<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="">Hello Grahame,</div><div class=""> Thank you for your reply, which is very much to the point. I’m off to teach so I will come back to this later in more detail. But I want to ask this question: Is there any experimental evidence at all that the z-component of the spin of the electron (at any speed) is anything other than + or - hbar/2 ? In my understanding there is no such experimental evidence, but I request John W to weigh in on this experimental fact question. Thanks.</div><div class=""> Richard</div><br class=""><div><blockquote type="cite" class=""><div class="">On Jul 12, 2016, at 6:23 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=""><div style="margin: 0cm 0cm 0pt;" class=""><span lang="EN-GB" style="font-family: Arial; color: navy; font-size: 10pt;" class="">Hi Chip, Richard, John W,<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: 10pt;" class=""> </span></div><div style="margin: 0cm 0cm 0pt;" class=""><span lang="EN-GB" style="font-family: Arial; color: navy; font-size: 10pt;" class="">I think we all realised, from Chip’s email if not before, that there’s an issue to be addressed with regard to a photon’s angular momentum in the overall behaviour of a photon-formed electron.<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: 10pt;" class=""> </span></div><div style="margin: 0cm 0cm 0pt;" class=""><span lang="EN-GB" style="font-family: Arial; color: navy; font-size: 10pt;" class="">It seems to me that, whatever photon-based electron model any one of us chooses to put forward, when that electron is in motion then there will be a component of that formative photon’s angular momentum in the direction of motion of the electron (i.e. about any axis in that direction).<span class=""> <span class="Apple-converted-space"> </span></span>More than this, my preliminary investigations suggest that it would take a very creative model indeed to ensure that the rise in that component with increase in electron speed would be exactly balanced by a drop-off in the component from the photon’s linear momentum to give the electron a constant angular momentum.<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: 10pt;" class=""> </span></div><div style="margin: 0cm 0cm 0pt;" class=""><span lang="EN-GB" style="font-family: Arial; color: navy; font-size: 10pt;" class="">[A ‘quick fix’ would of course be to propose a linearly polarized photon with zero spin – i.e. 50/50 superposition of left and right circularly polarized elements.<span class=""> <span class="Apple-converted-space"> </span></span>This, though, is rather a cop-out as it removes a possible explanation for other electron features, notably charge; it also doesn’t feel right.]<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: 10pt;" class=""> </span></div><div style="margin: 0cm 0cm 0pt;" class=""><span lang="EN-GB" style="font-family: Arial; color: navy; font-size: 10pt;" class="">I believe we’re all agreed that:<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: 10pt;" class="">(a) There’s more than enough evidence to confirm that the concept of an electron (and likely also other elementary particles) being formed from a closed-loop photon is totally valid;<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: 10pt;" class="">(b) Formation of an electron involves a double-loop per wavelength of the photon, at least for the static electron.<span class=""> <span class="Apple-converted-space"> </span></span>All else aside this is clearly indicated by zitterbewegung.<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: 10pt;" class=""> </span></div><div style="margin: 0cm 0cm 0pt;" class=""><span lang="EN-GB" style="font-family: Arial; color: navy; font-size: 10pt;" class="">I’m guessing we all also agree on the validity of the so-called Relativistic Energy-Momentum Relation (whether or not we subscribe to the idea of objective frame symmetry).<span class=""> <span class="Apple-converted-space"> </span></span>There are quite a few points that can be drawn from that, as I see it.<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: 10pt;" class=""> </span></div><div style="margin: 0cm 0cm 0pt;" class=""><span lang="EN-GB" style="font-family: Arial; color: navy; font-size: 10pt;" class="">Most importantly, the REMR represents the full momentum of a moving electron (i.e. momentum of its formative photon) in terms of linear and cyclic components.