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</o:shapelayout></xml><![endif]--></head><body lang=EN-US link="#0563C1" vlink="#954F72"><div class=WordSection1><p class=MsoNormal style='margin-bottom:0in;margin-bottom:.0001pt'><span style='font-size:14.0pt;line-height:106%;font-family:"Times New Roman",serif'>Hello Everyone,<o:p></o:p></span></p><p class=MsoNormal style='margin-bottom:0in;margin-bottom:.0001pt'><span style='font-size:14.0pt;line-height:106%;font-family:"Times New Roman",serif'><o:p> </o:p></span></p><p class=MsoNormal style='margin-bottom:0in;margin-bottom:.0001pt'><span style='font-size:14.0pt;line-height:106%;font-family:"Times New Roman",serif'>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:14.0pt;line-height:106%;font-family:"Cambria Math",serif'>ħ</span><span style='font-size:14.0pt;line-height:106%;font-family:"Times New Roman",serif'>/mc ≈ 3.86x10<sup>‑13</sup> m. 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:14.0pt;line-height:106%;font-family:"Cambria Math",serif'>ħ</span><span style='font-size:14.0pt;line-height:106%;font-family:"Times New Roman",serif'>/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. <o:p></o:p></span></p><p class=MsoNormal style='margin-bottom:0in;margin-bottom:.0001pt'><span style='font-size:14.0pt;line-height:106%;font-family:"Times New Roman",serif'><o:p> </o:p></span></p><p class=MsoNormal style='margin-bottom:0in;margin-bottom:.0001pt'><span style='font-size:14.0pt;line-height:106%;font-family:"Times New Roman",serif'>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><!--[if gte msEquation 12]><m:oMath><m:rad><m:radPr><m:degHide m:val="on"/><span style='font-size:14.0pt;font-family:"Cambria Math",serif;font-style:italic'><m:ctrlPr></m:ctrlPr></span></m:radPr><m:deg></m:deg><m:e><i><span style='font-size:14.0pt;line-height:106%;font-family:"Cambria Math",serif'><m:r>α</m:r></span></i></m:e></m:rad></m:oMath><![endif]--><![if !msEquation]><span style='font-size:11.0pt;line-height:106%;font-family:"Calibri",sans-serif;position:relative;top:4.5pt;mso-text-raise:-4.5pt;mso-fareast-language:EN-US'><img width=30 height=32 id="_x0000_i1025" src="cid:image002.png@01D07540.86973E80"></span><![endif]><span style='font-size:14.0pt;line-height:106%;font-family:"Times New Roman",serif'> 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><!--[if gte msEquation 12]><m:oMath><m:rad><m:radPr><m:degHide m:val="on"/><span style='font-size:14.0pt;font-family:"Cambria Math",serif;font-style:italic'><m:ctrlPr></m:ctrlPr></span></m:radPr><m:deg></m:deg><m:e><m:f><m:fPr><m:type m:val="lin"/><span style='font-size:14.0pt;font-family:"Cambria Math",serif;font-style:italic'><m:ctrlPr></m:ctrlPr></span></m:fPr><m:num><i><span style='font-size:14.0pt;line-height:106%;font-family:"Cambria Math",serif'><m:r>ħ</m:r></span></i><m:sSup><m:sSupPr><span style='font-size:14.0pt;font-family:"Cambria Math",serif;font-style:italic'><m:ctrlPr></m:ctrlPr></span></m:sSupPr><m:e><i><span style='font-size:14.0pt;line-height:106%;font-family:"Cambria Math",serif'><m:r>c</m:r></span></i></m:e><m:sup><i><span style='font-size:14.0pt;line-height:106%;font-family:"Cambria Math",serif'><m:r>5</m:r></span></i></m:sup></m:sSup></m:num><m:den><i><span style='font-size:14.0pt;line-height:106%;font-family:"Cambria Math",serif'><m:r>G</m:r></span></i></m:den></m:f></m:e></m:rad></m:oMath><![endif]--><![if !msEquation]><span style='font-size:11.0pt;line-height:106%;font-family:"Calibri",sans-serif;position:relative;top:5.0pt;mso-text-raise:-5.0pt;mso-fareast-language:EN-US'><img width=81 height=36 id="_x0000_i1025" src="cid:image004.png@01D07540.86973E80"></span><![endif]><span style='font-size:14.0pt;line-height:106%;font-family:"Times New Roman",serif'> ≈ 1.96x10<sup>9</sup> J.