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<p class="MsoNormal"><span style="font-size:11.0pt;font-family:"Calibri","sans-serif";color:#7030A0">Dear Andrew, I have been away for a few days.<o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-size:11.0pt;font-family:"Calibri","sans-serif";color:#7030A0">In your previous replies you tried to challenge me to be precise, and have questioned the correctness of my statements. That is very good.<o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-size:11.0pt;font-family:"Calibri","sans-serif";color:#7030A0"><o:p> </o:p></span></p>
<p class="MsoNormal"><span style="font-size:11.0pt;font-family:"Calibri","sans-serif";color:#7030A0">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.
<o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-size:11.0pt;font-family:"Calibri","sans-serif";color:#7030A0"><o:p> </o:p></span></p>
<p class="MsoNormal"><span style="font-size:11.0pt;font-family:"Calibri","sans-serif";color:#7030A0">I hope no one is color blind, yet another color will be used: purple! (just in case some haze troubles the mind…)<o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-size:11.0pt;font-family:"Calibri","sans-serif";color:#7030A0"><o:p> </o:p></span></p>
<p class="MsoNormal"><span style="font-size:11.0pt;font-family:"Calibri","sans-serif";color:#7030A0">So: purple (Martin) responds to
</span><span style="font-size:11.0pt;font-family:"Calibri","sans-serif";color:#984807;mso-style-textfill-fill-color:#984807;mso-style-textfill-fill-alpha:100.0%">brown (Andrew) responds to
</span><span style="font-size:11.0pt;font-family:"Calibri","sans-serif";color:#4F6228;mso-style-textfill-fill-color:#4F6228;mso-style-textfill-fill-alpha:100.0%">green (Martin) responds to
</span><span style="font-size:11.0pt;font-family:"Calibri","sans-serif";color:red">red (Andrew)</span><span style="font-size:11.0pt;font-family:"Calibri","sans-serif";color:#7030A0"><o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-size:11.0pt;font-family:"Calibri","sans-serif";color:#7030A0"><o:p> </o:p></span></p>
<p class="MsoNormal"><span style="font-size:11.0pt;font-family:"Calibri","sans-serif";color:#1F497D"><o:p> </o:p></span></p>
<p class="MsoNormal"><span lang="DE" style="font-size:10.0pt;font-family:"Arial","sans-serif";color:navy">Dr. Martin B. van der Mark</span><span lang="DE" style="color:navy"><o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-size:10.0pt;font-family:"Arial","sans-serif";color:navy">Principal Scientist, Minimally Invasive Healthcare</span><span style="font-size:11.0pt;font-family:"Calibri","sans-serif";color:navy"><o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-size:11.0pt;font-family:"Calibri","sans-serif";color:navy"> <o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-size:10.0pt;font-family:"Arial","sans-serif";color:navy">Philips Research Europe - Eindhoven</span><span style="font-size:11.0pt;font-family:"Calibri","sans-serif";color:navy"><o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-size:10.0pt;font-family:"Arial","sans-serif";color:navy">High Tech Campus, Building 34 (WB2.025)</span><span style="font-size:11.0pt;font-family:"Calibri","sans-serif";color:navy"><o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-size:10.0pt;font-family:"Arial","sans-serif";color:navy">Prof. Holstlaan 4</span><span style="font-size:11.0pt;font-family:"Calibri","sans-serif";color:navy"><o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-size:10.0pt;font-family:"Arial","sans-serif";color:navy">5656 AE Eindhoven, The Netherlands</span><span style="font-size:11.0pt;font-family:"Calibri","sans-serif";color:navy"><o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-size:10.0pt;font-family:"Arial","sans-serif";color:navy">Tel: +31 40 2747548</span><span style="font-size:11.0pt;font-family:"Calibri","sans-serif";color:#1F497D"><o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-size:11.0pt;font-family:"Calibri","sans-serif";color:#1F497D"><o:p> </o:p></span></p>
