<div dir="ltr"><div><div>Dear Andre,<br><br></div>In your replies to Chip, you show what I consider to be a sign of the true scholar "the desire and ability to acquire, remember, and utilize information from many diverse sources." Thank you for your link to de Broglie's 1923 paper. My French is not good enough to be sure that I was not interpreting his points as (rather than because of) his supporting of some of my views. In particular:<br><ol><li>His emphasis on frequency (or period) rather than wavelength.</li><li>His mention of closed path,</li><li>I'm not quite sure what to do with his association of the relativistic gamma factor with the wave frequency. It looks interesting; but, I need to figure out the implications. Do you have an answer? It does get included in his resonant energy relationship (which has a mv^2 rather than 1/2(mv^2) basis).<br></li></ol><p>His single mention of closed path, compared to his wave-based emphasis on frequency, misses statement of the importance of path independence of the closed or contour integral about non-singular regions. While his wave functions provide cyclic examples of these closed paths, the importance to conservation laws is seldom (if ever?) mentioned in physics. <br></p><p> </p><p>I also have a question on a comment you made to Chip. In <br></p><p style="margin-left:40px">"<span style="font-size:11pt"><span style="line-height:115%"><span style="font-family:"Calibri","sans-serif""><span style="font-size:12pt" lang="EN-US"><span style="line-height:115%"><span style="font-family:"Times New Roman","serif"">Heisenberg
equation turns out to be de Broglie's equation for the Bohr orbit
adapted to account for a<u> precision </u>drift of the chosen velocity on
either side of the selected velocity value on the ground orbital of the
hydrogen atom."</span></span></span></span></span></span></p>you mention "<span style="font-size:11pt"><span style="line-height:115%"><span style="font-family:"Calibri","sans-serif""><span style="font-size:12pt" lang="EN-US"><span style="line-height:115%"><span style="font-family:"Times New Roman","serif"">precision drift." Could you explain this a bit? I had originally thought that you meant <i>precession drift</i>, which I consider to be very important (the basis of the de Broglie frequency). However, I don't think you had that in mind.<br><br></span></span></span></span></span></span></div><span style="font-size:11pt"><span style="line-height:115%"><span style="font-family:"Calibri","sans-serif""><span style="font-size:12pt" lang="EN-US"><span style="line-height:115%"><span style="font-family:"Times New Roman","serif"">Andrew M.<br></span></span></span></span></span></span><div><div><div class="gmail-aju"><div class="gmail-aCi"><img id="gmail-:0_191-e" name=":0" src="https://ssl.gstatic.com/ui/v1/icons/mail/profile_mask2.png" class="gmail-ajn" style="background-color: rgb(204, 204, 204);"></div></div><table class="gmail-cf gmail-ix" cellpadding="0"><tbody><tr><td><h3 class="gmail-iw"><span name="André Michaud" class="gmail-gD">André Michaud</span> <span class="gmail-go"><span><</span><a href="mailto:srp2@srpinc.org">srp2@srpinc.org</a><span>></span></span> </h3></td></tr></tbody></table><table class="gmail-cf gmail-adz" cellpadding="0"><tbody><tr><td class="gmail-ady"><br></td></tr></tbody></table><div id="gmail-:23f" class="gmail-ii gmail-gt"><div id="gmail-:23g" class="gmail-a3s gmail-aXjCH gmail-m160e571d94250e8a"><div class="gmail-adM">
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</div><p style="margin:0cm 0cm 10pt"><span style="font-size:11pt"><span style="line-height:115%"><span style="font-family:"Calibri","sans-serif""><span style="font-size:12pt" lang="EN-US"><span style="line-height:115%"><span style="font-family:"Times New Roman","serif"">Hi Chip,</span></span></span></span></span></span></p>
<p style="margin:0cm 0cm 10pt"><span style="font-size:11pt"><span style="line-height:115%"><span style="font-family:"Calibri","sans-serif""><span style="font-size:12pt" lang="EN-US"><span style="line-height:115%"><span style="font-family:"Times New Roman","serif"">As