<span class=""> <span class="Apple-converted-space"> </span></span>Expressed diagrammatically, these three components form a right-angled triangle that defines the relative directions of the instantaneous velocity components (linear, cyclic, overall) of that photon (since these must necessarily follow momentum component directions).<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: 10pt;" class=""> </span></div><div style="margin: 0cm 0cm 0pt;" class=""><span lang="EN-GB" style="font-family: Arial; color: navy; font-size: 10pt;" class="">It’s pretty clear, first of all, that if the linear velocity component is v (as it is) and the overall velocity is anything other than c (in directions as given by REMR) then the cyclic velocity component will not be orthogonal to the linear component (as it must be).<span class=""> <span class="Apple-converted-space"> </span></span>From this I believe that we can confirm that the velocity (at least the mean velocity) of an electron-forming photon must be c; I think this rules out certain proposals.<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: 10pt;" class=""> </span></div><div style="margin: 0cm 0cm 0pt;" class=""><span lang="EN-GB" style="font-family: Arial; color: navy; font-size: 10pt;" class="">Secondly, that velocity triangle gives cyclic velocity component as c/gamma.<span class=""> <span class="Apple-converted-space"> </span></span>Those who subscribe to SR’s objective frame symmetry would presumably expect the double-loop to complete in a time gamma tau, where tau is the time for that double-loop for a static electron (since from the static perspective that double-loop in the moving electron would have to correspond with the time-dilated interval in the moving frame).<span class=""> <span class="Apple-converted-space"> </span></span>I also see the double-loop completing in that time, since I regard energy flow as the underlying mechanism driving the passage of time; a slower rate of time-experience (time dilation) is the consequence, rather than the cause, of that reduced looping rate.<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: 10pt;" class=""> </span></div><div style="margin: 0cm 0cm 0pt;" class=""><span lang="EN-GB" style="font-family: Arial; color: navy; font-size: 10pt;" class="">Whichever is the case, a looping rate reduced by a factor gamma and achieved by a flow speed component also reduced by a factor gamma indicates a constant path-length, i.e. a constant radius for the cyclic path of the formative photon.<span class=""> <span class="Apple-converted-space"> </span></span>This appears to be an inescapable conclusion from consideration of the REMR and time dilation.<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: 10pt;" class=""> </span></div><div style="margin: 0cm 0cm 0pt;" class=""><span lang="EN-GB" style="font-family: Arial; color: navy; font-size: 10pt;" class="">[For completeness I should add that SR frame symmetry requires that each double-loop is also seen as exactly one full single wavelength from within the moving frame; for me this raises an irreconcilable contradiction in SR.]<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: 10pt;" class=""> </span></div><div style="margin: 0cm 0cm 0pt;" class=""><span lang="EN-GB" style="font-family: Arial; color: navy; font-size: 10pt;" class="">Back to that photon spin<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: 10pt;" 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: 10pt;" class=""> </span></div><div style="margin: 0cm 0cm 0pt;" class=""><span lang="EN-GB" style="font-family: Arial; color: navy; font-size: 10pt;" class="">Clearly either electron spin increases with speed of the electron’s linear motion – or it doesn’t.<span class=""> <span class="Apple-converted-space"> </span></span>If it doesn’t then this implies some aspect of quantum mechanics that needs further consideration.<span class=""> <span class="Apple-converted-space"> </span></span>Rather more significantly for us, I believe it also rules out the whole concept of electrons being formed from looping photons.<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: 10pt;" class=""> </span></div><div style="margin: 0cm 0cm 0pt;" class=""><span lang="EN-GB" style="font-family: Arial; color: navy; font-size: 10pt;" class="">That last seemingly outrageous statement follows from the tendency towards flat-lining of the formative photon as an electron tends towards speed c.