<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="">Martin and John D and all,<div class=""> When an electron (charged photon) “falls" into a previously ionized atom, the total energy of the electron decreases as it becomes bound to the atom and gives off one or more photons as it drops from one atomic energy level to another, but the charged photon’s (electron’s) average kinetic energy and momentum increase as it goes into the negative potential energy well of the atom. The charged photon’s (electron’s) average de Broglie wavelength decreases as its momentum and kinetic energy increase. The charged photon (electron) gives off an uncharged photon each time it drops from one energy level of the atom to another, as described by QM. With each new lower total energy, increased average kinetic energy and decreased average de Broglie wavelength, the charged photon creates a kind of resonance state (quantum wave eigenfunction) throughout the atom corresponding to its particular energy eigenvalue. The charged photon as it circulates is continually generating plane waves corresponding to its energy. These plane waves from the charged photon generate the charged photon’s (electron’s) de Broglie wavelength and corresponding quantum wave functions along the helically circulating charged photon's longitudinal direction of motion. The probability density for detecting the electron (charged photon) is given by Psi*Psi of its particular eigenfunction in the atom. The charged photon appears to be spread out but when detected it is more localized (the resonant eigenstate produced by its de Broglie wavelength is destroyed) and the electron (charged photon) is back to being a non-resonant charged photon (electron), until it creates a new resonant state (new eigenfunction).</div><div class=""> Richard</div><div class=""><br class=""><div><blockquote type="cite" class=""><div class="">On May 12, 2015, at 4:20 PM, Mark, Martin van der <<a href="mailto:martin.van.der.mark@philips.com" class="">martin.van.der.mark@philips.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;" class="">Dear John D,</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;" class="">I completely agree with what you are saying, of course!</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;" class="">However i was only saying that, by experiment, the charge SEEMS to be distributed over the whole quantum state, ask John W the expert. So for the hydrogen atom in the ground state it is a sphere of one ångstrom diameter: the electron is delocalized.</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;" class="">I believe that the electron stays in its own box, just like you say with its compton wavelength, a box that fits in another box, the atomic orbital with its de Broglie wavelength. Indeed with corrections for binding energy that is lost in the process, as you point out correctly.</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;" class="">Cheers, Martin<br class=""><br class="">Verstuurd vanaf mijn iPhone</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;" class=""><br class="">Op 12 mei 2015 om 22:38 heeft John Duffield <<a href="mailto:johnduffield@btconnect.com" style="color: purple; text-decoration: underline;" class="">johnduffield@btconnect.com</a>> het volgende geschreven:<br class=""><br class=""></div><blockquote type="cite" 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;" class=""><div class=""><div class="WordSection1" style="page: WordSection1;"><div style="margin: 0cm 0cm 0.0001pt; font-size: 12pt; font-family: 'Times New Roman', serif;" class=""><span style="font-size: 11pt; font-family: Calibri, sans-serif; color: rgb(31, 73, 125);" class="">Martin:<o:p class=""></o:p></span></div><div style="margin: 0cm 0cm 0.0001pt; font-size: 12pt; font-family: 'Times New Roman', serif;" class=""><span style="font-size: 11pt; font-family: Calibri, sans-serif; color: rgb(31, 73, 125);" class=""> </span></div><div style="margin: 0cm 0cm 0.0001pt; font-size: 12pt; font-family: 'Times New Roman', serif;" class=""><span style="font-size: 11pt; font-family: Calibri, sans-serif; color: rgb(31, 73, 125);" class="">IMHO the electron in a<span class="Apple-converted-space"> </span><a href="http://www.antiprism.com/album/860_tori/index.html" style="color: purple; text-decoration: underline;" class="">spindle-sphere</a><span class="Apple-converted-space"> </span>S orbital is only a little larger than a free electron. It exists as a 511keV standing wave when it’s a free electron. When it’s a standing wave in an<span class="Apple-converted-space"> </span><a href="http://en.wikipedia.org/wiki/Atomic_orbital#Electron_properties" style="color: purple; text-decoration: underline;" class="">atomic orbital</a><span class="Apple-converted-space"> </span>it’s a mere 13.6ev less energy. So its Compton wavelength has only increased a little. IMHO you should remember<span class="Apple-converted-space"> </span><a href="http://www.tardyon.de/mirror/hooft/hooft.htm" style="color: purple; text-decoration: underline;" class="">the photon in the box for this</a>. Try to imagine jiggling the box around just so, such that the photon wavelength increases a little because the box is effectively a little bit bigger. Or imagine the electron around your waist, and you’re playing hula-hoop. <o:p class=""></o:p></span></div><div style="margin: 0cm 0cm 0.0001pt; font-size: 12pt; font-family: 'Times New Roman', serif;" class=""><span style="font-size: 11pt; font-family: Calibri, sans-serif; color: rgb(31, 73, 125);" class=""> </span></div><div style="margin: 0cm 0cm 0.0001pt; font-size: 12pt; font-family: 'Times New Roman', serif;" class=""><span style="font-size: 11pt; font-family: Calibri, sans-serif; color: rgb(31, 73, 125);" class=""><image001.jpg></span><span style="font-size: 11pt; font-family: Calibri, sans-serif; color: rgb(31, 73, 125);" class=""><span class="Apple-converted-space"> </span> <o:p class=""></o:p></span></div><div style="margin: 0cm 0cm 0.0001pt; font-size: 12pt; font-family: 'Times New Roman', serif;" class=""><span style="font-size: 11pt; font-family: Calibri, sans-serif; color: rgb(31, 73, 125);" class=""> </span></div><div style="margin: 0cm 0cm 0.0001pt; font-size: 12pt; font-family: 'Times New Roman', serif;" class=""><span style="font-size: 11pt; font-family: Calibri, sans-serif; color: rgb(31, 73, 125);" class="">Regards<o:p class=""></o:p></span></div><div style="margin: 0cm 0cm 0.0001pt; font-size: 12pt; font-family: 'Times New Roman', serif;" class=""><span style="font-size: 11pt; font-family: Calibri, sans-serif; color: rgb(31, 73, 125);" class="">John D<o:p class=""></o:p></span></div><div style="margin: 0cm 0cm 0.0001pt; font-size: 12pt; font-family: 'Times New Roman', serif;" class=""><span style="font-size: 11pt; font-family: Calibri, sans-serif; color: rgb(31, 73, 125);" class=""> </span></div><div style="margin: 0cm 0cm 0.0001pt; font-size: 12pt; font-family: 'Times New Roman', serif;" class=""><span style="font-size: 11pt; font-family: Calibri, sans-serif; color: rgb(31, 73, 125);" class=""> </span></div><div class=""><div style="border-style: solid none none; border-top-color: rgb(225, 225, 225); border-top-width: 1pt; padding: 3pt 0cm 0cm;" class=""><div style="margin: 0cm 0cm 0.0001pt; font-size: 12pt; font-family: 'Times New Roman', serif;" class=""><b class=""><span lang="EN-US" style="font-size: 11pt; font-family: Calibri, sans-serif;" class="">From:</span></b><span lang="EN-US" style="font-size: 11pt; font-family: Calibri, sans-serif;" class=""><span class="Apple-converted-space"> </span>General [<a href="mailto:general-bounces+johnduffield=btconnect.com@lists.natureoflightandparticles.org" style="color: purple; text-decoration: underline;" class="">mailto:general-bounces+johnduffield=btconnect.com@lists.natureoflightandparticles.org</a>]<b class="">On Behalf Of<span class="Apple-converted-space"> </span></b>Mark, Martin van der<br class=""><b class="">Sent:</b><span class="Apple-converted-space"> </span>12 May 2015 08:32<br class=""><b class="">To:</b><span class="Apple-converted-space"> </span>Nature of Light and Particles - General Discussion<br class=""><b class="">Subject:</b><span class="Apple-converted-space"> </span>Re: [General] Quantisation of classical electromagnetism<o:p class=""></o:p></span></div></div></div><div style="margin: 0cm 0cm 0.0001pt; font-size: 12pt; font-family: 'Times New Roman', serif;" class=""><o:p class=""> </o:p></div><div style="margin: 0cm 0cm 0.0001pt; font-size: 12pt; font-family: 'Times New Roman', serif;" class=""><span lang="EN-US" style="font-size: 11pt; font-family: Calibri, sans-serif; color: rgb(31, 73, 125);" class="">Hi Richard,</span><span lang="EN-US" class=""><o:p class=""></o:p></span></div><div style="margin: 0cm 0cm 0.0001pt; font-size: 12pt; font-family: 'Times New Roman', serif;" class=""><span lang="EN-US" style="font-size: 11pt; font-family: Calibri, sans-serif; color: rgb(31, 73, 125);" class="">You raise an important question. I cannot answer it yet, as I will try to explain.</span><span lang="EN-US" class=""><o:p class=""></o:p></span></div><div style="margin: 0cm 0cm 0.0001pt; font-size: 12pt; font-family: 'Times New Roman', serif;" class=""><span lang="EN-US" style="font-size: 11pt; font-family: Calibri, sans-serif; color: rgb(31, 73, 125);" class="">The structure of an electron inside an atom or in the conduction band of a metal or semi-conductor is different from that of the free electron. It manages to behave as it were much larger than the free electron, it can be measured that the charge is distributed over the whole atom or even the whole conductor.</span><span lang="EN-US" class=""><o:p class=""></o:p></span></div><div style="margin: 0cm 0cm 0.0001pt; font-size: 12pt; font-family: 'Times New Roman', serif;" class=""><span lang="EN-US" style="font-size: 11pt; font-family: Calibri, sans-serif; color: rgb(31, 73, 125);" class="">Does the electron really “disintegrate”? I do not believe so. But believing is quite different from knowing. What would have to happen is that the environment makes up for the binding forces inside the electron. I think those forces are far too weak. Moreover, the speed of light would come in the way to keep coherence over larger distances than the size of the free electron (at the Compton wavelength scale)…</span><span lang="EN-US" class=""><o:p class=""></o:p></span></div><div style="margin: 0cm 0cm 0.0001pt; font-size: 12pt; font-family: 'Times New Roman', serif;" class=""><span lang="EN-US" style="font-size: 11pt; font-family: Calibri, sans-serif; color: rgb(31, 73, 125);" class="">A proper theory must solve this. For the moment I think that the electron hardly changes its structure inside an atom or conductor and that only the external fiels have just the de Broglie wavelength that fits their imposed quantum state, as in the pilot wave picture.