<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="">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><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="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="">Yes Chip,</font></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> </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="">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="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> </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="">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="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> </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="">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 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="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> </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="">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="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> </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="">I hope that helps make things clearer.</font></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> </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="">Best regards,</font></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="">Grahame</font></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=""> </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="">----- Original Message -----<span class="Apple-converted-space"> </span></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; 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="chipakins@gmail.com" href="mailto:chipakins@gmail.com" style="color: purple; text-decoration: underline;" class="">Chip Akins</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" style="color: purple; text-decoration: underline;" 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>Wednesday, July 06, 2016 5:15 PM</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="WordSection1" style="page: WordSection1;"><div style="margin: 0in 0in 0pt; font-family: 'Times New Roman', serif; font-size: 12pt;" class=""><span style="" class="">Hi Grahame<o:p class=""></o:p></span></div><div style="margin: 0in 0in 0pt; font-family: 'Times New Roman', serif; font-size: 12pt;" class=""><span style="" class=""> </span></div><div style="margin: 0in 0in 0pt; font-family: 'Times New Roman', serif; font-size: 12pt;" class=""><span style="" class="">I think my problem is that I am not yet fully understanding your rationale.<o:p class=""></o:p></span></div><div style="margin: 0in 0in 0pt; font-family: 'Times New Roman', serif; font-size: 12pt;" class=""><span style="" class="">When I do the math, using my understanding of what you are saying, I get an increasing spin angular momentum, principally due to the momentum of the confined wave increasing. So I am not yet following your logic well enough to understand.<o:p class=""></o:p></span></div><div style="margin: 0in 0in 0pt; font-family: 'Times New Roman', serif; font-size: 12pt;" class=""><span style="" class=""> </span></div><div style="margin: 0in 0in 0pt; font-family: 'Times New Roman', serif; font-size: 12pt;" class=""><span style="" class="">Chip<o:p class=""></o:p></span></div><div style="margin: 0in 0in 0pt; font-family: 'Times New Roman', serif; font-size: 12pt;" class=""><span style="" class=""> </span></div><div class=""><div style="border-width: 1pt medium medium; border-style: solid none none; padding: 3pt 0in 0in; border-top-color: rgb(225, 225, 225);" class=""><div style="margin: 0in 0in 0pt; font-family: 'Times New Roman', serif; font-size: 12pt;" class=""><b class=""><span style="font-family: Calibri, sans-serif; font-size: 11pt;" class="">From:</span></b><span style="font-family: Calibri, sans-serif; font-size: 11pt;" class=""><span class="Apple-converted-space"> </span>General [<a href="mailto:general-bounces+chipakins=gmail.com@lists.natureoflightandparticles.org" style="color: purple; text-decoration: underline;" class="">mailto:general-bounces+chipakins=gmail.com@lists.natureoflightandparticles.org</a>]<span class="Apple-converted-space"> </span><b class="">On Behalf Of<span class="Apple-converted-space"> </span></b>Dr Grahame Blackwell<br class=""><b class="">Sent:</b><span class="Apple-converted-space"> </span>Wednesday, July 06, 2016 7:55 AM<br class=""><b class="">To:</b><span class="Apple-converted-space"> </span>Nature of Light and Particles - General Discussion <<a href="mailto:general@lists.natureoflightandparticles.org" style="color: purple; text-decoration: underline;" class="">general@lists.natureoflightandparticles.org</a>><br class=""><b class="">Subject:</b><span class="Apple-converted-space"> </span>Re: [General] double photon cycle, subjective v objective realities<o:p class=""></o:p></span></div></div></div><div style="margin: 0in 0in 0pt; font-family: 'Times New Roman', serif; font-size: 12pt;" class=""><o:p class=""> </o:p></div><div class=""><div style="margin: 0in 0in 0pt; font-family: 'Times New Roman', serif; font-size: 12pt;" class=""><span style="font-family: Arial, sans-serif; color: navy; font-size: 10pt;" class="">Hi Chip,</span><o:p class=""></o:p></div></div><div class=""><div style="margin: 0in 0in 0pt; font-family: 'Times New Roman', serif; font-size: 12pt;" class=""> <o:p class=""></o:p></div></div><div class=""><div style="margin: 0in 0in 0pt; font-family: 'Times New Roman', serif; font-size: 12pt;" class=""><span style="font-family: Arial, sans-serif; color: navy; font-size: 10pt;" class="">You and Richard have both referred to experiments demonstrating (or at least indicating) reduction in size of an electron with increasing speed.</span><o:p class=""></o:p></div></div><div class=""><div style="margin: 0in 0in 0pt; font-family: 'Times New Roman', serif; font-size: 12pt;" class=""> <o:p class=""></o:p></div></div><div class=""><div style="margin: 0in 0in 0pt; font-family: 'Times New Roman', serif; font-size: 12pt;" class=""><span style="font-family: Arial, sans-serif; color: navy; font-size: 10pt;" class="">I'm not familiar with these experimental findings, nor have I been able to find them by searching. I'm guessing that such findings must be made by inference, since direct measurement by any means is presumably out of the question. I'd be most interested to see any papers detailing these experimental findings and how they were derived, if either of you could send them to me. Many thanks.