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<P style="MARGIN: 0cm 0cm 0pt" class=MsoNormal><SPAN
style="FONT-FAMILY: Arial; COLOR: navy; FONT-SIZE: 10.5pt" lang=EN-GB>Hi Richard
(et al.),<?xml:namespace prefix = o ns =
"urn:schemas-microsoft-com:office:office" /><o:p></o:p></SPAN></P>
<P style="MARGIN: 0cm 0cm 0pt" class=MsoNormal><SPAN
style="FONT-FAMILY: Arial; COLOR: navy; FONT-SIZE: 10.5pt"
lang=EN-GB><o:p> </o:p></SPAN></P>
<P style="MARGIN: 0cm 0cm 0pt" class=MsoNormal><SPAN
style="FONT-FAMILY: Arial; COLOR: navy; FONT-SIZE: 10.5pt" lang=EN-GB>I feel I
need to address your reference to my constant-radius electron model with your
inference as to its apparently increasing spin angular momentum with increasing
velocity.<SPAN style="mso-spacerun: yes"> </SPAN>There is actually no
paradox there – in fact a clue as to the resolution of this issue is hidden in
your own candidate photon.<o:p></o:p></SPAN></P>
<P style="MARGIN: 0cm 0cm 0pt" class=MsoNormal><SPAN
style="FONT-FAMILY: Arial; COLOR: navy; FONT-SIZE: 10.5pt"
lang=EN-GB><o:p> </o:p></SPAN></P>
<P style="MARGIN: 0cm 0cm 0pt" class=MsoNormal><SPAN
style="FONT-FAMILY: Arial; COLOR: navy; FONT-SIZE: 10.5pt" lang=EN-GB>First I’d
like to query that electron model of yours, based as you say on a “spin-1/2
charged photon”.<SPAN style="mso-spacerun: yes"> </SPAN>I have no problem
with the spin-1/2 bit: as we know, the spin-1 (+ or -) characteristic of a
photon is a consequence of its own circular polarisation, clockwise or
anticlockwise.<SPAN style="mso-spacerun: yes"> </SPAN>So it follows that a
plane polarised photon, being an equal combination of + & -
circularly-polarised elements, will not exhibit any such spin; likewise an
elliptically polarised photon, consisting of unequal parts of + & -
polarisation, will somewhere between 0 and +/-1, depending on its
eccentricity.<SPAN style="mso-spacerun: yes"> </SPAN>So spin-1/2 is a
distinct possibility for a photon.<o:p></o:p></SPAN></P>
<P style="MARGIN: 0cm 0cm 0pt" class=MsoNormal><SPAN
style="FONT-FAMILY: Arial; COLOR: navy; FONT-SIZE: 10.5pt"
lang=EN-GB><o:p> </o:p></SPAN></P>
<P style="MARGIN: 0cm 0cm 0pt" class=MsoNormal><SPAN
style="FONT-FAMILY: Arial; COLOR: navy; FONT-SIZE: 10.5pt" lang=EN-GB>I’m not
clear, though, on what’s meant by a “charged photon”.<SPAN
style="mso-spacerun: yes"> </SPAN>I don’t know of any entities arising
from Maxwell’s equations that fit that term.<SPAN
style="mso-spacerun: yes"> </SPAN>Indeed, it’s increasingly apparent that
the phenomenon referred to as ‘static charge’ is itself an artefact arising from
the electromagnetic fields that form a ‘charged’ particle.<SPAN
style="mso-spacerun: yes"> </SPAN>I fully agree with John W & Martin
vdM on this* – more than that, I believe it would be pretty well impossible to
explain experimental findings showing the wavelike nature of an electron without
this being the case.<SPAN style="mso-spacerun: yes"> </SPAN>[* Also that
this formative photon must necessarily be circularly
polarised.]<o:p></o:p></SPAN></P>
<P style="MARGIN: 0cm 0cm 0pt" class=MsoNormal><SPAN
style="FONT-FAMILY: Arial; COLOR: navy; FONT-SIZE: 10.5pt"
lang=EN-GB><o:p> </o:p></SPAN></P>
<P style="MARGIN: 0cm 0cm 0pt" class=MsoNormal><SPAN
style="FONT-FAMILY: Arial; COLOR: navy; FONT-SIZE: 10.5pt" lang=EN-GB>If one
talks of a ‘charged photon’, presumably the photon itself is still an
electromagnetic construct?<SPAN style="mso-spacerun: yes"> </SPAN>In which
case we have an electromagnetic construct with an electric charge attached to it
(?) – two quite different electromagnetic constructs combined within the same
entity (if I’ve misunderstood this completely, please put me right).<SPAN
style="mso-spacerun: yes"> </SPAN>In this case, what’s the mechanism that
