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</o:shapelayout></xml><![endif]--></head><body lang=EN-US link="#0563C1" vlink="#954F72"><div class=WordSection1><p class=MsoNormal><span style='color:black'>Hi John M<o:p></o:p></span></p><p class=MsoNormal><span style='color:black'>Thank you. It is making more sense.<o:p></o:p></span></p><p class=MsoNormal><span style='color:black'>Are you saying that the energy density of space is greater outside of particles than inside, which causes space itself to “reflect” these waves and confine them? And that this implies a 0.2N gradient in space energy “pressure” at your electron radius?<o:p></o:p></span></p><p class=MsoNormal><span style='color:black'><o:p> </o:p></span></p><p class=MsoNormal><span style='color:black'>Chip<o:p></o:p></span></p><p class=MsoNormal><span style='color:black'><o:p> </o:p></span></p><p class=MsoNormal><span style='color:black'><o:p> </o:p></span></p><div><div style='border:none;border-top:solid #E1E1E1 1.0pt;padding:3.0pt 0in 0in 0in'><p class=MsoNormal style='margin-bottom:0in;margin-bottom:.0001pt;line-height:normal'><b>From:</b> General [mailto:general-bounces+chipakins=gmail.com@lists.natureoflightandparticles.org] <b>On Behalf Of </b>John Macken<br><b>Sent:</b> Thursday, April 16, 2015 8:16 PM<br><b>To:</b> 'Nature of Light and Particles - General Discussion'<br><b>Subject:</b> Re: [General] Support for Zitterbewegung<o:p></o:p></p></div></div><p class=MsoNormal><o:p> </o:p></p><p class=MsoNormal><span style='font-size:14.0pt;line-height:105%;font-family:"Times New Roman",serif'>Hi Chip,<o:p></o:p></span></p><p class=MsoNormal><span style='font-size:14.0pt;line-height:105%;font-family:"Times New Roman",serif'>You said, “<span style='color:#C00000'>I do not yet fully understand how you propose the standing waves are confined??</span>” As I stated in an earlier email, the implied internal pressure of an electron with energy of 8x10<sup>-14</sup> J and a radius of about <i><s>λ</s></i><sub>c</sub> is on the order of 10<sup>24</sup> N/m<sup>2</sup>. A proton exerts about 10<sup>34</sup> N/m<sup>3</sup> and a top quark is about 10<sup>45</sup> N/m<sup>2</sup>. The confinement of these tremendous pressures is no problem for my model. When I build the entire universe out of 4 dimensional spacetime, I start with the impedance of spacetime and the uncertainty principle. The uncertainty principle says that the distance between two points can vary by </span><span style='font-size:14.0pt;line-height:105%;font-family:"Cambria Math",serif'>±</span><span style='font-size:14.0pt;line-height:105%;font-family:"Times New Roman",serif'> L<sub>p</sub> (</span><span style='font-size:14.0pt;line-height:105%;font-family:"Cambria Math",serif'>±</span><span style='font-size:14.0pt;line-height:105%;font-family:"Times New Roman",serif'> Planck length) and the rate of time can vary such that two perfect clocks in flat spacetime can vary by </span><span style='font-size:14.0pt;line-height:105%;font-family:"Cambria Math",serif'>±</span><span style='font-size:14.0pt;line-height:105%;font-family:"Times New Roman",serif'> Planck time. These are the wave amplitude limits of waves in spacetime allowed by quantum mechanics. I go further and say that these waves actually exist and I proceed to quantify them, The rest is explained in my “foundation” paper and the book, but the result is that spacetime is modeled as a sea of these small amplitude waves at all frequencies up to Planck frequency. The implied energy density is about 10<sup>113</sup> J/m<sup>3</sup>. This sounds ridiculous, but it really is quite reasonable if you read the implications and model that explains the 10<sup>120</sup> difference between the observable energy density of the universe (</span><span style='font-size:14.0pt;line-height:105%;font-family:"Cambria Math",serif'>∿</span><span style='font-size:14.0pt;line-height:105%;font-family:"Times New Roman",serif'>10<sup>-9 </sup>J/M<sup>3</sup>) and the energy density of the quantum mechanical vacuum (</span><span style='font-size:14.0pt;line-height:105%;font-family:"Cambria Math",serif'>∿</span><span style='font-size:14.0pt;line-height:105%;font-family:"Times New Roman",serif'>10<sup>113</sup> J/m<sup>3</sup>). This model is initially justified by the uncertainty principle, but on a deeper level the sea of waves in the vacuum causes the uncertainty principle.