<p class="MsoNormal"><b><span style="font-size:10.0pt;font-family:"Tahoma","sans-serif"">From:</span></b><span style="font-size:10.0pt;font-family:"Tahoma","sans-serif""> General [mailto:general-bounces+martin.van.der.mark=philips.com@lists.natureoflightandparticles.org]
<b>On Behalf Of </b>Andrew Meulenberg<br>
<b>Sent:</b> donderdag 7 mei 2015 7:40<br>
<b>To:</b> Nature of Light and Particles - General Discussion<br>
<b>Subject:</b> Re: [General] Quantisation of classical electromagnetism<o:p></o:p></span></p>
<p class="MsoNormal"><o:p> </o:p></p>
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<p class="MsoNormal" style="margin-bottom:12.0pt">Dear Martin,<o:p></o:p></p>
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<p class="MsoNormal">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></o:p></p>
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<p class="MsoNormal"><o:p> </o:p></p>
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<p class="MsoNormal">On Thu, May 7, 2015 at 3:50 AM, Mark, Martin van der <<a href="mailto:martin.van.der.mark@philips.com" target="_blank">martin.van.der.mark@philips.com</a>> wrote:<o:p></o:p></p>
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<p class="MsoNormal" style="mso-margin-top-alt:auto;mso-margin-bottom-alt:auto"><span style="font-family:"Calibri","sans-serif";color:#77933C">Andrew, thanks, please see below, in green</span><span style="font-size:14.0pt"><o:p></o:p></span></p>
<p class="MsoNormal" style="mso-margin-top-alt:auto;mso-margin-bottom-alt:auto"><span lang="NL" style="font-size:11.0pt;font-family:"Calibri","sans-serif";color:#1F497D"> </span><span lang="DE" style="font-size:10.0pt;font-family:"Arial","sans-serif";color:navy">Dr.
Martin B. van der Mark</span><span lang="NL"><o:p></o:p></span></p>
<p class="MsoNormal" style="mso-margin-top-alt:auto;mso-margin-bottom-alt:auto"><span style="font-size:10.0pt;font-family:"Arial","sans-serif";color:navy">Principal Scientist, Minimally Invasive Healthcare</span><o:p></o:p></p>
<p class="MsoNormal" style="mso-margin-top-alt:auto;mso-margin-bottom-alt:auto"><b><span style="font-size:11.0pt;font-family:"Calibri","sans-serif";color:#1F497D"><o:p> </o:p></span></b></p>
<p class="MsoNormal" style="mso-margin-top-alt:auto;mso-margin-bottom-alt:auto"><b><span style="font-size:10.0pt;font-family:"Tahoma","sans-serif"">From:</span></b><span style="font-size:10.0pt;font-family:"Tahoma","sans-serif""> General [mailto:<a href="mailto:general-bounces%2Bmartin.van.der.mark" target="_blank">general-bounces+martin.van.der.mark</a>=<a href="mailto:philips.com@lists.natureoflightandparticles.org" target="_blank">philips.com@lists.natureoflightandparticles.org</a>]
<b>On Behalf Of </b>Andrew Meulenberg<br>
<b>Sent:</b> woensdag 6 mei 2015 19:46<br>
<b>To:</b> Nature of Light and Particles - General Discussion<br>
<b>Subject:</b> Re: [General] Quantisation of classical electromagnetism</span><span style="font-size:18.0pt"><o:p></o:p></span></p>
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<p class="MsoNormal" style="mso-margin-top-alt:auto;mso-margin-bottom-alt:auto"><span style="font-size:10.0pt"> <span style="color:red">Dear John W, Martin, et al.,</span></span><span style="font-size:18.0pt"><o:p></o:p></span></p>
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<p class="MsoNormal" style="mso-margin-top-alt:auto;margin-bottom:12.0pt"><span style="color:red">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><o:p></o:p></p>
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<p class="MsoNormal" style="mso-margin-top-alt:auto;margin-bottom:12.0pt"><span style="color:red">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,
<u>I </u>had been wrong and this smaller radius is probably correct.</span><o:p></o:p></p>
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<p class="MsoNormal" style="mso-margin-top-alt:auto;mso-margin-bottom-alt:auto"><span style="font-size:7.5pt;color:red">some comments below:</span><o:p></o:p></p>