persuades that charge to follow the interference-guided waveform to its
destination in the Davisson/Germer experiment?<SPAN
style="mso-spacerun: yes"> </SPAN>I just can’t see how it would work, on a
number of fronts. Surel that 'charge' must itself be wave-lie - so it's
just part of the photon wave?<o:p></o:p></SPAN></P>
<P style="MARGIN: 0cm 0cm 0pt" class=MsoNormal><SPAN
style="FONT-FAMILY: Arial; COLOR: navy; FONT-SIZE: 10.5pt"
lang=EN-GB><o:p> </o:p></SPAN></P>
<P style="MARGIN: 0cm 0cm 0pt" class=MsoNormal><SPAN
style="FONT-FAMILY: Arial; COLOR: navy; FONT-SIZE: 10.5pt" lang=EN-GB>The other
thing that’s quite puzzling is: when photons (possibly virtual) are added into
the electron to accelerate it, do they have to be these ‘charged photons’ as
well?<SPAN style="mso-spacerun: yes"> </SPAN>If so, where do they come
from?<SPAN style="mso-spacerun: yes"> </SPAN>If not, why not? How do
'non-charged' photons combine with a 'charged' photon to increase its
frequency?<o:p></o:p></SPAN></P>
<P style="MARGIN: 0cm 0cm 0pt" class=MsoNormal><SPAN
style="FONT-FAMILY: Arial; COLOR: navy; FONT-SIZE: 10.5pt"
lang=EN-GB><o:p> </o:p></SPAN></P>
<P style="MARGIN: 0cm 0cm 0pt" class=MsoNormal><SPAN
style="FONT-FAMILY: Arial; COLOR: navy; FONT-SIZE: 10.5pt" lang=EN-GB>With
regard to my own model, as you say it of course conforms with the
energy-momentum relation.<SPAN style="mso-spacerun: yes"> </SPAN>It also
creates the phenomenon experienced as ‘electric charge’ as an artefact of the
time-varying electromagnetic field effects of its formative photon.<SPAN
style="mso-spacerun: yes"> </SPAN>Those same effects, internally to the
electron, interfere with one another (non-linearly, of course – so not coherent
superposition) to create curvature in the photon path which, once initiated, is
self-perpetuating; hence the ‘confinement’ of the photon.<o:p></o:p></SPAN></P>
<P style="MARGIN: 0cm 0cm 0pt" class=MsoNormal><SPAN
style="FONT-FAMILY: Arial; COLOR: navy; FONT-SIZE: 10.5pt"
lang=EN-GB><o:p> </o:p></SPAN></P>
<P style="MARGIN: 0cm 0cm 0pt" class=MsoNormal><SPAN
style="FONT-FAMILY: Arial; COLOR: navy; FONT-SIZE: 10.5pt" lang=EN-GB>It’s clear
that the linear momentum of the cyclic photon, completing one wavelength in a
double-loop (as per zitterbewegung), gives the static electron an angular
momentum equivalent to spin-1/2.<SPAN style="mso-spacerun: yes">
</SPAN>The intrinsic spin of the photon itself (being circularly polarised) will
balance itself out over one cycle, contributing no additional spin to the
electron.<SPAN style="mso-spacerun: yes"> </SPAN>Additional energy,
leading to motion of the electron, will be plane polarised* – this is apparent
from other considerations, notably in relation to gravitational effects (which
fit very well with this model as extended electromagnetic effects of ‘massive’
objects), as well as non-increasing charge.<o:p></o:p></SPAN></P>
<P style="MARGIN: 0cm 0cm 0pt" class=MsoNormal><SPAN
style="FONT-FAMILY: Arial; COLOR: navy; FONT-SIZE: 10.5pt"
lang=EN-GB><o:p> </o:p></SPAN></P>
<P style="MARGIN: 0cm 0cm 0pt" class=MsoNormal><SPAN
style="FONT-FAMILY: Arial; COLOR: navy; FONT-SIZE: 10.5pt" lang=EN-GB>[* This
isn’t in any way a limitation on the energies that might accelerate an electron;
it’s anticipated that the structure of any elementary particle would be
self-regulated by interference effects that would mediate the energy exchange
between particles – both particles generally obeying matching constraints.<SPAN
style="mso-spacerun: yes"> </SPAN>Thus energy exchanges would be in the
form of plane polarised waves.]<o:p></o:p></SPAN></P>
<P style="MARGIN: 0cm 0cm 0pt" class=MsoNormal><SPAN
style="FONT-FAMILY: Arial; COLOR: navy; FONT-SIZE: 10.5pt"