<o:p></o:p></span></p><p class=MsoNormal><span style='font-size:14.0pt;line-height:105%;font-family:"Times New Roman",serif'><o:p> </o:p></span></p><p class=MsoNormal><span style='font-size:14.0pt;line-height:105%;font-family:"Times New Roman",serif'>In my book, I show how the tremendous vacuum pressure not only stabilized my spacetime-based particles, but this pressure is key to explaining all forces. In my model there is only one truly fundamental force. This is the force exerted by waves in spacetime propagating at the speed of light. I call this the “relativistic force <i>F</i><sub>r</sub>” where <i>F</i><sub>r</sub> = <i>P</i><sub>r</sub>/<i>c</i> where <i>P</i><sub>r</sub> is relativistic power propagating at the speed of light. For example, this force gives the force exerted by photon pressure or the force exerted by gravitational waves when they are emitted by rotating binary star systems. Most important, this is the force exerted by the small amplitude waves in spacetime that form the quantum mechanical vacuum. The relativistic force is always repulsive. I show how forces that appear to be attraction are actually a repulsive force caused by unequal pressure on opposite sides of a particle. <o:p></o:p></span></p><p class=MsoNormal><span style='font-size:14.0pt;line-height:105%;font-family:"Times New Roman",serif'><o:p> </o:p></span></p><p class=MsoNormal><span style='font-size:14.0pt;line-height:105%;font-family:"Times New Roman",serif'>This is not arm waving. For example, I calculate the gravitational force on an electron in the earth’s gravitational field by calculating the unequal pressure exerted on opposite sides of the electron. Everyone else in the group is satisfied in saying any model of an electron that postulates that an electron possesses 511,000 eV of energy has “explained” the gravitational force exerted by an electron. I say that this is merely quantifying the gravitational force without explaining anything. I know that others will bring up curved spacetime or gravitons, but this also is not an explanation. A real explanation must be able to start with a model of spacetime and a model of a particle, then show how the particle model produces curved spacetime. Even that is not the complete explanation because you then have to show how the force with the correct vector (attraction) is generated when a particle is prevented from following the geodesic. Assuming an analogy to acceleration also does nothing, but this is a long explanation and I have to cut it off. <o:p></o:p></span></p><p class=MsoNormal><span style='font-size:14.0pt;line-height:105%;font-family:"Times New Roman",serif'><o:p> </o:p></span></p><p class=MsoNormal><span style='font-size:14.0pt;line-height:105%;font-family:"Times New Roman",serif'>One last point. I did not proof read my last post carefully enough. There is one word that is out of place. In the second paragraph I said “<span style='color:black'>I am </span><span style='color:#C00000'>not</span><span style='color:black'> going to modify some of the points …” </span> The word “not” should be dropped, so it totally changes the meaning of the sentence to: “<span style='color:black'>I am going to modify some of the points …”</span><o:p></o:p></span></p><p class=MsoNormal><span style='font-size:14.0pt;line-height:105%;font-family:"Times New Roman",serif'><o:p> </o:p></span></p><p class=MsoNormal><span style='font-size:14.0pt;line-height:105%;font-family:"Times New Roman",serif'>John M. <o:p></o:p></span></p><p class=MsoNormal><span style='font-size:12.0pt;line-height:105%'><o:p> </o:p></span></p><p class=MsoNormal><span style='font-size:12.0pt;line-height:105%;font-family:"Times New Roman",serif;color:blue'><o:p> </o:p></span></p><p class=MsoNormal><span style='font-size:12.0pt;line-height:105%;font-family:"Times New Roman",serif;color:blue'><o:p> </o:p></span></p><div><div style='border:none;border-top:solid #E1E1E1 1.0pt;padding:3.0pt 0in 0in 0in'><p class=MsoNormal style='margin-bottom:0in;margin-bottom:.0001pt;line-height:normal'><b>From:</b> General [<a href="mailto:general-bounces+john=macken.com@lists.natureoflightandparticles.org">mailto:general-bounces+john=macken.com@lists.natureoflightandparticles.org</a>] <b>On Behalf Of </b>Chip Akins<br><b>Sent:</b> Thursday, April 16, 2015 4:35 PM<br><b>To:</b> 'Nature of Light and Particles - General Discussion'<br><b>Subject:</b> Re: [General] Support for Zitterbewegung<o:p></o:p></p></div></div><p