</span><span lang="EN-US" class=""><o:p class=""></o:p></span></div><div style="margin: 0cm 0cm 0.0001pt; font-size: 12pt; font-family: 'Times New Roman', serif;" class=""><span lang="EN-US" style="font-size: 11pt; font-family: Calibri, sans-serif; color: rgb(31, 73, 125);" class="">Cheers, Martin</span><span lang="EN-US" class=""><o:p class=""></o:p></span></div><div style="margin: 0cm 0cm 0.0001pt; font-size: 12pt; font-family: 'Times New Roman', serif;" class=""><span lang="EN-US" style="font-size: 11pt; font-family: Calibri, sans-serif; color: rgb(31, 73, 125);" class=""> </span><span lang="EN-US" class=""><o:p class=""></o:p></span></div><div class=""><div style="margin: 0cm 0cm 0.0001pt; font-size: 12pt; font-family: 'Times New Roman', serif;" class=""><span lang="DE" style="font-size: 10pt; font-family: Arial, sans-serif; color: navy;" class="">Dr. Martin B. van der Mark</span><span lang="EN-US" class=""><o:p class=""></o:p></span></div><div style="margin: 0cm 0cm 0.0001pt; font-size: 12pt; font-family: 'Times New Roman', serif;" class=""><span lang="EN-US" style="font-size: 10pt; font-family: Arial, sans-serif; color: navy;" class="">Principal Scientist, Minimally Invasive Healthcare</span><span lang="EN-US" class=""><o:p class=""></o:p></span></div><div style="margin: 0cm 0cm 0.0001pt; font-size: 12pt; font-family: 'Times New Roman', serif;" class=""><span lang="EN-US" style="font-size: 11pt; font-family: Calibri, sans-serif; color: navy;" class=""> </span><span lang="EN-US" class=""><o:p class=""></o:p></span></div><div style="margin: 0cm 0cm 0.0001pt; font-size: 12pt; font-family: 'Times New Roman', serif;" class=""><span lang="EN-US" style="font-size: 10pt; font-family: Arial, sans-serif; color: navy;" class="">Philips Research Europe - Eindhoven</span><span lang="EN-US" class=""><o:p class=""></o:p></span></div><div style="margin: 0cm 0cm 0.0001pt; font-size: 12pt; font-family: 'Times New Roman', serif;" class=""><span lang="EN-US" style="font-size: 10pt; font-family: Arial, sans-serif; color: navy;" class="">High Tech Campus, Building 34 (WB2.025)</span><span lang="EN-US" class=""><o:p class=""></o:p></span></div><div style="margin: 0cm 0cm 0.0001pt; font-size: 12pt; font-family: 'Times New Roman', serif;" class=""><span lang="EN-US" style="font-size: 10pt; font-family: Arial, sans-serif; color: navy;" class="">Prof. Holstlaan 4</span><span lang="EN-US" class=""><o:p class=""></o:p></span></div><div style="margin: 0cm 0cm 0.0001pt; font-size: 12pt; font-family: 'Times New Roman', serif;" class=""><span lang="EN-US" style="font-size: 10pt; font-family: Arial, sans-serif; color: navy;" class="">5656 AE Eindhoven, The Netherlands</span><span lang="EN-US" class=""><o:p class=""></o:p></span></div><div style="margin: 0cm 0cm 0.0001pt; font-size: 12pt; font-family: 'Times New Roman', serif;" class=""><span lang="EN-US" style="font-size: 10pt; font-family: Arial, sans-serif; color: navy;" class="">Tel: +31 40 2747548</span><span lang="EN-US" class=""><o:p class=""></o:p></span></div></div><div style="margin: 0cm 0cm 0.0001pt; font-size: 12pt; font-family: 'Times New Roman', serif;" class=""><span lang="EN-US" style="font-size: 11pt; font-family: Calibri, sans-serif; color: rgb(31, 73, 125);" class=""> </span><span lang="EN-US" class=""><o:p class=""></o:p></span></div><div class=""><div style="border-style: solid none none; border-top-color: rgb(181, 196, 223); border-top-width: 1pt; padding: 3pt 0cm 0cm;" class=""><div style="margin: 0cm 0cm 0.0001pt; font-size: 12pt; font-family: 'Times New Roman', serif;" class=""><b class=""><span lang="EN-US" style="font-size: 10pt; font-family: Tahoma, sans-serif;" class="">From:</span></b><span lang="EN-US" style="font-size: 10pt; font-family: Tahoma, sans-serif;" class=""><span class="Apple-converted-space"> </span>General [<a href="mailto:general-bounces+martin.van.der.mark=philips.com@lists.natureoflightandparticles.org" style="color: purple; text-decoration: underline;" class="">mailto:general-bounces+martin.van.der.mark=philips.com@lists.natureoflightandparticles.org</a>]<span class="Apple-converted-space"> </span><b class="">On Behalf Of<span class="Apple-converted-space"> </span></b>Richard Gauthier<br class=""><b class="">Sent:</b><span class="Apple-converted-space"> </span>dinsdag 12 mei 2015 8:23<br class=""><b class="">To:</b><span class="Apple-converted-space"> </span>Nature of Light and Particles - General Discussion<br class=""><b class="">Subject:</b><span class="Apple-converted-space"> </span>Re: [General] Quantisation of classical electromagnetism</span><span lang="EN-US" class=""><o:p class=""></o:p></span></div></div></div><div style="margin: 0cm 0cm 0.0001pt; font-size: 12pt; font-family: 'Times New Roman', serif;" class=""><span lang="EN-US" class=""> <o:p class=""></o:p></span></div><div style="margin: 0cm 0cm 0.0001pt; font-size: 12pt; font-family: 'Times New Roman', serif;" class=""><span lang="EN-US" class="">Andrew and Martin,<o:p class=""></o:p></span></div><div class=""><div style="margin: 0cm 0cm 0.0001pt; font-size: 12pt; font-family: 'Times New Roman', serif;" class=""><span lang="EN-US" class=""> I think it would be a good challenge for anyone with a single-looped or double-looped photon model of an electron to model their electron in the 1s atomic state of hydrogen (where n=1, l=0, ml=0 and ms = + or - 1/2 hbar) where the electron has zero hbar atomic angular momentum even though it has internal electron spin 1/2 hbar. I model the electron here as oscillating back and forth linearly through the center of the atom as a charged photon with a helical trajectory of variable pitch and radius, with a total energy of E=mc^2 -13.6 eV and a maximum kinetic energy when the helically circulating charged photon passes the nucleus, generating a variable de Broglie wavelength along its trajectory (because its longitudinal momentum is changing as it oscillates in the atom) and making one complete de Broglie path per oscillation. The most probable position of the charged photon (the electron) to be detected is at 1 Bohr radius ao (as predicted by QM for the hydrogen atom) because the charged photon obeys the Schrodinger equation (in the non-relativistic approximation). If the 1s electron (charged photon) absorbs an uncharged photon of energy 13.6 eV, the hydrogen atom is ionized with the charged photon now having energy E=mc^2 .<o:p class=""></o:p></span></div></div><div class=""><div style="margin: 0cm 0cm 0.0001pt; font-size: 12pt; font-family: 'Times New Roman', serif;" class=""><span lang="EN-US" class=""> Richard<o:p class=""></o:p></span></div></div><div class=""><div style="margin: 0cm 0cm 0.0001pt; font-size: 12pt; font-family: 'Times New Roman', serif;" class=""><span lang="EN-US" class=""> <o:p class=""></o:p></span></div><div class=""><blockquote style="margin-top: 5pt; margin-bottom: 5pt;" class=""><div class=""><div style="margin: 0cm 0cm 0.0001pt; font-size: 12pt; font-family: 'Times New Roman', serif;" class=""><span lang="EN-US" class="">On May 11, 2015, at 1:30 PM, Mark, Martin van der <<a href="mailto:martin.van.der.mark@philips.com" style="color: purple; text-decoration: underline;" class="">martin.van.der.mark@philips.com</a>> wrote:<o:p class=""></o:p></span></div></div><div style="margin: 0cm 0cm 0.0001pt; font-size: 12pt; font-family: 'Times New Roman', serif;" class=""><span lang="EN-US" class=""> <o:p class=""></o:p></span></div><div class=""><div class=""><div style="margin: 0cm 0cm 0.0001pt; font-size: 12pt; font-family: 'Times New Roman', serif;" class=""><span lang="EN-US" style="font-size: 11pt; font-family: Calibri, sans-serif; color: rgb(112, 48, 160);" class="">Dear Andrew, I have been away for a few days.</span><span lang="EN-US" class=""><o:p class=""></o:p></span></div></div><div class=""><div style="margin: 0cm 0cm 0.0001pt; font-size: 12pt; font-family: 'Times New Roman', serif;" class=""><span lang="EN-US" style="font-size: 11pt; font-family: Calibri, sans-serif; color: rgb(112, 48, 160);" class="">In your previous replies you tried to challenge me to be precise, and have questioned the correctness of my statements. That is very good.</span><span lang="EN-US" class=""><o:p class=""></o:p></span></div></div><div class=""><div style="margin: 0cm 0cm 0.0001pt; font-size: 12pt; font-family: 'Times New Roman', serif;" class=""><span lang="EN-US" style="font-size: 11pt; font-family: Calibri, sans-serif; color: rgb(112, 48, 160);" class=""> </span><span lang="EN-US" class=""><o:p class=""></o:p></span></div></div><div class=""><div style="margin: 0cm 0cm 0.0001pt; font-size: 12pt; font-family: 'Times New Roman', serif;" class=""><span lang="EN-US" style="font-size: 11pt; font-family: Calibri, sans-serif; color: rgb(112, 48, 160);" class="">But unfortunately you have put me in a position where I, in turn, have to correct you on all the things you say that are half baked or wrong. It is difficult to remain very polite since most of your brown replies, need “attention”. So brace, but remember that I only put in the effort because I respect you and because I think that your opinion matters.</span><span lang="EN-US" class=""><o:p class=""></o:p></span></div></div><div class=""><div style="margin: 0cm 0cm 0.0001pt; font-size: 12pt; font-family: 'Times New Roman', serif;" class=""><span lang="EN-US" style="font-size: 11pt; font-family: Calibri, sans-serif; color: rgb(112, 48, 160);" class=""> </span><span lang="EN-US" class=""><o:p class=""></o:p></span></div></div><div class=""><div style="margin: 0cm 0cm 0.0001pt; font-size: 12pt; font-family: 'Times New Roman', serif;" class=""><span lang="EN-US" style="font-size: 11pt; font-family: Calibri, sans-serif; color: rgb(112, 48, 160);" class="">I hope no one is color blind, yet another color will be used: purple! (just in case some haze troubles the mind…)</span><span lang="EN-US" class=""><o:p class=""></o:p></span></div></div><div class=""><div style="margin: 0cm 0cm 0.0001pt; font-size: 12pt; font-family: 'Times New Roman', serif;" class=""><span lang="EN-US" style="font-size: 11pt; font-family: Calibri, sans-serif; color: rgb(112, 48, 160);" class=""> </span><span lang="EN-US" class=""><o:p class=""></o:p></span></div></div><div class=""><div style="margin: 0cm 0cm 0.0001pt; font-size: 12pt; font-family: 'Times New Roman', serif;" class=""><span lang="EN-US" style="font-size: 11pt; font-family: Calibri, sans-serif; color: rgb(112, 48, 160);" class="">So: purple (Martin) responds to<span class="apple-converted-space"> </span></span><span lang="EN-US" style="font-size: 11pt; font-family: Calibri, sans-serif; color: rgb(152, 72, 7);" class="">brown (Andrew) responds to<span class="apple-converted-space"> </span></span><span lang="EN-US" style="font-size: 11pt; font-family: Calibri, sans-serif; color: rgb(79, 98, 40);" class="">green (Martin) responds to<span class="apple-converted-space"> </span></span><span lang="EN-US" style="font-size: 11pt; font-family: Calibri, sans-serif; color: red;" class="">red (Andrew)</span><span lang="EN-US" class=""><o:p class=""></o:p></span></div></div><div class=""><div style="margin: 0cm 0cm 0.0001pt; font-size: 12pt; font-family: 'Times New Roman', serif;" class=""><span lang="EN-US" style="font-size: 11pt; font-family: Calibri, sans-serif; color: rgb(112, 48, 160);" class=""> </span><span lang="EN-US" class=""><o:p class=""></o:p></span></div></div><div class=""><div style="margin: 0cm 0cm 0.0001pt; font-size: 12pt; font-family: 'Times New Roman', serif;" class=""><span lang="EN-US" style="font-size: 11pt; font-family: Calibri, sans-serif; color: rgb(31, 73, 125);" class=""> </span><span lang="EN-US" class=""><o:p class=""></o:p></span></div></div><div class=""><div style="margin: 0cm 0cm 0.0001pt; font-size: 12pt; font-family: 'Times New Roman', serif;" class=""><span lang="DE" style="font-size: 10pt; font-family: Arial, sans-serif; color: navy;" class="">Dr. Martin B. van der Mark</span><span lang="EN-US" class=""><o:p class=""></o:p></span></div></div><div class=""><div style="margin: 0cm 0cm 0.0001pt; font-size: 12pt; font-family: 'Times New Roman', serif;" class=""><span lang="EN-US" style="font-size: 10pt; font-family: Arial, sans-serif; color: navy;" class="">Principal Scientist, Minimally Invasive Healthcare</span><span lang="EN-US" class=""><o:p class=""></o:p></span></div></div><div class=""><div style="margin: 0cm 0cm 0.0001pt; font-size: 12pt; font-family: 'Times New Roman', serif;" class=""><span lang="EN-US" style="font-size: 11pt; font-family: Calibri, sans-serif; color: navy;" class=""> </span><span lang="EN-US" class=""><o:p class=""></o:p></span></div></div><div class=""><div style="margin: 0cm 0cm 0.0001pt; font-size: 12pt; font-family: 'Times New Roman', serif;" class=""><span lang="EN-US" style="font-size: 10pt; font-family: Arial, sans-serif; color: navy;" class="">Philips Research Europe - Eindhoven</span><span lang="EN-US" class=""><o:p class=""></o:p></span></div></div><div class=""><div style="margin: 0cm 0cm 0.0001pt; font-size: 12pt; font-family: 'Times New Roman', serif;" class=""><span lang="EN-US" style="font-size: 10pt; font-family: Arial, sans-serif; color: navy;" class="">High Tech Campus, Building 34 (WB2.025)</span><span lang="EN-US" class=""><o:p class=""></o:p></span></div></div><div class=""><div style="margin: 0cm 0cm 0.0001pt; font-size: 12pt; font-family: 'Times New Roman', serif;" class=""><span lang="EN-US" style="font-size: 10pt; font-family: Arial, sans-serif; color: navy;" class="">Prof. Holstlaan 4</span><span lang="EN-US" class=""><o:p class=""></o:p></span></div></div><div class=""><div style="margin: 0cm 0cm 0.0001pt; font-size: 12pt; font-family: 'Times New Roman', serif;" class=""><span lang="EN-US" style="font-size: 10pt; font-family: Arial, sans-serif; color: navy;" class="">5656 AE Eindhoven, The Netherlands</span><span lang="EN-US" class=""><o:p class=""></o:p></span></div></div><div class=""><div style="margin: 0cm 0cm 0.0001pt; font-size: 12pt; font-family: 'Times New