<html><head><meta http-equiv="Content-Type" content="text/html charset=windows-1252"></head><body style="word-wrap: break-word; -webkit-nbsp-mode: space; -webkit-line-break: after-white-space;" class=""><div class=""><br class=""></div><div class="">Hello Grahame,</div><div class=""><br class=""></div><div class=""> Here are some more replies to your earlier questions, which were deferred when I asked about the wavelength of the circulating photon in your electron model.</div><div class=""><br class=""></div><div class=""> I’m not sure what your problem is with the charge of the proposed spin 1/2 charged photon model (considered as a proposed new variety of photon that CAN carry an electric charge). You say that the spin 1/2 is not a problem for you but the charged part is. I would reply that you should have more of a problem with the charge of the circling spin 1 charged photon in your own electron model. (If your circling spin 1 photon is NOT charged then where does your electron model composed of this circling spin 1 photon model get its charge?) There is no experimental evidence I know of that a spin 1 photon can carry an electric charge , nor that a spin 1 photon can move in a double-looping circle. Non-linear “self-interference” is not a force that can keep a spin 1 photon moving in a circle, is it? My transluminal spin 1/2 charged photon model (with helical radius R= Lcompton/4pi = hbar/2mc for a resting electron) is proposed to make two helical turns per longitudinal photon wavelength, in a “linear-moving” spin 1/2 charged photon model. The spin 1/2 transluminal charged photon model curves its helical axis to form a double-looping spin 1/2 charged-photon model of the electron by making two circular loops of its helical axis (with two associated helical turns) for each Compton wavelength h/mc in a resting electron model. The transluminal spin 1/2 charged photon model doesn’t cancel itself out by destructive interference after going around the first loop, like a photon of one Compton wavelength normally would after using one-half of its wavelength to make the first loop and using the second half of its wavelength (180 degrees of of phase with the first half of its wavelength) to make the second loop. The electric charge of the transluminal spin 1/2 charged photon model could be what generates its two-helical-turns-per-wavelength proposed helical structure. </div><div class=""><br class=""></div><div class=""> In your electron-positron pair production model, it would be a violation of conservation of angular momentum for a single incoming spin 1 photon with sufficient energy to transform into two spin 1 charged photons (one positive and one negative) which then curl up to form a spin 1/2 electron and a spin 1/2 positron in ordinary electron-positron pair production. The nearby atomic nucleus generally needed for electron-positron pair production from a single sufficiently-energetic photon to occur only serves to absorb excess momentum from the electron-positron production process and not to supply angular momentum to the spin 1 uncharged photon in order to form two spin 1 charged photons. </div><div class=""><br class=""></div><div class=""> I am not at all convinced (is anyone else?) by your claim that the circularly polarized circling spin 1 photon in your resting electron model will be transformed gradually into an elliptically polarized photon and then into a spin 0 linearly-polarized photon as your electron model's speed increases relativistically so that the total spin of your relativistic electron model can be only 1/2. Perhaps your verbal explanation is correct but to me it is only words (“hand-waving”) and would need to be demonstrated mathematically. Plus, even when a light beam is linearly polarized, individual photons detected from such a light beam never have zero spin. The detected photons always have either spin 1/2 or spin -1/2 . At least that is my understanding. Do you know of any evidence for a spin zero photon ever being detected, or can a photon only have spin 0 in your highly relativistic electron model?