class=MsoNormal><o:p> </o:p></p><p class=MsoNormal><span style='color:black'>Hi John M<o:p></o:p></span></p><p class=MsoNormal><span style='color:black'>It occurs to me that when I look at the similarities in your electron model and the models proposed by Williamson/van der Mark, Vivian, and mine, and combine some of the concepts into a single model, we may come up with a description of how the “standing waves” concept bares some similarities to the circulating photon concept. It is my opinion that the electron is not made up of standing waves in the normal sense of the term, but of a circular or toroidal shaped circulating field structure, but the results may be similar. If the transport radius of the field structure is at approximately</span><!--[if gte msEquation 12]><m:oMath><i><span style='font-size:12.0pt;line-height:105%;font-family:"Cambria Math",serif'><m:r> </m:r></span></i><m:sSub><m:sSubPr><span style='font-size:12.0pt;font-family:"Cambria Math",serif;font-style:italic'><m:ctrlPr></m:ctrlPr></span></m:sSubPr><m:e><i><span style='font-size:12.0pt;line-height:105%;font-family:"Cambria Math",serif'><m:r>R</m:r></span></i></m:e><m:sub><i><span style='font-size:12.0pt;line-height:105%;font-family:"Cambria Math",serif'><m:r>0 =</m:r></span></i></m:sub></m:sSub><m:f><m:fPr><span style='font-size:12.0pt;font-family:"Cambria Math",serif'><m:ctrlPr></m:ctrlPr></span></m:fPr><m:num><m:sSub><m:sSubPr><span style='font-size:12.0pt;font-family:"Cambria Math",serif'><m:ctrlPr></m:ctrlPr></span></m:sSubPr><m:e><i><span style='font-size:12.0pt;line-height:105%;font-family:"Cambria Math",serif'><m:r>λ</m:r></span></i></m:e><m:sub><i><span style='font-size:12.0pt;line-height:105%;font-family:"Cambria Math",serif'><m:r>c</m:r></span></i></m:sub></m:sSub></m:num><m:den><span style='font-size:12.0pt;line-height:105%;font-family:"Cambria Math",serif'><m:r><m:rPr><m:scr m:val="roman"/><m:sty m:val="p"/></m:rPr>4π </m:r></span></m:den></m:f></m:oMath><![endif]--><![if !msEquation]><span style='font-size:11.0pt;line-height:105%;font-family:"Calibri",sans-serif;position:relative;top:7.5pt;mso-text-raise:-7.5pt;mso-fareast-language:EN-US'><img width=51 height=29 id="_x0000_i1025" src="cid:image002.png@01D078E2.2C5F4ED0"></span><![endif]><span style='font-size:12.0pt;line-height:105%'> </span><span style='color:black'>then the RMS radius for the fields could be approximately</span><!--[if gte msEquation 12]><m:oMath><i><span style='font-family:"Cambria Math",serif;color:black'><m:r> </m:r></span></i><m:f><m:fPr><span style='font-size:12.0pt;font-family:"Cambria Math",serif'><m:ctrlPr></m:ctrlPr></span></m:fPr><m:num><m:sSub><m:sSubPr><span style='font-size:12.0pt;font-family:"Cambria Math",serif'><m:ctrlPr></m:ctrlPr></span></m:sSubPr><m:e><i><span style='font-size:12.0pt;line-height:105%;font-family:"Cambria Math",serif'><m:r>λ</m:r></span></i></m:e><m:sub><i><span style='font-size:12.0pt;line-height:105%;font-family:"Cambria Math",serif'><m:r>c</m:r></span></i></m:sub></m:sSub></m:num><m:den><span style='font-size:12.0pt;line-height:105%;font-family:"Cambria Math",serif'><m:r><m:rPr><m:scr m:val="roman"/><m:sty m:val="p"/></m:rPr>2π </m:r></span></m:den></m:f></m:oMath><![endif]--><![if !msEquation]><span style='font-size:11.0pt;line-height:105%;font-family:"Calibri",sans-serif;position:relative;top:7.0pt;mso-text-raise:-7.0pt;mso-fareast-language:EN-US'><img width=19 height=27 id="_x0000_i1025" src="cid:image004.png@01D078E2.2C5F4ED0"></span><![endif]><span style='font-size:12.0pt;line-height:105%'>.<o:p></o:p></span></p><p class=MsoNormal><span style='font-size:12.0pt;line-height:105%'>For me it is easier to grasp how the circulating field model may be confined to become the electron, because the confinement for radial or transverse standing waves implies a barrier condition similar to a reflection, and this seems a bit more difficult to justify.<o:p></o:p></span></p><p class=MsoNormal><span style='font-size:12.0pt;line-height:105%'>I do not yet fully understand how you propose the standing waves are confined??