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<div class="userStyles" style=" font-family: Arial; font-size: 12pt; color: #000000;">Hi Andrew,<br>
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My answers embedded <strong><span style="color:#b22222;">in red</span></strong>.<br>
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Best Regards
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André Michaud<br>
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<span>On Sat, 13 Jan 2018 22:09:46 -0500, Andrew Meulenberg <mules333@gmail.com> wrote:</mules333@gmail.com></span><br>
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<div>Dear <span class="gmail-im">André,</span><br>
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<span class="gmail-im">comments below</span>
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<div class="gmail_quote">On Fri, Jan 12, 2018 at 4:43 PM, André Michaud <span dir="ltr"><<a href="mailto:srp2@srpinc.org" target="_blank">srp2@srpinc.org</a>></span> wrote:
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<div class="gmail-m_-5857549377844522026gmail-m_4573949240444522509m_4685593287220975574userStyles" style="font-family:Arial;font-size:12pt;color:rgb(0,0,0)">
<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%">Indeed, this is a fundamental question.</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%">I will try to explain how I see this. Note that my angle of "observation", so to speak, is strictly electromagnetic, meaning that to me energy, either free moving or stabilized as the invariant rest mass of elementary particles such as the electron, can only be "electromagnetic" in nature. <span style="color:rgb(255,0,0)"><b>[OK]</b></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%">We know that the electromagnetic oscillation is transverse with respect to the direction of motion. We know then that the "frequency" of a localized photon can only be the actual number of times the transverse electromagnetic mutual induction cycle of its electric and magnetic aspects occur in 1 second. </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" 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%"><span style="color:rgb(255,0,0)"><b>[OK]</b></span></span></span></span></span></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%">BUT, the wavelength that we associate with it happens to be the "longitudinal distance" that the photon will travel during one of its cycles at velocity c. </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" 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%"><span style="color:rgb(255,0,0)"><b>[OK]</b></span></span></span></span></span></span></span></span></span></span></span></p>
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<div class="gmail-m_-5857549377844522026gmail-m_4573949240444522509m_4685593287220975574userStyles" style="font-family:Arial;font-size:12pt;color:rgb(0,0,0)">
<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 deBroglie wavelength is of the same nature. It is the longitudinal distance that the carrying-photon of the electron can travel during one of its cycle, which happens to be the length of the Bohr orbit because it is now slowed down by having to "carry", so to speak, the inert mass of the electron.</span></span></span></span></span></p>
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<div>You appear to have taken the Bohr orbit to be fundamental rather than consequential. While that may not be wrong, I don't find it any more satisfying than the Planck constant being the universal.<br>
<p style="margin:0cm 0cm 10pt"><strong><span style="color:#b22222;"><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%;">I did not clarify enough here. I was talking of what deBroglie was talking about in his paper. He was taking the Bohr orbit as a reference, because it is at this radius distance that the energy of the ground states averages out to 4.359743805E-18 J. Of course, if the electron has any other value of carrying energy, it will move at the related velocity, and its wavelength (the distance it will cover during 1 cycle) will be in relation.</span></span></span></span></span></span></strong></p>
<p style="margin:0cm 0cm 10pt"><strong><span style="color:#b22222;"><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%;">I do not take the Bohr orbit as fundamental at the general level. its radius is just the mean resonance distance of the electron in the ground state of the hydrogen atom.</span></span></span></span></span> It just happens to coincide with the Planck constant as corresponding to the amount of energy that you get if you divide 1 second by the number of cycles of the energy induced at the Bohr orbit.</span></strong></p>
<p style="margin:0cm 0cm 10pt"><strong><span style="color:#b22222;"><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%;">But since all other metastable orbitals in the hydrogen atoms are multiples of this one, it is sort of fundamental in this atom, being the stable-rest-orbital. It is in this limited sense that I meant this.</span></span></span></span></span></span></strong></p>
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<div class="gmail-m_-5857549377844522026gmail-m_4573949240444522509m_4685593287220975574userStyles" style="font-family:Arial;font-size:12pt;color:rgb(0,0,0)">
<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%">Note: My blooper in my previous answer. the correct equations are of course: E= hf and E=(h c)/lambda.</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%">A free moving photon of 4.359743805E-18 J, has frequency of 6.579683917E15 Hz and a wavelength of 4.556335256E-8 m when calculated with lambda=hc</span></span><span style="font-size:12pt" lang="EN-CA"><span style="line-height:115%">/E.</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-CA"><span style="line-height:115%">A photon of 4.359743805E-18 j carrying an electron still has frequency of 6.579683917E15 Hz, but has an effective longitudinal wavelength of 3.32491846E-10 m only, that is the length of the Bohr orbit, whether you calculate it with Lambda=h/mv or with lambda = hv/E, because when you equate (h/mv)=(hv/E) and simplify, you end up with E=mv^2, which restitutes 4.359743805E-18j, that is the amount of electromagnetic energy that carries the electron.</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-CA"><span style="line-height:115%">My interpretation of the wavelength is that I don't think that anything is actually "longitudinally waving" with regard to the displacement of electromagnetic energy, whether free photons or electron carrier-photon. From my perspective, the "classical wavelength" simply is synonymous with "distance travelled in space on a longitudinal trajectory during one electromagnetic cycle of the photon energy".</span></span></span></span></span></p>