<o:p></o:p></span></p><p class=MsoNormal style='margin-bottom:0in;margin-bottom:.0001pt'><span style='font-size:14.0pt;line-height:106%;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%'><b><i><u><span style='font-size:14.0pt;line-height:115%'>F</span></u></i></b><sub><span style='font-size:14.0pt;line-height:115%'>g</span></sub><span style='font-size:12.0pt;line-height:115%;font-family:"Cambria Math",serif'> </span><span style='font-size:11.5pt;line-height:115%;font-family:"Cambria Math",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'><m:ctrlPr></m:ctrlPr></span></m:sSubPr><m:e><span style='font-size:16.0pt;line-height:115%;font-family:"Cambria Math",serif'><m:r><m:rPr><m:scr m:val="roman"/><m:sty m:val="p"/></m:rPr>F</m:r></span></m:e><m:sub><span style='font-size:16.0pt;line-height:115%;font-family:"Cambria Math",serif'><m:r><m:rPr><m:scr m:val="roman"/><m:sty m:val="p"/></m:rPr>g</m:r></span></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>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:106%;font-family:"Calibri",sans-serif;position:relative;top:14.0pt;mso-text-raise:-14.0pt;mso-fareast-language:EN-US'><img width=22 height=57 id="_x0000_i1025" src="cid:image006.png@01D07540.86973E80"></span><![endif]><span style='font-size:12.0pt;line-height:115%;font-family:"Cambria Math",serif'> = </span><!--[if gte msEquation 12]><m:oMath><m:d><m:dPr><span style='font-size:18.0pt;font-family:"Cambria Math",serif;font-style:italic'><m:ctrlPr></m:ctrlPr></span></m:dPr><m:e><m:f><m:fPr><span style='font-size:18.0pt;font-family:"Cambria Math",serif;font-style:italic'><m:ctrlPr></m:ctrlPr></span></m:fPr><m:num><i><span style='font-size:18.0pt;line-height:115%;font-family:"Cambria Math",serif'><m:r>G</m:r></span></i><m:sSup><m:sSupPr><span style='font-size:18.0pt;font-family:"Cambria Math",serif;font-style:italic'><m:ctrlPr></m:ctrlPr></span></m:sSupPr><m:e><i><span style='font-size:18.0pt;line-height:115%;font-family:"Cambria Math",serif'><m:r>m</m:r></span></i></m:e><m:sup><i><span style='font-size:18.0pt;line-height:115%;font-family:"Cambria Math",serif'><m:r>2</m:r></span></i></m:sup></m:sSup></m:num><m:den><m:sSubSup><m:sSubSupPr><span style='font-size:14.0pt;font-family:"Cambria Math",serif;font-style:italic'><m:ctrlPr></m:ctrlPr></span></m:sSubSupPr><m:e><i><s><span style='font-size:14.0pt;line-height:115%;font-family:"Cambria Math",serif'><m:r>λ</m:r></span></s></i></m:e><m:sub><i><span style='font-size:14.0pt;line-height:115%;font-family:"Cambria Math",serif'><m:r>c</m:r></span></i></m:sub><m:sup><i><span style='font-size:14.0pt;line-height:115%;font-family:"Cambria Math",serif'><m:r>2</m:r></span></i></m:sup></m:sSubSup></m:den></m:f></m:e></m:d><m:d><m:dPr><span style='font-size:18.0pt;font-family:"Cambria Math",serif;font-style:italic'><m:ctrlPr></m:ctrlPr></span></m:dPr><m:e><m:f><m:fPr><span style='font-size:18.0pt;font-family:"Cambria Math",serif;font-style:italic'><m:ctrlPr></m:ctrlPr></span></m:fPr><m:num><i><span