<span class=""> <span class="Apple-converted-space"> </span></span>Unless we consider that photon to be other than circularly polarized – which I believe raises serious difficulties with other aspects of the model – then this means that the electron’s angular momentum in its direction of motion tends to at least hbar – which is clearly inconsistent with constancy of electron angular momentum with increasing speed.<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: 10pt;" class=""> </span></div><div style="margin: 0cm 0cm 0pt;" class=""><span lang="EN-GB" style="font-family: Arial; color: navy; font-size: 10pt;" class="">Rather less problematic (as I see it) is the notion that the electron’s angular momentum in its direction of motion increases with its speed.<span class=""> <span class="Apple-converted-space"> </span></span>I don’t know of any experimental evidence showing conclusively that this is not the case, if others do then of course that would be of interest.<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: 10pt;" class=""> </span></div><div style="margin: 0cm 0cm 0pt;" class=""><span lang="EN-GB" style="font-family: Arial; color: navy; font-size: 10pt;" class="">Obviously if angular momentum does increase then that must be by virtue of its being transferred from elsewhere.<span class=""> <span class="Apple-converted-space"> </span></span>Since increase in velocity must be caused by an input of energy – a real or virtual photon – then the most obvious course is to consider a<span class="Apple-converted-space"> </span></span><st1:city class=""><st1:place class=""><span lang="EN-GB" style="font-family: Arial; color: navy; font-size: 10pt;" class="">Compton</span></st1:place></st1:city><span lang="EN-GB" style="font-family: Arial; color: navy; font-size: 10pt;" class=""><span class="Apple-converted-space"> </span>scattering event that increases the velocity of the electron.<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: 10pt;" class=""> </span></div><div style="margin: 0cm 0cm 0pt;" class=""><span lang="EN-GB" style="font-family: Arial; color: navy; font-size: 10pt;" class="">It’s known that in general<span class="Apple-converted-space"> </span></span><st1:city class=""><st1:place class=""><span lang="EN-GB" style="font-family: Arial; color: navy; font-size: 10pt;" class="">Compton</span></st1:place></st1:city><span lang="EN-GB" style="font-family: Arial; color: navy; font-size: 10pt;" class=""><span class="Apple-converted-space"> </span>scattering leads to a change in polarisation state of the scattered photon.<span class=""> <span class="Apple-converted-space"> </span></span>From what little I’ve seen, such changes have been calculated from theory and confirmed in principle by experiment; that theory doesn’t generally include the notion of an electron’s angular momentum varying with speed, as far as I know.<span class=""> <span class="Apple-converted-space"> </span></span>That (likely) omission would make negligible difference in all but the most extreme case: increase of electron speed from sub-relativistic to highly relativistic in a single step – since the change in scattered-photon spin would correspond to the change in v/c for the electron.<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: 10pt;" class=""> </span></div><div style="margin: 0cm 0cm 0pt;" class=""><span lang="EN-GB" style="font-family: Arial; color: navy; font-size: 10pt;" class="">To summarise: The concept of an electron formed from a circularly-polarised photon looping at constant radius for all speeds of the electron appears to be consistent with all experimental evidence, other than maybe definitive evidence on electron radius at speed* (unless electrons moving at high speed have been shown, and not just inferred, to have spin ½); this observation is based on the assumption that no evidence exists of photon polarisation state changes in high-energy Compton scattering events with sufficient powers of discrimination (i.e. accuracy) to definitively show that no angular momentum has been passed from the photon to the electron, other than that accounted for by a change in direction of motion of the electron.<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: 10pt;" class="">* I have yet to look at this.<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: 10pt;" class=""> </span></div><div style="margin: 0cm 0cm 0pt;" class=""><span lang="EN-GB" style="font-family: Arial; color: navy; font-size: 10pt;" class="">Of course this is just my view, based on my understanding of available scientific data.