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<p class="MsoNormal" style="mso-margin-top-alt:auto;mso-margin-bottom-alt:auto"><span style="font-size:7.5pt"> On Wed, May 6, 2015 at 3:28 PM, Mark, Martin van der <</span><a href="mailto:martin.van.der.mark@philips.com" target="_blank">martin.van.der.mark@philips.com</a><span style="font-size:7.5pt">>
wrote:</span><o:p></o:p></p>
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<p class="MsoNormal" style="mso-margin-top-alt:auto;mso-margin-bottom-alt:auto"><span style="font-size:7.5pt"> </span><span style="font-family:"Calibri","sans-serif";color:#1F497D">Andrew, John, all</span><o:p></o:p></p>
<p class="MsoNormal" style="mso-margin-top-alt:auto;mso-margin-bottom-alt:auto"><span style="font-family:"Calibri","sans-serif";color:#1F497D"> John W is quite right as well, just a small remark on the hydrogen atom.</span><o:p></o:p></p>
<p class="MsoNormal" style="mso-margin-top-alt:auto;mso-margin-bottom-alt:auto"><span style="font-family:"Calibri","sans-serif";color:#1F497D">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><o:p></o:p></p>
<p class="MsoNormal" style="mso-margin-top-alt:auto;mso-margin-bottom-alt:auto"><span style="font-family:"Calibri","sans-serif";color:#1F497D">For the structure of the atom there are three conditions, one of electromagnetic, and two of inertial nature.</span><o:p></o:p></p>
<p class="MsoNormal" style="mso-margin-top-alt:auto;mso-margin-bottom-alt:auto"><span style="font-family:"Calibri","sans-serif";color:#1F497D">1) The coulomb potential runs to minus infinity, that is very deep. It comes from the charge of proton and electron.</span><o:p></o:p></p>
<p class="MsoNormal" style="mso-margin-top-alt:auto;mso-margin-bottom-alt:auto"><span style="font-family:"Calibri","sans-serif";color:#1F497D">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><o:p></o:p></p>
<p class="MsoNormal" style="mso-margin-top-alt:auto;mso-margin-bottom-alt:auto"><span style="font-family:"Calibri","sans-serif";color:#1F497D">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><o:p></o:p></p>
<p class="MsoNormal" style="mso-margin-top-alt:auto;mso-margin-bottom-alt:auto"><span style="font-size:11.0pt;font-family:"Calibri","sans-serif";color:#1F497D">Cheers, Martin</span><span style="font-size:20.0pt"><o:p></o:p></span></p>
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<p class="MsoNormal" style="mso-margin-top-alt:auto;mso-margin-bottom-alt:auto"> <span style="color:red">I also have three basic conditions:</span><o:p></o:p></p>
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<span style="color:red">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><o:p></o:p></li><li class="MsoNormal" style="mso-margin-top-alt:auto;mso-margin-bottom-alt:auto;mso-list:l0 level1 lfo1">
<span style="color:red">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><o:p></o:p></li></ul>
<p class="MsoNormal" style="mso-margin-top-alt:auto;mso-margin-bottom-alt:auto"><span style="font-size:11.0pt;font-family:"Calibri","sans-serif";color:#77933C">I do not really understand what you mean by the double resonance.
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<p class="MsoNormal"><span style="color:#B45F06"> </span><span style="font-size:11.0pt;font-family:"Calibri","sans-serif";color:#B45F06">The levels identified with the classical description agree with those of the mechanical (QM) system.</span><span style="font-size:11.0pt;font-family:"Calibri","sans-serif""><o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-size:11.0pt;font-family:"Calibri","sans-serif";color:#7030A0">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.<o:p></o:p></span></p>
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<span style="color:red">the ground state is established by the requirement of a photon to have an angular momentum of hbar.</span><o:p></o:p></li></ul>
<p class="MsoNormal" style="mso-margin-top-alt:auto;mso-margin-bottom-alt:auto"><span style="font-size:11.0pt;font-family:"Calibri","sans-serif";color:#77933C">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!!!!!