style='font-size:18.0pt;line-height:115%;font-family:"Cambria Math",serif'><m:r>G</m:r></span></i></m:num><m:den><m:sSup><m:sSupPr><span style='font-size:18.0pt;font-family:"Cambria Math",serif;font-style:italic'><m:ctrlPr></m:ctrlPr></span></m:sSupPr><m:e><i><span style='font-size:18.0pt;line-height:115%;font-family:"Cambria Math",serif'><m:r>c</m:r></span></i></m:e><m:sup><i><span style='font-size:18.0pt;line-height:115%;font-family:"Cambria Math",serif'><m:r>4</m:r></span></i></m:sup></m:sSup></m:den></m:f></m:e></m:d><i><span style='font-size:18.0pt;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:106%;font-family:"Calibri",sans-serif;position:relative;top:13.5pt;mso-text-raise:-13.5pt;mso-fareast-language:EN-US'><img width=141 height=62 id="_x0000_i1025" src="cid:image008.png@01D07540.86973E80"></span><![endif]><span style='font-size:12.0pt;line-height:115%;font-family:"Cambria Math",serif'>= </span><span style='font-size:14.0pt;line-height:115%;font-family:"Cambria Math",serif'>Gm<sup>2</sup></span><!--[if gte msEquation 12]><m:oMath><m:d><m:dPr><span style='font-size:18.0pt;font-family:"Cambria Math",serif;font-style:italic'><m:ctrlPr></m:ctrlPr></span></m:dPr><m:e><m:f><m:fPr><span style='font-size:18.0pt;font-family:"Cambria Math",serif;font-style:italic'><m:ctrlPr></m:ctrlPr></span></m:fPr><m:num><m:sSup><m:sSupPr><span style='font-size:18.0pt;font-family:"Cambria Math",serif;font-style:italic'><m:ctrlPr></m:ctrlPr></span></m:sSupPr><m:e><i><span style='font-size:18.0pt;line-height:115%;font-family:"Cambria Math",serif'><m:r>m</m:r></span></i></m:e><m:sup><i><span style='font-size:18.0pt;line-height:115%;font-family:"Cambria Math",serif'><m:r>2</m:r></span></i></m:sup></m:sSup><m:sSup><m:sSupPr><span style='font-size:18.0pt;font-family:"Cambria Math",serif;font-style:italic'><m:ctrlPr></m:ctrlPr></span></m:sSupPr><m:e><i><span style='font-size:18.0pt;line-height:115%;font-family:"Cambria Math",serif'><m:r>c</m:r></span></i></m:e><m:sup><i><span style='font-size:18.0pt;line-height:115%;font-family:"Cambria Math",serif'><m:r>2</m:r></span></i></m:sup></m:sSup></m:num><m:den><m:sSup><m:sSupPr><span style='font-size:18.0pt;font-family:"Cambria Math",serif;font-style:italic'><m:ctrlPr></m:ctrlPr></span></m:sSupPr><m:e><i><span style='font-size:18.0pt;line-height:115%;font-family:"Cambria Math",serif'><m:r>ħ</m:r></span></i></m:e><m:sup><i><span style='font-size:18.0pt;line-height:115%;font-family:"Cambria Math",serif'><m:r>2</m:r></span></i></m:sup></m:sSup></m:den></m:f></m:e></m:d><m:d><m:dPr><span style='font-size:18.0pt;font-family:"Cambria Math",serif;font-style:italic'><m:ctrlPr></m:ctrlPr></span></m:dPr><m:e><m:f><m:fPr><span style='font-size:18.0pt;font-family:"Cambria Math",serif;font-style:italic'><m:ctrlPr></m:ctrlPr></span></m:fPr><m:num><i><span style='font-size:18.0pt;line-height:115%;font-family:"Cambria Math",serif'><m:r>G</m:r></span></i></m:num><m:den><m:sSup><m:sSupPr><span style='font-size:18.0pt;font-family:"Cambria Math",serif;font-style:italic'><m:ctrlPr></m:ctrlPr></span></m:sSupPr><m:e><i><span style='font-size:18.0pt;line-height:115%;font-family:"Cambria Math",serif'><m:r>c</m:r></span></i></m:e><m:sup><i><span style='font-size:18.0pt;line-height:115%;font-family:"Cambria Math",serif'><m:r>4</m:r></span></i></m:sup></m:sSup></m:den></m:f></m:e></m:d></m:oMath><![endif]--><![if !msEquation]><span style='font-size:11.0pt;line-height:106%;font-family:"Calibri",sans-serif;position:relative;top:11.5pt;mso-text-raise:-11.5pt;mso-fareast-language:EN-US'><img width=143 height=59 id="_x0000_i1025" src="cid:image010.png@01D07540.86973E80"></span><![endif]><span style='font-size:14.0pt;line-height:115%;font-family:"Cambria Math",serif'> = </span><!