lang=EN-GB><o:p> </o:p></SPAN></P>
<P style="MARGIN: 0cm 0cm 0pt" class=MsoNormal><SPAN
style="FONT-FAMILY: Arial; COLOR: navy; FONT-SIZE: 10.5pt" lang=EN-GB>This leads
to a formative photon for an electron that becomes progressively more elliptical
in its polarisation as the electron increases its speed.<SPAN
style="mso-spacerun: yes"> </SPAN>It should be apparent that the
increasing linear component of the formative photon itself thus has a
decreasing degree of angular momentum.<SPAN style="mso-spacerun: yes">
</SPAN>From this it should in turn be apparent that: (a) the formative photon
should asymptotically approach plane polarisation as the speed of the electron
approaches c (and the photon path approaches the unattainable ‘flatline’ state);
(b) the decreasing degree of circular polarisation will match the decreasing
proportion of that photon acting cyclically, as opposed to linearly – so
maintaining the balance between the reducing spin angular momentum of that
photon and the compensating cyclical component of photon motion; (c) the linear
momentum of the photon will contribute an unvarying element of angular momentum
(at constant radius) to the electron (translating into a constant spin-1/2,
regardless of electron speed), as already noted.<o:p></o:p></SPAN></P>
<P style="MARGIN: 0cm 0cm 0pt" class=MsoNormal><SPAN
style="FONT-FAMILY: Arial; COLOR: navy; FONT-SIZE: 10.5pt"
lang=EN-GB><o:p> </o:p></SPAN></P>
<P style="MARGIN: 0cm 0cm 0pt" class=MsoNormal><SPAN
style="FONT-FAMILY: Arial; COLOR: navy; FONT-SIZE: 10.5pt" lang=EN-GB>As
electron speed approaches arbitrarily close to c, its formative photon
approaches arbitrarily close to a flatlining plane polarised form – whilst still
maintaining a helical constant-radius path over an arbitrarily long cycle
interval, matched by an arbitrarily high frequency such that the two combine to
give a cyclic momentum component which gives a constant spin-1/2 at all electron
speeds.<o:p></o:p></SPAN></P>
<P style="MARGIN: 0cm 0cm 0pt" class=MsoNormal><SPAN
style="FONT-FAMILY: Arial; COLOR: navy; FONT-SIZE: 10.5pt"
lang=EN-GB><o:p> </o:p></SPAN></P>
<P style="MARGIN: 0cm 0cm 0pt" class=MsoNormal><SPAN
style="FONT-FAMILY: Arial; COLOR: navy; FONT-SIZE: 10.5pt" lang=EN-GB>In
contrast to all other models seen, this proposed electron structure requires
absolutely no add-ons or modifications to known features of a photon; the
proposal of self-interference as a mechanism for ‘confinement’ of the looping
photon seems virtually axiomatic, given the well-verified phenomenon of pair
production from two linear photons with no apparent injection of any additional
props.<SPAN style="mso-spacerun: yes"> </SPAN>Not least, this model with
its invariant loop radius for its formative photon offers a comprehensive
detailed explanation for ALL phenomena grouped under the heading of Special
Relativity (including, as Albrecht has observed, but not just, time dilation in
accordance with Lorentz factor).<o:p></o:p></SPAN></P>
<P style="MARGIN: 0cm 0cm 0pt" class=MsoNormal><SPAN
style="FONT-FAMILY: Arial; COLOR: navy; FONT-SIZE: 10.5pt"
lang=EN-GB><o:p> </o:p></SPAN></P>
<P style="MARGIN: 0cm 0cm 0pt" class=MsoNormal><SPAN
style="FONT-FAMILY: Arial; COLOR: navy; FONT-SIZE: 10.5pt" lang=EN-GB>More than
this, it offers a cogent and robust rationale for the phenomenon referred to as
‘gravitation’, including a full explanation for the highly useful concept of
‘curved spacetime’ as a tool for calculating trajectories through areas of space
subject to influences from massive bodies in motion.<SPAN
style="mso-spacerun: yes"> </SPAN>Not least, it offers a fully coherent
rationale for the phenomenon that we know as ‘time’, in a formulation that fits