</div><div class=""><br class=""></div><div class=""> I explained in my “Electrons are spin 1/2 charged photons generating the de Broglie wavelength” SPIE article that helically circling charged photons are proposed to generate quantum plane waves in the direction of their helical motion. As I showed in the article, these quantum plane waves intersect along the helical axis to mathematically produce quantum de Broglie waves with the de Brogile wavelength h/(gamma mv). These quantum de Broglie waves go through single slits or double slits or other slits etc to predict (via normal quantum mechanics) the statistical distribution of electrons detected on the other side of the slits. I propose that normal (spin 1) photons in a photon beam generate their own quantum waves in the forward direction of the photon beam to produce their own diffraction and interference quantum wave patterns at slits. These quantum wave patterns predict the statistical distribution of photons detected. The processes of diffraction and interference for electrons and photons are mathematically equivalent at the slits and beyond — only the wavelengths for electrons and photons are different. The quantum waves emitted from the helically circulating spin 1/2 charged photons predict the statistical distribution of charged photon (electron) detection, while the quantum waves emitted by uncharged photons predict the statistical distribution of the detection of uncharged photons.</div><div class=""><br class=""></div><div class=""> The circling spin 1/2 charged photon of an initially resting electron can absorb an uncharged spin 1 photon to increase the spin 1/2 charged photon's energy and internal frequency and therefore increase the electron’s velocity (as measured in the reference frame of the initially resting electron. The uncharged photon (if it has not been completely absorbed by the electron or an atom containing the electron) may then depart from the increased-energy electron with a decrease in the photon’s original energy and frequency. This is what happens in Compton scattering of an x-ray photon by an electron. I don’t have a model for spin 1 photon absorption by a spin 1/2 charged photon (i.e. electron). QED handles this and other similar electron-photon interactions mathematically, though without a description of the process itself, as in e-e pair production from a single photon. There’s a lot of room for further photon-electron modeling work here.</div><div class=""><br class=""></div><div class="">I won’t try to comment on the relation of your electron model to gravitation but wish you success with it.</div><div class=""><br class=""></div><div class="">I hope these answers to your earlier questions have been helpful.</div><div class=""><br class=""></div><div class="">Richard</div><div class=""><br class=""></div><br class=""><div><blockquote type="cite" class=""><div class="">On Jan 18, 2017, at 6:34 PM, Richard Gauthier <<a href="mailto:richgauthier@gmail.com" class="">richgauthier@gmail.com</a>> wrote:</div><br class="Apple-interchange-newline"><div class=""><meta http-equiv="Content-Type" content="text/html charset=windows-1252" class=""><div style="word-wrap: break-word; -webkit-nbsp-mode: space; -webkit-line-break: after-white-space;" class=""><div class="">Hi Grahame (and others)</div><div class=""><br class=""></div><div class=""> Thanks for the detailed critique of my electron model and further information on your model. It’s a lot to reply to so first I’ll start with one question about your electron model.</div><div class=""><br class=""></div><div class=""> Your electron model still doesn’t explicitly contain the relationship Lwavelength = h/(gamma mc) for the wavelength of your helically circulating photon, derived from hf= hc/Lwavelength = gamma m c^2 . Your photon’s constant-radius helical trajectory has a continuously DECREASING helically turning frequency as the energy of the electron increases. Your model's helical turning frequency decreases as 1/gamma with increasing electron energy, while its turning period T increases directly proportional to gamma. This implies that the length of one complete helical turn in your relativistic model is Lturn = gamma Lcompton). This means that with increasing gamma for your electron model, more and more of your helically moving photon's wavelengths of value Lwavelength = h/(gamma mc) = Lcompton/gamma are included on a single helical turn of length Lturn = gamma Lcompton of your helically moving photon. The number N of wavelengths per helical turn in your model moving with relativistic speed given by gamma can be seen easily to be N= Lturn/Lwavelength = (gamma Lcompton)/ (Lcompton/gamma) = gamma^2 . So if two people observe your electron model go by with two different high energies (say gamma = 10 and gamma = 100, the person observing the gamma=10 electron go by will count 10^2 = 100 photon