Roman', serif;" class=""><span lang="EN-US" style="font-size: 10pt; font-family: Arial, sans-serif; color: navy;" class="">Tel: +31 40 2747548</span><span lang="EN-US" class=""><o:p class=""></o:p></span></div></div><div class=""><div style="margin: 0cm 0cm 0.0001pt; font-size: 12pt; font-family: 'Times New Roman', serif;" class=""><span lang="EN-US" style="font-size: 11pt; font-family: Calibri, sans-serif; color: rgb(31, 73, 125);" class=""> </span><span lang="EN-US" class=""><o:p class=""></o:p></span></div></div><div class=""><div style="margin: 0cm 0cm 0.0001pt; font-size: 12pt; font-family: 'Times New Roman', serif;" class=""><b class=""><span lang="EN-US" style="font-size: 10pt; font-family: Tahoma, sans-serif;" class="">From:</span></b><span class="apple-converted-space"><span lang="EN-US" style="font-size: 10pt; font-family: Tahoma, sans-serif;" class=""> </span></span><span lang="EN-US" style="font-size: 10pt; font-family: Tahoma, sans-serif;" class="">General [<a href="mailto:general-bounces+martin.van.der.mark=philips.com@lists.natureoflightandparticles.org" style="color: purple; text-decoration: underline;" class=""><span style="color: purple;" class="">mailto:general-bounces+martin.van.der.mark=philips.com@lists.natureoflightandparticles.org</span></a>]<b class="">On Behalf Of<span class="apple-converted-space"> </span></b>Andrew Meulenberg<br class=""><b class="">Sent:</b><span class="apple-converted-space"> </span>donderdag 7 mei 2015 7:40<br class=""><b class="">To:</b><span class="apple-converted-space"> </span>Nature of Light and Particles - General Discussion<br class=""><b class="">Subject:</b><span class="apple-converted-space"> </span>Re: [General] Quantisation of classical electromagnetism</span><span lang="EN-US" class=""><o:p class=""></o:p></span></div></div><div class=""><div style="margin: 0cm 0cm 0.0001pt; font-size: 12pt; font-family: 'Times New Roman', serif;" class=""><span lang="EN-US" class=""> <o:p class=""></o:p></span></div></div><div class=""><div class=""><p class="MsoNormal" style="margin: 0cm 0cm 12pt; font-size: 12pt; font-family: 'Times New Roman', serif;"><span lang="EN-US" class="">Dear Martin,<o:p class=""></o:p></span></p></div><div class=""><div style="margin: 0cm 0cm 0.0001pt; font-size: 12pt; font-family: 'Times New Roman', serif;" class=""><span lang="EN-US" class="">It is great communicating with someone who has also thought about the issue. My comments are sometimes too cryptic because I assume that you would have come to the same conclusions. Let me try (in brown) to identify some of the differences below.<o:p class=""></o:p></span></div></div><div class=""><div class=""><div style="margin: 0cm 0cm 0.0001pt; font-size: 12pt; font-family: 'Times New Roman', serif;" class=""><span lang="EN-US" class=""> <o:p class=""></o:p></span></div></div><div class=""><div class=""><div style="margin: 0cm 0cm 0.0001pt; font-size: 12pt; font-family: 'Times New Roman', serif;" class=""><span lang="EN-US" class="">On Thu, May 7, 2015 at 3:50 AM, Mark, Martin van der <<a href="mailto:martin.van.der.mark@philips.com" target="_blank" style="color: purple; text-decoration: underline;" class=""><span style="color: purple;" class="">martin.van.der.mark@philips.com</span></a>> wrote:<o:p class=""></o:p></span></div></div><div class=""><div class=""><div class=""><div style="margin: 0cm 0cm 0.0001pt; font-size: 12pt; font-family: 'Times New Roman', serif;" class=""><span lang="EN-US" style="font-family: Calibri, sans-serif; color: rgb(119, 147, 60);" class="">Andrew, thanks, please see below, in green</span><span lang="EN-US" class=""><o:p class=""></o:p></span></div></div><div class=""><div style="margin: 0cm 0cm 0.0001pt; font-size: 12pt; font-family: 'Times New Roman', serif;" class=""><span lang="NL" style="font-size: 11pt; font-family: Calibri, sans-serif; color: rgb(31, 73, 125);" class=""> </span><span lang="DE" style="font-size: 10pt; font-family: Arial, sans-serif; color: navy;" class="">Dr. Martin B. van der Mark</span><span lang="EN-US" class=""><o:p class=""></o:p></span></div></div><div class=""><div style="margin: 0cm 0cm 0.0001pt; font-size: 12pt; font-family: 'Times New Roman', serif;" class=""><span lang="EN-US" style="font-size: 10pt; font-family: Arial, sans-serif; color: navy;" class="">Principal Scientist, Minimally Invasive Healthcare</span><span lang="EN-US" class=""><o:p class=""></o:p></span></div></div><div class=""><div style="margin: 0cm 0cm 0.0001pt; font-size: 12pt; font-family: 'Times New Roman', serif;" class=""><b class=""><span lang="EN-US" style="font-size: 11pt; font-family: Calibri, sans-serif; color: rgb(31, 73, 125);" class=""> </span></b><span lang="EN-US" class=""><o:p class=""></o:p></span></div></div><div class=""><div style="margin: 0cm 0cm 0.0001pt; font-size: 12pt; font-family: 'Times New Roman', serif;" class=""><b class=""><span lang="EN-US" style="font-size: 10pt; font-family: Tahoma, sans-serif;" class="">From:</span></b><span class="apple-converted-space"><span lang="EN-US" style="font-size: 10pt; font-family: Tahoma, sans-serif;" class=""> </span></span><span lang="EN-US" style="font-size: 10pt; font-family: Tahoma, sans-serif;" class="">General [mailto:<a href="mailto:general-bounces%2Bmartin.van.der.mark" target="_blank" style="color: purple; text-decoration: underline;" class=""><span style="color: purple;" class="">general-bounces+martin.van.der.mark</span></a>=<a href="mailto:philips.com@lists.natureoflightandparticles.org" target="_blank" style="color: purple; text-decoration: underline;" class=""><span style="color: purple;" class="">philips.com@lists.natureoflightandparticles.org</span></a>]<b class="">On Behalf Of<span class="apple-converted-space"> </span></b>Andrew Meulenberg<br class=""><b class="">Sent:</b><span class="apple-converted-space"> </span>woensdag 6 mei 2015 19:46<br class=""><b class="">To:</b><span class="apple-converted-space"> </span>Nature of Light and Particles - General Discussion<br class=""><b class="">Subject:</b><span class="apple-converted-space"> </span>Re: [General] Quantisation of classical electromagnetism</span><span lang="EN-US" class=""><o:p class=""></o:p></span></div></div><div class=""><div class=""><div class=""><div class=""><div class=""><div style="margin: 0cm 0cm 0.0001pt; font-size: 12pt; font-family: 'Times New Roman', serif;" class=""><span lang="EN-US" style="font-size: 10pt;" class=""> <span style="color: red;" class="">Dear John W, Martin, et al.,</span></span><span lang="EN-US" class=""><o:p class=""></o:p></span></div></div></div><p class="MsoNormal" style="margin: 0cm 0cm 12pt; font-size: 12pt; font-family: 'Times New Roman', serif;"><span lang="EN-US" style="color: red;" class="">I don't think that a week together in San Diego would be enough to transfer the information that we all need to share. And, I will probably miss even that. I am already learning so much and have so much to contribute that I feel frustrated that I have to divide my time.</span><span lang="EN-US" class=""><o:p class=""></o:p></span></p></div><p class="MsoNormal" style="margin: 0cm 0cm 12pt; font-size: 12pt; font-family: 'Times New Roman', serif;"><span lang="EN-US" style="color: red;" class="">Just this morning (my time), I changed my idea of the electron radius. After seeing it expressed many times by various members of this group as 1/2 the Compton radius (and considering that to be wrong), it finally hit me, when reading it again, that, even within my own model,<span class="apple-converted-space"> </span><u class="">I<span class="apple-converted-space"> </span></u>had been wrong and this smaller radius is probably correct.</span><span lang="EN-US" class=""><o:p class=""></o:p></span></p></div><div class=""><div style="margin: 0cm 0cm 0.0001pt; font-size: 12pt; font-family: 'Times New Roman', serif;" class=""><span lang="EN-US" style="font-size: 7.5pt; color: red;" class="">some comments below:</span><span lang="EN-US" class=""><o:p class=""></o:p></span></div></div><div class=""><div class=""><div class=""><div class=""><div class=""><div class=""><div class=""><div style="margin: 0cm 0cm 0.0001pt; font-size: 12pt; font-family: 'Times New Roman', serif;" class=""><span lang="EN-US" style="font-size: 7.5pt;" class=""> On Wed, May 6, 2015 at 3:28 PM, Mark, Martin van der <</span><span lang="EN-US" class=""><a href="mailto:martin.van.der.mark@philips.com" target="_blank" style="color: purple; text-decoration: underline;" class=""><span style="color: purple;" class="">martin.van.der.mark@philips.com</span></a></span><span lang="EN-US" style="font-size: 7.5pt;" class="">> wrote:</span><span lang="EN-US" class=""><o:p class=""></o:p></span></div></div><div class=""><div class=""><div class=""><div style="margin: 0cm 0cm 0.0001pt; font-size: 12pt; font-family: 'Times New Roman', serif;" class=""><span lang="EN-US" style="font-size: 7.5pt;" class=""> </span><span lang="EN-US" style="font-family: Calibri, sans-serif; color: rgb(31, 73, 125);" class="">Andrew, John, all</span><span lang="EN-US" class=""><o:p class=""></o:p></span></div></div><div class=""><div style="margin: 0cm 0cm 0.0001pt; font-size: 12pt; font-family: 'Times New Roman', serif;" class=""><span lang="EN-US" style="font-family: Calibri, sans-serif; color: rgb(31, 73, 125);" class=""> John W is quite right as well, just a small remark on the hydrogen atom.</span><span lang="EN-US" class=""><o:p class=""></o:p></span></div></div><div class=""><div style="margin: 0cm 0cm 0.0001pt; font-size: 12pt; font-family: 'Times New Roman', serif;" class=""><span lang="EN-US" style="font-family: Calibri, sans-serif; color: rgb(31, 73, 125);" class="">By the virial theorem, for a 1/r potential, potential energy is minus two times the kinetic energy and kinetic energy is equal to the binding energy (13.6 eV in the ground state).</span><span lang="EN-US" class=""><o:p class=""></o:p></span></div></div><div class=""><div style="margin: 0cm 0cm 0.0001pt; font-size: 12pt; font-family: 'Times New Roman', serif;" class=""><span lang="EN-US" style="font-family: Calibri, sans-serif; color: rgb(31, 73, 125);" class="">For the structure of the atom there are three conditions, one of electromagnetic, and two of inertial nature.</span><span lang="EN-US" class=""><o:p class=""></o:p></span></div></div><div class=""><div style="margin: 0cm 0cm 0.0001pt; font-size: 12pt; font-family: 'Times New Roman', serif;" class=""><span lang="EN-US" style="font-family: Calibri, sans-serif; color: rgb(31, 73, 125);" class="">1) The coulomb potential runs to minus infinity, that is very deep. It comes from the charge of proton and electron.</span><span lang="EN-US" class=""><o:p class=""></o:p></span></div></div><div class=""><div style="margin: 0cm 0cm 0.0001pt; font-size: 12pt; font-family: 'Times New Roman', serif;" class=""><span lang="EN-US" style="font-family: Calibri, sans-serif; color: rgb(31, 73, 125);" class="">2) Then the centrifugal force (depends on mass of proton and electron) must balance the Coulomb force, this could have been in a continuum of orbits if the electron and proton were just particles (without a wave nature) (see gravitation and solar system for an exact analogy),</span><span lang="EN-US" class=""><o:p class=""></o:p></span></div></div><div class=""><div style="margin: 0cm 0cm 0.0001pt; font-size: 12pt; font-family: 'Times New Roman', serif;" class=""><span lang="EN-US" style="font-family: Calibri, sans-serif; color: rgb(31, 73, 125);" class="">3) The mass of proton and electron set the scale of the de Broglie wavelength (which, incidentally, is exactly the same for proton and electron in the bound state), and hence the bound state has a finite size, 0.1 nm diameter for the ground state. The particle’s waves must interfere constructively within the boundary conditions: quantized energy levels appear.</span><span lang="EN-US" class=""><o:p class=""></o:p></span></div></div><div class=""><div style="margin: 0cm 0cm 0.0001pt; font-size: 12pt; font-family: 'Times New Roman', serif;" class=""><span lang="EN-US" style="font-size: 11pt; font-family: Calibri, sans-serif; color: rgb(31, 73, 125);" class="">Cheers, Martin</span><span lang="EN-US" class=""><o:p class=""></o:p></span></div></div></div></div><div class=""><div class=""><div style="margin: 0cm 0cm 0.0001pt; font-size: 12pt; font-family: 'Times New Roman', serif;" class=""><span lang="EN-US" class=""> <span style="color: red;" class="">I also have three basic conditions:</span><o:p class=""></o:p></span></div></div><ul type="disc" style="margin-bottom: 0cm; margin-top: 0cm;" class=""><li class="MsoNormal" style="margin: 0cm 0cm 0.0001pt; font-size: 12pt; font-family: 'Times New Roman', serif;"><span lang="EN-US" style="color: red;" class="">The QM description of the mechanical resonance of a body confined in a potential well. The reason for this resonance is not the interference with the nucleus (which does not appear in the fundamental equations). There is a simple physical and mathematical basis that is taught in 1st year calculus.