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<DIV><FONT color=#000080 size=2 face=Arial>Just realised that my reply only went
to Richard.</FONT></DIV>
<DIV><FONT color=#000080 size=2 face=Arial>Since his response went to all, some
may find my reply of interest.</FONT></DIV>
<DIV><FONT color=#000080 size=2 face=Arial></FONT> </DIV>
<DIV><FONT color=#000080 size=2 face=Arial>Best regards,</FONT></DIV>
<DIV><FONT color=#000080 size=2 face=Arial>Grahame</FONT></DIV>
<DIV><FONT color=#000080 size=2 face=Arial></FONT> </DIV>
<DIV><FONT color=#000080 size=2 face=Arial>===========</FONT></DIV>
<DIV><FONT color=#000080 size=2 face=Arial></FONT> </DIV>
<DIV style="FONT: 10pt arial">----- Original Message -----
<DIV style="BACKGROUND: #e4e4e4; font-color: black"><B>From:</B> <A
title=grahame@starweave.com href="mailto:grahame@starweave.com">Dr Grahame
Blackwell</A> </DIV>
<DIV><B>To:</B> <A title=richgauthier@gmail.com
href="mailto:richgauthier@gmail.com">Richard Gauthier</A> </DIV>
<DIV><B>Sent:</B> Monday, January 09, 2017 1:30 PM</DIV>
<DIV><B>Subject:</B> Re: [General] On particle radius</DIV></DIV>
<DIV><BR></DIV>
<DIV><FONT color=#000080 size=2 face=Arial>Hi Richard and all,</FONT></DIV>
<DIV><FONT color=#000080 size=2 face=Arial></FONT> </DIV>
<DIV><FONT color=#000080 size=2 face=Arial>Thanks for your detailed response,
most of which seems to be a re-run of your reasoning that you've presented
before rather than relating to my specific question (more on that below).
As with Chip's comments, I'll study this with interest in the light of my own
findings and understanding.</FONT></DIV>
<DIV><FONT color=#000080 size=2 face=Arial></FONT> </DIV>
<DIV><FONT color=#000080 size=2 face=Arial>With regard to my 'aperture'
question/thought-experiment: I agree completely that of course there's a
probabilistic element to passage of the electron through the gap - that's a good
point that you make. Unfortunately it doesn't do anything to reduce the
significance of my argument.</FONT></DIV>
<DIV><FONT color=#000080 size=2 face=Arial></FONT> </DIV>
<DIV><FONT color=#000080 size=2 face=Arial>In your final para you observe: "
<FONT color=#000000 size=3 face="Times New Roman">I think one would find a
higher probability of finding fast-moving (v=0.9c) electrons on the other
side of a small enough aperture as compared to the probability of finding
slow-moving (v=0.1c) electrons on the other side of the same small
aperture</FONT>"; on this we are agreed (if we accept the premise of reduced
particle size with speed - which I don't, but we'll run with that here).
If, in accordance with SR principles, we now shift to the perspective of the
electron's rest-frame, what we get is static electrons having a higher
probability of passing through a fast-moving orifice than they do of passing
through that orifice when it's moving more slowly. How do you explain
that, if it's not by virtue of that orifice increasing in size with increasing
speed? Probabilities don't simply change without circumstances changing,
and this appears to be the only credible explanation for such
variation.</FONT></DIV>
<DIV><FONT color=#000080 size=2 face=Arial></FONT> </DIV>
<DIV><FONT color=#000080 size=2 face=Arial>So I'm still waiting for the
explanation as to why that aperture increases in size with increasing speed,
which appears to be a necessary condition for satisfaction of SR reciprocity of
reference frames (without which SR breaks down). [If you have an
alternative explanation for probability of passage of static electrons through
an orifice varying in this way with speed of motion of that orifice, then of
course that would be of interest.]</FONT></DIV>
<DIV><FONT color=#000080 size=2 face=Arial></FONT> </DIV>
<DIV><FONT color=#000080 size=2 face=Arial>Best regards,</FONT></DIV>
<DIV><FONT color=#000080 size=2 face=Arial>Grahame</FONT></DIV>
<BLOCKQUOTE
style="BORDER-LEFT: #000080 2px solid; PADDING-LEFT: 5px; PADDING-RIGHT: 0px; MARGIN-LEFT: 5px; MARGIN-RIGHT: 0px">
<DIV style="FONT: 10pt arial">----- Original Message ----- </DIV>
<DIV
style="FONT: 10pt arial; BACKGROUND: #e4e4e4; font-color: black"><B>From:</B>
<A title=richgauthier@gmail.com href="mailto:richgauthier@gmail.com">Richard
Gauthier</A> </DIV>
<DIV style="FONT: 10pt arial"><B>To:</B> <A
title=general@lists.natureoflightandparticles.org
href="mailto:general@lists.natureoflightandparticles.org">Nature of Light and
Particles - General Discussion</A> ; <A title=grahame@starweave.com
href="mailto:grahame@starweave.com">Dr Grahame Blackwell</A> </DIV>
<DIV style="FONT: 10pt arial"><B>Sent:</B> Monday, January 09, 2017 6:26
AM</DIV>
<DIV style="FONT: 10pt arial"><B>Subject:</B> Re: [General] On particle
radius</DIV>
<DIV><BR></DIV>
<DIV>Hi Grahame and all,</DIV>
<DIV><BR></DIV>
<DIV> Thanks for your question about how I justify the reduced
transverse radius of the helical trajectory of the charged photon model with
velocity as R=Ro/gamma^2, where Ro=hbar/2mc (See below for the aperture
question.) All electron modelers need to keep in mind the experimentally
determined maximum size of the electron of about 10^-18 m as measured in high
energy electron-electron scattering experiments (at about 30GeV). The
R=Ro/gamma^2 result above for the trajectory radius of the spin 1/2 charged
photon, when added to the actual radius R1=L/4pi = Ro/gamma of my