</span><o:p class=""></o:p></div></div><div class=""><div style="margin: 0in 0in 0pt; font-family: 'Times New Roman', serif; font-size: 12pt;" class=""> <o:p class=""></o:p></div></div><div class=""><div style="margin: 0in 0in 0pt; font-family: 'Times New Roman', serif; font-size: 12pt;" class=""><span style="font-family: Arial, sans-serif; color: navy; font-size: 10pt;" class="">Chip, you also asked specifically how I could reconcile invariant electron spin momentum with photon momentum in the context of increasing frequency with increasing speed of motion. I'd be interested to hear what you thought of my rationale for that, based on linear and cyclic components of photon momentum - since this appears to me to exactly balance and give that invariant momentum with invariant electron diameter.</span><o:p class=""></o:p></div></div><div class=""><div style="margin: 0in 0in 0pt; font-family: 'Times New Roman', serif; font-size: 12pt;" class=""> <o:p class=""></o:p></div></div><div class=""><div style="margin: 0in 0in 0pt; font-family: 'Times New Roman', serif; font-size: 12pt;" class=""><span style="font-family: Arial, sans-serif; color: navy; font-size: 10pt;" class="">Best regards,</span><o:p class=""></o:p></div></div><div class=""><div style="margin: 0in 0in 0pt; font-family: 'Times New Roman', serif; font-size: 12pt;" class=""><span style="font-family: Arial, sans-serif; color: navy; font-size: 10pt;" class="">Grahame</span><o:p class=""></o:p></div></div><blockquote style="border-width: medium medium medium 1.5pt; border-style: none none none solid; border-left-color: navy; padding: 0in 0in 0in 4pt; margin: 5pt 0in 5pt 3.75pt;" class="" type="cite"><div class=""><div style="margin: 0in 0in 0pt; font-family: 'Times New Roman', serif; font-size: 12pt;" class=""><span style="font-family: Arial, sans-serif; font-size: 10pt;" class="">----- Original Message -----<span class="Apple-converted-space"> </span><o:p class=""></o:p></span></div></div><div class=""><div style="margin: 0in 0in 0pt; font-family: 'Times New Roman', serif; font-size: 12pt; background-color: rgb(228, 228, 228);" class=""><b class=""><span style="font-family: Arial, sans-serif; font-size: 10pt;" class="">From:</span></b><span style="font-family: Arial, sans-serif; font-size: 10pt;" class=""><span class="Apple-converted-space"> </span><a title="chipakins@gmail.com" href="mailto:chipakins@gmail.com" style="color: purple; text-decoration: underline;" class="">Chip Akins</a><o:p class=""></o:p></span></div></div><div class=""><div style="margin: 0in 0in 0pt; font-family: 'Times New Roman', serif; font-size: 12pt;" class=""><b class=""><span style="font-family: Arial, sans-serif; font-size: 10pt;" class="">To:</span></b><span style="font-family: Arial, sans-serif; font-size: 10pt;" class=""><span class="Apple-converted-space"> </span><a title="general@lists.natureoflightandparticles.org" href="mailto:general@lists.natureoflightandparticles.org" style="color: purple; text-decoration: underline;" class="">'Nature of Light and Particles - General Discussion'</a><o:p class=""></o:p></span></div></div><div class=""><div style="margin: 0in 0in 0pt; font-family: 'Times New Roman', serif; font-size: 12pt;" class=""><b class=""><span style="font-family: Arial, sans-serif; font-size: 10pt;" class="">Sent:</span></b><span style="font-family: Arial, sans-serif; font-size: 10pt;" class=""><span class="Apple-converted-space"> </span>Tuesday, July 05, 2016 2:15 PM<o:p class=""></o:p></span></div></div><div class=""><div style="margin: 0in 0in 0pt; font-family: 'Times New Roman', serif; font-size: 12pt;" class=""><b class=""><span style="font-family: Arial, sans-serif; font-size: 10pt;" class="">Subject:</span></b><span style="font-family: Arial, sans-serif; font-size: 10pt;" class=""><span class="Apple-converted-space"> </span>Re: [General] double photon cycle, subjective v objective realities<o:p class=""></o:p></span></div></div><div class=""><div style="margin: 0in 0in 0pt; font-family: 'Times New Roman', serif; font-size: 12pt;" class=""><o:p class=""> </o:p></div></div><div style="margin: 0in 0in 0pt; font-family: 'Times New Roman', serif; font-size: 12pt;" class=""><span style="" class="">Hi Richard and Grahame<o:p class=""></o:p></span></div><div style="margin: 0in 0in 0pt; font-family: 'Times New Roman', serif; font-size: 12pt;" class=""><span style="" class=""> </span></div><div style="margin: 0in 0in 0pt; font-family: 'Times New Roman', serif; font-size: 12pt;" class=""><span style="" class="">The three of us have different models for the confined energy propagation within the electron.<o:p class=""></o:p></span></div><div style="margin: 0in 0in 0pt; font-family: 'Times New Roman', serif; font-size: 12pt;" class=""><span style="font-family: Arial, sans-serif; color: navy; font-size: 10pt;" class="">... etc</span><span style="" class=""><o:p class=""></o:p></span></div></blockquote></div><div class=""><br class="webkit-block-placeholder"></div><hr class=""><div class=""><br class="webkit-block-placeholder"></div>_______________________________________________<br class="">If you no longer wish to receive communication from the Nature of Light and Particles General Discussion List at<span class="Apple-converted-space"> </span><a href="mailto:grahame@starweave.com" style="color: purple; text-decoration: underline;" class="">grahame@starweave.com</a><br class=""><a href="<a href="http://lists.natureoflightandparticles.org/options.cgi/general-natureoflightandparticles.org/grahame%40starweave.com?unsub=1&unsubconfirm=1" style="color: purple; text-decoration: underline;" class="">http://lists.natureoflightandparticles.org/options.cgi/general-natureoflightandparticles.org/grahame%40starweave.com?unsub=1&unsubconfirm=1</a>"><br class="">Click here to unsubscribe<br class=""></a><br class=""></blockquote><span 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); float: none; display: inline !important;" class="">_______________________________________________</span><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=""><span 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; 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