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</o:shapelayout></xml><![endif]--></head><body lang=EN-US link=blue vlink=purple><div class=WordSection1><p class=MsoNormal><span style='color:black'>Hi Andrew and all<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'>Regarding confinement force.<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'>So if we return to a more classical approach for a solution to the confinement of a photon to become an electron, we can start by considering the following:<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'>Your gradient refractive-index GRIN may be provided by a spacetime similar to John M’s. From a classical approach, if we consider the two momentum terms for the EM waves in the photon, longitudinal, and spin angular momentum, and imagine a helical path for the EM fields inside the photon, we arrive at the following for a photon with the energy of 0.511 MeV.<o:p></o:p></span></p><p class=MsoNormal><span style='color:black'><o:p> </o:p></span></p><p class=MsoNormal><!--[if gte msEquation 12]><m:oMath><m:sSub><m:sSubPr><span style='font-family:"Cambria Math",serif;font-style:italic'><m:ctrlPr></m:ctrlPr></span></m:sSubPr><m:e><i><span style='font-family:"Cambria Math",serif'><m:r>F</m:r></span></i></m:e><m:sub><i><span style='font-family:"Cambria Math",serif'><m:r>tw</m:r></span></i></m:sub></m:sSub><i><span style='font-family:"Cambria Math",serif'><m:r>=</m:r></span></i><m:f><m:fPr><span style='font-family:"Cambria Math",serif;font-style:italic'><m:ctrlPr></m:ctrlPr></span></m:fPr><m:num><i><span style='font-family:"Cambria Math",serif'><m:r>L</m:r><m:r> </m:r><m:r>c</m:r></span></i></m:num><m:den><m:sSub><m:sSubPr><span style='font-family:"Cambria Math",serif;font-style:italic'><m:ctrlPr></m:ctrlPr></span></m:sSubPr><m:e><i><span style='font-family:"Cambria Math",serif'><m:r>r</m:r></span></i></m:e><m:sub><i><span style='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:12.0pt;font-family:"Times New Roman",serif;position:relative;top:10.0pt;mso-text-raise:-10.0pt;mso-fareast-language:EN-US'><img width=59 height=31 id="_x0000_i1025" src="cid:image001.png@01D07CD1.C19438B0"></span><![endif]> Twist force<o:p></o:p></p><p class=MsoNormal><o:p> </o:p></p><p class=MsoNormal>Total mutual force <!--[if gte msEquation 12]><m:oMath><m:sSub><m:sSubPr><span style='font-family:"Cambria Math",serif'><m:ctrlPr></m:ctrlPr></span></m:sSubPr><m:e><i><span style='font-family:"Cambria Math",serif'><m:r>F</m:r></span></i></m:e><m:sub><i><span style='font-family:"Cambria Math",serif'><m:r>tp</m:r></span></i></m:sub></m:sSub><span style='font-family:"Cambria Math",serif'><m:r><m:rPr><m:scr m:val="roman"/><m:sty m:val="p"/></m:rPr> </m:r></span></m:oMath><![endif]--><![if !msEquation]><span style='font-size:12.0pt;font-family:"Times New Roman",serif;position:relative;top:4.5pt;mso-text-raise:-4.5pt;mso-fareast-language:EN-US'><img width=24 height=21 id="_x0000_i1025" src="cid:image003.png@01D07CD1.C19438B0"></span><![endif]>between E and M fields is then<!--[if gte msEquation 12]><m:oMath><span style='font-family:"Cambria Math",serif'><m:r><m:rPr><m:scr m:val="roman"/><m:sty m:val="p"/></m:rPr> </m:r></span><m:f><m:fPr><span style='font-family:"Cambria Math",serif'><m:ctrlPr></m:ctrlPr></span></m:fPr><m:num><span style='font-family:"Cambria Math",serif'><m:r><m:rPr><m:scr m:val="roman"/><m:sty m:val="p"/></m:rPr>1</m:r></span></m:num><m:den><span style='font-family:"Cambria Math",serif'><m:r><m:rPr><m:scr m:val="roman"/><m:sty m:val="p"/></m:rPr>cos(θ</m:r></span><span style='font-family:"Cambria Math",serif'><m:r><m:rPr><m:scr m:val="roman"/><m:sty m:val="p"/></m:rPr>)</m:r></span></m:den></m:f><m:sSub><m:sSubPr><span style='font-family:"Cambria Math",serif'><m:ctrlPr></m:ctrlPr></span></m:sSubPr><m:e><i><span style='font-family:"Cambria Math",serif'><m:r>F</m:r></span></i></m:e><m:sub><i><span style='font-family:"Cambria Math",serif'><m:r>tw</m:r></span></i></m:sub></m:sSub><span style='font-family:"Cambria Math",serif'><m:r><m:rPr><m:scr m:val="roman"/><m:sty m:val="p"/></m:rPr>=</m:r></span><m:rad><m:radPr><m:degHide m:val="on"/><span style='font-family:"Cambria Math",serif'><m:ctrlPr></m:ctrlPr></span></m:radPr><m:deg></m:deg><m:e><span style='font-family:"Cambria Math",serif'><m:r><m:rPr><m:scr m:val="roman"/><m:sty m:val="p"/></m:rPr>2</m:r></span></m:e></m:rad><m:sSub><m:sSubPr><span style='font-family:"Cambria Math",serif'><m:ctrlPr></m:ctrlPr></span></m:sSubPr><m:e><span style='font-family:"Cambria Math",serif'><m:r><m:rPr><m:scr m:val="roman"/><m:sty m:val="p"/></m:rPr> </m:r><m:r><i>F</i></m:r></span></m:e><m:sub><i><span style='font-family:"Cambria Math",serif'><m:r>tw</m:r></span></i></m:sub></m:sSub><span style='font-family:"Cambria Math",serif'><m:r><m:rPr><m:scr m:val="roman"/><m:sty m:val="p"/></m:rPr>.</m:r></span></m:oMath><![endif]--><![if !msEquation]><span style='font-size:12.0pt;font-family:"Times New Roman",serif;position:relative;top:8.5pt;mso-text-raise:-8.5pt;mso-fareast-language:EN-US'><img width=137 height=29 id="_x0000_i1025" src="cid:image005.png@01D07CD1.C19438B0"></span><![endif]><o:p></o:p></p><p class=MsoNormal><o:p> </o:p></p><p class=MsoNormal>The RMS action distance for the photon would be:<o:p></o:p></p><p class=MsoNormal><!--[if gte msEquation 12]><m:oMath><m:sSub><m:sSubPr><span style='font-family:"Cambria Math",serif'><m:ctrlPr></m:ctrlPr></span></m:sSubPr><m:e><i><span style='font-family:"Cambria Math",serif'><m:r>r</m:r></span></i></m:e><m:sub><i><span style='font-family:"Cambria Math",serif'><m:r>p</m:r></span></i></m:sub></m:sSub><span style='font-family:"Cambria Math",serif'><m:r><m:rPr><m:scr m:val="roman"/><m:sty m:val="p"/></m:rPr>=</m:r></span><m:f><m:fPr><span style='font-family:"Cambria Math",serif'><m:ctrlPr></m:ctrlPr></span></m:fPr><m:num><i><span style='font-family:"Cambria Math",serif'><m:r>λ</m:r></span></i></m:num><m:den><span style='font-family:"Cambria Math",serif'><m:r><m:rPr><m:scr m:val="roman"/><m:sty m:val="p"/></m:rPr>2</m:r><m:r><i>π</i></m:r></span></m:den></m:f></m:oMath><![endif]--><![if !msEquation]><span style='font-size:12.0pt;font-family:"Times New Roman",serif;position:relative;top:7.0pt;mso-text-raise:-7.0pt;mso-fareast-language:EN-US'><img width=48 height=28 id="_x0000_i1025" src="cid:image007.png@01D07CD1.C19438B0"></span><![endif]> Where <!--[if gte msEquation 12]><m:oMath><i><span style='font-family:"Cambria Math",serif'><m:r>λ</m:r></span></i><span style='font-family:"Cambria Math",serif'><m:r><m:rPr><m:scr m:val="roman"/><m:sty m:val="p"/></m:rPr>=</m:r><m:r><i>wavelengt</i></m:r><m:r><i>h</i></m:r><m:r><m:rPr><m:scr m:val="roman"/><m:sty m:val="p"/></m:rPr>=</m:r></span><m:f><m:fPr><span style='font-family:"Cambria Math",serif'><m:ctrlPr></m:ctrlPr></span></m:fPr><m:num><i><span style='font-family:"Cambria Math",serif'><m:r>E</m:r></span></i></m:num><m:den><i><span style='font-family:"Cambria Math",serif'><m:r>h</m:r></span></i></m:den></m:f></m:oMath><![endif]--><![if !msEquation]><span style='font-size:12.0pt;font-family:"Times New Roman",serif;position:relative;top:7.0pt;mso-text-raise:-7.0pt;mso-fareast-language:EN-US'><img width=143 height=27 id="_x0000_i1025" src="cid:image009.png@01D07CD1.C19438B0"></span><![endif]><o:p></o:p></p><p class=MsoNormal><o:p> </o:p></p><p class=MsoNormal>Working this out for my electron model: (this is assuming the helical wavefront velocity inside the photon is <!