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<span style="font-size:11.0pt;font-family:"Calibri","sans-serif";color:#B45F06">[Exactly, therefore it cannot radiate a photon except to a system w ang. mom. = hbar. No levels below gnd state have that value.]</span><br>
<span style="color:#7030A0">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).<o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-size:11.0pt;font-family:"Calibri","sans-serif";color:#7030A0">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. <o:p></o:p></span></p>
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<p class="MsoNormal" style="mso-margin-top-alt:auto;mso-margin-bottom-alt:auto"><span style="font-size:11.0pt;font-family:"Calibri","sans-serif";color:#77933C">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><o:p></o:p></p>
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<p class="MsoNormal"><span style="color:#B45F06">There is no reason <u>given</u> 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 style="color:#B45F06">This is the basis of Mill's hydrino states. The limiting factor is the photon.</span><o:p></o:p></p>
<p class="MsoNormal"><span style="font-size:11.0pt;font-family:"Calibri","sans-serif";color:#7030A0">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!<o:p></o:p></span></p>
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<p class="MsoNormal" style="mso-margin-top-alt:auto;mso-margin-bottom-alt:auto"><span style="font-size:11.0pt;font-family:"Calibri","sans-serif";color:#77933C">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><o:p></o:p></p>
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<p class="MsoNormal"><span style="color:#B45F06">The solution assuming an infinite mass nucleus (hence no deBroglie wavelength & no resonance) still produces discrete levels. Therefore that issue cannot be causal.</span><o:p></o:p></p>
<p class="MsoNormal"><span style="font-size:11.0pt;font-family:"Calibri","sans-serif";color:#7030A0">Bullshit, sorry, but here you should really know better since:<o:p></o:p></span></p>
<p class="MsoListParagraph" style="text-indent:-18.0pt;mso-list:l2 level1 lfo6"><![if !supportLists]><span style="font-size:11.0pt;font-family:"Calibri","sans-serif";color:#7030A0"><span style="mso-list:Ignore">1)<span style="font:7.0pt "Times New Roman"">
</span></span></span><![endif]><span style="font-size:11.0pt;font-family:"Calibri","sans-serif";color:#7030A0">I have told you already you are referring to the BORN APPROXIMATION<o:p></o:p></span></p>
<p class="MsoListParagraph" style="text-indent:-18.0pt;mso-list:l2 level1 lfo6"><![if !supportLists]><span style="font-size:11.0pt;font-family:"Calibri","sans-serif";color:#7030A0"><span style="mso-list:Ignore">2)<span style="font:7.0pt "Times New Roman"">
</span></span></span><![endif]><span style="font-size:11.0pt;font-family:"Calibri","sans-serif";color:#7030A0">It is in every basic textbook, second year physics<o:p></o:p></span></p>
<p class="MsoListParagraph" style="text-indent:-18.0pt;mso-list:l2 level1 lfo6"><![if !supportLists]><span style="font-size:11.0pt;font-family:"Calibri","sans-serif";color:#7030A0"><span style="mso-list:Ignore">3)<span style="font:7.0pt "Times New Roman"">
</span></span></span><![endif]><span style="font-size:11.0pt;font-family:"Calibri","sans-serif";color:#7030A0">The so-called reduced mass gives a slightly different set of levels, the correct levels. Remember the Rydbergconstant? And its slightly different
numbers?<o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-size:11.0pt;font-family:"Calibri","sans-serif";color:#7030A0">Just do your homework, and go to Wikipedia, that will be good enough.<o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-size:11.0pt;font-family:"Calibri","sans-serif";color:#7030A0"><o:p> </o:p></span></p>
<p class="MsoNormal"><span style="font-size:11.0pt;font-family:"Calibri","sans-serif";color:#7030A0">Here another remark regarding your earlier question, whether I was talking physics or mathematics. (see next question below)<o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-size:11.0pt;font-family:"Calibri","sans-serif";color:#7030A0">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.<o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-size:11.0pt;font-family:"Calibri","sans-serif";color:#7030A0">Sorry I just hate mediocrity.<o:p></o:p></span></p>
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<p class="MsoNormal" style="mso-margin-top-alt:auto;mso-margin-bottom-alt:auto"><span style="color:red">Looking at your conditions produced other thoughts.</span><o:p></o:p></p>
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<span style="color:red">The statement that "the coulomb potential runs to minus infinity" is a mathematician, not a physicist talking.