wavelengths per helical turn of your photon while the second person, observing the gamma = 100 electron go by, will count 100^2 = 10,000 photon wavelengths per helical turn of your model (not counting the factor of 1/2 in helical turns per photon wavelength due to zitterbewegung double-looping). In my spin-1/2 charged photon model, the number N of helical turns per wavelength is INDEPENDENT of gamma and always equals 1/2 helical turn per photon wavelength (including the zitterbewegung double-looping factor.) To me (and perhaps to others?) your N=gamma^2 result doesn’t make physical sense so I want to confirm with you that this result is in fact implied by your model. This result alone could disconfirm your model if it doesn’t make physical sense. Also in your model I still don’t see why the constant spin 1/2 of the orbital motion of the photon would not for very large gamma simply add to the intrinsic spin of the photon (either spin 1 or spin 1/2), whose spin vector is directed essentially longitudinally like that of the spin 1/2 orbital motion, to give a total relativistic electron-model spin 1 1/2 or spin 1 respectively . Please let me know. Thanks.</div><div class=""><br class=""></div><div class=""> Richard</div><br class=""><div class=""><blockquote type="cite" class=""><div class="">On Jan 18, 2017, at 7:29 AM, Dr Grahame Blackwell <<a href="mailto:grahame@starweave.com" class="">grahame@starweave.com</a>> wrote:</div><br class="Apple-interchange-newline"><div class=""><div style="font-family: Helvetica; font-size: 12px; font-style: normal; font-variant: normal; font-weight: normal; letter-spacing: normal; line-height: normal; orphans: auto; text-align: start; text-indent: 0px; text-transform: none; white-space: normal; widows: auto; word-spacing: 0px; -webkit-text-stroke-width: 0px; background-color: rgb(255, 255, 255);" class=""><font color="#000080" size="2" face="Arial" class=""><div style="margin: 0cm 0cm 0pt;" class=""><span lang="EN-GB" style="font-family: Arial; color: navy; font-size: 10.5pt;" class="">Hi Richard (et al.),<o:p class=""></o:p></span></div><div style="margin: 0cm 0cm 0pt;" class=""><span lang="EN-GB" style="font-family: Arial; color: navy; font-size: 10.5pt;" class=""><o:p class=""> </o:p></span></div><div style="margin: 0cm 0cm 0pt;" class=""><span lang="EN-GB" style="font-family: Arial; color: navy; font-size: 10.5pt;" class="">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 class=""> <span class="Apple-converted-space"> </span></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 class=""></o:p></span></div><div style="margin: 0cm 0cm 0pt;" class=""><span lang="EN-GB" style="font-family: Arial; color: navy; font-size: 10.5pt;" class=""><o:p class=""> </o:p></span></div><div style="margin: 0cm 0cm 0pt;" class=""><span lang="EN-GB" style="font-family: Arial; color: navy; font-size: 10.5pt;" class="">First I’d like to query that electron model of yours, based as you say on a “spin-1/2 charged photon”.<span class=""> <span class="Apple-converted-space"> </span></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 class=""> <span class="Apple-converted-space"> </span></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 class=""> <span class="Apple-converted-space"> </span></span>So spin-1/2 is a distinct possibility for a photon.<o:p class=""></o:p></span></div><div style="margin: 0cm 0cm 0pt;" class=""><span lang="EN-GB" style="font-family: Arial; color: navy; font-size: 10.5pt;" class=""><o:p class=""> </o:p></span></div><div style="margin: 0cm 0cm 0pt;" class=""><span lang="EN-GB" style="font-family: Arial; color: navy; font-size: 10.5pt;" class="">I’m not clear, though, on what’s meant by a “charged photon”.<span class=""> <span class="Apple-converted-space"> </span></span>I don’t know of any entities arising from Maxwell’s equations that fit that term.<span class=""> <span class="Apple-converted-space"> </span></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 class=""> <span class="Apple-converted-space"> </span></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 class=""> <span class="Apple-converted-space"> </span></span>[* Also that this formative photon must necessarily be circularly polarised.]<o:p class=""></o:p></span></div><div style="margin: 0cm 0cm 0pt;" class=""><span lang="EN-GB" style="font-family: Arial; color: navy; font-size: 10.5pt;" class=""><o:p class=""> </o:p></span></div><div style="margin: 0cm 0cm 0pt;" class=""><span lang="EN-GB" style="font-family: Arial; color: navy; font-size: 10.5pt;" class="">If one talks of a ‘charged photon’, presumably the photon itself is still an electromagnetic construct?