</span><span lang="EN-US" class=""><o:p class=""></o:p></span></li><li class="MsoNormal" style="margin: 0cm 0cm 0.0001pt; font-size: 12pt; font-family: 'Times New Roman', serif;"><span lang="EN-US" style="color: red;" class="">The classical description of the orbiting electron creates an EM field that is evolving into a photon as the electron decays to a deeper level. The resonance between the electron and emitted-photon frequencies, along with the virial theorem and conservation of energy and ang. mom., determine the allowed energy levels. The fact that these levels agree with the mechanical levels gives a double resonance.</span><span lang="EN-US" class=""><o:p class=""></o:p></span></li></ul><div class=""><div style="margin: 0cm 0cm 0.0001pt; font-size: 12pt; font-family: 'Times New Roman', serif;" class=""><span lang="EN-US" style="font-size: 11pt; font-family: Calibri, sans-serif; color: rgb(119, 147, 60);" class="">I do not really understand what you mean by the double resonance.</span><span lang="EN-US" class=""><o:p class=""></o:p></span></div></div></div></div></div></div></div></div></div></div></div></div><div class=""><div class=""><div style="margin: 0cm 0cm 0.0001pt; font-size: 12pt; font-family: 'Times New Roman', serif;" class=""><span lang="EN-US" style="color: rgb(180, 95, 6);" class=""> </span><span lang="EN-US" style="font-size: 11pt; font-family: Calibri, sans-serif; color: rgb(180, 95, 6);" class="">The levels identified with the classical description agree with those of the mechanical (QM) system.</span><span lang="EN-US" class=""><o:p class=""></o:p></span></div></div><div class=""><div style="margin: 0cm 0cm 0.0001pt; font-size: 12pt; font-family: 'Times New Roman', serif;" class=""><span lang="EN-US" style="font-size: 11pt; font-family: Calibri, sans-serif; color: rgb(112, 48, 160);" class="">To be precise: the mechanical part equals the mechanical part. No information in that at all, it is not a coincidence it is an incidence.</span><span lang="EN-US" class=""><o:p class=""></o:p></span></div></div></div><blockquote style="border-style: none none none solid; border-left-color: rgb(204, 204, 204); border-left-width: 1pt; padding: 0cm 0cm 0cm 6pt; margin: 5pt 0cm 5pt 4.8pt;" class=""><div class=""><div class=""><div class=""><div class=""><div class=""><div class=""><div class=""><div class=""><div class=""><div class=""><ul type="disc" style="margin-bottom: 0cm; margin-top: 0cm;" class=""><li class="MsoNormal" style="margin: 0cm 0cm 0.0001pt; font-size: 12pt; font-family: 'Times New Roman', serif;"><span lang="EN-US" style="color: red;" class="">the ground state is established by the requirement of a photon to have an angular momentum of hbar.</span><span lang="EN-US" class=""><o:p class=""></o:p></span></li></ul><div class=""><div style="margin: 0cm 0cm 0.0001pt; font-size: 12pt; font-family: 'Times New Roman', serif;" class=""><span lang="EN-US" style="font-size: 11pt; font-family: Calibri, sans-serif; color: rgb(119, 147, 60);" class="">Why is this fundamental? It depends on the system you are looking at. Circular orbits are a confusing thing o look at too, if you want to look at angular momentum. The real hydrogen atom has NO angular momentum (spin=0) in the ground state, contrary to the Bohr model of it!!!!! </span><span lang="EN-US" class=""><o:p class=""></o:p></span></div></div></div></div></div></div></div></div></div></div></div></div></blockquote><div class=""><div class=""><div style="margin: 0cm 0cm 0.0001pt; font-size: 12pt; font-family: 'Times New Roman', serif;" class=""><span lang="EN-US" class=""><br class=""></span><span lang="EN-US" style="font-size: 11pt; font-family: Calibri, sans-serif; color: rgb(180, 95, 6);" class="">[Exactly, therefore it cannot radiate a photon except to a system w ang. mom. = hbar. No levels below gnd state have that value.]</span><span lang="EN-US" class=""><br class=""><span style="color: rgb(112, 48, 160);" class="">Wrong answer to the given question. The ground state has IN THE FIRST PLACE nothing to do with the emitted energy part, but with what remains. What remains must be a mode of the system, a quantum state they call this in quantum mechanics. It means that a single wavelength, 3D resonance must be maintained. For the hydrogen atom (or for that matter any spherical system) must have simultaneous solutions for r, theta and phi, such that at least one has a single wave in it. It appears to be the radial solution, a breather (not the Bohr type phi solution with one wavelength on the circumference).</span><o:p class=""></o:p></span></div></div><div class=""><div style="margin: 0cm 0cm 0.0001pt; font-size: 12pt; font-family: 'Times New Roman', serif;" class=""><span lang="EN-US" style="font-size: 11pt; font-family: Calibri, sans-serif; color: rgb(112, 48, 160);" class="">To get from a higher state into this state the right combination of energy, momentum and angular momentum must be emitted, hence the selection rules as the are, and that is what your answer is about.<span class="apple-converted-space"> </span></span><span lang="EN-US" class=""><o:p class=""></o:p></span></div></div></div><blockquote style="border-style: none none none solid; border-left-color: rgb(204, 204, 204); border-left-width: 1pt; padding: 0cm 0cm 0cm 6pt; margin: 5pt 0cm 5pt 4.8pt;" class=""><div class=""><div class=""><div class=""><div class=""><div class=""><div class=""><div class=""><div class=""><div class=""><div class=""><div class=""><div style="margin: 0cm 0cm 0.0001pt; font-size: 12pt; font-family: 'Times New Roman', serif;" class=""><span lang="EN-US" style="font-size: 11pt; font-family: Calibri, sans-serif; color: rgb(119, 147, 60);" class="">The groundstate of the atom is the groundstate because it is the lowest energy state, with just the fundamental tone (one wavelength) fitting to the boundary conditions.</span><span lang="EN-US" class=""><o:p class=""></o:p></span></div></div></div></div></div></div></div></div></div></div></div></div></blockquote><div class=""><div class=""><div style="margin: 0cm 0cm 0.0001pt; font-size: 12pt; font-family: 'Times New Roman', serif;" class=""><span lang="EN-US" class=""> <o:p class=""></o:p></span></div></div></div><div class=""><div class=""><div style="margin: 0cm 0cm 0.0001pt; font-size: 12pt; font-family: 'Times New Roman', serif;" class=""><span lang="EN-US" style="color: rgb(180, 95, 6);" class="">There is no reason<span class="apple-converted-space"> </span><u class="">given</u><span class="apple-converted-space"> </span>that the wavelength cannot fit 2 cycles rather than one. Is it more difficult than having n wavelengths in a single cycle? (ref Lissajou figures)</span><span class="apple-converted-space"><span lang="EN-US" class=""> </span></span><span lang="EN-US" style="color: rgb(180, 95, 6);" class="">This is the basis of Mill's hydrino states. The limiting factor is the photon.</span><span lang="EN-US" class=""><o:p class=""></o:p></span></div></div><div class=""><div style="margin: 0cm 0cm 0.0001pt; font-size: 12pt; font-family: 'Times New Roman', serif;" class=""><span lang="EN-US" style="font-size: 11pt; font-family: Calibri, sans-serif; color: rgb(112, 48, 160);" class="">See previous answer and understand that the reason is implicitly given there already. A mode of a resonator or waveguide, a quantum state, these ar the same sort of things. They have Q or quality factor that tells you how broad or narrow the resonance is and how long it lives. For a very long live time such as the ground state hydrogen atom, the Q is very very high, and the level is very precisely defined. The wave must therefore fit very very very very precisely on the mode. Not a factor of two difference, no, minus dozens of orders of magnitude precise!</span><span lang="EN-US" class=""><o:p class=""></o:p></span></div></div></div><div class=""><div class=""><div style="margin: 0cm 0cm 0.0001pt; font-size: 12pt; font-family: 'Times New Roman', serif;" class=""><span lang="EN-US" class=""> <o:p class=""></o:p></span></div></div></div><blockquote style="border-style: none none none solid; border-left-color: rgb(204, 204, 204); border-left-width: 1pt; padding: 0cm 0cm 0cm 6pt; margin: 5pt 0cm 5pt 4.8pt;" class=""><div class=""><div class=""><div class=""><div class=""><div class=""><div class=""><div class=""><div class=""><div class=""><div class=""><div class=""><div style="margin: 0cm 0cm 0.0001pt; font-size: 12pt; font-family: 'Times New Roman', serif;" class=""><span lang="EN-US" style="font-size: 11pt; font-family: Calibri, sans-serif; color: rgb(119, 147, 60);" class="">The one wavelength holds for the complete atom, electron and proton: the electron is light and moving fast, the proton id heavy and slow, but both have the same momentum! Hence they have the same de Broglie wavelength…</span><span lang="EN-US" class=""><o:p class=""></o:p></span></div></div></div></div></div></div></div></div></div></div></div></div></blockquote><div class=""><div class=""><div style="margin: 0cm 0cm 0.0001pt; font-size: 12pt; font-family: 'Times New Roman', serif;" class=""><span lang="EN-US" class=""> <o:p class=""></o:p></span></div></div></div><div class=""><div class=""><div style="margin: 0cm 0cm 0.0001pt; font-size: 12pt; font-family: 'Times New Roman', serif;" class=""><span lang="EN-US" style="color: rgb(180, 95, 6);" class="">The solution assuming an infinite mass nucleus (hence no deBroglie wavelength & no resonance) still produces discrete levels. Therefore that issue cannot be causal.</span><span lang="EN-US" class=""><o:p class=""></o:p></span></div></div><div class=""><div style="margin: 0cm 0cm 0.0001pt; font-size: 12pt; font-family: 'Times New Roman', serif;" class=""><span lang="EN-US" style="font-size: 11pt; font-family: Calibri, sans-serif; color: rgb(112, 48, 160);" class="">Bullshit, sorry, but here you should really know better since:</span><span lang="EN-US" class=""><o:p class=""></o:p></span></div></div><div style="margin-left: 36pt;" class=""><div style="margin: 0cm 0cm 0.0001pt; font-size: 12pt; font-family: 'Times New Roman', serif; text-indent: -18pt;" class=""><span lang="EN-US" style="font-size: 11pt; font-family: Calibri, sans-serif; color: rgb(112, 48, 160);" class="">1)</span><span lang="EN-US" style="font-size: 7pt; color: rgb(112, 48, 160);" class=""> <span class="apple-converted-space"> </span></span><span lang="EN-US" style="font-size: 11pt; font-family: Calibri, sans-serif; color: rgb(112, 48, 160);" class="">I have told you already you are referring to the BORN APPROXIMATION</span><span lang="EN-US" class=""><o:p class=""></o:p></span></div></div><div style="margin-left: 36pt;" class=""><div style="margin: 0cm 0cm 0.0001pt; font-size: 12pt; font-family: 'Times New Roman', serif; text-indent: -18pt;" class=""><span lang="EN-US" style="font-size: 11pt; font-family: Calibri, sans-serif; color: rgb(112, 48, 160);" class="">2)</span><span lang="EN-US" style="font-size: 7pt; color: rgb(112, 48, 160);" class=""> <span class="apple-converted-space"> </span></span><span lang="EN-US" style="font-size: 11pt; font-family: Calibri, sans-serif; color: rgb(112, 48, 160);" class="">It is in every basic textbook, second year physics</span><span lang="EN-US" class=""><o:p class=""></o:p></span></div></div><div style="margin-left: 36pt;" class=""><div style="margin: 0cm 0cm 0.0001pt; font-size: 12pt; font-family: 'Times New Roman', serif; text-indent: -18pt;" class=""><span lang="EN-US" style="font-size: 11pt; font-family: Calibri, sans-serif; color: rgb(112, 48, 160);" class="">3)</span><span lang="EN-US" style="font-size: 7pt; color: rgb(112, 48, 160);" class=""> <span class="apple-converted-space"> </span></span><span lang="EN-US" style="font-size: 11pt; font-family: Calibri, sans-serif; color: rgb(112, 48, 160);" class="">The so-called reduced mass gives a slightly different set of levels, the correct levels. Remember the Rydbergconstant? And its slightly different numbers?