--[if gte msEquation 12]><m:oMath><m:rad><m:radPr><m:degHide m:val="on"/><span style='font-family:"Cambria Math",serif'><m:ctrlPr></m:ctrlPr></span></m:radPr><m:deg></m:deg><m:e><span style='font-family:"Cambria Math",serif'><m:r><m:rPr><m:scr m:val="roman"/><m:sty m:val="p"/></m:rPr>2</m:r></span></m:e></m:rad><i><span style='font-family:"Cambria Math",serif'><m:r> </m:r><m:r>c</m:r></span></i></m:oMath><![endif]--><![if !msEquation]><span style='font-size:12.0pt;font-family:"Times New Roman",serif;position:relative;top:3.0pt;mso-text-raise:-3.0pt;mso-fareast-language:EN-US'><img width=31 height=21 id="_x0000_i1025" src="cid:image011.png@01D07CD1.C19438B0"></span><![endif]> so that the photon moves forward at c. But the system seems to work for other models as well if properly implemented.)<o:p></o:p></p><p class=MsoNormal><o:p> </o:p></p><p class=MsoNormal><!--[if gte msEquation 12]><m:oMath><i><span style='font-family:"Cambria Math",serif'><m:r>E</m:r></span></i><span style='font-family:"Cambria Math",serif'><m:r><m:rPr><m:scr m:val="roman"/><m:sty m:val="p"/></m:rPr>= </m:r></span></m:oMath><![endif]--><![if !msEquation]><span style='font-size:12.0pt;font-family:"Times New Roman",serif;position:relative;top:3.0pt;mso-text-raise:-3.0pt;mso-fareast-language:EN-US'><img width=31 height=19 id="_x0000_i1025" src="cid:image013.png@01D07CD1.C19438B0"></span><![endif]>8.18710478684500E-14J<o:p></o:p></p><p class=MsoNormal><o:p> </o:p></p><p class=MsoNormal><!--[if gte msEquation 12]><m:oMath><i><span style='font-family:"Cambria Math",serif'><m:r>E</m:r></span></i><span style='font-family:"Cambria Math",serif'><m:r><m:rPr><m:scr m:val="roman"/><m:sty m:val="p"/></m:rPr>=</m:r><m:r><i>h</i></m:r><m:r><i>f</i></m:r></span></m:oMath><![endif]--><![if !msEquation]><span style='font-size:12.0pt;font-family:"Times New Roman",serif;position:relative;top:3.0pt;mso-text-raise:-3.0pt;mso-fareast-language:EN-US'><img width=50 height=19 id="_x0000_i1025" src="cid:image015.png@01D07CD1.C19438B0"></span><![endif]> and <!--[if gte msEquation 12]><m:oMath><i><span style='font-family:"Cambria Math",serif'><m:r>λ</m:r></span></i><span style='font-family:"Cambria Math",serif'><m:r><m:rPr><m:scr m:val="roman"/><m:sty m:val="p"/></m:rPr>=</m:r><m:r><i>wavelengt</i></m:r><m:r><i>h</i></m:r><m:r><m:rPr><m:scr m:val="roman"/><m:sty m:val="p"/></m:rPr>=</m:r></span><m:f><m:fPr><span style='font-family:"Cambria Math",serif'><m:ctrlPr></m:ctrlPr></span></m:fPr><m:num><i><span style='font-family:"Cambria Math",serif'><m:r>E</m:r></span></i></m:num><m:den><i><span style='font-family:"Cambria Math",serif'><m:r>h</m:r></span></i></m:den></m:f></m:oMath><![endif]--><![if !msEquation]><span style='font-size:12.0pt;font-family:"Times New Roman",serif;position:relative;top:7.0pt;mso-text-raise:-7.0pt;mso-fareast-language:EN-US'><img width=143 height=27 id="_x0000_i1025" src="cid:image009.png@01D07CD1.C19438B0"></span><![endif]> so the frequency of the confined photon is:<o:p></o:p></p><p class=MsoNormal><o:p> </o:p></p><p class=MsoNormal> <!--[if gte msEquation 12]><m:oMath><i><span style='font-family:"Cambria Math",serif'><m:r>f</m:r></span></i><span style='font-family:"Cambria Math",serif'><m:r><m:rPr><m:scr m:val="roman"/><m:sty m:val="p"/></m:rPr>= </m:r></span></m:oMath><![endif]--><![if !msEquation]><span style='font-size:12.0pt;font-family:"Times New Roman",serif;position:relative;top:3.0pt;mso-text-raise:-3.0pt;mso-fareast-language:EN-US'><img width=29 height=19 id="_x0000_i1025" src="cid:image017.png@01D07CD1.C19438B0"></span><![endif]>1.23558997290369E+20Hz<o:p></o:p></p><p class=MsoNormal><o:p> </o:p></p><p class=MsoNormal>And the wavelength at c is: <!--[if gte msEquation 12]><m:oMath><i><span style='font-family:"Cambria Math",serif'><m:r>λ</m:r></span></i><span style='font-family:"Cambria Math",serif'><m:r><m:rPr><m:scr m:val="roman"/><m:sty m:val="p"/></m:rPr>=</m:r></span></m:oMath><![endif]--><![if !msEquation]><span style='font-size:12.0pt;font-family:"Times New Roman",serif;position:relative;top:3.0pt;mso-text-raise:-3.0pt;mso-fareast-language:EN-US'><img width=25 height=19 id="_x0000_i1025" src="cid:image019.png@01D07CD1.C19438B0"></span><![endif]> 2.42631022082086E-12m<o:p></o:p></p><p class=MsoNormal><o:p> </o:p></p><p class=MsoNormal>So the helical radius of the photon is: <!--[if gte msEquation 12]><m:oMath><m:sSub><m:sSubPr><span style='font-family:"Cambria Math",serif'><m:ctrlPr></m:ctrlPr></span></m:sSubPr><m:e><i><span style='font-family:"Cambria Math",serif'><m:r>r</m:r></span></i></m:e><m:sub><i><span style='font-family:"Cambria Math",serif'><m:r>p</m:r></span></i></m:sub></m:sSub><span style='font-family:"Cambria Math",serif'><m:r><m:rPr><m:scr m:val="roman"/><m:sty m:val="p"/></m:rPr>=</m:r></span><m:f><m:fPr><span style='font-family:"Cambria Math",serif'><m:ctrlPr></m:ctrlPr></span></m:fPr><m:num><i><span style='font-family:"Cambria Math",serif'><m:r>λ</m:r></span></i></m:num><m:den><span style='font-family:"Cambria Math",serif'><m:r><m:rPr><m:scr m:val="roman"/><m:sty m:val="p"/></m:rPr>2</m:r><m:r><i>π</i></m:r></span></m:den></m:f><span style='font-family:"Cambria Math",serif'><m:r><m:rPr><m:scr m:val="roman"/><m:sty m:val="p"/></m:rPr>=</m:r></span></m:oMath><![endif]--><![if !msEquation]><span style='font-size:12.0pt;font-family:"Times New Roman",serif;position:relative;top:7.0pt;mso-text-raise:-7.0pt;mso-fareast-language:EN-US'><img width=64 height=28 id="_x0000_i1025" src="cid:image021.png@01D07CD1.C19438B0"></span><![endif]> 3.86159265118028E-13m<o:p></o:p></p><p class=MsoNormal>And the electron transport radius: <!--[if gte msEquation 12]><m:oMath><m:sSub><m:sSubPr><span style='font-family:"Cambria Math",serif'><m:ctrlPr></m:ctrlPr></span></m:sSubPr><m:e><i><span style='font-family:"Cambria Math",serif'><m:r>r</m:r></span></i></m:e><m:sub><i><span style='font-family:"Cambria Math",serif'><m:r>e</m:r></span></i></m:sub></m:sSub><span style='font-family:"Cambria Math",serif'><m:r><m:rPr><m:scr m:val="roman"/><m:sty m:val="p"/></m:rPr>= </m:r></span><m:rad><m:radPr><m:degHide m:val="on"/><span style='font-family:"Cambria Math",serif'><m:ctrlPr></m:ctrlPr></span></m:radPr><m:deg></m:deg><m:e><span style='font-family:"Cambria Math",serif'><m:r><m:rPr><m:scr m:val="roman"/><m:sty m:val="p"/></m:rPr>2</m:r></span></m:e></m:rad></m:oMath><![endif]--><![if !msEquation]><span style='font-size:12.0pt;font-family:"Times New Roman",serif;position:relative;top:3.0pt;mso-text-raise:-3.0pt;mso-fareast-language:EN-US'><img width=56 height=21 id="_x0000_i1025" src="cid:image023.png@01D07CD1.C19438B0"></span><![endif]> <!--[if gte msEquation 12]><m:oMath><m:f><m:fPr><span style='font-family:"Cambria Math",serif'><m:ctrlPr></m:ctrlPr></span></m:fPr><m:num><i><span style='font-family:"Cambria Math",serif'><m:r>λ</m:r></span></i></m:num><m:den><span style='font-family:"Cambria Math",serif'><m:r><m:rPr><m:scr m:val="roman"/><m:sty m:val="p"/></m:rPr>4</m:r><m:r><i>π</i></m:r></span></m:den></m:f><span style='font-family:"Cambria Math",serif'><m:r><m:rPr><m:scr m:val="roman"/><m:sty m:val="p"/></m:rPr>=</m:r></span></m:oMath><![endif]--><![if !msEquation]><span style='font-size:12.0pt;font-family:"Times New Roman",serif;position:relative;top:7.0pt;mso-text-raise:-7.0pt;mso-fareast-language:EN-US'><img width=31 height=28 id="_x0000_i1025" src="cid:image025.png@01D07CD1.C19438B0"></span><![endif]> 2.73055834982987E-13m<o:p></o:p></p><p class=MsoNormal>This <!