<o:p></o:p></span></p><p class=MsoNormal><span style='font-size:12.0pt;line-height:105%'><o:p> </o:p></span></p><p class=MsoNormal><span style='font-size:12.0pt;line-height:105%'>Chip</span><span style='color:black'><o:p></o:p></span></p><p class=MsoNormal><span style='color:black'><o:p> </o:p></span></p><p class=MsoNormal><span style='color:black'><o:p> </o:p></span></p><div><div style='border:none;border-top:solid #E1E1E1 1.0pt;padding:3.0pt 0in 0in 0in'><p class=MsoNormal style='margin-bottom:0in;margin-bottom:.0001pt;line-height:normal'><b>From:</b> General [<a href="mailto:general-bounces+chipakins=gmail.com@lists.natureoflightandparticles.org">mailto:general-bounces+chipakins=gmail.com@lists.natureoflightandparticles.org</a>] <b>On Behalf Of </b>John Macken<br><b>Sent:</b> Thursday, April 16, 2015 6:00 PM<br><b>To:</b> Nature of Light and Particles<br><b>Subject:</b> [General] Support for Zitterbewegung<o:p></o:p></p></div></div><p class=MsoNormal><o:p> </o:p></p><p class=MsoNormal><span style='font-size:14.0pt;line-height:105%;font-family:"Times New Roman",serif'>Hello Everyone,<o:p></o:p></span></p><p class=MsoNormal><span style='font-size:14.0pt;line-height:105%;font-family:"Times New Roman",serif'><o:p> </o:p></span></p><p class=MsoNormal><span style='font-size:14.0pt;line-height:105%;font-family:"Times New Roman",serif'>Most people in this group would feel more comfortable if I explained my ideas using terms like “zitterbewegung<span style='color:black'>” and quoting Dirac. OK, here goes. I can prove that an electron has a vibration that you are welcome to call “zitterbewegung”. In my model there is no particle going through a trembling motion, but I agree that there is a pulsation so we can move on. If there is zitterbewegung then there should be some waves in the surrounding volume of space. If no power is being radiated, then the electron must achieve standing waves. If these standing waves exist, then they should reveal themselves by causing a disturbance that we would call a “field”. The obvious answer is: an electric/magnetic field and a gravitational field. If these fields are caused by “zitterbewegung” disturbances, then we should find some evidence connecting the electron’s electrostatic force and its gravitational force to the wavelength of the zitterbewegung standing waves. <o:p></o:p></span></span></p><p class=MsoNormal><span style='font-size:14.0pt;line-height:105%;font-family:"Times New Roman",serif;color:black'><o:p> </o:p></span></p><p class=MsoNormal><span style='font-size:14.0pt;line-height:105%;font-family:"Times New Roman",serif;color:black'>What is the wavelength of the zitterbewegung waves? Depending on who you listen to, it is either <i>ħ/mc</i> or <i>ħ/2mc</i>. OK, a factor of 2 difference can be tolerated. When the rest of the world does not believe in zitterbewegung waves, we should consider models which differ by only a factor of 2 as being the equivalent of first cousins. So where is the proof that these waves exist? In the email that I wrote on Sunday, April 12, I made the case that the electrostatic force and the gravitational force are connected. So far there has been no comments on this, but it should be of great interest to this group. I am not going to modify some of the points using different emphasis. The conclusion will be that when the separation distance between two particles is expressed as the number of reduced Compton wavelengths <i><s>λ</s></i><sub>c</sub> = </span><span style='font-size:14.0pt;line-height:105%;font-family:"Cambria Math",serif;color:black'>ħ</span><span style='font-size:14.0pt;line-height:105%;font-family:"Times New Roman",serif;color:black'>/mc, then wonderful things happen. I consider this to be the electron’s radius, but you are welcome to define this as the electron’s diameter, so we can proceed. Suppose that we start with the simplest case. We are going to compare the electrostatic force <i>F</i><sub>e</sub> of two electrons (charge<i> e</i>) to the gravitational force <i>F</i><sub>g</sub> when the two electrons are separated by a distance of <i><s>λ</s></i><sub>c</sub> ≈3.8616x10<sup>-13</sup> m. This is chosen because N = 1 at this distance. We will also be using Planck force <i>F</i><sub>p</sub> = c<sup>4</sup>/G and α, the fine structure constant. So how do these forces compare at this distance? <o:p></o:p></span></p><p class=MsoNormal><!