<span class=""> <span class="Apple-converted-space"> </span></span>I’d be interested to hear other views on these observations<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: 10pt;" class=""> </span></div><div style="margin: 0cm 0cm 0pt;" class=""><span lang="EN-GB" style="font-family: Arial; color: navy; font-size: 10pt;" class="">[Richard, I hope it’s clear from the above why I have reservations over your proposed v=sqrt(2)c spin-1/2 photon model of the electron.<span class=""> <span class="Apple-converted-space"> </span></span>In particular I can’t see how that model can be reconciled with the Relativistic Energy-Momentum Relation in terms of correspondence of directions for components of momentum and velocity.]<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: 10pt;" class=""> </span></div><div style="margin: 0cm 0cm 0pt;" class=""><span lang="EN-GB" style="font-family: Arial; color: navy; font-size: 10pt;" class="">Regards to all,<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: 10pt;" class="">Grahame<o:p class=""></o:p></span></div></div><blockquote 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); border-left-color: rgb(0, 0, 128); border-left-width: 2px; border-left-style: solid; padding-left: 5px; padding-right: 0px; margin-left: 5px; margin-right: 0px;" class="" type="cite"><div style="font-style: normal; font-variant: normal; font-weight: normal; font-size: 10pt; line-height: normal; font-family: arial;" class="">----- Original Message -----<span class="Apple-converted-space"> </span></div><div style="font-style: normal; font-variant: normal; font-weight: normal; font-size: 10pt; line-height: normal; font-family: arial; 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 style="font-style: normal; font-variant: normal; font-weight: normal; font-size: 10pt; line-height: normal; font-family: arial;" 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 style="font-style: normal; font-variant: normal; font-weight: normal; font-size: 10pt; line-height: normal; font-family: arial;" class=""><b class="">Sent:</b><span class="Apple-converted-space"> </span>Friday, July 08, 2016 6:13 AM</div><div style="font-style: normal; font-variant: normal; font-weight: normal; font-size: 10pt; line-height: normal; font-family: arial;" class=""><b class="">Subject:</b><span class="Apple-converted-space"> </span>Re: [General] double photon cycle, subjective v objective realities</div><div class=""><br class=""></div><div class="">Hello Grahame,</div><div class=""><br class=""></div><div class=""> Unfortunately the situation is not so simple. Neither of our published electron models includes a specific photon model with its own spin, where this photon model moves along the helical trajectory described in our models. If that photon moving along the helical trajectory has a spin that is is independent of the energy of the photon (which is the nature of photons) then as the photon's trajectory in the your double-loop constant helical radius electron model gets more and more straight with increasing electron speed, then the spin of this circulating photon adds more and more to the spin 1/2 of your electron model produced by its circling transverse component of momentum mc at constant radius R. The result is that a circulating spin 1 photon along your constant radius R helical trajectory would give your electron model a total spin of one and a half units of spin hbar at highly relativistic velocities. A circulating spin 1/2 photon traveling along your constant radius R trajectory would give your electron model a total spin of 1/2 + 1/2 = 1 unit of hbar of spin at highly relativistic velocities. It is only if the radius R of the photon’s helical trajectory decreases with increasing velocity to become insignificant (compared to R in a resting electron) at relativistic velocities that the spin of the electron model at relativistic velocities will equal only the spin of the photon composing the electron model. Ideally the helically circulating photon model of the electron will have longitudinal spin component 1/2 hbar at all velocities of the electron model from very slow velocities to very highly relativistic velocities. </div><div class=""><br class=""></div><div class=""> I have an unpublished internally superluminal (v=c sqrt(2) ) helically circulating spin-1/2 photon model whose spin remains 1/2 at all energies, which may be suitable for modeling the electron. I described this photon model in this email list in the past. The radius of my published spin-1/2 charged-photon electron model’s photon trajectory decreases as 1/gamma^2 with increasing electron velocity, so this does not produce the complication described above when the helical radius of the photon’s trajectory is a constant R at all electron velocities.