--[if gte msEquation 12]><m:oMath><m:sSub><m:sSubPr><span style='font-family:"Cambria Math",serif'><m:ctrlPr></m:ctrlPr></span></m:sSubPr><m:e><i><span style='font-family:"Cambria Math",serif'><m:r>r</m:r></span></i></m:e><m:sub><i><span style='font-family:"Cambria Math",serif'><m:r>e</m:r></span></i></m:sub></m:sSub><span style='font-family:"Cambria Math",serif'><m:r><m:rPr><m:scr m:val="roman"/><m:sty m:val="p"/></m:rPr> </m:r></span></m:oMath><![endif]--><![if !msEquation]><span style='font-size:12.0pt;font-family:"Times New Roman",serif;position:relative;top:3.0pt;mso-text-raise:-3.0pt;mso-fareast-language:EN-US'><img width=16 height=19 id="_x0000_i1025" src="cid:image027.png@01D07CD1.C19438B0"></span><![endif]>is a smaller action distance than that of the photon <!--[if gte msEquation 12]><m:oMath><m:sSub><m:sSubPr><span style='font-family:"Cambria Math",serif'><m:ctrlPr></m:ctrlPr></span></m:sSubPr><m:e><i><span style='font-family:"Cambria Math",serif'><m:r>r</m:r></span></i></m:e><m:sub><i><span style='font-family:"Cambria Math",serif'><m:r>p</m:r></span></i></m:sub></m:sSub><span style='font-family:"Cambria Math",serif'><m:r><m:rPr><m:scr m:val="roman"/><m:sty m:val="p"/></m:rPr> </m:r></span></m:oMath><![endif]--><![if !msEquation]><span style='font-size:12.0pt;font-family:"Times New Roman",serif;position:relative;top:4.5pt;mso-text-raise:-4.5pt;mso-fareast-language:EN-US'><img width=16 height=21 id="_x0000_i1025" src="cid:image029.png@01D07CD1.C19438B0"></span><![endif]>since the electron is a spin ½ particle. If we assume that the total mutual force follows the inverse square rule, which seems reasonable, we can estimate the E and M confinement forces for the electron model by using the ratio of the square of the photon radius over the square of the electron radius:<!--[if gte msEquation 12]><m:oMath><span style='font-family:"Cambria Math",serif'><m:r><m:rPr><m:scr m:val="roman"/><m:sty m:val="p"/></m:rPr> </m:r></span><m:f><m:fPr><span style='font-family:"Cambria Math",serif'><m:ctrlPr></m:ctrlPr></span></m:fPr><m:num><m:sSup><m:sSupPr><span style='font-family:"Cambria Math",serif'><m:ctrlPr></m:ctrlPr></span></m:sSupPr><m:e><m:sSub><m:sSubPr><span style='font-family:"Cambria Math",serif'><m:ctrlPr></m:ctrlPr></span></m:sSubPr><m:e><i><span style='font-family:"Cambria Math",serif'><m:r>r</m:r></span></i></m:e><m:sub><i><span style='font-family:"Cambria Math",serif'><m:r>p</m:r></span></i></m:sub></m:sSub></m:e><m:sup><span style='font-family:"Cambria Math",serif'><m:r><m:rPr><m:scr m:val="roman"/><m:sty m:val="p"/></m:rPr>2</m:r></span></m:sup></m:sSup></m:num><m:den><m:sSup><m:sSupPr><span style='font-family:"Cambria Math",serif'><m:ctrlPr></m:ctrlPr></span></m:sSupPr><m:e><m:sSub><m:sSubPr><span style='font-family:"Cambria Math",serif'><m:ctrlPr></m:ctrlPr></span></m:sSubPr><m:e><i><span style='font-family:"Cambria Math",serif'><m:r>r</m:r></span></i></m:e><m:sub><i><span style='font-family:"Cambria Math",serif'><m:r>e</m:r></span></i></m:sub></m:sSub></m:e><m:sup><span style='font-family:"Cambria Math",serif'><m:r><m:rPr><m:scr m:val="roman"/><m:sty m:val="p"/></m:rPr>2</m:r></span></m:sup></m:sSup></m:den></m:f></m:oMath><![endif]--><![if !msEquation]><span style='font-size:12.0pt;font-family:"Times New Roman",serif;position:relative;top:8.5pt;mso-text-raise:-8.5pt;mso-fareast-language:EN-US'><img width=21 height=33 id="_x0000_i1025" src="cid:image030.png@01D07CD1.C19438B0"></span><![endif]><o:p></o:p></p><p class=MsoNormal><!--[if gte msEquation 12]><m:oMath><m:sSub><m:sSubPr><span style='font-family:"Cambria Math",serif'><m:ctrlPr></m:ctrlPr></span></m:sSubPr><m:e><i><span style='font-family:"Cambria Math",serif'><m:r>F</m:r></span></i></m:e><m:sub><i><span style='font-family:"Cambria Math",serif'><m:r>E</m:r></span></i></m:sub></m:sSub><span style='font-family:"Cambria Math",serif'><m:r><m:rPr><m:scr m:val="roman"/><m:sty m:val="p"/></m:rPr>= </m:r></span><m:f><m:fPr><span style='font-family:"Cambria Math",serif'><m:ctrlPr></m:ctrlPr></span></m:fPr><m:num><m:sSub><m:sSubPr><span style='font-family:"Cambria Math",serif'><m:ctrlPr></m:ctrlPr></span></m:sSubPr><m:e><i><span style='font-family:"Cambria Math",serif'><m:r>F</m:r></span></i></m:e><m:sub><i><span style='font-family:"Cambria Math",serif'><m:r>tp</m:r></span></i></m:sub></m:sSub></m:num><m:den><span style='font-family:"Cambria Math",serif'><m:r><m:rPr><m:scr m:val="roman"/><m:sty m:val="p"/></m:rPr>2</m:r></span></m:den></m:f><span style='font-family:"Cambria Math",serif'><m:r><m:rPr><m:scr m:val="roman"/><m:sty m:val="p"/></m:rPr> </m:r></span><m:f><m:fPr><span style='font-family:"Cambria Math",serif'><m:ctrlPr></m:ctrlPr></span></m:fPr><m:num><m:sSup><m:sSupPr><span style='font-family:"Cambria Math",serif'><m:ctrlPr></m:ctrlPr></span></m:sSupPr><m:e><m:sSub><m:sSubPr><span style='font-family:"Cambria Math",serif'><m:ctrlPr></m:ctrlPr></span></m:sSubPr><m:e><i><span style='font-family:"Cambria Math",serif'><m:r>r</m:r></span></i></m:e><m:sub><i><span style='font-family:"Cambria Math",serif'><m:r>p</m:r></span></i></m:sub></m:sSub></m:e><m:sup><span style='font-family:"Cambria Math",serif'><m:r><m:rPr><m:scr m:val="roman"/><m:sty m:val="p"/></m:rPr>2</m:r></span></m:sup></m:sSup></m:num><m:den><m:sSup><m:sSupPr><span style='font-family:"Cambria Math",serif'><m:ctrlPr></m:ctrlPr></span></m:sSupPr><m:e><m:sSub><m:sSubPr><span style='font-family:"Cambria Math",serif'><m:ctrlPr></m:ctrlPr></span></m:sSubPr><m:e><i><span style='font-family:"Cambria Math",serif'><m:r>r</m:r></span></i></m:e><m:sub><i><span style='font-family:"Cambria Math",serif'><m:r>e</m:r></span></i></m:sub></m:sSub></m:e><m:sup><span style='font-family:"Cambria Math",serif'><m:r><m:rPr><m:scr m:val="roman"/><m:sty m:val="p"/></m:rPr>2</m:r></span></m:sup></m:sSup></m:den></m:f></m:oMath><![endif]--><![if !msEquation]><span style='font-size:12.0pt;font-family:"Times New Roman",serif;position:relative;top:8.5pt;mso-text-raise:-8.5pt;mso-fareast-language:EN-US'><img width=81 height=33 id="_x0000_i1025" src="cid:image031.png@01D07CD1.C19438B0"></span><![endif]> And <!--[if gte msEquation 12]><m:oMath><m:sSub><m:sSubPr><span style='font-family:"Cambria Math",serif'><m:ctrlPr></m:ctrlPr></span></m:sSubPr><m:e><i><span style='font-family:"Cambria Math",serif'><m:r>F</m:r></span></i></m:e><m:sub><i><span style='font-family:"Cambria Math",serif'><m:r>m</m:r></span></i></m:sub></m:sSub><span style='font-family:"Cambria Math",serif'><m:r><m:rPr><m:scr m:val="roman"/><m:sty m:val="p"/></m:rPr>= </m:r></span><m:f><m:fPr><span style='font-family:"Cambria Math",serif'><m:ctrlPr></m:ctrlPr></span></m:fPr><m:num><m:sSub><m:sSubPr><span style='font-family:"Cambria Math",serif'><m:ctrlPr></m:ctrlPr></span></m:sSubPr><m:e><i><span style='font-family:"Cambria Math",serif'><m:r>F</m:r></span></i></m:e><m:sub><i><span style='font-family:"Cambria Math",serif'><m:r>tp</m:r></span></i></m:sub></m:sSub></m:num><m:den><span style='font-family:"Cambria Math",serif'><m:r><m:rPr><m:scr m:val="roman"/><m:sty m:val="p"/></m:rPr>2</m:r></span></m:den></m:f><span style='font-family:"Cambria Math",serif'><m:r><m:rPr><m:scr m:val="roman"/><m:sty m:val="p"/></m:rPr> </m:r></span><m:f><m:fPr><span style='font-family:"Cambria Math",serif'><m:ctrlPr></m:ctrlPr></span></m:fPr><m:num><m:sSup><m:sSupPr><span style='font-family:"Cambria Math",serif'><m:ctrlPr></m:ctrlPr></span></m:sSupPr><m:e><m:sSub><m:sSubPr><span style='font-family:"Cambria Math",serif'><m:ctrlPr></m:ctrlPr></span></m:sSubPr><m:e><i><span