<span class=""> <span class="Apple-converted-space"> </span></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 class=""> <span class="Apple-converted-space"> </span></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 class=""> <span class="Apple-converted-space"> </span></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 class=""></o:p></span></div><div style="margin: 0cm 0cm 0pt;" class=""><span lang="EN-GB" style="font-family: Arial; color: navy; font-size: 10.5pt;" class=""><o:p class=""> </o:p></span></div><div style="margin: 0cm 0cm 0pt;" class=""><span lang="EN-GB" style="font-family: Arial; color: navy; font-size: 10.5pt;" class="">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 class=""> <span class="Apple-converted-space"> </span></span>If so, where do they come from?<span class=""> <span class="Apple-converted-space"> </span></span>If not, why not? How do 'non-charged' photons combine with a 'charged' photon to increase its frequency?<o:p class=""></o:p></span></div><div style="margin: 0cm 0cm 0pt;" class=""><span lang="EN-GB" style="font-family: Arial; color: navy; font-size: 10.5pt;" class=""><o:p class=""> </o:p></span></div><div style="margin: 0cm 0cm 0pt;" class=""><span lang="EN-GB" style="font-family: Arial; color: navy; font-size: 10.5pt;" class="">With regard to my own model, as you say it of course conforms with the energy-momentum relation.<span class=""> <span class="Apple-converted-space"> </span></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 class=""> <span class="Apple-converted-space"> </span></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 class=""></o:p></span></div><div style="margin: 0cm 0cm 0pt;" class=""><span lang="EN-GB" style="font-family: Arial; color: navy; font-size: 10.5pt;" class=""><o:p class=""> </o:p></span></div><div style="margin: 0cm 0cm 0pt;" class=""><span lang="EN-GB" style="font-family: Arial; color: navy; font-size: 10.5pt;" class="">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 class=""> <span class="Apple-converted-space"> </span></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 class=""> <span class="Apple-converted-space"> </span></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 class=""></o:p></span></div><div style="margin: 0cm 0cm 0pt;" class=""><span lang="EN-GB" style="font-family: Arial; color: navy; font-size: 10.5pt;" class=""><o:p class=""> </o:p></span></div><div style="margin: 0cm 0cm 0pt;" class=""><span lang="EN-GB" style="font-family: Arial; color: navy; font-size: 10.5pt;" class="">[* 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 class=""> <span class="Apple-converted-space"> </span></span>Thus energy exchanges would be in the form of plane polarised waves.]<o:p class=""></o:p></span></div><div style="margin: 0cm 0cm 0pt;" class=""><span lang="EN-GB" style="font-family: Arial; color: navy; font-size: 10.5pt;" class=""><o:p class=""> </o:p></span></div><div style="margin: 0cm 0cm 0pt;" class=""><span lang="EN-GB" style="font-family: Arial; color: navy; font-size: 10.5pt;" class="">This leads to a formative photon for an electron that becomes progressively more elliptical in its polarisation as the electron increases its speed.<span class=""> <span class="Apple-converted-space"> </span></span>It should be apparent that the increasing linear component of the formative photon itself thus has a decreasing degree of angular momentum.<span class=""> <span class="Apple-converted-space"> </span></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 class=""></o:p></span></div><div style="margin: 0cm 0cm 0pt;" class=""><span lang="EN-GB" style="font-family: Arial; color: navy; font-size: 10.5pt;" class=""><o:p class=""> </o:p></span></div><div style="margin: 0cm 0cm 0pt;" class=""><span lang="EN-GB" style="font-family: Arial; color: navy; font-size: 10.5pt;" class="">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 class=""></o:p></span></div><div style="margin: 0cm 0cm 0pt;" class=""><span lang="EN-GB" style="font-family: Arial; color: navy; font-size: 10.5pt;" class=""><o:p class=""> </o:p></span></div><div style="margin: 0cm 0cm 0pt;" class=""><span lang="EN-GB" style="font-family: Arial; color: navy; font-size: 10.5pt;" class="">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 class=""> <span class="Apple-converted-space"> </span></span>Not