</div><div class=""><br class=""></div><div class=""> Richard</div><br class=""><div class=""><blockquote type="cite" class=""><div class="">On Jul 7, 2016, at 1:00 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="text-transform: none; background-color: rgb(255, 255, 255); text-indent: 0px; font-style: normal; font-variant: normal; font-weight: normal; font-size: 12px; line-height: normal; font-family: Helvetica; white-space: normal; letter-spacing: normal; word-spacing: 0px; -webkit-text-stroke-width: 0px;" class=""><font color="#000080" size="2" face="Arial" class="">Thanks Richard,</font></div><div style="text-transform: none; background-color: rgb(255, 255, 255); text-indent: 0px; font-style: normal; font-variant: normal; font-weight: normal; font-size: 12px; line-height: normal; font-family: Helvetica; white-space: normal; letter-spacing: normal; word-spacing: 0px; -webkit-text-stroke-width: 0px;" class=""><font color="#000080" size="2" face="Arial" class=""></font> </div><div style="text-transform: none; background-color: rgb(255, 255, 255); text-indent: 0px; font-style: normal; font-variant: normal; font-weight: normal; font-size: 12px; line-height: normal; font-family: Helvetica; white-space: normal; letter-spacing: normal; word-spacing: 0px; -webkit-text-stroke-width: 0px;" class=""><font color="#000080" size="2" face="Arial" class="">That's precisely what I've been trying to say, without in any way resting on any generally-accepted results that might be regarded as consequences of SR (and so open to question).</font></div><div style="text-transform: none; background-color: rgb(255, 255, 255); text-indent: 0px; font-style: normal; font-variant: normal; font-weight: normal; font-size: 12px; line-height: normal; font-family: Helvetica; white-space: normal; letter-spacing: normal; word-spacing: 0px; -webkit-text-stroke-width: 0px;" class=""><font color="#000080" size="2" face="Arial" class=""></font> </div><div style="text-transform: none; background-color: rgb(255, 255, 255); text-indent: 0px; font-style: normal; font-variant: normal; font-weight: normal; font-size: 12px; line-height: normal; font-family: Helvetica; white-space: normal; letter-spacing: normal; word-spacing: 0px; -webkit-text-stroke-width: 0px;" class=""><font color="#000080" size="2" face="Arial" class="">If we agree that the transverse momentum component of the electron is a direct consequence of the rotational component of its formative photon (as I hope we do!) then that rotational component is acting at radius R of the electron at that time from its centre. Angular momentum is given by linear tangential momentum multiplied by radius - so angular momentum of the electron is mcR. Since mc is constant, R must also be constant if angular momentum is invariant (which I believe we agree it is).</font></div><div style="text-transform: none; background-color: rgb(255, 255, 255); text-indent: 0px; font-style: normal; font-variant: normal; font-weight: normal; font-size: 12px; line-height: normal; font-family: Helvetica; white-space: normal; letter-spacing: normal; word-spacing: 0px; -webkit-text-stroke-width: 0px;" class=""><font color="#000080" size="2" face="Arial" class=""></font> </div><div style="text-transform: none; background-color: rgb(255, 255, 255); text-indent: 0px; font-style: normal; font-variant: normal; font-weight: normal; font-size: 12px; line-height: normal; font-family: Helvetica; white-space: normal; letter-spacing: normal; word-spacing: 0px; -webkit-text-stroke-width: 0px;" class=""><font color="#000080" size="2" face="Arial" class="">Just one further point: Richard, you refer to m as the electron's invariant mass. If we regard mass as that quality of an object that resists acceleration (and so is proportional to the instantaneous force required to induce an instantaneous acceleration), then my research indicates that the mass is<span class="Apple-converted-space"> </span><em class="">not</em><span class="Apple-converted-space"> </span>invariant - though it will appear so from measurements taken within the electron's moving frame. My analysis shows that objective mass varies with speed and the relationship E = mc^2 is applicable only for an objectively static object/particle. The m referred to above, as I see it, is the objective rest-mass of the electron (i.e. its mass when objectively static), which corresponds to the energy required to maintain the formative structure of the electron (as opposed to that required to maintain its linear motion). This is of course constant.