detailed spin 1/2 charged photon model (described briefly in this forum in the
past), gives a total transverse helical radius Rtotal = Ro/gamma^2 + Ro/gamma
= Ro ( 1/gamma^2 + 1/gamma) where Ro=hbar/2mc . This total transverse
radius Rtotal of the charged photon electron model is dominated by the spin
1/2 photon's radius in high electron energy scattering to give Rtotal
-> Ro/gamma , consistent with these experimental results.</DIV>
<DIV> </DIV>
<DIV> On the theoretical side, the R=Ro/gamma^2 result is derived
from setting the circulating charged photon's energy E=hf equal to electron's
total energy formula E=gamma mc^2 and solving for the photon's wavelength
L=h/(gamma mc). This result of decreasing charged photon wavelength L with
increasing electron velocity is used together with the increasing
double-looping frequency f=2 gamma mc^2 with increasing electron
velocity of the helically double-looping photon . The result is a quantitative
geometrical helical model for the trajectory of the spin 1/2 charged photon.
The helical radius R=Ro/gamma^2 of the trajectory emerges naturally from both
the increasing double-looping frequency and the decreasing wavelength of the
spin 1/2 charged photon with increasing electron speed. I showed that this
result is also the case for Vivian’s helically-circulating-photon particle
model when it is corrected to include the decreasing wavelength of the
circulating photon associated with the particle’s increasing speed, which he
had left out of his derivation. The de Broglie wavelength L-compton = h/(gamma
mv) falls out easily from this spin 1/2 charged photon wavelength L=h/(gamma
mc) result. I don’t think John and Martin used this reduced photon-wavelength
relationship L=h/gamma mc in their 1997 electron-modeling article. You also
don’t use it in your particle model. </DIV>
<DIV><BR></DIV>
<DIV> Your circulating-photon-like object particle model maintains
a constant transverse radius as the speed (and energy) of the moving particle
increases. The frequency of helical rotation of your photon-like object
therefore actually decreases as 1/gamma with increasing particle speed.
But based on energy considerations the circulating photon frequency of a
helically-moving-photon model should INCREASE with the particle’s energy in
proportion to gamma due to E=gamma mc^2 for the total energy of a moving
particle with mass. De Broglie’s own derivation of the de Broglie wavelength
incorporated both an increasing frequency (due to increasing electron energy)
with electron speed, and also a seemingly contradictory decreasing frequency
with increasing electron speed (due to the relativistic time dilation effect.)
He rationalized both of these frequencies using his “harmony of phases”
argument. But your particle model doesn’t contain the increasing frequency
with photon energy or particle energy at all (as far as I know). We have
previously discussed the problem of your particle model’s spin at relativistic
energies. If your particle is composed of a spin 1 hbar circulating photon (or
even a spin 1/2 hbar circulating photon) , either of these spins will add to
the orbital spin of your electron model that (due to its constant radius with
increasing particle speed) remains a constant 1/2 hbar with increasing speed
of your electron model. This gives your electron model a total spin of 1 1/2
hbar or 1 hbar (depending the spin 1 or spin 1/2 of the photon model you
use) at highly relativistic velocities, which contradicts the experimental
spin 1/2 for an electron at all velocities. With my model (and Vivian’s
corrected model) the orbital contribution of spin 1/2 hbar (which is
correct for a slowly moving electron) decreases rapidly to zero (as 1/gamma^2)
at relativistic particle velocities, and the spin 1/2 of the helically
circulating photon becomes the spin 1/2 of the electron model itself at
relativistic energies.</DIV>
<DIV> </DIV>
<DIV> As for the question of whether a fast-moving (with v=0.9c)
electron can go through an aperture with a radial size that might block a
slower moving electron (with v=0.1c) , I think that one has to appeal to the
photon-like quantum wave nature of the electron to answer the question. My
charged-photon electron model is proposed to generate de Broglie wavelength
quantum waves in its longitudinal direction of motion that would interact with
an aperture or slit (or 2 slits) and predict (by quantum wave diffraction and
interference effects) the probability of detecting electrons at a screen on
the other side of the aperture, whether for slow moving electrons or for fast
moving electrons. Moving electrons are not like wooden pegs that one tries to
fit through various hole sizes relative to the size of the electron peg. But
In general I think one would find a higher probability of finding
fast-moving (v=0.9c) electrons on the other side of a small enough
aperture as compared to the probability of finding slow-moving (v=0.1c)
electrons on the other side of the same small aperture. There should be
no contradiction in this result, whether an observer is in the inertial frame
of the moving electron, or stands next to the aperture that individual
electrons are passing (or not passing) through.</DIV>
<DIV><BR></DIV>
<DIV> Richard</DIV>
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