least, this model with<span class="Apple-converted-space"> </span> 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 class=""></o:p></span></div><div style="margin: 0cm 0cm 0pt;" class=""><span lang="EN-GB" style="font-family: Arial; color: navy; font-size: 10.5pt;" class=""><o:p class=""> </o:p></span></div><div style="margin: 0cm 0cm 0pt;" class=""><span lang="EN-GB" style="font-family: Arial; color: navy; font-size: 10.5pt;" class="">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 class=""> <span class="Apple-converted-space"> </span></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></div><p class="MsoNormal" style="margin: 0cm 0cm 0pt;"><span lang="EN-GB" style="font-family: Arial; color: navy; font-size: 10.5pt;" class=""></span> </p><div style="margin: 0cm 0cm 0pt;" class=""><span lang="EN-GB" style="font-family: Arial; color: navy; font-size: 10.5pt;" class="">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></div><div style="margin: 0cm 0cm 0pt;" class=""><span lang="EN-GB" style="font-family: Arial; color: navy; font-size: 10.5pt;" class=""><o:p class=""> </o:p></span></div><div style="margin: 0cm 0cm 0pt;" class=""><span lang="EN-GB" style="font-family: Arial; color: navy; font-size: 10.5pt;" class="">Grahame</span></div><p class="MsoNormal" style="margin: 0cm 0cm 0pt;"><span lang="EN-GB" style="font-family: Arial; color: navy; font-size: 10.5pt;" class=""></span> </p><div style="margin: 0cm 0cm 0pt;" class=""><span lang="EN-GB" style="font-family: Arial; color: navy; font-size: 10.5pt;" class="">========</span></div><div style="margin: 0cm 0cm 0pt;" class=""><span lang="EN-GB" style="font-family: Arial; color: navy; font-size: 10.5pt;" class=""><o:p class=""></o:p></span> </div></font></div><div style="font-style: normal; font-variant: normal; font-weight: normal; letter-spacing: normal; line-height: normal; orphans: auto; text-align: start; text-indent: 0px; text-transform: none; white-space: normal; widows: auto; word-spacing: 0px; -webkit-text-stroke-width: 0px; background-color: rgb(255, 255, 255); font-size: 10pt; font-family: arial;" class="">----- Original Message -----<span class="Apple-converted-space"> </span><div style="background-color: rgb(228, 228, 228); background-position: initial initial; background-repeat: initial initial;" class=""><b class="">From:</b><span class="Apple-converted-space"> </span><a title="richgauthier@gmail.com" href="mailto:richgauthier@gmail.com" class="">Richard Gauthier</a></div><div class=""><b class="">To:</b><span class="Apple-converted-space"> </span><a title="general@lists.natureoflightandparticles.org" href="mailto:general@lists.natureoflightandparticles.org" class="">Nature of Light and Particles - General Discussion</a></div><div class=""><b class="">Sent:</b><span class="Apple-converted-space"> </span>Monday, January 16, 2017 2:27 AM</div><div class=""><b class="">Subject:</b><span class="Apple-converted-space"> </span>Re: [General] Reply to Chip on particle radius & spin</div></div><div style="font-family: Helvetica; font-size: 12px; font-style: normal; font-variant: normal; font-weight: normal; letter-spacing: normal; line-height: normal; orphans: auto; text-align: start; text-indent: 0px; text-transform: none; white-space: normal; widows: auto; word-spacing: 0px; -webkit-text-stroke-width: 0px; background-color: rgb(255, 255, 255);" class=""><font color="#000080" size="2" face="Arial" class=""></font><br class=""> </div><div style="font-family: Helvetica; font-size: 12px; font-style: normal; font-variant: normal; font-weight: normal; letter-spacing: normal; line-height: normal; orphans: auto; text-align: start; text-indent: 0px; text-transform: none; white-space: normal; widows: auto; word-spacing: 0px; -webkit-text-stroke-width: 0px; background-color: rgb(255, 255, 255);" class="">Hello Chip, Grahame, Vivian, John W, Alex, Hodge and others,</div><div style="font-family: Helvetica; font-size: 12px; font-style: normal; font-variant: normal; font-weight: normal; letter-spacing: normal; line-height: normal; orphans: auto; text-align: start; text-indent: 0px; text-transform: none; white-space: normal; widows: auto; word-spacing: 0px; -webkit-text-stroke-width: 0px; background-color: rgb(255, 255, 255);" class=""><br class=""></div><div style="font-family: Helvetica; font-size: 12px; font-style: normal; font-variant: normal; font-weight: normal; letter-spacing: normal; line-height: normal; orphans: auto; text-align: start; text-indent: 0px; text-transform: none; white-space: normal; widows: auto; word-spacing: 0px; -webkit-text-stroke-width: 0px; background-color: rgb(255, 255, 255);" class=""> 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<span class="Apple-converted-space"> </span><a href="http://academia.edu/" class="">Academia.edu</a><span class="Apple-converted-space"> </span>article discussion group I am in asked me if I had heard of your work. I was pleased to say “yes”.