--[if gte msEquation 12]><m:oMathPara><m:oMath><m:f><m:fPr><span style='font-size:16.0pt;font-family:"Cambria Math",serif;font-style:italic'><m:ctrlPr></m:ctrlPr></span></m:fPr><m:num><m:sSub><m:sSubPr><span style='font-size:16.0pt;font-family:"Cambria Math",serif;font-style:italic'><m:ctrlPr></m:ctrlPr></span></m:sSubPr><m:e><i><span style='font-size:16.0pt;line-height:105%;font-family:"Cambria Math",serif'><m:r>F</m:r></span></i></m:e><m:sub><i><span style='font-size:16.0pt;line-height:105%;font-family:"Cambria Math",serif'><m:r>g</m:r></span></i></m:sub></m:sSub></m:num><m:den><m:sSub><m:sSubPr><span style='font-size:16.0pt;font-family:"Cambria Math",serif;font-style:italic'><m:ctrlPr></m:ctrlPr></span></m:sSubPr><m:e><i><span style='font-size:16.0pt;line-height:105%;font-family:"Cambria Math",serif'><m:r>F</m:r></span></i></m:e><m:sub><i><span style='font-size:16.0pt;line-height:105%;font-family:"Cambria Math",serif'><m:r>e</m:r></span></i></m:sub></m:sSub><m:sSup><m:sSupPr><span style='font-size:16.0pt;font-family:"Cambria Math",serif;font-style:italic'><m:ctrlPr></m:ctrlPr></span></m:sSupPr><m:e><i><span style='font-size:16.0pt;line-height:105%;font-family:"Cambria Math",serif'><m:r>α</m:r></span></i></m:e><m:sup><i><span style='font-size:16.0pt;line-height:105%;font-family:"Cambria Math",serif'><m:r>-</m:r><m:r>1</m:r></span></i></m:sup></m:sSup></m:den></m:f><i><span style='font-size:16.0pt;line-height:105%;font-family:"Cambria Math",serif'><m:r>= </m:r></span></i><m:f><m:fPr><span style='font-size:16.0pt;font-family:"Cambria Math",serif;font-style:italic'><m:ctrlPr></m:ctrlPr></span></m:fPr><m:num><m:sSub><m:sSubPr><span style='font-size:16.0pt;font-family:"Cambria Math",serif;font-style:italic'><m:ctrlPr></m:ctrlPr></span></m:sSubPr><m:e><i><span style='font-size:16.0pt;line-height:105%;font-family:"Cambria Math",serif'><m:r>F</m:r></span></i></m:e><m:sub><i><span style='font-size:16.0pt;line-height:105%;font-family:"Cambria Math",serif'><m:r>e</m:r><m:r> </m:r></span></i></m:sub></m:sSub><m:sSup><m:sSupPr><span style='font-size:16.0pt;font-family:"Cambria Math",serif;font-style:italic'><m:ctrlPr></m:ctrlPr></span></m:sSupPr><m:e><i><span style='font-size:16.0pt;line-height:105%;font-family:"Cambria Math",serif'><m:r>α</m:r></span></i></m:e><m:sup><i><span style='font-size:16.0pt;line-height:105%;font-family:"Cambria Math",serif'><m:r>-</m:r><m:r>1</m:r></span></i></m:sup></m:sSup></m:num><m:den><m:sSub><m:sSubPr><span style='font-size:16.0pt;font-family:"Cambria Math",serif;font-style:italic'><m:ctrlPr></m:ctrlPr></span></m:sSubPr><m:e><i><span style='font-size:16.0pt;line-height:105%;font-family:"Cambria Math",serif'><m:r>F</m:r></span></i></m:e><m:sub><i><span style='font-size:16.0pt;line-height:105%;font-family:"Cambria Math",serif'><m:r>p</m:r></span></i></m:sub></m:sSub></m:den></m:f></m:oMath></m:oMathPara><![endif]--><![if !msEquation]><span style='font-size:11.0pt;line-height:105%;font-family:"Calibri",sans-serif;mso-fareast-language:EN-US'><img width=142 height=60 id="_x0000_i1025" src="cid:image006.png@01D078E2.2C5F4ED0"></span><![endif]><o:p></o:p></p><p class=MsoNormal style='margin-bottom:0in;margin-bottom:.0001pt;text-align:justify;line-height:115%'><span style='font-size:16.0pt;line-height:115%'><o:p> </o:p></span></p><p class=MsoNormal style='margin-bottom:0in;margin-bottom:.0001pt;text-align:justify;line-height:115%'><span style='font-size:14.0pt;line-height:115%;font-family:"Times New Roman",serif'>It is easy to do a numerical example since we are dealing with a specific separation distance of 3.8616x10<sup>-13</sup> m. At this distance we have: <o:p></o:p></span></p><p class=MsoNormal style='margin-bottom:0in;margin-bottom:.0001pt;text-align:justify;line-height:115%'><span style='font-size:14.0pt;line-height:115%;font-family:"Times New Roman",serif'><o:p> </o:p></span></p><p class=MsoNormal style='margin-bottom:0in;margin-bottom:.0001pt;text-align:justify;line-height:115%'><span style='font-size:14.0pt;line-height:115%;font-family:"Times New Roman",serif'>F<sub>g</sub> = 3.713x10<sup>-46</sup> N, <o:p></o:p></span></p><p class=MsoNormal style='margin-bottom:0in;margin-bottom:.0001pt;text-align:justify;line-height:115%'><span style='font-size:14.0pt;line-height:115%;font-family:"Times New Roman",serif'>F<sub>e</sub> = 1.547x10<sup>-3</sup> N therefore F<sub>e</sub>α<sup>-1</sup> = 0.21201 N and<o:p></o:p></span></p><p class=MsoNormal style='margin-bottom:0in;margin-bottom:.0001pt;text-align:justify;line-height:115%'><span style='font-size:14.0pt;line-height:115%;font-family:"Times New Roman",serif'>F<sub>p</sub> = 1.2105x10<sup>44</sup> N <o:p></o:p></span></p><p class=MsoNormal style='margin-bottom:0in;margin-bottom:.0001pt;text-align:justify;line-height:115%'><span style='font-size:14.0pt;line-height:115%;font-family:"Times New Roman",serif'><o:p> </o:p></span></p><p class=MsoNormal style='margin-bottom:0in;margin-bottom:.0001pt;text-align:justify;line-height:115%'><span style='font-size:14.0pt;line-height:115%;font-family:"Times New Roman",serif'>To test the above equation, we will calculate the ratios.