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<div>I agree with both the distance traveled during one cycle and the no <span style="font-size:11pt"><span style="line-height:115%"><span style="font-family:"Calibri","sans-serif""><span style="font-size:12pt" lang="EN-CA"><span style="line-height:115%">"longitudinal waving"</span></span></span></span></span>. However, your use of "carrying energy" (non-mass portion of total energy?) as a photon with a wavelength does not seem to match for particles with mass. (Consider a 1 eV photon with ~ 1 micron wavelength compared to a KE = 1 eV electron with a very long de Broglie wavelength.) So, we disagree on what cycle must be used. There must be another cycle that we need to consider. (This goes to the 'forbidden' variable of QM.)<br>
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<strong><span style="color:#b22222;"><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%;">If we agree with the previous mention that a free moving 1 eV photon and an electron 1 eV carrying energy have the same frequency, as in the comparison I made with the Bohr orbit energy, then we should agree that the wavelength of the 1 eV electron carrying energy will be shorter. that is, "the distance it will cover during 1 cycle" because it is slowed down by having to drag the inert electron mass along.<br>
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(Sorry, I am getting mixed up now with these "longer" and "shorter" switching. But doing the calculations can sort this out.).</span></span></span></span></span></span></strong><br>
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<div class="gmail-m_-5857549377844522026gmail-m_4573949240444522509m_4685593287220975574userStyles" style="font-family:Arial;font-size:12pt;color:rgb(0,0,0)">
<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-CA"><span style="line-height:115%">The actual "waving" can only be cyclically transverse in my view and I found that the maximum amplitude of this waving for any photon corresponds to (lambda alpha)/(2 pi), so the longitudinal wavelength is nevertheless related to the EM transverse frequency when related to alpha/(2 pi). </span></span></span></span></span></p>
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<div>I can consider the waving to be a rotation (but not that of a circularly-polarized photon), a change in orientation rather than any transverse or longitudinal motion. I consider the radius of a photon to be <span style="font-size:11pt"><span style="line-height:115%"><span style="font-family:"Calibri","sans-serif""><span style="font-size:12pt" lang="EN-CA"><span style="line-height:115%">(lambda)/(2 pi), so the alpha in your <span style="font-size:11pt"><span style="line-height:115%"><span style="font-family:"Calibri","sans-serif""><span style="font-size:12pt" lang="EN-CA"><span style="line-height:115%">(lambda alpha)/(2 pi) might still relate to the lowest stable condensation of light into matter.</span></span></span></span></span></span></span><br>
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<strong><span style="color:#b22222;"><span style="font-size: 12pt;" lang="EN-US"><span style="line-height: 115%;">Here, it would be too long to explain locally why in the trispatial geometry </span></span><span style="font-size: 12pt;" lang="EN-CA"><span style="line-height: 115%;">(lambda alpha)/(2 pi)</span></span><span style="font-size: 12pt;" lang="EN-US"><span style="line-height: 115%;"> is the only possible maximum distance between both charges of the moving photon, but this is partially adressed in the paper I will give reference to further down.</span></span></span></strong><span style="font-size:12pt" lang="EN-CA"><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-CA"><span style="line-height:115%"> </span></span></span></span></span></span></span></span></span></span><br>
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<div class="gmail-m_-5857549377844522026gmail-m_4573949240444522509m_4685593287220975574userStyles" style="font-family:Arial;font-size:12pt;color:rgb(0,0,0)">
<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%">I analyse this from another perspective in section "Defining a Distance Based Quantum of Action" in pages 8 and 9 of this paper:</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%"><a href="https://www.omicsonline.org/open-access/the-last-challenge-of-modern-physics-2090-0902-1000217.pdf" style="color:blue;text-decoration:underline" target="_blank">https://www.omicsonline.org/op<wbr>en-access/the-last-challenge-o<wbr>f-modern-physics-2090-0902-100<wbr>0217.pdf</a></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%">I hope I am not confusing things still more with my unorthodox viewpoints.</span></span></span></span></span></p>
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<div>I do have some questions about your equations 11 & 12 (I have had the same questions in conventional descriptions, sometimes including that of the Poynting vector). You have <b>E </b>& <b>B</b> values as steady state. However, these EM fields both either oscillate in magnitude (for linearly-polarized light) or rotate in direction (for circularly-polarized light). How do you rationalize the fixed values of eq. 11 for light in your system? Eq 12 has a fixed value of both for an electron. How does that agree with the zero magnetic field of the electron? I must assume that you are considering the fields of the composite photon rather than those of the electron.<br>
<p style="margin:0cm 0cm 10pt"><strong><span style="color:#b22222;"><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%;">Note that there is a typo in equations 12: Both lambdas should have been lambda_Compton of the electron, as mentioned in the previous paragraph. I have been unable to get the editors to correct this transcript typo before they published the paper.</span></span></span></span></span></span></strong></p>