</font></div><div style="text-transform: none; background-color: rgb(255, 255, 255); text-indent: 0px; font-style: normal; font-variant: normal; font-weight: normal; font-size: 12px; line-height: normal; font-family: Helvetica; white-space: normal; letter-spacing: normal; word-spacing: 0px; -webkit-text-stroke-width: 0px;" class=""><font color="#000080" size="2" face="Arial" class=""></font> </div><div style="text-transform: none; background-color: rgb(255, 255, 255); text-indent: 0px; font-style: normal; font-variant: normal; font-weight: normal; font-size: 12px; line-height: normal; font-family: Helvetica; white-space: normal; letter-spacing: normal; word-spacing: 0px; -webkit-text-stroke-width: 0px;" class=""><font color="#000080" size="2" face="Arial" class="">Best regards,</font></div><div style="text-transform: none; background-color: rgb(255, 255, 255); text-indent: 0px; font-style: normal; font-variant: normal; font-weight: normal; font-size: 12px; line-height: normal; font-family: Helvetica; white-space: normal; letter-spacing: normal; word-spacing: 0px; -webkit-text-stroke-width: 0px;" class=""><font color="#000080" size="2" face="Arial" class="">Grahame</font></div><blockquote type="cite" style="border-left-color: rgb(0, 0, 128); border-left-width: 2px; border-left-style: solid; text-transform: none; background-color: rgb(255, 255, 255); text-indent: 0px; padding-left: 5px; padding-right: 0px; font-style: normal; font-variant: normal; font-weight: normal; font-size: 12px; line-height: normal; font-family: Helvetica; white-space: normal; letter-spacing: normal; margin-left: 5px; margin-right: 0px; word-spacing: 0px; -webkit-text-stroke-width: 0px;" class=""><div style="font-style: normal; font-variant: normal; font-weight: normal; font-size: 10pt; line-height: normal; font-family: arial;" class="">----- Original Message -----<span class="Apple-converted-space"> </span></div><div style="background-color: rgb(228, 228, 228); font-style: normal; font-variant: normal; font-weight: normal; font-size: 10pt; line-height: normal; font-family: arial;" 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 style="font-style: normal; font-variant: normal; font-weight: normal; font-size: 10pt; line-height: normal; font-family: arial;" 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 style="font-style: normal; font-variant: normal; font-weight: normal; font-size: 10pt; line-height: normal; font-family: arial;" class=""><b class="">Sent:</b><span class="Apple-converted-space"> </span>Thursday, July 07, 2016 6:42 AM</div><div style="font-style: normal; font-variant: normal; font-weight: normal; font-size: 10pt; line-height: normal; font-family: arial;" class=""><b class="">Subject:</b><span class="Apple-converted-space"> </span>Re: [General] double photon cycle, subjective v objective realities</div><div class=""><br class=""></div><div class="">Chip and Grahame,</div><div class=""> Lets be specific to the electron to avoid unnecessary vagueness. The moving electron (composed of a circulating photon) has a constant transverse internal momentum component mc and a longitudinal external momentum component p=gamma mv. These two momenta add vectorially (by the Pythagorean theorem) to give P^2 = p^2 + (mc)^2 where P=E/c is the momentum P=gamma mc of the helically circulating photon of energy E = gamma mc^2 that is the total energy of the linearly moving electron, modeled by the helically moving photon. This relationship is equivalent to the relativistic energy-momentum equation for a moving electron: E^2 = (pc)^2 + m^2 c^4 which, substituting E=Pc, gives (Pc)^2 = (pc)^2 + (mc^2) c^2 .. Dividing by c^2 gives P^2 = p^2 + (mc)^2 as given above. So as the electron speeds up, the transverse momentum component mc of the electron’s total (internal plus external) momentum P remains constant even for a highly relativistic electron. The electron’s constant transverse internal momentum component mc corresponds to (and leads to a derivation of) the electron’s invariant mass m.