</span><span lang="EN-US" class=""><o:p class=""></o:p></span></div></div><div class=""><div style="margin: 0cm 0cm 0.0001pt; font-size: 12pt; font-family: 'Times New Roman', serif;" class=""><span lang="EN-US" style="font-size: 11pt; font-family: Calibri, sans-serif; color: rgb(112, 48, 160);" class="">Just do your homework, and go to Wikipedia, that will be good enough.</span><span lang="EN-US" class=""><o:p class=""></o:p></span></div></div><div class=""><div style="margin: 0cm 0cm 0.0001pt; font-size: 12pt; font-family: 'Times New Roman', serif;" class=""><span lang="EN-US" style="font-size: 11pt; font-family: Calibri, sans-serif; color: rgb(112, 48, 160);" class=""> </span><span lang="EN-US" class=""><o:p class=""></o:p></span></div></div><div class=""><div style="margin: 0cm 0cm 0.0001pt; font-size: 12pt; font-family: 'Times New Roman', serif;" class=""><span lang="EN-US" style="font-size: 11pt; font-family: Calibri, sans-serif; color: rgb(112, 48, 160);" class="">Here another remark regarding your earlier question, whether I was talking physics or mathematics. (see next question below)</span><span lang="EN-US" class=""><o:p class=""></o:p></span></div></div><div class=""><div style="margin: 0cm 0cm 0.0001pt; font-size: 12pt; font-family: 'Times New Roman', serif;" class=""><span lang="EN-US" style="font-size: 11pt; font-family: Calibri, sans-serif; color: rgb(112, 48, 160);" class="">Here you see I get the physics right because I think physics. Then I get the numbers right because I understand the approximations, the calculus and the details. That can only be if you know how to the mathematics right.</span><span lang="EN-US" class=""><o:p class=""></o:p></span></div></div><div class=""><div style="margin: 0cm 0cm 0.0001pt; font-size: 12pt; font-family: 'Times New Roman', serif;" class=""><span lang="EN-US" style="font-size: 11pt; font-family: Calibri, sans-serif; color: rgb(112, 48, 160);" class="">Sorry I just hate mediocrity.</span><span lang="EN-US" class=""><o:p class=""></o:p></span></div></div></div><div class=""><div class=""><div style="margin: 0cm 0cm 0.0001pt; font-size: 12pt; font-family: 'Times New Roman', serif;" class=""><span lang="EN-US" class=""> <o:p class=""></o:p></span></div></div></div><blockquote style="border-style: none none none solid; border-left-color: rgb(204, 204, 204); border-left-width: 1pt; padding: 0cm 0cm 0cm 6pt; margin: 5pt 0cm 5pt 4.8pt;" class=""><div class=""><div class=""><div class=""><div class=""><div class=""><div class=""><div class=""><div class=""><div class=""><div class=""><div class=""><div style="margin: 0cm 0cm 0.0001pt; font-size: 12pt; font-family: 'Times New Roman', serif;" class=""><span lang="EN-US" style="color: red;" class="">Looking at your conditions produced other thoughts.</span><span lang="EN-US" class=""><o:p class=""></o:p></span></div></div></div><div class=""><ol start="1" type="1" style="margin-bottom: 0cm; margin-top: 0cm;" class=""><li class="MsoNormal" style="margin: 0cm 0cm 0.0001pt; font-size: 12pt; font-family: 'Times New Roman', serif;"><span lang="EN-US" style="color: red;" class="">The statement that "the coulomb potential runs to minus infinity" is a mathematician, not a physicist talking.</span><span lang="EN-US" class=""><o:p class=""></o:p></span></li></ol><div class=""><div style="margin: 0cm 0cm 0.0001pt; font-size: 12pt; font-family: 'Times New Roman', serif;" class=""><span lang="EN-US" style="font-size: 11pt; font-family: Calibri, sans-serif; color: rgb(119, 147, 60);" class="">True. The Coulomb potential is a mathematical concept that models reality quite perfectly. Mathematics is the language of physics. Further, the electron has an almost 1/r dependent potential still at TeV collision energies, this is why people say it has point-like behavior.</span><span lang="EN-US" class=""><o:p class=""></o:p></span></div></div></div></div></div></div></div></div></div></div></div></div></blockquote><div class=""><div class=""><div style="margin: 0cm 0cm 0.0001pt; font-size: 12pt; font-family: 'Times New Roman', serif;" class=""><span lang="EN-US" class=""> <o:p class=""></o:p></span></div></div></div><div class=""><div class=""><div style="margin: 0cm 0cm 0.0001pt; font-size: 12pt; font-family: 'Times New Roman', serif;" class=""><span lang="EN-US" style="color: rgb(180, 95, 6);" class="">And, it will be considered valid until experimental evidence show otherwise. Then, 60 years of mathematical 'proofs' will immediately disappear. Do you know of any nuclear physicist who would consider the nuclear Coulomb potential to be a singularity? Even before the quark model became popular? What is reality, a singular potential that contains all of the energy in the universe, or a presently measured finite charge density of the proton and neutron? Feynman jested that the whole universe consisted of a single electron oscillating back and forth in time. If it was singular and contained all of the energy in the universe, maybe Feynman's jest was correct.</span><span lang="EN-US" class=""><o:p class=""></o:p></span></div></div></div><div class=""><div class=""><div style="margin: 0cm 0cm 0.0001pt; font-size: 12pt; font-family: 'Times New Roman', serif;" class=""><span lang="EN-US" class=""> <o:p class=""></o:p></span></div></div><div class=""><div style="margin: 0cm 0cm 0.0001pt; font-size: 12pt; font-family: 'Times New Roman', serif;" class=""><span lang="EN-US" style="font-size: 11pt; font-family: Calibri, sans-serif; color: rgb(112, 48, 160);" class="">The Coulomb potential is BY DEFINITION a 1/r potential associated with a POINT CHARGE.</span><span lang="EN-US" class=""><o:p class=""></o:p></span></div></div><div class=""><div style="margin: 0cm 0cm 0.0001pt; font-size: 12pt; font-family: 'Times New Roman', serif;" class=""><span lang="EN-US" style="font-size: 11pt; font-family: Calibri, sans-serif; color: rgb(112, 48, 160);" class="">It therefore runs, by definition, to minus infinity.</span><span lang="EN-US" class=""><o:p class=""></o:p></span></div></div><div class=""><div style="margin: 0cm 0cm 0.0001pt; font-size: 12pt; font-family: 'Times New Roman', serif;" class=""><span lang="EN-US" style="font-size: 11pt; font-family: Calibri, sans-serif; color: rgb(112, 48, 160);" class=""> </span><span lang="EN-US" class=""><o:p class=""></o:p></span></div></div><div class=""><div style="margin: 0cm 0cm 0.0001pt; font-size: 12pt; font-family: 'Times New Roman', serif;" class=""><span lang="EN-US" style="font-size: 11pt; font-family: Calibri, sans-serif; color: rgb(112, 48, 160);" class="">Real charges, like the proton or a charged party balloon, rubbed-up on a cat, have a cut-off at their respective charge radii of 0.87 fm and 10 cm: at smaller size the potential may be or is quite constant. There is always a reason in the physics of things that will avoid infinities naturally.</span><span lang="EN-US" class=""><o:p class=""></o:p></span></div></div><div class=""><div style="margin: 0cm 0cm 0.0001pt; font-size: 12pt; font-family: 'Times New Roman', serif;" class=""><span lang="EN-US" style="font-size: 11pt; font-family: Calibri, sans-serif; color: rgb(112, 48, 160);" class="">I know you want to make that point, and I fully agree. But please do not misuse the argument or definition of things.</span><span lang="EN-US" class=""><o:p class=""></o:p></span></div></div></div><blockquote style="border-style: none none none solid; border-left-color: rgb(204, 204, 204); border-left-width: 1pt; padding: 0cm 0cm 0cm 6pt; margin: 5pt 0cm 5pt 4.8pt;" class=""><div class=""><div class=""><div class=""><div class=""><div class=""><div class=""><div class=""><div class=""><div class=""><div class=""><div class=""><div style="margin: 0cm 0cm 0.0001pt; font-size: 12pt; font-family: 'Times New Roman', serif;" class=""><span lang="EN-US" style="font-size: 11pt; font-family: Calibri, sans-serif; color: rgb(119, 147, 60);" class="">Further your remark is irrelevant because the binding energy of the ground state of hydrogen (or any atom) is alpha^2 times smaller than the electron’s classical radius (which incidentally is close to the charge radius of the proton)</span><span lang="EN-US" class=""><o:p class=""></o:p></span></div></div></div></div></div></div></div></div></div></div></div></div></blockquote><div class=""><div class=""><div style="margin: 0cm 0cm 0.0001pt; font-size: 12pt; font-family: 'Times New Roman', serif;" class=""><span lang="EN-US" class=""> <o:p class=""></o:p></span></div></div></div><div class=""><div class=""><div style="margin: 0cm 0cm 0.0001pt; font-size: 12pt; font-family: 'Times New Roman', serif;" class=""><span lang="EN-US" style="color: rgb(180, 95, 6);" class="">Do you consider the proton charge radius to be its field-energy density or the major extent of its<b class="">Coulomb potential</b><span class="apple-converted-space"> </span>(e.g., the electron Compton radius)?</span><span class="apple-converted-space"><span lang="EN-US" class=""> </span></span><span lang="EN-US" style="color: rgb(180, 95, 6);" class="">We haven't defined charge yet have we? [Am I being the mathematician now for insisting on a valid definition?]</span><span lang="EN-US" class=""><o:p class=""></o:p></span></div></div><div class=""><div style="margin: 0cm 0cm 0.0001pt; font-size: 12pt; font-family: 'Times New Roman', serif;" class=""><span lang="EN-US" style="font-size: 11pt; font-family: Calibri, sans-serif; color: rgb(31, 73, 125);" class=""> </span><span lang="EN-US" class=""><o:p class=""></o:p></span></div></div><div class=""><div style="margin: 0cm 0cm 0.0001pt; font-size: 12pt; font-family: 'Times New Roman', serif;" class=""><span lang="EN-US" style="font-size: 11pt; font-family: Calibri, sans-serif; color: rgb(112, 48, 160);" class="">It is the proton’s START of the Coulomb potential! Look it Up in a book on high energy physics if you really want to know exactly what they mean by it.</span><span lang="EN-US" class=""><o:p class=""></o:p></span></div></div></div><div class=""><div class=""><div style="margin: 0cm 0cm 0.0001pt; font-size: 12pt; font-family: 'Times New Roman', serif;" class=""><span lang="EN-US" class=""> <o:p class=""></o:p></span></div></div></div><blockquote style="border-style: none none none solid; border-left-color: rgb(204, 204, 204); border-left-width: 1pt; padding: 0cm 0cm 0cm 6pt; margin: 5pt 0cm 5pt 4.8pt;" class=""><div class=""><div class=""><div class=""><div class=""><div class=""><div class=""><div class=""><div class=""><div class=""><div class=""><div style="margin-left: 36pt;" class=""><div style="margin: 0cm 0cm 0.0001pt; font-size: 12pt; font-family: 'Times New Roman', serif;" class=""><span lang="EN-US" style="color: red;" class="">The potential energy PE must come from the energies, as expressed by the mass and charge, of proton and electron. Since the largest energy is the mass, the PE is limited to a GeV. Therefore, the electrical potential cannot exceed this value.<span class="apple-converted-space"> </span></span><span lang="EN-US" class=""><o:p class=""></o:p></span></div></div><div class=""><div style="margin: 0cm 0cm 0.0001pt; font-size: 12pt; font-family: 'Times New Roman', serif;" class=""><span lang="EN-US" style="font-size: 11pt; font-family: Calibri, sans-serif; color: rgb(119, 147, 60);" class="">Yes it can exceed its RESTmass , and will be precisely gamma m0, see above, not exceeding its relativistic mass, of course.</span><span lang="EN-US" class=""><o:p class=""></o:p></span></div></div></div></div></div></div></div></div></div></div></div></div></blockquote><div class=""><div class=""><div style="margin: 0cm 0cm 0.0001pt; font-size: 12pt; font-family: 'Times New Roman', serif;" class=""><span lang="EN-US" class=""> <o:p class=""></o:p></span></div></div></div><div class=""><p class="MsoNormal" style="margin: 0cm 0cm 12pt; font-size: 12pt; font-family: 'Times New Roman', serif;"><span lang="EN-US" style="color: rgb(180, 95, 6);" class="">In some frame of reference, the relativistic mass is infinite. However, the charge field changes in that frame also. In the rest frame, PE is finite and 1/r must be limited.