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<p class="MsoNormal" style="mso-margin-top-alt:auto;mso-margin-bottom-alt:auto"><span style="font-size:11.0pt;font-family:"Calibri","sans-serif";color:#77933C">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><o:p></o:p></p>
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<p class="MsoNormal"><span style="color:#B45F06">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><o:p></o:p></p>
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<p class="MsoNormal"><span style="font-size:11.0pt;font-family:"Calibri","sans-serif";color:#7030A0">The Coulomb potential is BY DEFINITION a 1/r potential associated with a POINT CHARGE.<o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-size:11.0pt;font-family:"Calibri","sans-serif";color:#7030A0">It therefore runs, by definition, to minus infinity.<o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-size:11.0pt;font-family:"Calibri","sans-serif";color:#7030A0"><o:p> </o:p></span></p>
<p class="MsoNormal"><span style="font-size:11.0pt;font-family:"Calibri","sans-serif";color:#7030A0">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.<o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-size:11.0pt;font-family:"Calibri","sans-serif";color:#7030A0">I know you want to make that point, and I fully agree. But please do not misuse the argument or definition of things.
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<p class="MsoNormal" style="mso-margin-top-alt:auto;mso-margin-bottom-alt:auto"><span style="font-size:11.0pt;font-family:"Calibri","sans-serif";color:#77933C">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><o:p></o:p></p>
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<p class="MsoNormal"><span style="color:#B45F06">Do you consider the proton charge radius to be its field-energy density or the major extent of its
<b>Coulomb potential</b> (e.g., the electron Compton radius)?</span> <span style="color:#B45F06">
We haven't defined charge yet have we? [Am I being the mathematician now for insisting on a valid definition?]</span><o:p></o:p></p>
<p class="MsoNormal"><span style="font-size:11.0pt;font-family:"Calibri","sans-serif";color:#1F497D"><o:p> </o:p></span></p>
<p class="MsoNormal"><span style="font-size:11.0pt;font-family:"Calibri","sans-serif";color:#7030A0">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.<o:p></o:p></span></p>
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<span style="color:red">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><o:p></o:p></p>
<p class="MsoNormal" style="mso-margin-top-alt:auto;mso-margin-bottom-alt:auto"><span style="font-size:11.0pt;font-family:"Calibri","sans-serif";color:#77933C">Yes it can exceed its RESTmass , and will be precisely gamma m0, see above, not exceeding its relativistic
mass, of course.</span><o:p></o:p></p>
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<p class="MsoNormal" style="margin-bottom:12.0pt"><span style="color:#B45F06">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><o:p></o:p></p>
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<span style="color:red">This, like relativity, makes a big difference in some fields of physics.</span><o:p></o:p></p>
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<span style="color:red">The source of the wave nature of the electron is never defined in QM. Is it the 'hidden variable"?