</div><div class=""> Richard</div><br class=""><div class=""><blockquote type="cite" class=""><div class="">On Jul 6, 2016, at 10:18 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="text-transform: none; background-color: rgb(255, 255, 255); text-indent: 0px; font-style: normal; font-variant: normal; font-weight: normal; font-size: 12px; line-height: normal; font-family: Helvetica; white-space: normal; letter-spacing: normal; word-spacing: 0px; -webkit-text-stroke-width: 0px;" class=""><font color="#000080" size="2" face="Arial" class="">Yes Chip,</font></div><div style="text-transform: none; background-color: rgb(255, 255, 255); text-indent: 0px; font-style: normal; font-variant: normal; font-weight: normal; font-size: 12px; line-height: normal; font-family: Helvetica; white-space: normal; letter-spacing: normal; word-spacing: 0px; -webkit-text-stroke-width: 0px;" class=""><font color="#000080" size="2" face="Arial" class=""></font> </div><div style="text-transform: none; background-color: rgb(255, 255, 255); text-indent: 0px; font-style: normal; font-variant: normal; font-weight: normal; font-size: 12px; line-height: normal; font-family: Helvetica; white-space: normal; letter-spacing: normal; word-spacing: 0px; -webkit-text-stroke-width: 0px;" class=""><font color="#000080" size="2" face="Arial" class="">Certainly the momentum of the confined wave increases - but that increased momentum should not ALL be reckoned as ANGULAR momentum of the electron.</font></div><div style="text-transform: none; background-color: rgb(255, 255, 255); text-indent: 0px; font-style: normal; font-variant: normal; font-weight: normal; font-size: 12px; line-height: normal; font-family: Helvetica; white-space: normal; letter-spacing: normal; word-spacing: 0px; -webkit-text-stroke-width: 0px;" class=""><font color="#000080" size="2" face="Arial" class=""></font> </div><div style="text-transform: none; background-color: rgb(255, 255, 255); text-indent: 0px; font-style: normal; font-variant: normal; font-weight: normal; font-size: 12px; line-height: normal; font-family: Helvetica; white-space: normal; letter-spacing: normal; word-spacing: 0px; -webkit-text-stroke-width: 0px;" class=""><font color="#000080" size="2" face="Arial" class="">We know that a component of the momentum of that photon is linear - it's the linear momentum of the electron in motion. There is another component of that photon that's orthogonal to that, i.e. in the direction of the cyclic motion of the photon. As the linear velocity of the electron increases, the linear component of the photon momentum increases - however the orthogonal, cyclic, component of that photon momentum does NOT increase, since the 'pitch angle' of the helical motion of that photon increases with linear electron velocity, and so also with photon frequency, so as to precisely cancel out the effect of that increased frequency in the resolved-component cyclic direction.</font></div><div style="text-transform: none; background-color: rgb(255, 255, 255); text-indent: 0px; font-style: normal; font-variant: normal; font-weight: normal; font-size: 12px; line-height: normal; font-family: Helvetica; white-space: normal; letter-spacing: normal; word-spacing: 0px; -webkit-text-stroke-width: 0px;" class=""><font color="#000080" size="2" face="Arial" class=""></font> </div><div style="text-transform: none; background-color: rgb(255, 255, 255); text-indent: 0px; font-style: normal; font-variant: normal; font-weight: normal; font-size: 12px; line-height: normal; font-family: Helvetica; white-space: normal; letter-spacing: normal; word-spacing: 0px; -webkit-text-stroke-width: 0px;" class=""><font color="#000080" size="2" face="Arial" class="">The angular momentum of the electron, dictated by the angular momentum contribution of the photon, does NOT depend on the FULL momentum of the photon - it ONLY depends on that <span class="Apple-converted-space"> </span> <span class="Apple-converted-space"> </span><span class="Apple-converted-space"> </span> <span class="Apple-converted-space"> </span><span class="Apple-converted-space"> </span> <span class="Apple-converted-space"> </span>component of the photon that acts cyclically, i.e. the component that's orthogonal to the linear motion of the photon. That component remains constant (as long as the radius of the photon cycle remains constant).