</span><span lang="EN-US" class=""><o:p class=""></o:p></span></p></div><blockquote style="border-style: none none none solid; border-left-color: rgb(204, 204, 204); border-left-width: 1pt; padding: 0cm 0cm 0cm 6pt; margin: 5pt 0cm 5pt 4.8pt;" class=""><div class=""><div class=""><div class=""><div class=""><div class=""><div class=""><div class=""><div class=""><div class=""><div class=""><div style="margin-left: 36pt;" class=""><div style="margin: 0cm 0cm 0.0001pt; font-size: 12pt; font-family: 'Times New Roman', serif;" class=""><span lang="EN-US" style="color: red;" class="">This, like relativity, makes a big difference in some fields of physics.</span><span lang="EN-US" class=""><o:p class=""></o:p></span></div></div><ol start="2" type="1" style="margin-bottom: 0cm; margin-top: 0cm;" class=""><li class="MsoNormal" style="margin: 0cm 0cm 0.0001pt; font-size: 12pt; font-family: 'Times New Roman', serif;"><span lang="EN-US" style="color: red;" class="">The source of the wave nature of the electron is never defined in QM. Is it the 'hidden variable"?</span><span lang="EN-US" class=""><o:p class=""></o:p></span></li></ol><div class=""><div style="margin: 0cm 0cm 0.0001pt; font-size: 12pt; font-family: 'Times New Roman', serif;" class=""><span lang="EN-US" style="font-size: 11pt; font-family: Calibri, sans-serif; color: rgb(119, 147, 60);" class="">No it is not, but almost, what the real structure is, well we have our ideas,,,, The hidden variable has to do with phase coherence in the measurement process. Will explain that over a glass of beer, it is worth a good set of papers.</span><span lang="EN-US" class=""><o:p class=""></o:p></span></div></div><div style="margin-left: 36pt;" class=""><div style="margin: 0cm 0cm 0.0001pt; font-size: 12pt; font-family: 'Times New Roman', serif;" class=""><span lang="EN-US" style="color: red;" class="">It can be defined classically, if spin is a real angular momentum, not just a Q#, and relativity is more than just a mind game.</span><span lang="EN-US" class=""><o:p class=""></o:p></span></div></div><div class=""><div style="margin: 0cm 0cm 0.0001pt; font-size: 12pt; font-family: 'Times New Roman', serif;" class=""><span lang="EN-US" style="font-size: 11pt; font-family: Calibri, sans-serif; color: rgb(119, 147, 60);" class="">Quantum spin is angular momentum, but not that of a rigid body. For spin ½ you need something like a fluid that is circulating in 2 directions at the same time, like a spinning, rotating , twisting torus. Think of a smoke ring with a twist and rotating like a wheel</span><span lang="EN-US" class=""><o:p class=""></o:p></span></div></div><div class=""><div style="margin: 0cm 0cm 0.0001pt; font-size: 12pt; font-family: 'Times New Roman', serif;" class=""><span lang="EN-US" style="font-size: 11pt; font-family: Calibri, sans-serif; color: rgb(119, 147, 60);" class="">More beer required here too</span><span lang="EN-US" class=""><o:p class=""></o:p></span></div></div></div></div></div></div></div></div></div></div></div></div></blockquote><div class=""><div class=""><div style="margin: 0cm 0cm 0.0001pt; font-size: 12pt; font-family: 'Times New Roman', serif;" class=""><span lang="EN-US" class=""> <o:p class=""></o:p></span></div></div></div><div class=""><div class=""><div style="margin: 0cm 0cm 0.0001pt; font-size: 12pt; font-family: 'Times New Roman', serif;" class=""><span lang="EN-US" style="color: rgb(180, 95, 6);" class="">I think of the surface of a ball of yarn! Only photons can pass thru each other (or itself), thus the electron is more than a fluid. It is circulating in<span class="apple-converted-space"> </span><b class=""><u class="">all</u></b><span class="apple-converted-space"> </span>directions. Uniquely, it can have an infinity of angular momenta. That is why it can have spin 1/2 in<span class="apple-converted-space"> </span><b class=""><u class="">any</u></b><span class="apple-converted-space"> </span>direction you wish to chose. That question puzzled since college days; but, I was too 'young' to properly question the 'cant' being fed us. I don't think that the professors, bright as they were, could have understood my question, much less answered it. (What about a spin axis along the time direction?)</span><span lang="EN-US" class=""><o:p class=""></o:p></span></div></div><div class=""><div style="margin: 0cm 0cm 0.0001pt; font-size: 12pt; font-family: 'Times New Roman', serif;" class=""><span lang="EN-US" style="font-size: 11pt; font-family: Calibri, sans-serif; color: rgb(31, 73, 125);" class=""> </span><span lang="EN-US" class=""><o:p class=""></o:p></span></div></div><div class=""><div style="margin: 0cm 0cm 0.0001pt; font-size: 12pt; font-family: 'Times New Roman', serif;" class=""><span lang="EN-US" style="font-family: Calibri, sans-serif; color: rgb(112, 48, 160);" class="">Who are you trying to convince here? Surely not me. Look at the 1997 Williamson van der Mark paper and find all you try to say. Incidentally the word fluid refers to something you apparently do not know: It is well known that electromagnetic fields behave like a so-called INVISCID FLUID.</span><span lang="EN-US" class=""><o:p class=""></o:p></span></div></div><div class=""><div style="margin: 0cm 0cm 0.0001pt; font-size: 12pt; font-family: 'Times New Roman', serif;" class=""><span lang="EN-US" style="font-family: Calibri, sans-serif; color: rgb(112, 48, 160);" class="">Other fluids are useful too: more beer required ;-) I do agree that spin ½ is not easy, I know the problems and the salient details. It is one of the key things in physics to understand!</span><span lang="EN-US" class=""><o:p class=""></o:p></span></div></div></div><blockquote style="border-style: none none none solid; border-left-color: rgb(204, 204, 204); border-left-width: 1pt; padding: 0cm 0cm 0cm 6pt; margin: 5pt 0cm 5pt 4.8pt;" class=""><div class=""><div class=""><div class=""><div class=""><div class=""><div class=""><div class=""><div class=""><div class=""><div class=""><ol start="3" type="1" style="margin-bottom: 0cm; margin-top: 0cm;" class=""><li class="MsoNormal" style="margin: 0cm 0cm 0.0001pt; font-size: 12pt; font-family: 'Times New Roman', serif;"><span lang="EN-US" style="font-size: 7.5pt; color: red;" class="">I do not believe that looking at the system in center-of-mass (momentum) coordinates introduces quantized levels in two dimensions. Can only adding 1 or 2 more dimensions produce the fixed levels? Can you describe how such levels might occur? If you define a bell as quantized, then the levels can be quantized. However, they still can have a continuum of values unless the structure is fixed. I have to admit that this is like my condition 1 and both are weak w/o a better reason for discrete values. The 'standing wave' concept is attractive, but misleading.</span><span lang="EN-US" class=""><o:p class=""></o:p></span></li></ol><div style="margin: 0cm 0cm 0.0001pt; font-size: 12pt; font-family: 'Times New Roman', serif;" class=""><span lang="EN-US" style="color: red;" class="">More below:</span><span lang="EN-US" class=""><o:p class=""></o:p></span></div></div><blockquote style="border-style: none none none solid; border-left-color: windowtext; border-left-width: 1pt; padding: 0cm 0cm 0cm 6pt; margin: 5pt 0cm 5pt 4.8pt;" class=""><div class=""><div class=""><div class=""><div style="border-style: solid none none; border-top-color: windowtext; border-top-width: 1pt; padding: 3pt 0cm 0cm;" class=""><div class=""><div style="margin: 0cm 0cm 0.0001pt; font-size: 12pt; font-family: 'Times New Roman', serif;" class=""><b class=""><span lang="EN-US" style="font-size: 7.5pt; font-family: Tahoma, sans-serif;" class="">From:</span></b><span class="apple-converted-space"><span lang="EN-US" style="font-size: 7.5pt; font-family: Tahoma, sans-serif;" class=""> </span></span><span lang="EN-US" style="font-size: 7.5pt; font-family: Tahoma, sans-serif;" class="">General [mailto:<a href="mailto:general-bounces%2Bmartin.van.der.mark" target="_blank" style="color: purple; text-decoration: underline;" class=""><span style="color: purple;" class="">general-bounces+martin.van.der.mark</span></a>=<a href="mailto:philips.com@lists.natureoflightandparticles.org" target="_blank" style="color: purple; text-decoration: underline;" class=""><span style="color: purple;" class="">philips.com@lists.natureoflightandparticles.org</span></a>]<span class="apple-converted-space"> </span><b class="">On Behalf Of<span class="apple-converted-space"> </span></b>John Williamson<br class=""><b class="">Sent:</b><span class="apple-converted-space"> </span>woensdag 6 mei 2015 11:12</span><span lang="EN-US" class=""><o:p class=""></o:p></span></div></div><div class=""><div class=""><div class=""><div style="margin: 0cm 0cm 0.0001pt; font-size: 12pt; font-family: 'Times New Roman', serif;" class=""><span lang="EN-US" style="font-size: 7.5pt;" class=""><br class=""><b class="">To:</b><span class="apple-converted-space"> </span>Nature of Light and Particles - General Discussion<br class=""><b class="">Cc:</b><span class="apple-converted-space"> </span>Nick Bailey; Kyran Williamson; Michael Wright; Manohar .; Ariane Mandray<br class=""><b class="">Subject:</b><span class="apple-converted-space"> </span>Re: [General] Quantisation of classical electromagnetism</span><span lang="EN-US" class=""><o:p class=""></o:p></span></div></div></div></div></div></div><div class=""><div class=""><div class=""><div style="margin: 0cm 0cm 0.0001pt; font-size: 12pt; font-family: 'Times New Roman', serif;" class=""><span lang="EN-US" style="font-size: 7.5pt;" class=""> </span><span lang="EN-US" class=""><o:p class=""></o:p></span></div></div><div class=""><div class=""><div style="margin: 0cm 0cm 0.0001pt; font-size: 12pt; font-family: 'Times New Roman', serif;" class=""><span lang="EN-US" style="font-size: 7.5pt; font-family: Tahoma, sans-serif;" class="">Hihi,<br class=""><br class="">A lot of questions there Andrew.<br class=""><br class="">All quantised means is "countable".</span><span lang="EN-US" class=""><o:p class=""></o:p></span></div></div></div></div></div></div></div></blockquote><div class=""><div class=""><div style="margin: 0cm 0cm 0.0001pt; font-size: 12pt; font-family: 'Times New Roman', serif;" class=""><span lang="EN-US" style="font-size: 7.5pt;" class=""> </span><span lang="EN-US" class=""><o:p class=""></o:p></span></div></div></div><div class=""><div class=""><div style="margin: 0cm 0cm 0.0001pt; font-size: 12pt; font-family: 'Times New Roman', serif;" class=""><span lang="EN-US" style="font-size: 7.5pt; color: red;" class="">QM is certainly putting a lot more weight to the word than that. Pointing out resonances has a physical meaning that can be useful.</span><span lang="EN-US" class=""><o:p class=""></o:p></span></div></div></div><blockquote style="border-style: none none none solid; border-left-color: windowtext; border-left-width: 1pt; padding: 0cm 0cm 0cm 6pt; margin: 5pt 0cm 5pt 4.8pt;" class=""><div class=""><div class=""><div class=""><div class=""><div class=""><div class=""><div style="margin: 0cm 0cm 0.0001pt; font-size: 12pt; font-family: 'Times New Roman', serif;" class=""><span lang="EN-US" style="font-size: 7.5pt; font-family: Tahoma, sans-serif;" class=""><br class="">Yes there are exceptions. Mostly exceptions! The quantised electron charge comes, for me, from an interaction rate. Hence the reason all charges in contact have the same value.</span><span lang="EN-US" class=""><o:p class=""></o:p></span></div></div></div></div></div></div></div></blockquote><div class=""><div class=""><div style="margin: 0cm 0cm 0.0001pt; font-size: 12pt; font-family: 'Times New Roman', serif;" class=""><span lang="EN-US" class=""> <o:p class=""></o:p></span></div></div></div><div class=""><div class=""><div style="margin: 0cm 0cm 0.0001pt; font-size: 12pt; font-family: 'Times New Roman', serif;" class=""><span lang="EN-US" style="font-size: 7.5pt; color: red;" class="">I would say that this looks at effect, not cause or definition.</span><span lang="EN-US" class=""><o:p class=""></o:p></span></div></div></div><div class=""><div class=""><div style="margin: 0cm 0cm 0.0001pt; font-size: 12pt; font-family: 'Times New Roman', serif;" class=""><span lang="EN-US" class=""> <o:p class=""></o:p></span></div></div></div><blockquote style="border-style: none none none solid; border-left-color: windowtext; border-left-width: 1pt; padding: 0cm 0cm 0cm 6pt; margin: 5pt 0cm 5pt 4.8pt;" class=""><div class=""><div class=""><div class=""><div class=""><div class=""><div class=""><div style="margin: 0cm 0cm 0.0001pt; font-size: 12pt; font-family: 'Times New Roman', serif;" class=""><span lang="EN-US" style="font-size: 7.5pt; font-family: Tahoma, sans-serif;" class="">Other quantum numbers may just be an intrinsic sign- such as the lepton number difference between the positron and the electron. Quantised states in atoms and quantum wells are resonant states, indeed. In the FQHE these are bound quasi-particle-flux-quantum states. These are more musical ratios, than integer numbers. Quantised conductance, for example, is simply a rate-per-single-electron. The popular press and Wikipedia tends to sweep all the unknowns into one big unknown. That thing which cannot be known - the great UNCERTAINTY! Assigning a quantum number to something is tantamount to putting all your lack of understanding into a single number. Too much of this kind of shit passes as understanding!