<o:p></o:p></span></p><p class=MsoNormal style='margin-bottom:0in;margin-bottom:.0001pt;text-align:justify;line-height:115%'><span style='font-size:14.0pt;line-height:115%;font-family:"Times New Roman",serif'><o:p> </o:p></span></p><p class=MsoNormal style='margin-bottom:0in;margin-bottom:.0001pt;text-align:justify;line-height:115%'><span style='font-size:14.0pt;line-height:115%;font-family:"Times New Roman",serif'> </span><!--[if gte msEquation 12]><m:oMath><m:f><m:fPr><span style='font-size:16.0pt;font-family:"Cambria Math",serif;font-style:italic'><m:ctrlPr></m:ctrlPr></span></m:fPr><m:num><m:sSub><m:sSubPr><span style='font-size:16.0pt;font-family:"Cambria Math",serif;font-style:italic'><m:ctrlPr></m:ctrlPr></span></m:sSubPr><m:e><i><span style='font-size:16.0pt;line-height:115%;font-family:"Cambria Math",serif'><m:r>F</m:r></span></i></m:e><m:sub><i><span style='font-size:16.0pt;line-height:115%;font-family:"Cambria Math",serif'><m:r>g</m:r></span></i></m:sub></m:sSub></m:num><m:den><m:sSub><m:sSubPr><span style='font-size:16.0pt;font-family:"Cambria Math",serif;font-style:italic'><m:ctrlPr></m:ctrlPr></span></m:sSubPr><m:e><i><span style='font-size:16.0pt;line-height:115%;font-family:"Cambria Math",serif'><m:r>F</m:r></span></i></m:e><m:sub><i><span style='font-size:16.0pt;line-height:115%;font-family:"Cambria Math",serif'><m:r>e</m:r></span></i></m:sub></m:sSub><m:sSup><m:sSupPr><span style='font-size:16.0pt;font-family:"Cambria Math",serif;font-style:italic'><m:ctrlPr></m:ctrlPr></span></m:sSupPr><m:e><i><span style='font-size:16.0pt;line-height:115%;font-family:"Cambria Math",serif'><m:r>α</m:r></span></i></m:e><m:sup><i><span style='font-size:16.0pt;line-height:115%;font-family:"Cambria Math",serif'><m:r>-</m:r><m:r>1</m:r></span></i></m:sup></m:sSup></m:den></m:f><i><span style='font-size:16.0pt;line-height:115%;font-family:"Cambria Math",serif'><m:r>=1.7513</m:r><m:r>x</m:r></span></i><m:sSup><m:sSupPr><span style='font-size:16.0pt;font-family:"Cambria Math",serif;font-style:italic'><m:ctrlPr></m:ctrlPr></span></m:sSupPr><m:e><i><span style='font-size:16.0pt;line-height:115%;font-family:"Cambria Math",serif'><m:r>10</m:r></span></i></m:e><m:sup><i><span style='font-size:16.0pt;line-height:115%;font-family:"Cambria Math",serif'><m:r>-</m:r><m:r>45</m:r></span></i></m:sup></m:sSup></m:oMath><![endif]--><![if !msEquation]><span style='font-size:11.0pt;line-height:105%;font-family:"Calibri",sans-serif;position:relative;top:11.5pt;mso-text-raise:-11.5pt;mso-fareast-language:EN-US'><img width=200 height=42 id="_x0000_i1025" src="cid:image008.png@01D078E2.2C5F4ED0"></span><![endif]><span style='font-size:16.0pt;line-height:115%;font-family:"Times New Roman",serif'> N</span><span style='font-size:14.0pt;line-height:115%;font-family:"Times New Roman",serif'><o:p></o:p></span></p><p class=MsoNormal style='margin-bottom:0in;margin-bottom:.0001pt;text-align:justify;line-height:115%'><span style='font-size:14.0pt;line-height:115%;font-family:"Times New Roman",serif'> </span><!--[if gte msEquation 12]><m:oMath><m:f><m:fPr><span style='font-size:16.0pt;font-family:"Cambria Math",serif;font-style:italic'><m:ctrlPr></m:ctrlPr></span></m:fPr><m:num><m:sSub><m:sSubPr><span style='font-size:16.0pt;font-family:"Cambria Math",serif;font-style:italic'><m:ctrlPr></m:ctrlPr></span></m:sSubPr><m:e><i><span style='font-size:16.0pt;line-height:115%;font-family:"Cambria Math",serif'><m:r>F</m:r></span></i></m:e><m:sub><i><span style='font-size:16.0pt;line-height:115%;font-family:"Cambria Math",serif'><m:r>e</m:r><m:r> </m:r></span></i></m:sub></m:sSub><m:sSup><m:sSupPr><span style='font-size:16.0pt;font-family:"Cambria Math",serif;font-style:italic'><m:ctrlPr></m:ctrlPr></span></m:sSupPr><m:e><i><span style='font-size:16.0pt;line-height:115%;font-family:"Cambria Math",serif'><m:r>α</m:r></span></i></m:e><m:sup><i><span style='font-size:16.0pt;line-height:115%;font-family:"Cambria Math",serif'><m:r>-</m:r><m:r>1</m:r></span></i></m:sup></m:sSup></m:num><m:den><m:sSub><m:sSubPr><span style='font-size:16.0pt;font-family:"Cambria