style='font-family:"Cambria Math",serif'><m:r>r</m:r></span></i></m:e><m:sub><i><span style='font-family:"Cambria Math",serif'><m:r>p</m:r></span></i></m:sub></m:sSub></m:e><m:sup><span style='font-family:"Cambria Math",serif'><m:r><m:rPr><m:scr m:val="roman"/><m:sty m:val="p"/></m:rPr>2</m:r></span></m:sup></m:sSup></m:num><m:den><m:sSup><m:sSupPr><span style='font-family:"Cambria Math",serif'><m:ctrlPr></m:ctrlPr></span></m:sSupPr><m:e><m:sSub><m:sSubPr><span style='font-family:"Cambria Math",serif'><m:ctrlPr></m:ctrlPr></span></m:sSubPr><m:e><i><span style='font-family:"Cambria Math",serif'><m:r>r</m:r></span></i></m:e><m:sub><i><span style='font-family:"Cambria Math",serif'><m:r>e</m:r></span></i></m:sub></m:sSub></m:e><m:sup><span style='font-family:"Cambria Math",serif'><m:r><m:rPr><m:scr m:val="roman"/><m:sty m:val="p"/></m:rPr>2</m:r></span></m:sup></m:sSup></m:den></m:f></m:oMath><![endif]--><![if !msEquation]><span style='font-size:12.0pt;font-family:"Times New Roman",serif;position:relative;top:8.5pt;mso-text-raise:-8.5pt;mso-fareast-language:EN-US'><img width=83 height=33 id="_x0000_i1025" src="cid:image032.png@01D07CD1.C19438B0"></span><![endif]> . Where <!--[if gte msEquation 12]><m:oMath><m:sSub><m:sSubPr><span style='font-family:"Cambria Math",serif'><m:ctrlPr></m:ctrlPr></span></m:sSubPr><m:e><i><span style='font-family:"Cambria Math",serif'><m:r>F</m:r></span></i></m:e><m:sub><i><span style='font-family:"Cambria Math",serif'><m:r>E</m:r></span></i></m:sub></m:sSub><span style='font-family:"Cambria Math",serif'><m:r><m:rPr><m:scr m:val="roman"/><m:sty m:val="p"/></m:rPr> </m:r></span></m:oMath><![endif]--><![if !msEquation]><span style='font-size:12.0pt;font-family:"Times New Roman",serif;position:relative;top:3.0pt;mso-text-raise:-3.0pt;mso-fareast-language:EN-US'><img width=20 height=19 id="_x0000_i1025" src="cid:image033.png@01D07CD1.C19438B0"></span><![endif]>is the electrical contribution to the force, and <!--[if gte msEquation 12]><m:oMath><m:sSub><m:sSubPr><span style='font-family:"Cambria Math",serif'><m:ctrlPr></m:ctrlPr></span></m:sSubPr><m:e><i><span style='font-family:"Cambria Math",serif'><m:r>F</m:r></span></i></m:e><m:sub><i><span style='font-family:"Cambria Math",serif'><m:r>m</m:r></span></i></m:sub></m:sSub><span style='font-family:"Cambria Math",serif'><m:r><m:rPr><m:scr m:val="roman"/><m:sty m:val="p"/></m:rPr> </m:r></span></m:oMath><![endif]--><![if !msEquation]><span style='font-size:12.0pt;font-family:"Times New Roman",serif;position:relative;top:3.0pt;mso-text-raise:-3.0pt;mso-fareast-language:EN-US'><img width=22 height=19 id="_x0000_i1025" src="cid:image034.png@01D07CD1.C19438B0"></span><![endif]>is the magnetic contribution. <o:p></o:p></p><p class=MsoNormal><o:p> </o:p></p><p class=MsoNormal>When simplified, this expression shows that the <b>total mutual confinement force</b> of the electron<!--[if gte msEquation 12]><m:oMath><m:sSub><m:sSubPr><span style='font-family:"Cambria Math",serif'><m:ctrlPr></m:ctrlPr></span></m:sSubPr><m:e><span style='font-family:"Cambria Math",serif'><m:r><m:rPr><m:scr m:val="roman"/><m:sty m:val="p"/></m:rPr> </m:r><m:r><i>F</i></m:r></span></m:e><m:sub><i><span style='font-family:"Cambria Math",serif'><m:r>te</m:r></span></i><span style='font-family:"Cambria Math",serif'><m:r><m:rPr><m:scr m:val="roman"/><m:sty m:val="p"/></m:rPr> </m:r></span></m:sub></m:sSub></m:oMath><![endif]--><![if !msEquation]><span style='font-size:12.0pt;font-family:"Times New Roman",serif;position:relative;top:3.0pt;mso-text-raise:-3.0pt;mso-fareast-language:EN-US'><img width=26 height=19 id="_x0000_i1025" src="cid:image035.png@01D07CD1.C19438B0"></span><![endif]> is:<o:p></o:p></p><p class=MsoNormal><!--[if gte msEquation 12]><m:oMath><m:sSub><m:sSubPr><span style='font-family:"Cambria Math",serif'><m:ctrlPr></m:ctrlPr></span></m:sSubPr><m:e><i><span style='font-family:"Cambria Math",serif'><m:r>F</m:r></span></i></m:e><m:sub><i><span style='font-family:"Cambria Math",serif'><m:r>te</m:r></span></i><span style='font-family:"Cambria Math",serif'><m:r><m:rPr><m:scr m:val="roman"/><m:sty m:val="p"/></m:rPr> </m:r></span></m:sub></m:sSub><span style='font-family:"Cambria Math",serif'><m:r><m:rPr><m:scr m:val="roman"/><m:sty m:val="p"/></m:rPr>= </m:r></span><m:sSub><m:sSubPr><span style='font-family:"Cambria Math",serif'><m:ctrlPr></m:ctrlPr></span></m:sSubPr><m:e><span style='font-family:"Cambria Math",serif'><m:r><m:rPr><m:scr m:val="roman"/><m:sty m:val="p"/></m:rPr>2</m:r><m:r><i>F</i></m:r></span></m:e><m:sub><i><span style='font-family:"Cambria Math",serif'><m:r>tp</m:r></span></i></m:sub></m:sSub></m:oMath><![endif]--><![if !msEquation]><span style='font-size:12.0pt;font-family:"Times New Roman",serif;position:relative;top:4.5pt;mso-text-raise:-4.5pt;mso-fareast-language:EN-US'><img width=77 height=21 id="_x0000_i1025" src="cid:image036.png@01D07CD1.C19438B0"></span><![endif]> = 0.59966525068799 <span style='font-size:11.0pt'><o:p></o:p></span></p><p class=MsoNormal><span style='font-family:"Calibri",sans-serif;color:black'><o:p> </o:p></span></p><p class=MsoNormal>Then we find the <b>required confinement force</b> <!--[if gte msEquation 12]><m:oMath><m:sSub><m:sSubPr><span style='font-family:"Cambria Math",serif'><m:ctrlPr></m:ctrlPr></span></m:sSubPr><m:e><i><span style='font-family:"Cambria Math",serif'><m:r>F</m:r></span></i></m:e><m:sub><i><span style='font-family:"Cambria Math",serif'><m:r>ce</m:r></span></i><span style='font-family:"Cambria Math",serif'><m:r><m:rPr><m:scr m:val="roman"/><m:sty m:val="p"/></m:rPr> </m:r></span></m:sub></m:sSub></m:oMath><![endif]--><![if !msEquation]><span style='font-size:12.0pt;font-family:"Times New Roman",serif;position:relative;top:3.0pt;mso-text-raise:-3.0pt;mso-fareast-language:EN-US'><img width=22 height=19 id="_x0000_i1025" src="cid:image037.png@01D07CD1.C19438B0"></span><![endif]>for the electron model using the photon angular momentum <!--[if gte msEquation 12]><m:oMath><i><span style='font-family:"Cambria Math",serif'><m:r>L</m:r></span></i></m:oMath><![endif]--><![if !msEquation]><span style='font-size:12.0pt;font-family:"Times New Roman",serif;position:relative;top:3.0pt;mso-text-raise:-3.0pt;mso-fareast-language:EN-US'><img width=9 height=19 id="_x0000_i1025" src="cid:image038.png@01D07CD1.C19438B0"></span><![endif]> at the velocity<!--[if gte msEquation 12]><m:oMath><span style='font-family:"Cambria Math",serif'><m:r><m:rPr><m:scr m:val="roman"/><m:sty m:val="p"/></m:rPr> </m:r></span><m:rad><m:radPr><m:degHide m:val="on"/><span style='font-family:"Cambria Math",serif'><m:ctrlPr></m:ctrlPr></span></m:radPr><m:deg></m:deg><m:e><span style='font-family:"Cambria Math",serif'><m:r><m:rPr><m:scr m:val="roman"/><m:sty m:val="p"/></m:rPr>2</m:r></span></m:e></m:rad><span style='font-family:"Cambria Math",serif'><m:r><m:rPr><m:scr m:val="roman"/><m:sty m:val="p"/></m:rPr> </m:r><m:r><i>c</i></m:r></span></m:oMath><![endif]--><![if !msEquation]><span style='font-size:12.0pt;font-family:"Times New Roman",serif;position:relative;top:3.0pt;mso-text-raise:-3.0pt;mso-fareast-language:EN-US'><img width=34 height=21 id="_x0000_i1025" src="cid:image039.png@01D07CD1.C19438B0"></span><![endif]>.<span style='font-family:"Calibri",sans-serif'><o:p></o:p></span></p><p class=MsoNormal>Preserving wavefront velocity<!