</font></div><div style="text-transform: none; background-color: rgb(255, 255, 255); text-indent: 0px; font-style: normal; font-variant: normal; font-weight: normal; font-size: 12px; line-height: normal; font-family: Helvetica; white-space: normal; letter-spacing: normal; word-spacing: 0px; -webkit-text-stroke-width: 0px;" class=""><font color="#000080" size="2" face="Arial" class=""></font> </div><div style="text-transform: none; background-color: rgb(255, 255, 255); text-indent: 0px; font-style: normal; font-variant: normal; font-weight: normal; font-size: 12px; line-height: normal; font-family: Helvetica; white-space: normal; letter-spacing: normal; word-spacing: 0px; -webkit-text-stroke-width: 0px;" class=""><font color="#000080" size="2" face="Arial" class="">For example, if an electron is travelling with linear speed 0.6c then its formative photon is travelling in a helical path which, if we were to flatten it out (as in relativistic energy-momentum relation) we'd find that formative photon having a linear motion component of 0.6c and cyclic speed component of 0.8c. This means that the ANGULAR momentum imparted by the photon will only be 0.8 of that which it would give if it were travelling fully cyclically at speed c (as for a static particle). Since the frequency of the photon will be increased by a gamma factor of 1/0.8 for such motion, the decreased (0.8) contribution of momentum for increased (1/0.8) frequency will be exactly what it was for the static particle.</font></div><div style="text-transform: none; background-color: rgb(255, 255, 255); text-indent: 0px; font-style: normal; font-variant: normal; font-weight: normal; font-size: 12px; line-height: normal; font-family: Helvetica; white-space: normal; letter-spacing: normal; word-spacing: 0px; -webkit-text-stroke-width: 0px;" class=""><font color="#000080" size="2" face="Arial" class=""></font> </div><div style="text-transform: none; background-color: rgb(255, 255, 255); text-indent: 0px; font-style: normal; font-variant: normal; font-weight: normal; font-size: 12px; line-height: normal; font-family: Helvetica; white-space: normal; letter-spacing: normal; word-spacing: 0px; -webkit-text-stroke-width: 0px;" class=""><font color="#000080" size="2" face="Arial" class="">I hope that helps make things clearer.</font></div><div style="text-transform: none; background-color: rgb(255, 255, 255); text-indent: 0px; font-style: normal; font-variant: normal; font-weight: normal; font-size: 12px; line-height: normal; font-family: Helvetica; white-space: normal; letter-spacing: normal; word-spacing: 0px; -webkit-text-stroke-width: 0px;" class=""><font color="#000080" size="2" face="Arial" class=""></font> </div><div style="text-transform: none; background-color: rgb(255, 255, 255); text-indent: 0px; font-style: normal; font-variant: normal; font-weight: normal; font-size: 12px; line-height: normal; font-family: Helvetica; white-space: normal; letter-spacing: normal; word-spacing: 0px; -webkit-text-stroke-width: 0px;" class=""><font color="#000080" size="2" face="Arial" class="">Best regards,</font></div><div style="text-transform: none; background-color: rgb(255, 255, 255); text-indent: 0px; font-style: normal; font-variant: normal; font-weight: normal; font-size: 12px; line-height: normal; font-family: Helvetica; white-space: normal; letter-spacing: normal; word-spacing: 0px; -webkit-text-stroke-width: 0px;" class=""><font color="#000080" size="2" face="Arial" class="">Grahame</font></div><div style="text-transform: none; background-color: rgb(255, 255, 255); text-indent: 0px; font-style: normal; font-variant: normal; font-weight: normal; font-size: 12px; line-height: normal; font-family: Helvetica; white-space: normal; letter-spacing: normal; word-spacing: 0px; -webkit-text-stroke-width: 0px;" class=""><font color="#000080" size="2" face="Arial" class=""></font> </div></div></blockquote></div></blockquote><span style="text-transform: none; background-color: rgb(255, 255, 255); text-indent: 0px; font-style: normal; font-variant: normal; font-weight: normal; font-size: 12px; line-height: normal; font-family: Helvetica; white-space: normal; float: none; letter-spacing: normal; word-spacing: 0px; -webkit-text-stroke-width: 0px; display: inline !important;" class="">_______________________________________________</span><br style="text-transform: none; 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