precisely with all known experimental and other empirical findings. To
cover ALL these bases without having to introduce ANY new concepts would, I
believe, warm the heart of William of Ockham.</SPAN></P>
<P style="MARGIN: 0cm 0cm 0pt" class=MsoNormal><SPAN
style="FONT-FAMILY: Arial; COLOR: navy; FONT-SIZE: 10.5pt"
lang=EN-GB></SPAN> </P>
<P style="MARGIN: 0cm 0cm 0pt" class=MsoNormal><SPAN
style="FONT-FAMILY: Arial; COLOR: navy; FONT-SIZE: 10.5pt" lang=EN-GB>Just to
push the boat out a little further, this model also gives a sensible explanation
of 'quantum indeterminacy' - without either of the antiquated myths of
exponentially-increasing alternative universes OR 'God playing dice' (I'm with
Einstein on the latter of these).</SPAN></P>
<P style="MARGIN: 0cm 0cm 0pt" class=MsoNormal><SPAN
style="FONT-FAMILY: Arial; COLOR: navy; FONT-SIZE: 10.5pt"
lang=EN-GB><o:p> </o:p></SPAN></P>
<P style="MARGIN: 0cm 0cm 0pt" class=MsoNormal><SPAN
style="FONT-FAMILY: Arial; COLOR: navy; FONT-SIZE: 10.5pt"
lang=EN-GB>Grahame</SPAN></P>
<P style="MARGIN: 0cm 0cm 0pt" class=MsoNormal><SPAN
style="FONT-FAMILY: Arial; COLOR: navy; FONT-SIZE: 10.5pt"
lang=EN-GB></SPAN> </P>
<P style="MARGIN: 0cm 0cm 0pt" class=MsoNormal><SPAN
style="FONT-FAMILY: Arial; COLOR: navy; FONT-SIZE: 10.5pt"
lang=EN-GB>========</SPAN></P>
<P style="MARGIN: 0cm 0cm 0pt" class=MsoNormal><SPAN
style="FONT-FAMILY: Arial; COLOR: navy; FONT-SIZE: 10.5pt"
lang=EN-GB><o:p></o:p></SPAN> </P></FONT></DIV>
<DIV style="FONT: 10pt arial">----- Original Message -----
<DIV style="BACKGROUND: #e4e4e4; font-color: black"><B>From:</B> <A
title=richgauthier@gmail.com href="mailto:richgauthier@gmail.com">Richard
Gauthier</A> </DIV>
<DIV><B>To:</B> <A title=general@lists.natureoflightandparticles.org
href="mailto:general@lists.natureoflightandparticles.org">Nature of Light and
Particles - General Discussion</A> </DIV>
<DIV><B>Sent:</B> Monday, January 16, 2017 2:27 AM</DIV>
<DIV><B>Subject:</B> Re: [General] Reply to Chip on particle radius &
spin</DIV></DIV>
<DIV><FONT color=#000080 size=2 face=Arial></FONT><BR> </DIV>
<DIV>Hello Chip, Grahame, Vivian, John W, Alex, Hodge and others,</DIV>
<DIV><BR></DIV>
<DIV> Alex, congratulations on your latest “bag model” article on
arXiv. Do you have any suggestions on how we can get on arXiv? Does your bag
model’s radius change by increasing the model's speed relativistically? Someone
in an <A href="http://Academia.edu">Academia.edu</A> article discussion group I
am in asked me if I had heard of your work. I was pleased to say “yes”.</DIV>
<DIV><BR></DIV>
<DIV> The below diagram (figure 1 in my SPIE article at <A
href="https://www.academia.edu/15686831/Electrons_are_spin_1_2_charged_photons_generating_the_de_Broglie_wavelength">https://www.academia.edu/15686831/Electrons_are_spin_1_2_charged_photons_generating_the_de_Broglie_wavelength</A>
) represents the relationships among momentum, energy and velocity for the
relativistic spin-1/2 charged photon model of the electron. The figure also
applies to some other helical photon-like object models of the relativistic
electron because the total photon-like object’s momentum P=gamma mc is the
hypotenuse of a momentum triangle where p=gamma mv is the longitudinal component
of the photon-like object's momentum (and equals the the momentum of the
relativistic electron being modeled), while mc is the transverse component of
the photon-like object’s total momentum P=gamma mc, as shown by the pythagorean
formula P^2 = p^2 + (mc)^2 . Since P=E/c for the photon-like object,
where the energy of the helically-moving photon-like object is E=gamma
mc^2 , the 90-degree momentum triangle relating P, p and mc corresponds to the
relativistic energy-momentum equation for an electron: E^2 = p^2 c^2 + m^2 c^4