Math",serif;font-style:italic'><m:ctrlPr></m:ctrlPr></span></m:sSubPr><m:e><i><span style='font-size:16.0pt;line-height:115%;font-family:"Cambria Math",serif'><m:r>F</m:r></span></i></m:e><m:sub><i><span style='font-size:16.0pt;line-height:115%;font-family:"Cambria Math",serif'><m:r>p</m:r></span></i></m:sub></m:sSub></m:den></m:f><i><span style='font-size:16.0pt;line-height:115%;font-family:"Cambria Math",serif'><m:r>=1.7514</m:r><m:r>x</m:r></span></i><m:sSup><m:sSupPr><span style='font-size:16.0pt;font-family:"Cambria Math",serif;font-style:italic'><m:ctrlPr></m:ctrlPr></span></m:sSupPr><m:e><i><span style='font-size:16.0pt;line-height:115%;font-family:"Cambria Math",serif'><m:r>10</m:r></span></i></m:e><m:sup><i><span style='font-size:16.0pt;line-height:115%;font-family:"Cambria Math",serif'><m:r>-</m:r><m:r>45</m:r></span></i></m:sup></m:sSup><i><span style='font-size:16.0pt;line-height:115%;font-family:"Cambria Math",serif'><m:r> </m:r></span></i></m:oMath><![endif]--><![if !msEquation]><span style='font-size:11.0pt;line-height:105%;font-family:"Calibri",sans-serif;position:relative;top:13.5pt;mso-text-raise:-13.5pt;mso-fareast-language:EN-US'><img width=208 height=47 id="_x0000_i1025" src="cid:image010.png@01D078E2.2C5F4ED0"></span><![endif]><span style='font-size:16.0pt;line-height:115%;font-family:"Times New Roman",serif'>N<o:p></o:p></span></p><p class=MsoNormal style='margin-bottom:0in;margin-bottom:.0001pt;text-align:justify;line-height:115%'><span style='font-size:14.0pt;line-height:115%;font-family:"Times New Roman",serif'><o:p> </o:p></span></p><p class=MsoNormal style='margin-bottom:0in;margin-bottom:.0001pt;text-align:justify;line-height:115%'><span style='font-size:14.0pt;line-height:115%;font-family:"Times New Roman",serif'>This equality is exact, but I did not incorporate enough accuracy to achieve perfect agreement to 5 significant figures. There is another way to think of this. Suppose we place the vastly different forces on a log scale of force. At one end of this log scale we place the largest possible force, Planck force. At the other end we place the weakest force between two electrons at a separation distance of <i><s>λ</s></i><sub>c</sub>. This weakest force is the gravitational force. Then at the exact midpoint between these forces we have the electrostatic force between two electrons times α<sup>-1</sup> ≈ 137.036. Remember, that this simplicity happens only when the separation equals <i><s>λ</s></i><sub>c</sub>, the electron’s radius or diameter, depending on your model. <o:p></o:p></span></p><p class=MsoNormal style='margin-bottom:0in;margin-bottom:.0001pt;text-align:justify;line-height:115%'><span style='font-size:14.0pt;line-height:115%;font-family:"Times New Roman",serif'><o:p> </o:p></span></p><p class=MsoNormal style='margin-bottom:0in;margin-bottom:.0001pt;text-align:justify;line-height:115%'><span style='font-size:14.0pt;line-height:115%;font-family:"Times New Roman",serif'>If we had used Planck charge rather than charge <i>e</i>, then we would have a coupling constant of 1 and α<sup>-1</sup> disappears. Suppose that we go to arbitrary separation. Since both the gravitational force and the electrostatic force are caused by the standing <span style='color:black'>zitterbewegung waves, we still need to express the separation distance as the number N of reduced Compton wavelengths N = r/<i><s>λ</s></i><sub>c</sub>.</span> then this equation becomes: <o:p></o:p></span></p><p class=MsoNormal style='margin-bottom:0in;margin-bottom:.0001pt;text-align:justify;line-height:115%'><span style='font-size:16.0pt;line-height:115%'> </span><!--[if gte msEquation 12]><m:oMath><i><span style='font-size:16.0pt;line-height:115%;font-family:"Cambria Math",serif'><br></span></i></m:oMath><![endif]--><![if !msEquation]><br><![endif]> <!