--[if gte msEquation 12]><m:oMath><span style='font-family:"Cambria Math",serif'><m:r><m:rPr><m:scr m:val="roman"/><m:sty m:val="p"/></m:rPr> </m:r></span><m:rad><m:radPr><m:degHide m:val="on"/><span style='font-family:"Cambria Math",serif'><m:ctrlPr></m:ctrlPr></span></m:radPr><m:deg></m:deg><m:e><span style='font-family:"Cambria Math",serif'><m:r><m:rPr><m:scr m:val="roman"/><m:sty m:val="p"/></m:rPr>2</m:r></span></m:e></m:rad><i><span style='font-family:"Cambria Math",serif'><m:r>c</m:r></span></i></m:oMath><![endif]--><![if !msEquation]><span style='font-size:12.0pt;font-family:"Times New Roman",serif;position:relative;top:3.0pt;mso-text-raise:-3.0pt;mso-fareast-language:EN-US'><img width=31 height=21 id="_x0000_i1025" src="cid:image040.png@01D07CD1.C19438B0"></span><![endif]>, the momentum for the confined photon in the electron model is:<o:p></o:p></p><p class=MsoNormal><!--[if gte msEquation 12]><m:oMath><i><span style='font-family:"Cambria Math",serif'><m:r>L</m:r></span></i><span style='font-family:"Cambria Math",serif'><m:r><m:rPr><m:scr m:val="roman"/><m:sty m:val="p"/></m:rPr>= </m:r></span><m:rad><m:radPr><m:degHide m:val="on"/><span style='font-family:"Cambria Math",serif'><m:ctrlPr></m:ctrlPr></span></m:radPr><m:deg></m:deg><m:e><span style='font-family:"Cambria Math",serif'><m:r><m:rPr><m:scr m:val="roman"/><m:sty m:val="p"/></m:rPr>2</m:r></span></m:e></m:rad><span style='font-family:"Cambria Math",serif'><m:r><m:rPr><m:scr m:val="roman"/><m:sty m:val="p"/></m:rPr> </m:r></span><m:f><m:fPr><span style='font-family:"Cambria Math",serif'><m:ctrlPr></m:ctrlPr></span></m:fPr><m:num><i><span style='font-family:"Cambria Math",serif'><m:r>h</m:r></span></i></m:num><m:den><i><span style='font-family:"Cambria Math",serif'><m:r>λ</m:r></span></i></m:den></m:f><span style='font-family:"Cambria Math",serif'><m:r><m:rPr><m:scr m:val="roman"/><m:sty m:val="p"/></m:rPr>=</m:r></span></m:oMath><![endif]--><![if !msEquation]><span style='font-size:12.0pt;font-family:"Times New Roman",serif;position:relative;top:7.0pt;mso-text-raise:-7.0pt;mso-fareast-language:EN-US'><img width=82 height=27 id="_x0000_i1025" src="cid:image069.png@01D07CD1.C19438B0"></span><![endif]>3.86211004218299E-22 <span style='font-size:11.0pt'><o:p></o:p></span></p><p class=MsoNormal><o:p> </o:p></p><p class=MsoNormal>So the <b>binding force required</b> is: <!--[if gte msEquation 12]><m:oMath><m:sSub><m:sSubPr><span style='font-family:"Cambria Math",serif'><m:ctrlPr></m:ctrlPr></span></m:sSubPr><m:e><i><span style='font-family:"Cambria Math",serif'><m:r>F</m:r></span></i></m:e><m:sub><i><span style='font-family:"Cambria Math",serif'><m:r>ce</m:r></span></i><span style='font-family:"Cambria Math",serif'><m:r><m:rPr><m:scr m:val="roman"/><m:sty m:val="p"/></m:rPr> </m:r></span></m:sub></m:sSub><span style='font-family:"Cambria Math",serif'><m:r><m:rPr><m:scr m:val="roman"/><m:sty m:val="p"/></m:rPr>=</m:r></span><m:f><m:fPr><span style='font-family:"Cambria Math",serif'><m:ctrlPr></m:ctrlPr></span></m:fPr><m:num><i><span style='font-family:"Cambria Math",serif'><m:r>L</m:r></span></i><span style='font-family:"Cambria Math",serif'><m:r><m:rPr><m:scr m:val="roman"/><m:sty m:val="p"/></m:rPr> </m:r></span><m:rad><m:radPr><m:degHide m:val="on"/><span style='font-family:"Cambria Math",serif'><m:ctrlPr></m:ctrlPr></span></m:radPr><m:deg></m:deg><m:e><span style='font-family:"Cambria Math",serif'><m:r><m:rPr><m:scr m:val="roman"/><m:sty m:val="p"/></m:rPr>2</m:r></span></m:e></m:rad><span style='font-family:"Cambria Math",serif'><m:r><m:rPr><m:scr m:val="roman"/><m:sty m:val="p"/></m:rPr> </m:r><m:r><i>c</i></m:r></span></m:num><m:den><m:sSub><m:sSubPr><span style='font-family:"Cambria Math",serif'><m:ctrlPr></m:ctrlPr></span></m:sSubPr><m:e><i><span style='font-family:"Cambria Math",serif'><m:r>r</m:r></span></i></m:e><m:sub><i><span style='font-family:"Cambria Math",serif'><m:r>e</m:r></span></i></m:sub></m:sSub></m:den></m:f><span style='font-family:"Cambria Math",serif'><m:r><m:rPr><m:scr m:val="roman"/><m:sty m:val="p"/></m:rPr>= </m:r></span></m:oMath><![endif]--><![if !msEquation]><span style='font-size:12.0pt;font-family:"Times New Roman",serif;position:relative;top:8.5pt;mso-text-raise:-8.5pt;mso-fareast-language:EN-US'><img width=94 height=33 id="_x0000_i1025" src="cid:image070.png@01D07CD1.C19438B0"></span><![endif]>0.59966525068799 <o:p></o:p></p><p class=MsoNormal> <o:p></o:p></p><p class=MsoNormal>Which equals the calculated confinement force providing a stable balance of forces.<o:p></o:p></p><p class=MsoNormal><o:p> </o:p></p><p class=MsoNormal>Which leads us again to John W’s twist term and new field formulation, being required for a full understanding of EM forces and for a correct definition of confinement.<o:p></o:p></p><p class=MsoNormal><o:p> </o:p></p><p class=MsoNormal>Chip<o:p></o:p></p><p class=MsoNormal><o:p> </o:p></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><p class=MsoNormal><b><span style='font-size:11.0pt;font-family:"Calibri",sans-serif'>From:</span></b><span style='font-size:11.0pt;font-family:"Calibri",sans-serif'> General [mailto:general-bounces+chipakins=gmail.com@lists.natureoflightandparticles.org] <b>On Behalf Of </b>Andrew Meulenberg<br><b>Sent:</b> Tuesday, April 21, 2015 10:50 PM<br><b>To:</b> Nature of Light and Particles - General Discussion<br><b>Subject:</b> Re: [General] Attack on Virtual Phonon Force Carriers<o:p></o:p></span></p><p class=MsoNormal><o:p> </o:p></p><div><div><div><p class=MsoNormal style='margin-bottom:12.0pt'><span style='font-size:10.0pt'>Dear John M,</span><o:p></o:p></p></div><p class=MsoNormal style='margin-bottom:12.0pt'><span style='font-size:10.0pt'>A couple comments below.</span><o:p></o:p></p></div><p class=MsoNormal><span style='font-size:10.0pt'>Andrew</span><o:p></o:p></p><div><div><div><div><p class=MsoNormal><span style='font-size:10.0pt'>_ _ _ </span><o:p></o:p></p><div><p class=MsoNormal><span style='font-size:10.0pt'>On Mon, Apr 13, 2015 at 5:18 AM, John Macken <<a href="mailto:john@macken.com" target="_blank">john@macken.com</a>> wrote:</span><o:p></o:p></p><blockquote style='border:none;border-left:solid #CCCCCC 1.0pt;padding:0in 0in 0in 6.0pt;margin-left:4.8pt;margin-right:0in'><div><div><p class=MsoNormal style='mso-margin-top-alt:auto'><span style='font-size:10.0pt'>Hello Everyone,</span><o:p></o:p></p><p class=MsoNormal style='mso-margin-top-alt:auto'><span style='font-size:10.0pt'> </span><o:p></o:p></p><p class=MsoNormal style='mso-margin-top-alt:auto'><span style='font-size:10.0pt'>I am going to defend the position that an electron’s electric and gravitational fields are caused by waves in spacetime and not by virtual photons and gravitons. I also will support the claim that the “mathematical radius” of an electron is equal to the electron’s reduced Compton wavelength <i><s>λ</s></i><sub>c</sub> = </span><span style='font-size:10.0pt;font-family:"Cambria Math",serif'>ħ</span><span style='font-size:10.0pt'>/mc ≈ 3.86x10<sup>‑13</sup> m. </span><span style='font-size:7.5pt'>The first step in this proof is to calculate the gravitational force F<sub>g</sub> and electrostatic force F<sub>E</sub> between two of the same particles separated by their single loop radius (r = <i><s>λ</s></i><sub>c</sub> = </span><span style='font-size:7.5pt;font-family:"Cambria Math",serif'>ħ</span><span style='font-size:7.5pt'>/mc). The claim is that this is the natural unit of length for a particle and the forces should scale as a fundamental function of the particle’s radius. This distance is the transition where quantum