--[if gte msEquation 12]><m:oMath><m:sSup><m:sSupPr><span style='font-size:18.0pt;font-family:"Cambria Math",serif'><m:ctrlPr></m:ctrlPr></span></m:sSupPr><m:e><m:d><m:dPr><span style='font-size:18.0pt;font-family:"Cambria Math",serif;font-style:italic'><m:ctrlPr></m:ctrlPr></span></m:dPr><m:e><m:f><m:fPr><span style='font-size:18.0pt;font-family:"Cambria Math",serif;font-style:italic'><m:ctrlPr></m:ctrlPr></span></m:fPr><m:num><i><span style='font-size:18.0pt;line-height:115%;font-family:"Cambria Math",serif'><m:r>G</m:r><m:r> </m:r></span></i><m:sSup><m:sSupPr><span style='font-size:18.0pt;font-family:"Cambria Math",serif;font-style:italic'><m:ctrlPr></m:ctrlPr></span></m:sSupPr><m:e><i><span style='font-size:18.0pt;line-height:115%;font-family:"Cambria Math",serif'><m:r>m</m:r></span></i></m:e><m:sup><i><span style='font-size:18.0pt;line-height:115%;font-family:"Cambria Math",serif'><m:r>2</m:r></span></i></m:sup></m:sSup></m:num><m:den><i><span style='font-size:18.0pt;line-height:115%;font-family:"Cambria Math",serif'><m:r>ħ</m:r><m:r>c</m:r><m:r> </m:r></span></i></m:den></m:f></m:e></m:d></m:e><m:sup><span style='font-size:18.0pt;line-height:115%;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:oMath><![endif]--><![if !msEquation]><span style='font-size:11.0pt;line-height:106%;font-family:"Calibri",sans-serif;position:relative;top:11.5pt;mso-text-raise:-11.5pt;mso-fareast-language:EN-US'><img width=95 height=66 id="_x0000_i1025" src="cid:image012.png@01D07540.86973E80"></span><![endif]><i><span style='font-size:11.5pt;line-height:115%;font-family:"Cambria Math",serif'><o:p></o:p></span></i></p><p class=MsoNormal style='margin-bottom:0in;margin-bottom:.0001pt;text-align:justify;line-height:115%'><b><i><u><span style='font-size:14.0pt;line-height:115%'>F</span></u></i></b><i><sub><span style='font-size:12.0pt;line-height:115%'>E</span></sub></i><span style='font-size:14.0pt;line-height:115%;font-family:"Cambria Math",serif'> </span><span style='font-size:11.5pt;line-height:115%;font-family:"Cambria Math",serif'>=</span><span style='font-size:12.0pt;line-height:115%;font-family:"Cambria Math",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></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>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> </m:r></span></i></m:oMath><![endif]--><![if !msEquation]><span style='font-size:11.0pt;line-height:106%;font-family:"Calibri",sans-serif;position:relative;top:14.0pt;mso-text-raise:-14.0pt;mso-fareast-language:EN-US'><img width=30 height=54 id="_x0000_i1025" src="cid:image014.png@01D07540.86973E80"></span><![endif]><span style='font-size:12.0pt;line-height:115%;font-family:"Cambria Math",serif'>= </span><!