--[if gte msEquation 12]><m:oMath><m:f><m:fPr><span style='font-size:16.0pt;font-family:"Cambria Math",serif;font-style:italic'><m:ctrlPr></m:ctrlPr></span></m:fPr><m:num><m:sSub><m:sSubPr><span style='font-size:16.0pt;font-family:"Cambria Math",serif;font-style:italic'><m:ctrlPr></m:ctrlPr></span></m:sSubPr><m:e><i><span style='font-size:16.0pt;line-height:115%;font-family:"Cambria Math",serif'><m:r>F</m:r></span></i></m:e><m:sub><i><span style='font-size:16.0pt;line-height:115%;font-family:"Cambria Math",serif'><m:r>g</m:r></span></i></m:sub></m:sSub></m:num><m:den><m:sSub><m:sSubPr><span style='font-size:16.0pt;font-family:"Cambria Math",serif;font-style:italic'><m:ctrlPr></m:ctrlPr></span></m:sSubPr><m:e><i><span style='font-size:16.0pt;line-height:115%;font-family:"Cambria Math",serif'><m:r>F</m:r></span></i></m:e><m:sub><i><span style='font-size:16.0pt;line-height:115%;font-family:"Cambria Math",serif'><m:r>e</m:r></span></i></m:sub></m:sSub><m:sSup><m:sSupPr><span style='font-size:16.0pt;font-family:"Cambria Math",serif;font-style:italic'><m:ctrlPr></m:ctrlPr></span></m:sSupPr><m:e><i><span style='font-size:16.0pt;line-height:115%;font-family:"Cambria Math",serif'><m:r>Nα</m:r></span></i></m:e><m:sup><i><span style='font-size:16.0pt;line-height:115%;font-family:"Cambria Math",serif'><m:r>-</m:r><m:r>1</m:r></span></i></m:sup></m:sSup></m:den></m:f><i><span style='font-size:16.0pt;line-height:115%;font-family:"Cambria Math",serif'><m:r>= </m:r></span></i><m:f><m:fPr><span style='font-size:16.0pt;font-family:"Cambria Math",serif;font-style:italic'><m:ctrlPr></m:ctrlPr></span></m:fPr><m:num><m:sSub><m:sSubPr><span style='font-size:16.0pt;font-family:"Cambria Math",serif;font-style:italic'><m:ctrlPr></m:ctrlPr></span></m:sSubPr><m:e><i><span style='font-size:16.0pt;line-height:115%;font-family:"Cambria Math",serif'><m:r>F</m:r></span></i></m:e><m:sub><i><span style='font-size:16.0pt;line-height:115%;font-family:"Cambria Math",serif'><m:r>e</m:r><m:r> </m:r></span></i></m:sub></m:sSub><m:sSup><m:sSupPr><span style='font-size:16.0pt;font-family:"Cambria Math",serif;font-style:italic'><m:ctrlPr></m:ctrlPr></span></m:sSupPr><m:e><i><span style='font-size:16.0pt;line-height:115%;font-family:"Cambria Math",serif'><m:r>Nα</m:r></span></i></m:e><m:sup><i><span style='font-size:16.0pt;line-height:115%;font-family:"Cambria Math",serif'><m:r>-</m:r><m:r>1</m:r></span></i></m:sup></m:sSup></m:num><m:den><m:sSub><m:sSubPr><span style='font-size:16.0pt;font-family:"Cambria Math",serif;font-style:italic'><m:ctrlPr></m:ctrlPr></span></m:sSubPr><m:e><i><span style='font-size:16.0pt;line-height:115%;font-family:"Cambria Math",serif'><m:r>F</m:r></span></i></m:e><m:sub><i><span style='font-size:16.0pt;line-height:115%;font-family:"Cambria Math",serif'><m:r>p</m:r></span></i></m:sub></m:sSub></m:den></m:f></m:oMath><![endif]--><![if !msEquation]><span style='font-size:11.0pt;line-height:105%;font-family:"Calibri",sans-serif;position:relative;top:13.5pt;mso-text-raise:-13.5pt;mso-fareast-language:EN-US'><img width=146 height=47 id="_x0000_i1025" src="cid:image012.png@01D078E2.2C5F4ED0"></span><![endif]><span style='font-size:14.0pt;line-height:115%;font-family:"Times New Roman",serif'><o:p></o:p></span></p><p class=MsoNormal><!--[if gte msEquation 12]><m:oMathPara><m:oMath><i><span style='font-size:20.0pt;line-height:105%;font-family:"Cambria Math",serif'><br></span></i></m:oMath></m:oMathPara><![endif]--><![if !msEquation]><br><![endif]><span style='font-size:14.0pt;line-height:105%;font-family:"Times New Roman",serif'>There is another set of equations which show that the only difference between the gravitational force and the electrostatic force is that wave amplitude is squared in the gravitational force equation and not squared in the electrostatic equation. These equations were predicted by my wave-based analysis. However, the previous equations are independent of the model that first generated them. Therefore you are welcome to use them to support the contention that an electron is a confined photon possessing zitterbewegung that affects the forces generated by an electron.<o:p></o:p></span></p><p class=MsoNormal><span style='font-size:14.0pt;line-height:105%;font-family:"Times New Roman",serif'><o:p> </o:p></span></p><p class=MsoNormal><span style='font-size:14.0pt;line-height:105%;font-family:"Times New Roman",serif'>On another subject, John D. sent out an email earlier today disputing some of my ideas. I will respond to that at a later date, but now I am trying to prove that I share a common ground with the rest of the group.<o:p></o:p></span></p><p class=MsoNormal><span style='font-size:14.0pt;line-height:105%;font-family:"Times New Roman",serif'><o:p> </o:p></span></p><p class=MsoNormal><span style='font-size:14.0pt;line-height:105%;font-family:"Times New Roman",serif'>John M.<o:p></o:p></span></p><p class=MsoNormal><span style='font-size:14.0pt;line-height:105%;font-family:"Times New Roman",serif'><o:p> </o:p></span></p></div></body></html>