span></p>
</div>
<div>
<p class="MsoNormal" style="background:#E4E4E4"><b><span
style="font-size:10.0pt;font-family:"Arial",sans-serif">From:</span></b><span
style="font-size:10.0pt;font-family:"Arial",sans-serif"> <a
moz-do-not-send="true"
href="mailto:chipakins@gmail.com"
title="chipakins@gmail.com">Chip Akins</a> <o:p></o:p></span></p>
</div>
<div>
<p class="MsoNormal"><b><span
style="font-size:10.0pt;font-family:"Arial",sans-serif">To:</span></b><span
style="font-size:10.0pt;font-family:"Arial",sans-serif"> <a
moz-do-not-send="true"
href="mailto:general@lists.natureoflightandparticles.org"
title="general@lists.natureoflightandparticles.org">'Nature
of Light and Particles - General Discussion'</a> <o:p></o:p></span></p>
</div>
<div>
<p class="MsoNormal"><b><span
style="font-size:10.0pt;font-family:"Arial",sans-serif">Sent:</span></b><span
style="font-size:10.0pt;font-family:"Arial",sans-serif">
Sunday, January 08, 2017 9:22 PM<o:p></o:p></span></p>
</div>
<div>
<p class="MsoNormal"><b><span
style="font-size:10.0pt;font-family:"Arial",sans-serif">Subject:</span></b><span
style="font-size:10.0pt;font-family:"Arial",sans-serif"> Re:
[General] On particle radius<o:p></o:p></span></p>
</div>
<div>
<p class="MsoNormal"><o:p> </o:p></p>
</div>
<p class="MsoNormal"><span style="color:black" lang="EN-GB">Hi
Dr Graham Blackwell<o:p></o:p></span></p>
<p class="MsoNormal"><span style="color:black"><o:p> </o:p></span></p>
<p class="MsoNormal"><span style="color:black">I like the way
you clearly and succinctly write.<o:p></o:p></span></p>
<p class="MsoNormal"><span style="color:black"><o:p> </o:p></span></p>
<p class="MsoNormal"><span style="color:black">Let me explain
some of the reasons why I feel the radius of the electron
decreases with velocity.<o:p></o:p></span></p>
<p class="MsoNormal"><span style="color:black"><o:p> </o:p></span></p>
<p class="MsoNormal"><span style="color:black">In order to
accelerate the electron at rest, we must apply energy
(force through distance).<o:p></o:p></span></p>
<p class="MsoNormal"><span style="color:black">The only way to
apply energy to the electron, when we get down to the
basis, is to add energy to its existing confined wave
structure. Plancks rule suggests that this confined wave
structure with energy added has a wavelength which is (h
c)/E. If this is the case and the momentum of this wave
remains p=E/c, then in order to be a spin ½ hbar particle,
it seems the electron must have a radius which is r = (h
c)/(4 pi E). Where E is the new total energy with velocity
throughout this paragraph.<o:p></o:p></span></p>
<p class="MsoNormal"><span style="color:black"><o:p> </o:p></span></p>
<p class="MsoNormal"><span style="color:black">Then when we
calculate the mass of this particle from its confined
momentum (as Richard has pointed out) we get the expected
relativistic (total) mass of the moving particle. m = E/(r
w c) = E/c^2= E Eo Uo. Which is exactly equivalent to m =
y m. [where w = c/r (angular frequency)].<o:p></o:p></span></p>
<p class="MsoNormal"><span style="color:black"><o:p> </o:p></span></p>
<p class="MsoNormal"><span style="color:black">This is the
only scenario I have found where all of the expected
parameters are accommodated, and I have searched
extensively for other possibilities.<o:p></o:p></span></p>
<p class="MsoNormal"><span style="color:black"><o:p> </o:p></span></p>
<p class="MsoNormal"><span style="color:black">We also note
that the scattering cross-section of an electron at
relativistic velocities is very small, and agrees with
these assumptions quite well.<o:p></o:p></span></p>
<p class="MsoNormal"><span style="color:black"><o:p> </o:p></span></p>
<p class="MsoNormal"><span style="color:black">In order for
the electron radius to remain the same size with velocity
I think we have to ignore things which seem quite
important, and these specific things appear to be required
in order to tie several of the pieces of the puzzle
together. It seems the picture is just not complete unless
the radius of the electron is reduced with velocity.<o:p></o:p></span></p>
<p class="MsoNormal"><span style="color:black"><o:p> </o:p></span></p>
<p class="MsoNormal"><span style="color:black">Thoughts?<o:p></o:p></span></p>
<p class="MsoNormal"><span style="color:black"><o:p> </o:p></span></p>
<p class="MsoNormal"><span style="color:black">Chip<o:p></o:p></span></p>
<p class="MsoNormal"><span style="color:black"><o:p> </o:p></span></p>
</blockquote>
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