mechanics becomes dominant so an actual experiment at this distance is unrealistic. However, it is possible to calculate the forces at this important distance using the Newtonian gravitational equation and the Coulomb law equation. </span><o:p></o:p></p><p class=MsoNormal style='mso-margin-top-alt:auto'><span style='font-size:7.5pt'> </span><o:p></o:p></p><p class=MsoNormal style='mso-margin-top-alt:auto'><span style='font-size:7.5pt'>The first calculation will not be for an electron, but the more general case of two of the same mass (m<sub>1</sub> = m<sub>2</sub>) particles, each particle with Planck charge <i>q</i><sub>p</sub> rather than elementary charge <i>e</i>. This charge is chosen because Planck charge has a coupling constant of 1 while elementary charge <i>e</i> has a coupling constant of alpha α ≈ <sup>1</sup>/<sub>137</sub>. Planck charge is about 11.7 times (</span><span style='font-size:7.5pt;font-family:"Calibri",sans-serif'><img border=0 width=12 height=12 id="_x0000_i1025" src="cid:image002.png@01D07CCF.C8425810"></span><span style='font-size:7.5pt'> times) larger than charge<i> e</i>. Later we will convert this to charge <i>e</i> for comparison. When Planck charge is assumed, then the symbol used for electrostatic force will be <i>F</i><sub>E</sub>. Besides using Planck charge, we will also express these forces using natural dimensionless Planck units which will be designated by an underline. For example, <b><i><u>F</u></i></b><sub>g</sub> = <i>F</i><sub>g</sub>/<i>F</i><sub>p</sub> where <i>F</i><sub>p</sub> = <i>c</i><sup>4</sup>/<i>G</i> ≈1.2x10<sup>44</sup> J. Also the particle’s internal energy (<i>E</i><sub>i</sub> = <i>m<sub>o</sub>c</i><sup>2</sup>) in dimensionless Planck units of energy is <b><i><u>E</u></i></b><sub>i </sub>= <i>E</i><sub>i</sub>/<i>E</i><sub>p</sub> where <i>E</i><sub>p</sub> is Planck energy <i>E</i><sub>p</sub> = </span><span style='font-size:7.5pt;font-family:"Calibri",sans-serif'><img border=0 width=32 height=14 id="_x0000_i1026" src="cid:image004.png@01D07CCF.C8425810"></span><span style='font-size:7.5pt'>≈ 1.96x10<sup>9</sup> J.</span><o:p></o:p></p><p class=MsoNormal style='mso-margin-top-alt:auto'><span style='font-size:7.5pt'> </span><o:p></o:p></p><p class=MsoNormal style='mso-margin-top-alt:auto;text-align:justify;line-height:115%'><b><i><u><span style='font-size:7.5pt;line-height:115%'>F</span></u></i></b><sub><span style='font-size:7.5pt;line-height:115%'>g</span></sub><span style='font-size:7.5pt;line-height:115%;font-family:"Cambria Math",serif'> = </span><span style='font-size:7.5pt;line-height:115%;font-family:"Calibri",sans-serif'><img border=0 width=8 height=22 id="_x0000_i1027" src="cid:image006.png@01D07CCF.C8425810"></span><span style='font-size:7.5pt;line-height:115%;font-family:"Cambria Math",serif'>= </span><span style='font-size:7.5pt;line-height:115%;font-family:"Calibri",sans-serif'><img border=0 width=56 height=24 id="_x0000_i1028" src="cid:image008.png@01D07CCF.C8425810"></span><span style='font-size:7.5pt;line-height:115%;font-family:"Cambria Math",serif'>= Gm<sup>2</sup></span><span style='font-size:7.5pt;line-height:115%;font-family:"Calibri",sans-serif'><img border=0 width=57 height=23 id="_x0000_i1029" src="cid:image010.png@01D07CCF.C8425810"></span><span style='font-size:7.5pt;line-height:115%;font-family:"Cambria Math",serif'> = </span><span style='font-size:7.5pt;line-height:115%;font-family:"Calibri",sans-serif'><img border=0 width=38 height=26 id="_x0000_i1030" src="cid:image012.png@01D07CCF.C8425810"></span><o:p></o:p></p><p class=MsoNormal style='mso-margin-top-alt:auto;text-align:justify;line-height:115%'><b><i><u><span style='font-size:7.5pt;line-height:115%'>F</span></u></i></b><i><sub><span style='font-size:7.5pt;line-height:115%'>E</span></sub></i><span style='font-size:7.5pt;line-height:115%;font-family:"Cambria Math",serif'> = </span><span style='font-size:7.5pt;line-height:115%;font-family:"Calibri",sans-serif'><img border=0 width=12 height=21 id="_x0000_i1031" src="cid:image014.png@01D07CCF.C8425810"></span><span style='font-size:7.5pt;line-height:115%;font-family:"Cambria Math",serif'>= </span><span style='font-size:7.5pt;line-height:115%;font-family:"Calibri",sans-serif'><img border=0 width=61 height=25 id="_x0000_i1032" src="cid:image016.png@01D07CCF.C8425810"></span><span style='font-size:7.5pt;line-height:115%;font-family:"Cambria Math",serif'>= (ħc)</span><span style='font-size:7.5pt;line-height:115%;font-family:"Calibri",sans-serif'><img border=0 width=52 height=25 id="_x0000_i1033" src="cid:image018.png@01D07CCF.C8425810"></span><span style='font-size:7.5pt;line-height:115%;font-family:"Cambria Math",serif'> = </span><span style='font-size:7.5pt;line-height:115%;font-family:"Calibri",sans-serif'><img border=0 width=18 height=23 id="_x0000_i1034" src="cid:image020.png@01D07CCF.C8425810"></span><o:p></o:p></p><p class=MsoNormal style='mso-margin-top-alt:auto;text-align:justify;line-height:115%;background:white;background-attachment:scroll;background-position-x:0%;background-position-y:0%'><b><i><u><span style='font-size:7.5pt;line-height:115%'>E</span></u></i></b><sub><span style='font-size:7.5pt;line-height:115%'>i</span></sub><i><span style='font-size:7.5pt;line-height:115%;font-family:"Cambria Math",serif'> </span></i><span style='font-size:7.5pt;line-height:115%;font-family:"Cambria Math",serif'>=</span><span style='font-size:7.5pt;line-height:115%;font-family:"Calibri",sans-serif'><img border=0 width=10 height=24 id="_x0000_i1035" src="cid:image022.png@01D07CCF.C8425810"></span><span style='font-size:7.5pt;line-height:115%;font-family:"Cambria Math",serif'> =</span><span style='font-size:7.5pt;line-height:115%;font-family:"Calibri",sans-serif'><img border=0 width=46 height=23 id="_x0000_i1036" src="cid:image024.png@01D07CCF.C8425810"></span><span style='font-size:7.5pt;line-height:115%;font-family:"Cambria Math",serif'> = </span><span style='font-size:7.5pt;line-height:115%;font-family:"Calibri",sans-serif'><img border=0 width=28 height=30 id="_x0000_i1037" src="cid:image026.png@01D07CCF.C8425810"></span><span style='font-size:7.5pt;line-height:115%;font-family:"Cambria Math",serif'> </span><o:p></o:p></p><p class=MsoNormal style='mso-margin-top-alt:auto;text-align:justify;line-height:115%;background:white;background-attachment:scroll;background-position-x:0%;background-position-y:0%'><span style='font-size:7.5pt;line-height:115%;font-family:"Cambria Math",serif'>Therefore:</span><o:p></o:p></p><p class=MsoNormal style='mso-margin-top-alt:auto;text-align:justify;line-height:115%'><b><i><u><span style='font-size:7.5pt;line-height:115%'>F</span></u></i></b><sub><span style='font-size:7.5pt;line-height:115%'>g</span></sub><span style='font-size:7.5pt;line-height:115%;font-family:"Cambria Math",serif'> =</span><b><i><u><span style='font-size:7.5pt;line-height:115%'> F</span></u></i></b><i><sub><span style='font-size:7.5pt;line-height:115%'>E</span></sub></i><sup><span style='font-size:7.5pt;line-height:115%'>2</span></sup><span style='font-size:7.5pt;line-height:115%;font-family:"Cambria Math",serif'> =</span><b><i><u><span style='font-size:7.5pt;line-height:115%'> E</span></u></i></b><sub><span style='font-size:7.5pt;line-height:115%'>i</span></sub><i><sup><span style='font-size:7.5pt;line-height:115%'>4</span></sup></i><span style='font-size:7.5pt;line-height:115%;font-family:"Cambria Math",serif'> </span><o:p></o:p></p><p class=MsoNormal