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<p class="MsoNormal" style="mso-margin-top-alt:auto;mso-margin-bottom-alt:auto"><span style="font-size:11.0pt;font-family:"Calibri","sans-serif";color:#77933C">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><o:p></o:p></p>
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<span style="color:red">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><o:p></o:p></p>
<p class="MsoNormal" style="mso-margin-top-alt:auto;mso-margin-bottom-alt:auto"><span style="font-size:11.0pt;font-family:"Calibri","sans-serif";color:#77933C">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><o:p></o:p></p>
<p class="MsoNormal" style="mso-margin-top-alt:auto;mso-margin-bottom-alt:auto"><span style="font-size:11.0pt;font-family:"Calibri","sans-serif";color:#77933C">More beer required here too</span><o:p></o:p></p>
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<p class="MsoNormal"><span style="color:#B45F06">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
<b><u>all</u></b> directions. Uniquely, it can have an infinity of angular momenta. That is why it can have spin 1/2 in
<b><u>any</u></b> 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><o:p></o:p></p>
<p class="MsoNormal"><span style="font-size:11.0pt;font-family:"Calibri","sans-serif";color:#1F497D"><o:p> </o:p></span></p>
<p class="MsoNormal"><span style="font-family:"Calibri","sans-serif";color:#7030A0">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.<o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-family:"Calibri","sans-serif";color:#7030A0">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!<o:p></o:p></span></p>
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<span style="font-size:7.5pt;color:red">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><o:p></o:p></li></ol>
<p><span style="color:red">More below:</span><o:p></o:p></p>
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<p class="MsoNormal" style="mso-margin-top-alt:auto;mso-margin-bottom-alt:auto"><b><span style="font-size:7.5pt;font-family:"Tahoma","sans-serif"">From:</span></b><span style="font-size:7.5pt;font-family:"Tahoma","sans-serif""> General [mailto:<a href="mailto:general-bounces%2Bmartin.van.der.mark" target="_blank">general-bounces+martin.van.der.mark</a>=<a href="mailto:philips.com@lists.natureoflightandparticles.org" target="_blank">philips.com@lists.natureoflightandparticles.org</a>]
<b>On Behalf Of </b>John Williamson<br>
<b>Sent:</b> woensdag 6 mei 2015 11:12</span><o:p></o:p></p>
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<b>To:</b> Nature of Light and Particles - General Discussion<br>
<b>Cc:</b> Nick Bailey; Kyran Williamson; Michael Wright; Manohar .; Ariane Mandray<br>
<b>Subject:</b> Re: [General] Quantisation of classical electromagnetism</span><o:p></o:p></p>
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<p class="MsoNormal" style="mso-margin-top-alt:auto;mso-margin-bottom-alt:auto"><span style="font-size:7.5pt;font-family:"Tahoma","sans-serif";color:black">Hihi,<br>
<br>
A lot of questions there Andrew.<br>
<br>
All quantised means is "countable".</span><o:p></o:p></p>
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<p class="MsoNormal" style="mso-margin-top-alt:auto;mso-margin-bottom-alt:auto"><span style="font-size:7.5pt;color:red">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><o:p></o:p></p>
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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.
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<p class="MsoNormal" style="mso-margin-top-alt:auto;mso-margin-bottom-alt:auto"><span style="font-size:7.5pt;color:red">I would say that this looks at effect, not cause or definition.</span><o:p></o:p></p>
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<p class="MsoNormal" style="mso-margin-top-alt:auto;mso-margin-bottom-alt:auto"><span style="font-size:7.5pt;font-family:"Tahoma","sans-serif";color:black">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><o:p></o:p></p>
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<p class="MsoNormal" style="mso-margin-top-alt:auto;mso-margin-bottom-alt:auto"><span style="color:red">Agreed!
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</span><span style="font-size:10.0pt;font-family:"Tahoma","sans-serif";color:black">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><o:p></o:p></p>
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<p class="MsoNormal" style="mso-margin-top-alt:auto;mso-margin-bottom-alt:auto"><span style="color:red">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.