as is evident if you just substitute P=E/c into the momentum triangle formula
P^2 = p^2 + (mc)^2 .</DIV>
<DIV><BR></DIV>
<DIV> If the above momentum triangle relationship is agreed for all
our helical models of the relativistic electron , the only quantitative
difference among Graham’s, Vivian’s, Chip’s and my helical photon models in this
regard is the helical radius R's dependence on gamma, compared to the resting
electron’s trajectory radius Ro=hbar/2mc (shown by the oval’s transverse radius
at the left end of the figure). My spin-1/2 charged photon model predicts
that the helical radius R is given by R=Ro/gamma^2 = hbar/(2mc gamma^2) as shown
in the figure, (which equals 1/2 in this diagram where the value used for
gamma in the diagram is gamma = sqrt(2) = 1.414 so also v= c/sqrt(2) =
0.707c in the diagram. The value of theta in the figure is therefore 45 degrees.
Grahame’s electron model predicts that R=Ro for all values of gamma. Vivian
predicts that R=Ro/gamma which would equal 0.707 Ro in this example. I’m
not sure what Chip’s model predicts for the radius of the helically trajectory
(I think it is R=Ro/gamma) which however is not necessarily the same as the
radius of the helically moving photon-like object itself. Chip, Vivian and I
seem to agree that the photon radius decreases as R=Ro/gamma for highly
relativistic values of gamma, while Grahame doesn’t as far as I know have a
prediction for the radius of a photon-like object (as distinct for his
prediction of the constant radius of the trajectory of the photon-like object of
Ro for all values of gamma. </DIV>
<DIV><BR></DIV>
<DIV> In Graham’s electron model, the orbital value alone for the
angular momentum is always mc x Ro = hbar/2 even at highly relativistic
velocities. Any additional angular momentum such as spin-1 or even spin-1/2 of
the helically-moving photon would add a component of this spin at highly
relativistic velocities to this orbital angular momentum value of hbar/2, giving
a total z-component of spin greater than hbar/2 at highly relativistic
velocities, which is contrary to experiment. Chip also doesn’t seem to take into
account the spin of the photon-like object itself in his calculation of the
total spin of his relativistic model of the photon as the electron’s momentum
increases, which forces him to decrease the radius of his photon model as
Ro/gamma (as I understand him) to keep the total spin of his electron model
equal to hbar/2. But it is clear from the diagram that the transverse momentum
component of the circulating photon-like object remains mc even at highly
relativistic electron values, so his calculated value of orbital spin should
actually decrease if his R decreases with increasing gamma.</DIV>
<DIV><BR></DIV>
<DIV> I would also like to know if John W agrees with the momentum
right triangle relations here for a relativistic electron model. I believe that
he thinks that the radius of a photon decreases as 1/gamma from various energy
considerations. And Hodge? John M?</DIV>
<DIV><BR></DIV>
<DIV> Richard</DIV>
<DIV></DIV>
<P>
<HR>
<P></P>
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<P style="MARGIN-LEFT: 13.5pt" class=MsoNormal><SPAN
style="FONT-FAMILY: 'Times New Roman'; FONT-SIZE: 9pt">Figure 1. Velocity,
momentum and energy relationships for the charged photon model moving along its
helical trajectory. The velocity and momentum </SPAN></P>
<P style="MARGIN-LEFT: 13.5pt" class=MsoNormal><SPAN
style="FONT-FAMILY: 'Times New Roman'; FONT-SIZE: 9pt">vectors of the charged
photon and its components related to the electron being modeled are
indicated.<O:P></O:P></SPAN></P><!--EndFragment--></DIV>
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