style='mso-margin-top-alt:auto;text-align:justify;line-height:115%'><span style='font-size:7.5pt;line-height:115%;font-family:"Cambria Math",serif'> </span><o:p></o:p></p><p class=MsoNormal style='mso-margin-top-alt:auto;text-align:justify;line-height:115%'><span style='font-size:7.5pt;line-height:115%;font-family:"Cambria Math",serif'>This is an amazing result that needs to be stated in words. We assume two particles with equal mass (<i>m</i><sub>1</sub> = <i>m</i><sub>2</sub>). Also, both hypothetical particles have Planck charge. They are separated by a distance equal to the particle’s reduced Compton wavelength r = <i><s>λ</s></i><sub>c</sub>. Then, when <i>dimensionless</i> natural Planck units are used, the gravitational force equals the square of the electrostatic force and the fourth power of the particle’s energy. Notice that this relationship only holds if the separation distance is equal to the single loop radius. If a double loop design is chosen, then separating the two particles by their radius shortens the separation distance to <i>r</i> = <i><s>λ</s></i><sub>c</sub>/2 and the equation becomes: </span><b><i><u><span style='font-size:7.5pt;line-height:115%'>F</span></u></i></b><sub><span style='font-size:7.5pt;line-height:115%'>g</span></sub><span style='font-size:7.5pt;line-height:115%;font-family:"Cambria Math",serif'> = </span><b><i><u><span style='font-size:7.5pt;line-height:115%'>F</span></u></i></b><i><sub><span style='font-size:7.5pt;line-height:115%'>E</span></sub></i><sup><span style='font-size:7.5pt;line-height:115%'>2</span></sup><span style='font-size:7.5pt;line-height:115%'>/</span><span style='font-size:7.5pt;line-height:115%;font-family:"Cambria Math",serif'>4 = 4</span><b><i><u><span style='font-size:7.5pt;line-height:115%'>E</span></u></i></b><sub><span style='font-size:7.5pt;line-height:115%'>i</span></sub><i><sup><span style='font-size:7.5pt;line-height:115%'>4</span></sup></i><span style='font-size:7.5pt;line-height:115%'>. </span><o:p></o:p></p></div></div></blockquote><blockquote style='border:none;border-left:solid #CCCCCC 1.0pt;padding:0in 0in 0in 6.0pt;margin-left:4.8pt;margin-right:0in'><div><div><p class=MsoNormal style='mso-margin-top-alt:auto;text-align:justify;line-height:115%'><span style='font-size:7.5pt;line-height:115%;font-family:"Cambria Math",serif'> </span><o:p></o:p></p><p class=MsoNormal style='mso-margin-top-alt:auto;text-align:justify;line-height:115%'><span style='font-size:7.5pt;line-height:115%;font-family:"Cambria Math",serif'>Next we will express the force relationship for the conditions stated without using dimensionless Planck units (no underline).</span><o:p></o:p></p><p class=MsoNormal style='mso-margin-top-alt:auto;text-align:justify;line-height:115%'><span style='font-size:7.5pt;line-height:115%;font-family:"Cambria Math",serif'> </span><o:p></o:p></p><p class=MsoNormal style='mso-margin-top-alt:auto;text-align:justify;line-height:115%'><span style='font-size:7.5pt;line-height:115%;font-family:"Calibri",sans-serif'><img border=0 width=35 height=22 id="_x0000_i1038" src="cid:image028.png@01D07CCF.C8425810"></span><span style='font-size:7.5pt;line-height:115%;font-family:"Cambria Math",serif'> </span><o:p></o:p></p><p class=MsoNormal style='mso-margin-top-alt:auto;text-align:justify;line-height:115%'><span style='font-size:7.5pt;line-height:115%;font-family:"Cambria Math",serif'> </span><o:p></o:p></p><p class=MsoNormal style='mso-margin-top-alt:auto;text-align:justify;line-height:115%'><span style='font-size:7.5pt;line-height:115%;font-family:"Cambria Math",serif'>The ratio of the gravitational force divided by the electrostatic force equals the ratio of the electrostatic force divided by Planck force. Another way of visualizing this is to imagine representing these forces on a log scale. One end of this scale will represent the largest possible force which is Planck force. The opposite end of this log scale will represents the weakest force between these two particles which is the gravitational force. Now, on this log scale, where do you think that the electrostatic force needs to be placed? The answer is exactly midway between these two extremes on this log scale. If the double loop radius is chosen for the separation distance, then this relationship would not hold.</span><o:p></o:p></p><p class=MsoNormal style='mso-margin-top-alt:auto;text-align:justify;line-height:115%'><span style='font-size:7.5pt;line-height:115%;font-family:"Cambria Math",serif'> </span><o:p></o:p></p><p class=MsoNormal style='mso-margin-top-alt:auto;text-align:justify;line-height:115%'><span style='font-size:7.5pt;line-height:115%;font-family:"Cambria Math",serif'>Now suppose that we want to express these relationships at arbitrary separation distance. The way to keep a connection to the particle’s single loop radius is to express the separation distance <i>r</i> as the number (<i>N</i>) of reduced Compton wavelengths therefore <i>N</i> = <i>r</i>/<i><s>λ</s></i><sub>c</sub>. The equation</span><b><i><u><span style='font-size:7.5pt;line-height:115%'> F</span></u></i></b><sub><span style='font-size:7.5pt;line-height:115%'>g</span></sub><span style='font-size:7.5pt;line-height:115%;font-family:"Cambria Math",serif'> =</span><b><i><u><span style='font-size:7.5pt;line-height:115%'> F</span></u></i></b><i><sub><span style='font-size:7.5pt;line-height:115%'>E</span></sub></i><sup><span style='font-size:7.5pt;line-height:115%'>2</span></sup><span style='font-size:7.5pt;line-height:115%;font-family:"Cambria Math",serif'> =</span><b><i><u><span style='font-size:7.5pt;line-height:115%'> E</span></u></i></b><sub><span style='font-size:7.5pt;line-height:115%'>i</span></sub><i><sup><span style='font-size:7.5pt;line-height:115%'>4</span></sup></i><span style='font-size:7.5pt;line-height:115%;font-family:"Cambria Math",serif'> becomes:</span><o:p></o:p></p><p class=MsoNormal style='mso-margin-top-alt:auto;text-align:justify;line-height:115%'><b><i><u><span style='font-size:7.5pt;line-height:115%'>F</span></u></i></b><sub><span style='font-size:7.5pt;line-height:115%'>g</span></sub><i><span style='font-size:7.5pt;line-height:115%'>N</span></i><sup><span style='font-size:7.5pt;line-height:115%'>2</span></sup><span style='font-size:7.5pt;line-height:115%;font-family:"Cambria Math",serif'> = (</span><b><i><u><span style='font-size:7.5pt;line-height:115%'>F</span></u></i></b><i><sub><span style='font-size:7.5pt;line-height:115%'>E</span></sub></i><i><span style='font-size:7.5pt;line-height:115%'>N<sup>2</sup></span></i><span style='font-size:7.5pt;line-height:115%'>)<sup>2</sup></span><span style='font-size:7.5pt;line-height:115%;font-family:"Cambria Math",serif'> =</span><b><i><u><span style='font-size:7.5pt;line-height:115%'> E</span></u></i></b><sub><span style='font-size:7.5pt;line-height:115%'>i</span></sub><i><sup><span style='font-size:7.5pt;line-height:115%'>4</span></sup></i><o:p></o:p></p><p class=MsoNormal style='mso-margin-top-alt:auto;text-align:justify;line-height:115%'><span style='font-size:7.5pt;line-height:115%;font-family:"Cambria Math",serif'> </span><o:p></o:p></p><p class=MsoNormal style='mso-margin-top-alt:auto;text-align:justify;line-height:115%'><span style='font-size:7.5pt;line-height:115%;font-family:"Cambria Math",serif'>Note the square relationship between forces is retained. Again, this only works if we assume that <i>N</i> is defined by the single loop radius, not the double loop radius. Finally, we