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<p class="MsoNormal" style="mso-margin-top-alt:auto;mso-margin-bottom-alt:auto"><span style="font-size:11.0pt;font-family:"Calibri","sans-serif";color:#1F497D"> </span><o:p></o:p></p>
<p class="MsoNormal" style="mso-margin-top-alt:auto;mso-margin-bottom-alt:auto"><span style="font-size:11.0pt;font-family:"Calibri","sans-serif";color:#77933C">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><o:p></o:p></p>
<p class="MsoNormal" style="mso-margin-top-alt:auto;mso-margin-bottom-alt:auto"><span style="font-size:11.0pt;font-family:"Calibri","sans-serif";color:#77933C">Oh and KE = -PE/2, PE is negative!!!</span><o:p></o:p></p>
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<p class="MsoNormal"><span style="color:#B45F06">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><o:p></o:p></p>
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<p class="MsoNormal"><span style="font-size:11.0pt;font-family:"Calibri","sans-serif";color:#7030A0">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 style="font-size:11.0pt;font-family:"Calibri","sans-serif";color:#1F497D"> </span><o:p></o:p></p>
<p class="MsoNormal" style="mso-margin-top-alt:auto;mso-margin-bottom-alt:auto"><span style="color:red">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><o:p></o:p></p>
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</span><span style="font-size:10.0pt;font-family:"Tahoma","sans-serif";color:black">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 style="font-size:18.0pt"><o:p></o:p></span></p>
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<p class="MsoNormal" style="mso-margin-top-alt:auto;mso-margin-bottom-alt:auto"><span style="color:red">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.)
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<p class="MsoNormal" style="mso-margin-top-alt:auto;mso-margin-bottom-alt:auto"><span style="font-family:"Calibri","sans-serif";color:#77933C">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 style="font-size:16.0pt"><o:p></o:p></span></p>
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<p class="MsoNormal"><span style="color:#B45F06">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> <o:p></o:p></p>
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<p class="MsoNormal"><span style="font-family:"Calibri","sans-serif";color:#7030A0">The electron is a wave and a particle at the same time, right?!<o:p></o:p></span></p>
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</span><span style="font-size:10.0pt;color:red">More below:</span><o:p></o:p></p>
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Martin is, as usual, right in (pretty much) everything he says. Especially in that it is very important!<br>
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Regards, John W.</span><o:p></o:p></p>
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<p class="MsoNormal" style="mso-margin-top-alt:auto;margin-bottom:12.0pt"><b><span style="font-family:"Tahoma","sans-serif";color:black">From:</span></b><span style="font-family:"Tahoma","sans-serif";color:black"> General [general-bounces+john.williamson=<a href="mailto:glasgow.ac.uk@lists.natureoflightandparticles.org" target="_blank">glasgow.ac.uk@lists.natureoflightandparticles.org</a>]
on behalf of Mark, Martin van der [<a href="mailto:martin.van.der.mark@philips.com" target="_blank">martin.van.der.mark@philips.com</a>]<br>
<b>Sent:</b> Wednesday, May 06, 2015 8:48 AM<br>
<b>To:</b> Nature of Light and Particles - General Discussion<br>
<b>Cc:</b> Nick Bailey; Kyran Williamson; Michael Wright; Manohar .; Ariane Mandray<br>
<b>Subject:</b> Re: [General] Quantisation of classical electromagnetism</span><o:p></o:p></p>
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<p class="MsoNormal" style="mso-margin-top-alt:auto;mso-margin-bottom-alt:auto"><span style="font-family:"Calibri","sans-serif";color:#1F497D">Dear Andrew,</span><o:p></o:p></p>
<p class="MsoNormal" style="mso-margin-top-alt:auto;mso-margin-bottom-alt:auto"><span style="font-family:"Calibri","sans-serif";color:#1F497D">I have good answers to most of your questions, but have no time right now to write them down,<br>
we must come back to this, it is very important indeed.</span><o:p></o:p></p>
<p class="MsoNormal" style="mso-margin-top-alt:auto;mso-margin-bottom-alt:auto"><span style="font-size:7.5pt;font-family:"Calibri","sans-serif";color:#1F497D">In any case it comes down to the following:</span><o:p></o:p></p>
<p><span style="font-size:11.0pt;font-family:Symbol;color:#1F497D">·</span><span style="font-size:7.0pt;color:#1F497D">
</span><span style="font-size:11.0pt;font-family:"Calibri","sans-serif";color:#1F497D">Quantization comes from any wave equation with imposed boundary conditions.