<p style="margin:0cm 0cm 10pt"><strong><span style="color:#b22222;"><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 two fields of equations 12 are fixed and they are the E and B fields of the rest mass of the electron.</span></span></span></span></span></span></strong></p>
<p style="margin:0cm 0cm 10pt"><strong><span style="color:#b22222;"><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%;">Equations 11 represent the varying E and B fields of the carrying energy of the photon.</span></span></span></span></span> Here, lambda is the lambda of the free moving photon of the related energy -----> Note it is important to note here that in equations 13 and 15, it is this wavelength that must be used even when calculating the combined E and B fields of the moving electron.</span></strong></p>
<p style="margin:0cm 0cm 10pt"><strong><span style="color:#b22222;"><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%;">Note that it is impossible for the electron to have a zero magnetic field because it is an electromagnetic particle. It has a fixed magnetic field equal to the B equation 12 (with lambda_Compton).</span></span></span></span></span></span></strong></p>
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Do you describe somewhere how the composite fields of the photon sum to those of the electron?<br>
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<p style="margin:0cm 0cm 10pt"><strong><span style="color:#b22222;"><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%;">Yes. Equation 13 provides the product of both B fields of the electron and that of its variable carrying energy (Lambda_compton is fixed, but lambda of its carrying energy varies with the energy of the carrying energy). </span></span></span></span></span></span></strong></p>
<p style="margin:0cm 0cm 10pt"><strong><span style="color:#b22222;"><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%;">And equation 15 provides the complex product of both E fields of the electron and that of its variable carrying energy.</span></span></span></span></span></span></strong></p>
<p style="margin:0cm 0cm 10pt"><strong><span style="color:#b22222;"><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%;">These equations for the separate B and E fields of the electron and its carrying energy are derived in this paper, as well as how they can be combined:</span></span></span></span></span></span></strong></p>
<p style="margin:0cm 0cm 10pt"><strong><span style="font-size:11pt"><span style="line-height:115%"><span style="font-family:"Calibri","sans-serif""><span style="font-size:12.0pt" lang="EN-US"><span style="line-height:115%"><a href="http://www.gsjournal.net/Science-Journals/Research%20Papers-Relativity%20Theory/Download/2257" style="color:blue; text-decoration:underline"><span style="color:#b22222;">http://www.gsjournal.net/Science-Journals/Research%20Papers-Relativity%20Theory/Download/2257</span></a></span></span></span></span></span></strong></p>
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<div><strong><span style="color:#b22222;">Best Regards<br>
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André</span></strong><br>
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<div>Andrew M.</div>
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<p style="margin:0cm 0cm 10pt"><span><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></span></p>
<p style="margin:0cm 0cm 10pt"><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%">André</span></span></span></span></span></span></p>
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<span>---<br>
André Michaud<br>
GSJournal admin<br>
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<span>On Fri, 12 Jan 2018 15:29:33 -0500, Andrew Meulenberg wrote:</span>
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<div>Dear André,</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.</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.</span></span></span></span></span></span></span></span></span></span></div>
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<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.</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.</span></span></span></span></span></span></span></span></span></span>
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<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:
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<div class="gmail-m_-5857549377844522026gmail-m_4573949240444522509m_4685593287220975574gmail-m_6484677386908469894userStyles" style="font-family:Arial;font-size:12pt;color:rgb(0,0,0)">
<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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André Michaud<br>
GSJournal admin</span><br>
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<span>On Thu, 11 Jan 2018 14:39:08 -0500, Andrew Meulenberg wrote:</span>
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<div>Dear Andre,</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:
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<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>
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<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></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.</span></span></span></span></span></span>
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<h3 class="gmail-m_-5857549377844522026gmail-m_4573949240444522509m_4685593287220975574gmail-m_6484677386908469894gmail-iw"><span class="gmail-m_-5857549377844522026gmail-m_4573949240444522509m_4685593287220975574gmail-m_6484677386908469894gmail-gD" name="André Michaud">André Michaud</span> <span class="gmail-m_-5857549377844522026gmail-m_4573949240444522509m_4685593287220975574gmail-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>
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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_-5857549377844522026gmail-m_4573949240444522509m_4685593287220975574gmail-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>
<span class="gmail-m_-5857549377844522026gmail-m_4573949240444522509m_4685593287220975574gmail-m_6484677386908469894gmail-im">---<br>
André Michaud<br>
GSJournal admin</span></div>
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