</span><span lang="EN-US" class=""><o:p class=""></o:p></span></div></div></div></div></div></div></div></blockquote><div class=""><div class=""><div style="margin: 0cm 0cm 0.0001pt; font-size: 12pt; font-family: 'Times New Roman', serif;" class=""><span lang="EN-US" style="font-size: 7.5pt;" class=""> </span><span lang="EN-US" class=""><o:p class=""></o:p></span></div></div></div><div class=""><div class=""><div style="margin: 0cm 0cm 0.0001pt; font-size: 12pt; font-family: 'Times New Roman', serif;" class=""><span lang="EN-US" style="color: red;" class="">Agreed!</span><span lang="EN-US" class=""><o:p class=""></o:p></span></div></div></div><blockquote style="border-style: none none none solid; border-left-color: windowtext; border-left-width: 1pt; padding: 0cm 0cm 0cm 6pt; margin: 5pt 0cm 5pt 4.8pt;" class=""><div class=""><div class=""><div class=""><div class=""><div class=""><div class=""><div style="margin: 0cm 0cm 0.0001pt; font-size: 12pt; font-family: 'Times New Roman', serif;" class=""><span lang="EN-US" style="font-family: Tahoma, sans-serif;" class=""><br class=""></span><span lang="EN-US" style="font-size: 10pt; font-family: Tahoma, sans-serif;" class="">The ground state of the Hydrogen atom is that energy where potential= kinetic, and the de Broglie wavelength of the electron equals the de Broglie wavelength of the proton. A single wavelength with periodic boundary conditions - for both! What a beautiful resonance! Simple, singing resonance - with no dissipation. Physics tries indeed to mystify this, but it is really a simple congruence. Engineers know better!</span><span lang="EN-US" class=""><o:p class=""></o:p></span></div></div></div></div></div></div></div></blockquote><div class=""><div class=""><div style="margin: 0cm 0cm 0.0001pt; font-size: 12pt; font-family: 'Times New Roman', serif;" class=""><span lang="EN-US" class=""> <o:p class=""></o:p></span></div></div></div><div class=""><div class=""><div style="margin: 0cm 0cm 0.0001pt; font-size: 12pt; font-family: 'Times New Roman', serif;" class=""><span lang="EN-US" style="color: red;" class="">For a 1/r potential the virial thm states that KE = PE/2. You and Martin agree about the relationship between proton and electron as being important. Is this a claim of QM or something that you both simply agreed on? The basic Schrodinger equation assumes an infinite proton mass.</span><span lang="EN-US" class=""><o:p class=""></o:p></span></div></div><div class=""><div style="margin: 0cm 0cm 0.0001pt; font-size: 12pt; font-family: 'Times New Roman', serif;" class=""><span lang="EN-US" style="font-size: 11pt; font-family: Calibri, sans-serif; color: rgb(31, 73, 125);" class=""> </span><span lang="EN-US" class=""><o:p class=""></o:p></span></div></div><div class=""><div style="margin: 0cm 0cm 0.0001pt; font-size: 12pt; font-family: 'Times New Roman', serif;" class=""><span lang="EN-US" style="font-size: 11pt; font-family: Calibri, sans-serif; color: rgb(119, 147, 60);" class="">This has nothing to do with the Schroedinger equation but with the Born approximation, which is not necessary to make, the proton mass is finite, and it can be taken into account by introducing the reduced mass: m_p x m_e/(m_p + m_e)</span><span lang="EN-US" class=""><o:p class=""></o:p></span></div></div><div class=""><div style="margin: 0cm 0cm 0.0001pt; font-size: 12pt; font-family: 'Times New Roman', serif;" class=""><span lang="EN-US" style="font-size: 11pt; font-family: Calibri, sans-serif; color: rgb(119, 147, 60);" class="">Oh and KE = -PE/2, PE is negative!!!</span><span lang="EN-US" class=""><o:p class=""></o:p></span></div></div></div></div></div></div></div></div></div></div></div></div></blockquote><div class=""><div class=""><div style="margin: 0cm 0cm 0.0001pt; font-size: 12pt; font-family: 'Times New Roman', serif;" class=""><span lang="EN-US" class=""> <o:p class=""></o:p></span></div></div></div><div class=""><div class=""><div style="margin: 0cm 0cm 0.0001pt; font-size: 12pt; font-family: 'Times New Roman', serif;" class=""><span lang="EN-US" style="color: rgb(180, 95, 6);" class="">Introducing the reduced mass (and a nuclear deBroglie wavelength for 'resonance') changes the values, but not the nature, of the discrete energy levels. The nucleus travels~2000 orbits before it completes a single deBroglie wavelength. How come the electron is only allowed a maximum of a single cycle?</span><span lang="EN-US" class=""><o:p class=""></o:p></span></div></div><div class=""><div style="margin: 0cm 0cm 0.0001pt; font-size: 12pt; font-family: 'Times New Roman', serif;" class=""><span lang="EN-US" style="font-size: 11pt; font-family: Calibri, sans-serif; color: rgb(31, 73, 125);" class=""> </span><span lang="EN-US" class=""><o:p class=""></o:p></span></div></div></div><blockquote style="border-style: none none none solid; border-left-color: rgb(204, 204, 204); border-left-width: 1pt; padding: 0cm 0cm 0cm 6pt; margin: 5pt 0cm 5pt 4.8pt;" class=""><div class=""><div class=""><div class=""><div class=""><div class=""><div class=""><div class=""><div class=""><div class=""><div class=""><div class=""><div style="margin: 0cm 0cm 0.0001pt; font-size: 12pt; font-family: 'Times New Roman', serif;" class=""><span lang="EN-US" style="font-size: 11pt; font-family: Calibri, sans-serif; color: rgb(112, 48, 160);" class="">I have given you all the clues, now please do the work! The nucleus is slow and heavy, the electron light and fast, oscillating about their common centre of mass with EXACTLY the same momentum and hence the same de Broglie wavelength.</span><span lang="EN-US" style="font-size: 11pt; font-family: Calibri, sans-serif; color: rgb(31, 73, 125);" class=""> </span><span lang="EN-US" class=""><o:p class=""></o:p></span></div></div><div class=""><div style="margin: 0cm 0cm 0.0001pt; font-size: 12pt; font-family: 'Times New Roman', serif;" class=""><span lang="EN-US" style="color: red;" class="">There is no nuclear wavelength, yet the solution has discrete levels. You are correct about a resonance between two wavelengths (frequencies). But I think that they are between the electron and EM wave becoming a photon.</span><span lang="EN-US" class=""><o:p class=""></o:p></span></div></div></div><blockquote style="border-style: none none none solid; border-left-color: windowtext; border-left-width: 1pt; padding: 0cm 0cm 0cm 6pt; margin: 5pt 0cm 5pt 4.8pt;" class=""><div class=""><div class=""><div class=""><div class=""><div class=""><div class=""><div style="margin: 0cm 0cm 0.0001pt; font-size: 12pt; font-family: 'Times New Roman', serif;" class=""><span lang="EN-US" style="font-size: 10pt; font-family: Tahoma, sans-serif;" class=""><br class="">Indeed the Coulomb potential goes way down (as you argue so beautifully in your paper). Shorter lengths, however, are less than one wavelength and hence, though they could be resonant, actually at a higher energy, through interference. The one wavelength state is the ground state. For this state the Coulomb field, cancelled outside the Bohr radius corresponds exactly to the 13.6 eV binding energy of the Hydrogen atom. All very simple and very beautiful!</span><span lang="EN-US" class=""><o:p class=""></o:p></span></div></div></div></div></div></div></div></blockquote><div class=""><div class=""><div style="margin: 0cm 0cm 0.0001pt; font-size: 12pt; font-family: 'Times New Roman', serif;" class=""><span lang="EN-US" class=""> <o:p class=""></o:p></span></div></div></div><div class=""><div class=""><div style="margin: 0cm 0cm 0.0001pt; font-size: 12pt; font-family: 'Times New Roman', serif;" class=""><span lang="EN-US" style="color: red;" class="">What prevents the 1/2 wavelength state from existing and being occupied? (Or for 1/n, with a single wavelength being completed in n orbits.)</span><span lang="EN-US" class=""><o:p class=""></o:p></span></div></div><div class=""><div style="margin: 0cm 0cm 0.0001pt; font-size: 12pt; font-family: 'Times New Roman', serif;" class=""><span lang="EN-US" style="font-size: 13.5pt; font-family: Calibri, sans-serif; color: rgb(31, 73, 125);" class=""> </span><span lang="EN-US" class=""><o:p class=""></o:p></span></div></div><div class=""><div style="margin: 0cm 0cm 0.0001pt; font-size: 12pt; font-family: 'Times New Roman', serif;" class=""><span lang="EN-US" style="font-family: Calibri, sans-serif; color: rgb(119, 147, 60);" class="">If you do that, it simply interferes away, then that energy has to go somewhere, it cannot be destroyed, so it will be radiated. This is why atoms radiate while an electron changes “orbit” : temporarily there is no fit, but energy must be conserved.</span><span lang="EN-US" class=""><o:p class=""></o:p></span></div></div></div></div></div></div></div></div></div></div></div></div></blockquote><div class=""><div class=""><div style="margin: 0cm 0cm 0.0001pt; font-size: 12pt; font-family: 'Times New Roman', serif;" class=""><span lang="EN-US" style="font-size: 16pt;" class=""> </span><span lang="EN-US" class=""><o:p class=""></o:p></span></div></div></div><div class=""><div class=""><div style="margin: 0cm 0cm 0.0001pt; font-size: 12pt; font-family: 'Times New Roman', serif;" class=""><span lang="EN-US" style="color: rgb(180, 95, 6);" class="">Are you assuming that the electron is a wave and not localized? That its wave function, distributed around the atom and extended to 2 orbits per cycle, would cancel because of phase reversal? Then what about 3 (or any odd integer) orbits?</span><span lang="EN-US" class=""> <o:p class=""></o:p></span></div></div><div class=""><div style="margin: 0cm 0cm 0.0001pt; font-size: 12pt; font-family: 'Times New Roman', serif;" class=""><span lang="EN-US" style="font-size: 11pt; font-family: Calibri, sans-serif; color: rgb(31, 73, 125);" class=""> </span><span lang="EN-US" class=""><o:p class=""></o:p></span></div></div><div class=""><div style="margin: 0cm 0cm 0.0001pt; font-size: 12pt; font-family: 'Times New Roman', serif;" class=""><span lang="EN-US" style="font-family: Calibri, sans-serif; color: rgb(112, 48, 160);" class="">The electron is a wave and a particle at the same time, right?!</span><span lang="EN-US" class=""><o:p class=""></o:p></span></div></div></div><blockquote style="border-style: none none none solid; border-left-color: rgb(204, 204, 204); border-left-width: 1pt; padding: 0cm 0cm 0cm 6pt; margin: 5pt 0cm 5pt 4.8pt;" class=""><div class=""><div class=""><div class=""><div class=""><div class=""><div class=""><div class=""><div class=""><div class=""><div class=""><div class=""><div style="margin: 0cm 0cm 0.0001pt; font-size: 12pt; font-family: 'Times New Roman', serif;" class=""><span lang="EN-US" style="font-size: 9pt; color: red;" class=""><br class=""></span><span lang="EN-US" style="font-size: 10pt; color: red;" class="">More below:</span><span lang="EN-US" class=""><o:p class=""></o:p></span></div></div></div><blockquote style="border-style: none none none solid; border-left-color: windowtext; border-left-width: 1pt; padding: 0cm 0cm 0cm 6pt; margin: 5pt 0cm 5pt 4.8pt;" class=""><div class=""><div class=""><div class=""><div class=""><div class=""><div class=""><div style="margin: 0cm 0cm 0.0001pt; font-size: 12pt; font-family: 'Times New Roman', serif;" class=""><span lang="EN-US" style="font-family: Tahoma, sans-serif;" class=""><br class="">Martin is, as usual, right in (pretty much) everything he says. Especially in that it is very important!<br class=""><br class="">Regards, John W.