can convert all these force equations to charge <i>e</i> by substituting <i>F</i><sub>E</sub> = <i>F</i><sub>e</sub>/<i>α</i> where <i>F</i><sub>e</sub> is the electrostatic force between two particles with elementary charge <i>e</i> rather than the Planck charge force <i>F</i><sub>E</sub>. The various conversions will not be made here, but another interesting equation utilizing <i>N</i> and charge <i>e</i> that works directly with electrons is:</span><o:p></o:p></p><p class=MsoNormal style='mso-margin-top-alt:auto;text-align:justify;line-height:115%'><i><span style='font-size:7.5pt;line-height:115%;font-family:"Cambria Math",serif'>F</span></i><sub><span style='font-size:7.5pt;line-height:115%;font-family:"Cambria Math",serif'>g</span></sub><i><span style='font-size:7.5pt;line-height:115%;font-family:"Cambria Math",serif'>F</span></i><sub><span style='font-size:7.5pt;line-height:115%;font-family:"Cambria Math",serif'>p</span></sub><span style='font-size:7.5pt;line-height:115%;font-family:"Cambria Math",serif'> = (<i>F</i><sub>e</sub></span><i><span style='font-size:7.5pt;line-height:115%'>N<sup>2</sup></span></i><span style='font-size:7.5pt;line-height:115%;font-family:"Cambria Math",serif'>/α)<sup>2</sup></span><o:p></o:p></p><p class=MsoNormal style='mso-margin-top-alt:auto'><span style='font-size:10.0pt'> </span><o:p></o:p></p><p class=MsoNormal style='mso-margin-top-alt:auto'><span style='font-size:10.0pt'>Much of this is explained in more detail in the “foundation paper”. However, now I want to return to my contention that the electrostatic and gravitational forces are not transferred by messenger particles such as virtual photons and gravitons. Virtual photons <u>do</u> exist and have a wave-based explanation. They just do not transfer the electrostatic force. These equations were first derived from a purely wave-based analysis which <i><u>predicted</u></i> that there should be this square relationship between the electrostatic and gravitational force. These equations are all logically derived from the spacetime-based model of the universe. I believe that these equations and other equations in the “Foundation” paper are incompatible with virtual photons and gravitons being force messenger particles. If you believe otherwise, please suggest a model of virtual photons and gravitons which is compatible with these equations. If there is no logical connection, then force explanations based on virtual photons and gravitons must be wrong.</span><o:p></o:p></p></div></div></blockquote><div><p class=MsoNormal><o:p> </o:p></p></div><div><p class=MsoNormal style='margin-bottom:12.0pt'><span style='font-size:10.0pt'>Messenger particles are QM 'jargon'. If you recognize (most people do not) that this is simply a means of QM's usurping useful classical physics processes (virtual photons are classical evanescent waves), then the concept has a rational basis. I would propose that the infinite-range evanescent wave (which intensity decays at a rate dependent on the source geometry) is a unique structure created by light traveling along a <u>g</u>radient <u>r</u>efractive-<u>in</u>dex. This GRIN results in self-focusing (or total internal reflection) of light that produces the self-generated 'light-pipe' and EM soliton called a photon. The same process allows a spherically confined photon to produce the uniform 'charge wave' basic to the electron and positron.</span><o:p></o:p></p></div><div><p class=MsoNormal style='margin-bottom:12.0pt'><span style='font-size:10.0pt'>I agree with you that gravity is only the second-order effect of the charge and physically appears as the residue of immense numbers of balanced charges. I don't know if vibration of this field can cause evanescent waves and its propagation speed in space. I doubt if it is quantized at anything less than stellar size (assuming that it can form a solitonic structure).</span><o:p></o:p></p></div><div><p class=MsoNormal><span style='font-size:10.0pt'>If your model of gravity being the square of the electrostatic force is valid, then is it possible that, at nuclear distances, it is even larger than the <b>E</b>-field and perhaps becomes the strong nuclear forces?</span><o:p></o:p></p></div><blockquote style='border:none;border-left:solid #CCCCCC 1.0pt;padding:0in 0in 0in 6.0pt;margin-left:4.8pt;margin-right:0in'><div><div><p class=MsoNormal style='mso-margin-top-alt:auto'><span style='font-size:10.0pt'> </span><o:p></o:p></p><p class=MsoNormal style='mso-margin-top-alt:auto'><span style='font-size:10.0pt'>Here is another flaw in the concept that a cloud of virtual photons are responsible for an electron’s electric field. Here is a logical syllogism. </span><o:p></o:p></p><p><span style='font-size:10.0pt'>1) Virtual particles come into existence and go out of existence in a time so short that there is no violation of the conservation of energy as modified by the uncertainty principle. (</span><span style='font-size:10.0pt;font-family:"Cambria Math",serif'>Δ</span><span style='font-size:10.0pt'>E</span><span style='font-size:10.0pt;font-family:"Cambria Math",serif'>Δ</span><span style='font-size:10.0pt'>t = ½ </span><span style='font-size:10.0pt;font-family:"Cambria Math",serif'>ħ</span><span style='font-size:10.0pt'>). In other words, virtual photons can never produce measurable energy. </span><o:p></o:p></p><p><span style='font-size:10.0pt'>2) Electric fields have energy density which can be experimentally measured. </span><o:p></o:p></p><p><span style='font-size:10.0pt'>3) Therefore, electric fields cannot be created by a cloud of virtual photons.</span><o:p></o:p></p></div></div></blockquote><div><p class=MsoNormal>But, the<span style='font-size:10.0pt'> <b>E</b>-fields</span> <u>can</u> be the steady-state evanescent waves from a bound photon. <o:p></o:p></p></div><blockquote style='border:none;border-left:solid #CCCCCC 1.0pt;padding:0in 0in 0in 6.0pt;margin-left:4.8pt;margin-right:0in'><div><div><p class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto'><span style='font-size:10.0pt'> </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'>Finally, I want to point out that even the standard model considers that spacetime is filled with fields. The 17 named particles in the standard model are considered to be “excitations” in the 17 overlapping fields that exist in the vacuum. These fields all have large energy density. For example, the Higgs field has been calculated to have energy density of about 10<sup>46</sup> J/m<sup>3</sup>. QED and QCD require even higher energy densities in the vacuum. Zero point energy has harmonic oscillators, each with energy E = ½ ħω and each harmonic oscillator occupies a volume V of: V = k<i><s>λ</s></i><sup>3</sup> = kc<sup>3</sup>/ω<sup>3</sup>. If the maximum angular frequency is Planck frequency, then the implied energy density is approximately Planck energy density ≈ 10<sup>113</sup> J/m<sup>3</sup>. I have proposed a single field (the spacetime field) with resonances to replace the 17 fields of the standard model. This single “spacetime field” has been quantified and forms the basis of my model of the universe. </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'> </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'>John M.</span><o:p></o:p></p><p class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto'><span style='font-size:10.0pt'> </span><o:p></o:p></p></div></div></blockquote></div></div></div></div></div></div></div></body></html>