<div dir="ltr"><div><div><div>Dear André,<span style="font-size:11pt"><span style="line-height:115%"><span style="font-family:"Calibri","sans-serif""><span style="font-size:12pt"><span style="line-height:115%"><br><br></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"><span style="line-height:115%">Thanks for your comments; even tho they reflect our differing models.<br><br></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"><span style="line-height:115%">A question, which answer was/is important to me, comes from your response to item 1. If "</span></span></span></span></span><span style="font-size:11pt"><span style="line-height:115%"><span style="font-family:"Calibri","sans-serif""><span style="font-size:12pt"><span style="line-height:115%"><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%">E=(lambda h)/c," then this refers only to light speed items (light) in a medium with refractive index of 1. However, the de Broglie wavelength (</span></span></span></span></span></span></span></span></span></span><span style="font-size:11pt"><span style="line-height:115%"><span style="font-family:"Calibri","sans-serif""><span style="font-size:12pt"><span style="line-height:115%"><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-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%">lambda = h)/mv) </span></span></span></span></span>only applies to bodies with mass. The de Broglie frequency is independent of medium and applies to massive items. So, I doubt that de Broglie would have equated the frequency and wavelength relations.<br></span></span></span></span></span></span></span></span></span></span></div><div><span style="font-size:11pt"><span style="line-height:115%"><span style="font-family:"Calibri","sans-serif""><span style="font-size:12pt"><span style="line-height:115%"><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%"><br></span></span></span></span></span></span></span></span></span></span></div><div><span style="font-size:11pt"><span style="line-height:115%"><span style="font-family:"Calibri","sans-serif""><span style="font-size:12pt"><span style="line-height:115%"><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%">How do you interpret physic's emphasis on the wavelength and the ignoring of the frequency and what is actually waving? What is your guess/interpretation as to what is waving? Despite some good descriptions and meaning of the deBroglie wavelength, I've not seen anyone in this group (or anywhere) give what I consider to be a valid answer to the frequency question, which I consider to be fundamental to the nature of the electron.<br><br></span></span></span></span></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"><span style="line-height:115%"><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%">Andrew M.<br></span></span></span></span></span></span></span></span></span></span><div><div><div><span style="font-size:11pt"><span style="line-height:115%"><span style="font-family:"Calibri","sans-serif""><span style="font-size:12pt"><span style="line-height:115%"><br>_ _ _ <br></span></span></span></span></span><div class="gmail_extra"><br><div class="gmail_quote">On Fri, Jan 12, 2018 at 1:15 PM, André Michaud <span dir="ltr"><<a href="mailto:srp2@srpinc.org" target="_blank">srp2@srpinc.org</a>></span> wrote:<br><blockquote class="gmail_quote" style="margin:0px 0px 0px 0.8ex;border-left:1px solid rgb(204,204,204);padding-left:1ex">
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<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%">Dear Andrew,</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%">Thank you so much for your appreciation. I think no lead should be neglected in trying to figure out what is really happening at the fundamental level. I simply share those that I know of, when occasion arises.</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%">Relative to what you perceive as missing in relation to path independence, remember </span></span><span style="font-size:12pt"><span style="line-height:115%">where de Broglie was at when he wrote this. </span></span><span style="font-size:12pt" lang="EN-CA"><span style="line-height:115%">This was 2 years before Schrödinger came up with the wave function. He was ears deep in the same sort of research that we are in now, about the same issues, but without the knowledge accumulated since. This paper plus one other, I think, is what inspired Schrödinger to use the wave equation.</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%">To the 3 points you raised, here is what I think:</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%">1. I think that he saw frequency and wavelength as amounting to two equivalent references to the related amount of energy, and that he considered that mentioning one always implied the other. Lets remember that E= hf, but that also E=(lambda h)/c.</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%">2. On page 509, when he writes : "the wave of frequency nu and of velocity c/beta must be in resonance over the whole length of the trajectory. This leads to condition", he was talking about the Bohr orbit in the Bohr atom as a starting point, thus his reference to a "closed path" no doubt. This is how I interpret this.</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%">3. As for his use of the gamma factor, I have not specifically analyzed this particular issue, but I know now that he was deeply aware of Special relativity (thanks to Albrecht) and certainly was aware that the energy level calculable for the Bohr orbit was sufficient to warrant a relativistic velocity of the electron on this orbit, if the electron actually ran this orbit (Heisenberg came to the conclusion in the same decade that it was possible that the electron may not have been running this orbit, but could be stabilized at this distance without translating about the proton). Indeed, I also think that this is possible. What seems to matter is that in both cases, the energy level is the same. But yes, I also think that the implications of his use of the gamma factor warrants investigation.</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%">For my mention of a "precision drift" of the velocity, I simply refer to the fact that if the electron were to orbit at Chip' inner radius limit distance, the more energetic electron's velocity would be higher, while as the radius expands towards his outer radius limit, the less and less energetic electron's velocity would diminish in sync.</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%">The word precision, simply highlight that the velocity on the exact Bohr orbit is precise, while the possible spread of all orbits between r_outer and r_inner of Chip and Heisenberg equation amount to a precision drift of this velocity.</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%">Hope this helps.</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%">Best Regards</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"><span style="line-height:115%">André</span></span></span></span></span></p>
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<span>On Thu, 11 Jan 2018 14:39:08 -0500, Andrew Meulenberg <u></u> wrote:<u></u></span><br>
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<div>Dear Andre,<br>
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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:
<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).</li>
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<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.</p>
<p> </p>
<p>I also have a question on a comment you made to Chip. In</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.</span></span></span></span></span></span><br>
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<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.</span></span></span></span></span></span>
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<h3 class="gmail-m_6484677386908469894gmail-iw"><span class="gmail-m_6484677386908469894gmail-gD" name="André Michaud">André Michaud</span> <span class="gmail-m_6484677386908469894gmail-go"><span><</span><a href="mailto:srp2@srpinc.org" target="_blank">srp2@srpinc.org</a><span>></span></span></h3>
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<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.f<wbr>r/pdf/dossiers/Broglie/Broglie<wbr>_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>
<p style="margin:0cm 0cm 10pt"><span class="gmail-m_6484677386908469894gmail-im"><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></span></p>
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