</span><span lang="EN-US" class=""><o:p class=""></o:p></span></div></div><div class=""><div class="MsoNormal" align="center" style="margin: 0cm 0cm 0.0001pt; font-size: 12pt; font-family: 'Times New Roman', serif; text-align: center;"><span lang="EN-US" style="font-size: 7.5pt;" class=""><hr size="2" width="100%" align="center" class=""></span></div><div class=""><p class="MsoNormal" style="margin: 0cm 0cm 12pt; font-size: 12pt; font-family: 'Times New Roman', serif;"><b class=""><span lang="EN-US" style="font-family: Tahoma, sans-serif;" class="">From:</span></b><span class="apple-converted-space"><span lang="EN-US" style="font-family: Tahoma, sans-serif;" class=""> </span></span><span lang="EN-US" style="font-family: Tahoma, sans-serif;" class="">General [general-bounces+john.williamson=<a href="mailto:glasgow.ac.uk@lists.natureoflightandparticles.org" target="_blank" style="color: purple; text-decoration: underline;" class=""><span style="color: purple;" class="">glasgow.ac.uk@lists.natureoflightandparticles.org</span></a>] on behalf of Mark, Martin van der [<a href="mailto:martin.van.der.mark@philips.com" target="_blank" style="color: purple; text-decoration: underline;" class=""><span style="color: purple;" class="">martin.van.der.mark@philips.com</span></a>]<br class=""><b class="">Sent:</b><span class="apple-converted-space"> </span>Wednesday, May 06, 2015 8:48 AM<br class=""><b class="">To:</b><span class="apple-converted-space"> </span>Nature of Light and Particles - General Discussion<br class=""><b class="">Cc:</b><span class="apple-converted-space"> </span>Nick Bailey; Kyran Williamson; Michael Wright; Manohar .; Ariane Mandray<br class=""><b class="">Subject:</b><span class="apple-converted-space"> </span>Re: [General] Quantisation of classical electromagnetism</span><span lang="EN-US" class=""><o:p class=""></o:p></span></p></div><div class=""><div class=""><div class=""><div style="margin: 0cm 0cm 0.0001pt; font-size: 12pt; font-family: 'Times New Roman', serif;" class=""><span lang="EN-US" style="font-family: Calibri, sans-serif; color: rgb(31, 73, 125);" class="">Dear Andrew,</span><span lang="EN-US" class=""><o:p class=""></o:p></span></div></div><div class=""><div style="margin: 0cm 0cm 0.0001pt; font-size: 12pt; font-family: 'Times New Roman', serif;" class=""><span lang="EN-US" style="font-family: Calibri, sans-serif; color: rgb(31, 73, 125);" class="">I have good answers to most of your questions, but have no time right now to write them down,<br class="">we must come back to this, it is very important indeed.</span><span lang="EN-US" class=""><o:p class=""></o:p></span></div></div><div class=""><div style="margin: 0cm 0cm 0.0001pt; font-size: 12pt; font-family: 'Times New Roman', serif;" class=""><span lang="EN-US" style="font-size: 7.5pt; font-family: Calibri, sans-serif; color: rgb(31, 73, 125);" class="">In any case it comes down to the following:</span><span lang="EN-US" class=""><o:p class=""></o:p></span></div></div><div style="margin: 0cm 0cm 0.0001pt; font-size: 12pt; font-family: 'Times New Roman', serif;" class=""><span lang="EN-US" style="font-size: 11pt; font-family: Symbol; color: rgb(31, 73, 125);" class="">·</span><span lang="EN-US" style="font-size: 7pt; color: rgb(31, 73, 125);" class=""> <span class="apple-converted-space"> </span></span><span lang="EN-US" style="font-size: 11pt; font-family: Calibri, sans-serif; color: rgb(31, 73, 125);" class="">Quantization comes from any wave equation with imposed boundary conditions.<span class="apple-converted-space"> </span></span><span lang="EN-US" style="font-size: 11pt; font-family: Calibri, sans-serif; color: red;" class="">[if you can establish standing waves?]</span><span lang="EN-US" style="font-size: 11pt; font-family: Calibri, sans-serif; color: rgb(31, 73, 125);" class=""> </span><span lang="EN-US" style="font-size: 11pt; font-family: Calibri, sans-serif; color: rgb(119, 147, 60);" class="">stationary waves may do already</span><span lang="EN-US" class=""><o:p class=""></o:p></span></div><div style="margin: 0cm 0cm 0.0001pt; font-size: 12pt; font-family: 'Times New Roman', serif;" class=""><span lang="EN-US" style="font-size: 11pt; font-family: Symbol; color: rgb(31, 73, 125);" class="">·</span><span lang="EN-US" style="font-size: 7pt; color: rgb(31, 73, 125);" class=""> <span class="apple-converted-space"> </span></span><span lang="EN-US" style="font-size: 11pt; font-family: Calibri, sans-serif; color: rgb(31, 73, 125);" class="">Uncertainty is no more than what the Fourier limit tells you.<span class="apple-converted-space"> </span></span><span lang="EN-US" style="font-size: 11pt; font-family: Calibri, sans-serif; color: red;" class="">[agreed]</span><span lang="EN-US" class=""><o:p class=""></o:p></span></div><div style="margin: 0cm 0cm 0.0001pt; font-size: 12pt; font-family: 'Times New Roman', serif;" class=""><span lang="EN-US" style="font-size: 11pt; font-family: Symbol; color: rgb(31, 73, 125);" class="">·</span><span lang="EN-US" style="font-size: 7pt; color: rgb(31, 73, 125);" class=""> <span class="apple-converted-space"> </span></span><span lang="EN-US" style="font-size: 11pt; font-family: Calibri, sans-serif; color: rgb(31, 73, 125);" class="">Copenhagen interpretation is Copenhagen mystification: although it is not very wrong at the simple level, it takes away any possibility for improvement by dogma.</span><span lang="EN-US" style="font-size: 11pt; font-family: Calibri, sans-serif; color: red;" class="">[agreed]</span><span lang="EN-US" class=""><o:p class=""></o:p></span></div><div style="margin: 0cm 0cm 0.0001pt; font-size: 12pt; font-family: 'Times New Roman', serif;" class=""><span lang="EN-US" style="font-size: 11pt; font-family: Symbol; color: rgb(31, 73, 125);" class="">·</span><span lang="EN-US" style="font-size: 7pt; color: rgb(31, 73, 125);" class=""> <span class="apple-converted-space"> </span></span><span lang="EN-US" style="font-size: 11pt; font-family: Calibri, sans-serif; color: rgb(31, 73, 125);" class="">Wave/particle dualism is the consequence of special relativity, see Louis de Broglie.</span><span class="apple-converted-space"><span lang="EN-US" style="font-size: 11pt; font-family: Calibri, sans-serif; color: red;" class=""> </span></span><span lang="EN-US" style="font-size: 11pt; font-family: Calibri, sans-serif; color: red;" class="">[do you have a particular reference? I have not seen this statement before.]</span><span lang="EN-US" style="font-size: 11pt; font-family: Calibri, sans-serif; color: rgb(31, 73, 125);" class=""> </span><span lang="EN-US" style="font-size: 11pt; font-family: Calibri, sans-serif; color: rgb(119, 147, 60);" class="">Thesis of Louis de Broglie, more beer would also help. Niels Bohr and his gang were successful enough to make people forget about this or so, it is a mystery why it has not become common knowledge among physicists.</span><span lang="EN-US" class=""><o:p class=""></o:p></span></div></div></div></div></div></div></div></div></div></blockquote></div></div></div></div></div></div></div></div></div></blockquote><div class=""><p class="MsoNormal" style="margin: 0cm 0cm 12pt; font-size: 12pt; font-family: 'Times New Roman', serif;"><span lang="EN-US" style="color: rgb(180, 95, 6);" class="">I think that I had heard that before, but not really registered on it. I had thought of relativity as applied to the deBroglie wavelength rather than being fundamental to it. I'm finding that my youthful disinterest in the history of physics is extracting a penalty now.</span><span lang="EN-US" class=""><o:p class=""></o:p></span></p><p class="MsoNormal" style="margin: 0cm 0cm 12pt; font-size: 12pt; font-family: 'Times New Roman', serif;"><span lang="EN-US" style="font-size: 11pt; font-family: Calibri, sans-serif; color: rgb(112, 48, 160);" class="">It is not your fault, it is mentioned rarely. But since I have, now you know.</span><span lang="EN-US" class=""><o:p class=""></o:p></span></p><p class="MsoNormal" style="margin: 0cm 0cm 12pt; font-size: 12pt; font-family: 'Times New Roman', serif;"><span lang="EN-US" style="color: rgb(180, 95, 6);" class="">I don't have his Thesis handy; but, in his "Theory of Quanta," he does provide support for your earlier statement about resonance between the nucleus and electron.</span><span lang="EN-US" class=""><o:p class=""></o:p></span></p><div style="margin-left: 30pt;" class=""><div class=""><div style="margin: 0cm 0cm 0.0001pt; font-size: 12pt; font-family: 'Times New Roman', serif;" class=""><span lang="EN-US" style="color: rgb(180, 95, 6);" class="">"This is exactly BOHR’s formula that he deduced from the theorem mentioned above<br class="">and which again can be regarded as a phase wave resonance condition for an electron in</span><span lang="EN-US" class=""><o:p class=""></o:p></span></div></div></div><div style="margin-left: 30pt;" class=""><p class="MsoNormal" style="margin: 0cm 0cm 12pt; font-size: 12pt; font-family: 'Times New Roman', serif;"><span lang="EN-US" style="color: rgb(180, 95, 6);" class="">orbit about a proton."</span><span lang="EN-US" class=""><o:p class=""></o:p></span></p></div><div class=""><div style="margin: 0cm 0cm 0.0001pt; font-size: 12pt; font-family: 'Times New Roman', serif;" class=""><span lang="EN-US" style="color: rgb(180, 95, 6);" class="">If this is also considered resonance, rather than just strict mechanics, then the energy levels have 3 resonances in coincidence.</span><span lang="EN-US" class=""><o:p class=""></o:p></span></div></div></div><div class=""><div class=""><div style="margin: 0cm 0cm 0.0001pt; font-size: 12pt; font-family: 'Times New Roman', serif;" class=""><span lang="EN-US" class=""> <o:p class=""></o:p></span></div></div></div><div class=""><div class=""><div style="margin: 0cm 0cm 0.0001pt; font-size: 12pt; font-family: 'Times New Roman', serif;" class=""><span lang="EN-US" class="">Andrew<o:p class=""></o:p></span></div></div></div><blockquote style="border-style: none none none solid; border-left-color: rgb(204, 204, 204); border-left-width: 1pt; padding: 0cm 0cm 0cm 6pt; margin: 5pt 0cm 5pt 4.8pt;" class=""><div class=""><div class=""><div class=""><div class=""><div class=""><div class=""><div class=""><div class=""><div class=""><div class=""><div class=""><blockquote style="border-style: none none none solid; border-left-color: windowtext; border-left-width: 1pt; padding: 0cm 0cm 0cm 6pt; margin: 5pt 0cm 5pt 4.8pt;" class=""><div class=""><div class=""><div class=""><div class=""><div class=""><div class=""><div class=""><div class=""><div class=""><div class=""><div class=""><div class=""><div class=""><div class=""><div class=""><div class=""><div class=""><div class=""><div class=""><div class=""><div class=""><div class=""><div style="margin: 0cm 0cm 0.0001pt; font-size: 12pt; font-family: 'Times New Roman', serif;" class=""><span lang="EN-US" style="font-family: Cambria, serif; color: rgb(112, 48, 160);" class="">Dear Andrew I hope to have cleared up a few things, surely we should talk about them some more,</span><span lang="EN-US" class=""><o:p class=""></o:p></span></div></div><div class=""><div style="margin: 0cm 0cm 0.0001pt; font-size: 12pt; font-family: 'Times New Roman', serif;" class=""><span lang="EN-US" style="font-family: Cambria, serif; color: rgb(112, 48, 160);" class="">Very best regards, Martin</span><span lang="EN-US" class=""><o:p class=""></o:p></span></div></div></div></div></div></div></div></div></div></div></div></div></div></div></div></div></div></div></div></div></div></div></div></blockquote></div></div></div></div></div></div></div></div></div></div></div><div class=""><div style="margin: 0cm 0cm 0.0001pt; font-size: 12pt; font-family: 'Times New Roman', serif;" class=""><span lang="EN-US" class=""> <o:p class=""></o:p></span></div></div></blockquote></div><div class=""><div style="margin: 0cm 0cm 0.0001pt; font-size: 12pt; font-family: 'Times New Roman', serif;" class=""><span lang="EN-US" class=""> <o:p class=""></o:p></span></div></div></div></div><div style="margin: 0cm 0cm 0.0001pt; font-size: 12pt; font-family: 'Times New Roman', serif;" class=""><span lang="EN-US" class=""> <o:p class=""></o:p></span></div><div class="MsoNormal" align="center" style="margin: 0cm 0cm 0.0001pt; font-size: 12pt; font-family: 'Times New Roman', serif; text-align: center;"><span lang="EN-US" class=""><hr size="2" width="100%" align="center" class=""></span></div><div style="margin: 0cm 0cm 0.0001pt; font-size: 12pt; font-family: 'Times New Roman', serif;" class=""><span lang="EN-US" style="font-size: 7.5pt; font-family: Arial, sans-serif; color: gray;" class="">The information contained in this message may be confidential and legally protected under applicable law. 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