</div><div style="font-family: Helvetica; font-size: 12px; font-style: normal; font-variant: normal; font-weight: normal; letter-spacing: normal; line-height: normal; orphans: auto; text-align: start; text-indent: 0px; text-transform: none; white-space: normal; widows: auto; word-spacing: 0px; -webkit-text-stroke-width: 0px; background-color: rgb(255, 255, 255);" class=""><br class=""></div><div style="font-family: Helvetica; font-size: 12px; font-style: normal; font-variant: normal; font-weight: normal; letter-spacing: normal; line-height: normal; orphans: auto; text-align: start; text-indent: 0px; text-transform: none; white-space: normal; widows: auto; word-spacing: 0px; -webkit-text-stroke-width: 0px; background-color: rgb(255, 255, 255);" class=""> The below diagram (figure 1 in my SPIE article at<span class="Apple-converted-space"> </span><a href="https://www.academia.edu/15686831/Electrons_are_spin_1_2_charged_photons_generating_the_de_Broglie_wavelength" class="">https://www.academia.edu/15686831/Electrons_are_spin_1_2_charged_photons_generating_the_de_Broglie_wavelength</a><span class="Apple-converted-space"> </span>) 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 style="font-family: Helvetica; font-size: 12px; font-style: normal; font-variant: normal; font-weight: normal; letter-spacing: normal; line-height: normal; orphans: auto; text-align: start; text-indent: 0px; text-transform: none; white-space: normal; widows: auto; word-spacing: 0px; -webkit-text-stroke-width: 0px; background-color: rgb(255, 255, 255);" class=""><br class=""></div><div style="font-family: Helvetica; font-size: 12px; font-style: normal; font-variant: normal; font-weight: normal; letter-spacing: normal; line-height: normal; orphans: auto; text-align: start; text-indent: 0px; text-transform: none; white-space: normal; widows: auto; word-spacing: 0px; -webkit-text-stroke-width: 0px; background-color: rgb(255, 255, 255);" class=""> 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 style="font-family: Helvetica; font-size: 12px; font-style: normal; font-variant: normal; font-weight: normal; letter-spacing: normal; line-height: normal; orphans: auto; text-align: start; text-indent: 0px; text-transform: none; white-space: normal; widows: auto; word-spacing: 0px; -webkit-text-stroke-width: 0px; background-color: rgb(255, 255, 255);" class=""><br class=""></div><div style="font-family: Helvetica; font-size: 12px; font-style: normal; font-variant: normal; font-weight: normal; letter-spacing: normal; line-height: normal; orphans: auto; text-align: start; text-indent: 0px; text-transform: none; white-space: normal; widows: auto; word-spacing: 0px; -webkit-text-stroke-width: 0px; background-color: rgb(255, 255, 255);" class=""> 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 style="font-family: Helvetica; font-size: 12px; font-style: normal; font-variant: normal; font-weight: normal; letter-spacing: normal; line-height: normal; orphans: auto; text-align: start; text-indent: 0px; text-transform: none; white-space: normal; widows: auto; word-spacing: 0px; -webkit-text-stroke-width: 0px; background-color: rgb(255, 255, 255);" class=""><br class=""></div><div style="font-family: Helvetica; font-size: 12px; font-style: normal; font-variant: normal; font-weight: normal; letter-spacing: normal; line-height: normal; orphans: auto; text-align: start; text-indent: 0px; text-transform: none; white-space: normal; widows: auto; word-spacing: 0px; -webkit-text-stroke-width: 0px; background-color: rgb(255, 255, 255);" class=""> 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 style="font-family: Helvetica; font-size: 12px; font-style: normal; font-variant: normal; font-weight: normal; letter-spacing: normal; line-height: normal; orphans: auto; text-align: start; text-indent: 0px; text-transform: none; white-space: normal; widows: auto; word-spacing: 0px; -webkit-text-stroke-width: 0px; background-color: rgb(255, 255, 255);" class=""><br class=""></div><div style="font-family: Helvetica; font-size: 