I signaled the typo in your equation on page 36, I forgot to mention
something else that struck me (this is a part that I read carefully)</span></span></span></span></span></span></p>
<p style="margin:0cm 0cm 10pt"><span style="font-size:11pt"><span style="line-height:115%"><span style="font-family:"Calibri","sans-serif""><span style="font-size:12pt" lang="EN-US"><span style="line-height:115%"><span style="font-family:"Times New Roman","serif"">I notice that you mention that you noticed what you named a "beat frequency" with regard to the hydrogen ground state.</span></span></span></span></span></span></p>
<p style="margin:0cm 0cm 10pt"><span style="font-size:11pt"><span style="line-height:115%"><span style="font-family:"Calibri","sans-serif""><span style="font-size:12pt" lang="EN-US"><span style="line-height:115%"><span style="font-family:"Times New Roman","serif"">Just
to mention that this the exact term that de Broglie used in French (un
battement) to describe the resonance state that he associated with the
hydrogen ground state. Here is a link to the paper that inspired
Schrödinger to introduce the wave function on account of this
observation by de Broglie:</span></span></span></span></span></span></p>
<p style="margin:0cm 0cm 10pt"><span style="font-size:11pt"><span style="line-height:115%"><span style="font-family:"Calibri","sans-serif""><span style="font-size:12pt" lang="EN-US"><span style="line-height:115%"><span style="font-family:"Times New Roman","serif""><a href="http://www.academie-sciences.fr/pdf/dossiers/Broglie/Broglie_pdf/CR1923_p507.pdf" style="color:blue;text-decoration:underline" target="_blank">http://www.academie-sciences.<wbr>fr/pdf/dossiers/Broglie/<wbr>Broglie_pdf/CR1923_p507.pdf</a></span></span></span></span></span></span></p>
<p style="margin:0cm 0cm 10pt"><span style="font-size:11pt"><span style="line-height:115%"><span style="font-family:"Calibri","sans-serif""><span style="font-size:12pt" lang="EN-US"><span style="line-height:115%"><span style="font-family:"Times New Roman","serif"">The interesting part is in page 509.</span></span></span></span></span></span></p>
<p style="margin:0cm 0cm 10pt"><span style="font-size:11pt"><span style="line-height:115%"><span style="font-family:"Calibri","sans-serif""><span style="font-size:12pt" lang="EN-US"><span style="line-height:115%"><span style="font-family:"Times New Roman","serif"">I also noted that your outer and inner radii for the ground state can be directly related to Heisenberg's equation </span></span></span></span></span></span></p>
<p style="margin:0cm 0cm 10pt"><img></p>
<p style="margin:0cm 0cm 10pt"><span style="font-size:11pt"><span style="line-height:115%"><span style="font-family:"Calibri","sans-serif""><span style="font-size:12pt" lang="EN-US"><span style="line-height:115%"><span style="font-family:"Times New Roman","serif"">Heisenberg
equation turns out to be de Broglie's equation for the Bohr orbit
adapted to account for a precision drift of the chosen velocity on
either side of the selected velocity value on the ground orbital of the
hydrogen atom.</span></span></span></span></span></span></p>
<p style="margin:0cm 0cm 10pt"><span style="font-size:11pt"><span style="line-height:115%"><span style="font-family:"Calibri","sans-serif""><span style="font-size:12pt" lang="EN-US"><span style="line-height:115%"><span style="font-family:"Times New Roman","serif"">This range lies between your outer and inner radii.<br>
<br>
But you probably already were aware of this latter detail</span></span></span></span></span></span></p><span class="gmail-im">
<p style="margin:0cm 0cm 10pt"><span style="font-size:11pt"><span style="line-height:115%"><span style="font-family:"Calibri","sans-serif""><span style="font-size:12pt" lang="EN-US"><span style="line-height:115%"><span style="font-family:"Times New Roman","serif"">Best Regards</span></span></span></span></span></span></p>
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