</span><span style="font-size:11.0pt;font-family:"Calibri","sans-serif";color:red">[if you can establish standing waves?]</span><span style="font-size:11.0pt;font-family:"Calibri","sans-serif";color:#1F497D">
</span><span style="font-size:11.0pt;font-family:"Calibri","sans-serif";color:#77933C">stationary waves may do already</span><o:p></o:p></p>
<p><span style="font-size:11.0pt;font-family:Symbol;color:#1F497D">·</span><span style="font-size:7.0pt;color:#1F497D">
</span><span style="font-size:11.0pt;font-family:"Calibri","sans-serif";color:#1F497D">Uncertainty is no more than what the Fourier limit tells you.
</span><span style="font-size:11.0pt;font-family:"Calibri","sans-serif";color:red">[agreed]</span><o:p></o:p></p>
<p><span style="font-size:11.0pt;font-family:Symbol;color:#1F497D">·</span><span style="font-size:7.0pt;color:#1F497D">
</span><span style="font-size:11.0pt;font-family:"Calibri","sans-serif";color:#1F497D">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 style="font-size:11.0pt;font-family:"Calibri","sans-serif";color:red">[agreed]</span><o:p></o:p></p>
<p><span style="font-size:11.0pt;font-family:Symbol;color:#1F497D">·</span><span style="font-size:7.0pt;color:#1F497D">
</span><span style="font-size:11.0pt;font-family:"Calibri","sans-serif";color:#1F497D">Wave/particle dualism is the consequence of special relativity, see Louis de Broglie.</span><span style="font-size:11.0pt;font-family:"Calibri","sans-serif";color:red"> [do
you have a particular reference? I have not seen this statement before.]</span><span style="font-size:11.0pt;font-family:"Calibri","sans-serif";color:#1F497D">
</span><span style="font-size:11.0pt;font-family:"Calibri","sans-serif";color:#77933C">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><o:p></o:p></p>
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<p class="MsoNormal" style="margin-bottom:12.0pt"><span style="color:#B45F06">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 style="color:#1F497D"><o:p></o:p></span></p>
<p class="MsoNormal" style="margin-bottom:12.0pt"><span style="font-size:11.0pt;font-family:"Calibri","sans-serif";color:#7030A0">It is not your fault, it is mentioned rarely. But since I have, now you know.<o:p></o:p></span></p>
<p class="MsoNormal" style="margin-bottom:12.0pt"><span style="color:#B45F06">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><o:p></o:p></p>
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<p class="MsoNormal"><span style="color:#B45F06">"This is exactly BOHR’s formula that he deduced from the theorem mentioned above<br>
and which again can be regarded as a phase wave resonance condition for an electron in</span><o:p></o:p></p>
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<p class="MsoNormal" style="margin-bottom:12.0pt"><span style="color:#B45F06">orbit about a proton."</span><o:p></o:p></p>
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<p class="MsoNormal"><span style="color:#B45F06">If this is also considered resonance, rather than just strict mechanics, then the energy levels have 3 resonances in coincidence.</span><o:p></o:p></p>
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<p class="MsoNormal">Andrew<o:p></o:p></p>
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<p class="MsoNormal" style="mso-margin-top-alt:auto;mso-margin-bottom-alt:auto"><span style="font-family:"Cambria","serif";color:#7030A0">Dear Andrew I hope to have cleared up a few things, surely we should talk about them some more,<o:p></o:p></span></p>
<p class="MsoNormal" style="mso-margin-top-alt:auto;mso-margin-bottom-alt:auto"><span style="font-family:"Cambria","serif";color:#7030A0">Very best regards, Martin<o:p></o:p></span></p>
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