12px; font-style: normal; font-variant: normal; font-weight: normal; letter-spacing: normal; line-height: normal; orphans: auto; text-align: start; text-indent: 0px; text-transform: none; white-space: normal; widows: auto; word-spacing: 0px; -webkit-text-stroke-width: 0px; background-color: rgb(255, 255, 255);" class=""> Richard</div><div style="font-family: Helvetica; font-size: 12px; font-style: normal; font-variant: normal; font-weight: normal; letter-spacing: normal; line-height: normal; orphans: auto; text-align: start; text-indent: 0px; text-transform: none; white-space: normal; widows: auto; word-spacing: 0px; -webkit-text-stroke-width: 0px; background-color: rgb(255, 255, 255);" class=""></div><div style="font-family: Helvetica; font-size: 12px; font-style: normal; font-variant: normal; font-weight: normal; letter-spacing: normal; line-height: normal; orphans: auto; text-align: start; text-indent: 0px; text-transform: none; white-space: normal; widows: auto; word-spacing: 0px; -webkit-text-stroke-width: 0px; background-color: rgb(255, 255, 255);" class=""><br class="webkit-block-placeholder"></div><hr style="font-family: Helvetica; font-size: 12px; font-style: normal; font-variant: normal; font-weight: normal; letter-spacing: normal; line-height: normal; orphans: auto; text-align: start; text-indent: 0px; text-transform: none; white-space: normal; widows: auto; word-spacing: 0px; -webkit-text-stroke-width: 0px; background-color: rgb(255, 255, 255);" class=""><div style="font-family: Helvetica; font-size: 12px; font-style: normal; font-variant: normal; font-weight: normal; letter-spacing: normal; line-height: normal; orphans: auto; text-align: start; text-indent: 0px; text-transform: none; white-space: normal; widows: auto; word-spacing: 0px; -webkit-text-stroke-width: 0px; background-color: rgb(255, 255, 255);" class=""><br class="webkit-block-placeholder"></div><div style="font-family: Helvetica; font-size: 12px; font-style: normal; font-variant: normal; font-weight: normal; letter-spacing: normal; line-height: normal; orphans: auto; text-align: start; text-indent: 0px; text-transform: none; white-space: normal; widows: auto; word-spacing: 0px; -webkit-text-stroke-width: 0px; background-color: rgb(255, 255, 255);" class=""></div><div style="font-family: Helvetica; font-size: 12px; font-style: normal; font-variant: normal; font-weight: normal; letter-spacing: normal; line-height: normal; orphans: auto; text-align: start; text-indent: 0px; text-transform: none; white-space: normal; widows: auto; word-spacing: 0px; -webkit-text-stroke-width: 0px; background-color: rgb(255, 255, 255);" class=""><p class="MsoNormal" style="margin-left: 13.5pt;"><span style="font-family: 'Times New Roman'; font-size: 9pt;" class="">Figure 1. Velocity, momentum and energy relationships for the charged photon model moving along its helical trajectory. The velocity and momentum </span></p><p class="MsoNormal" style="margin-left: 13.5pt;"><span style="font-family: 'Times New Roman'; font-size: 9pt;" class="">vectors of the charged photon and its components related to the electron being modeled are indicated.<o:p class=""></o:p></span></p></div><div style="font-family: Helvetica; font-size: 12px; font-style: normal; font-variant: normal; font-weight: normal; letter-spacing: normal; line-height: normal; orphans: auto; text-align: start; text-indent: 0px; text-transform: none; white-space: normal; widows: auto; word-spacing: 0px; -webkit-text-stroke-width: 0px; background-color: rgb(255, 255, 255);" class=""><br class=""></div><br style="font-family: Helvetica; font-size: 12px; font-style: normal; font-variant: normal; font-weight: normal; letter-spacing: normal; line-height: normal; orphans: auto; text-align: start; text-indent: 0px; text-transform: none; white-space: normal; widows: auto; word-spacing: 0px; -webkit-text-stroke-width: 0px; background-color: rgb(255, 255, 255);" class=""><div style="font-family: Helvetica; font-size: 12px; font-style: normal; font-variant: normal; font-weight: normal; letter-spacing: normal; line-height: normal; orphans: auto; text-align: start; text-indent: 0px; text-transform: none; white-space: normal; widows: auto; word-spacing: 0px; -webkit-text-stroke-width: 0px; background-color: rgb(255, 255, 255);" class=""><blockquote type="cite" class=""><font color="#000080" size="2" face="Arial" class=""></font> </blockquote></div></div></blockquote></div><br class=""></div></div></blockquote></div><br class=""></body></html>