--[if gte msEquation 12]><m:oMath><m:d><m:dPr><span style='font-size:18.0pt;font-family:"Cambria Math",serif;font-style:italic'><m:ctrlPr></m:ctrlPr></span></m:dPr><m:e><m:f><m:fPr><span style='font-size:18.0pt;font-family:"Cambria Math",serif;font-style:italic'><m:ctrlPr></m:ctrlPr></span></m:fPr><m:num><m:sSubSup><m:sSubSupPr><span style='font-size:18.0pt;font-family:"Cambria Math",serif;font-style:italic'><m:ctrlPr></m:ctrlPr></span></m:sSubSupPr><m:e><i><span style='font-size:18.0pt;line-height:115%;font-family:"Cambria Math",serif'><m:r>q</m:r></span></i></m:e><m:sub><i><span style='font-size:18.0pt;line-height:115%;font-family:"Cambria Math",serif'><m:r>p</m:r></span></i></m:sub><m:sup><i><span style='font-size:18.0pt;line-height:115%;font-family:"Cambria Math",serif'><m:r>2</m:r></span></i></m:sup></m:sSubSup></m:num><m:den><i><span style='font-size:18.0pt;line-height:115%;font-family:"Cambria Math",serif'><m:r>4</m:r><m:r>π</m:r></span></i><m:sSub><m:sSubPr><span style='font-size:18.0pt;font-family:"Cambria Math",serif;font-style:italic'><m:ctrlPr></m:ctrlPr></span></m:sSubPr><m:e><i><span style='font-size:18.0pt;line-height:115%;font-family:"Cambria Math",serif'><m:r>ε</m:r></span></i></m:e><m:sub><i><span style='font-size:18.0pt;line-height:115%;font-family:"Cambria Math",serif'><m:r>o</m:r></span></i></m:sub></m:sSub><m:sSubSup><m:sSubSupPr><span style='font-size:14.0pt;font-family:"Cambria Math",serif;font-style:italic'><m:ctrlPr></m:ctrlPr></span></m:sSubSupPr><m:e><i><s><span style='font-size:14.0pt;line-height:115%;font-family:"Cambria Math",serif'><m:r>λ</m:r></span></s></i></m:e><m:sub><i><span style='font-size:14.0pt;line-height:115%;font-family:"Cambria Math",serif'><m:r>c</m:r></span></i></m:sub><m:sup><i><span style='font-size:14.0pt;line-height:115%;font-family:"Cambria Math",serif'><m:r>2</m:r></span></i></m:sup></m:sSubSup></m:den></m:f></m:e></m:d><m:d><m:dPr><span style='font-size:18.0pt;font-family:"Cambria Math",serif;font-style:italic'><m:ctrlPr></m:ctrlPr></span></m:dPr><m:e><m:f><m:fPr><span style='font-size:18.0pt;font-family:"Cambria Math",serif;font-style:italic'><m:ctrlPr></m:ctrlPr></span></m:fPr><m:num><i><span style='font-size:18.0pt;line-height:115%;font-family:"Cambria Math",serif'><m:r>G</m:r></span></i></m:num><m:den><m:sSup><m:sSupPr><span style='font-size:18.0pt;font-family:"Cambria Math",serif;font-style:italic'><m:ctrlPr></m:ctrlPr></span></m:sSupPr><m:e><i><span style='font-size:18.0pt;line-height:115%;font-family:"Cambria Math",serif'><m:r>c</m:r></span></i></m:e><m:sup><i><span style='font-size:18.0pt;line-height:115%;font-family:"Cambria Math",serif'><m:r>4</m:r></span></i></m:sup></m:sSup></m:den></m:f></m:e></m:d></m:oMath><![endif]--><![if !msEquation]><span style='font-size:11.0pt;line-height:106%;font-family:"Calibri",sans-serif;position:relative;top:13.5pt;mso-text-raise:-13.5pt;mso-fareast-language:EN-US'><img width=154 height=64 id="_x0000_i1025" src="cid:image016.png@01D07540.86973E80"></span><![endif]><span style='font-size:12.0pt;line-height:115%;font-family:"Cambria Math",serif'> = </span><span style='font-size:14.0pt;line-height:115%;font-family:"Cambria Math",serif'>(ħc)</span><!--[if gte msEquation 12]><m:oMath><m:sSup><m:sSupPr><span style='font-size:18.0pt;font-family:"Cambria Math",serif;font-style:italic'><m:ctrlPr></m:ctrlPr></span></m:sSupPr><m:e><m:d><m:dPr><span style='font-size:18.0pt;font-family:"Cambria Math",serif;font-style:italic'><m:ctrlPr></m:ctrlPr></span></m:dPr><m:e><m:f><m:fPr><span style='font-size:18.0pt;font-family:"Cambria Math",serif;font-style:italic'><m:ctrlPr></m:ctrlPr></span></m:fPr><m:num><i><span style='font-size:20.0pt;line-height:115%;font-family:"Cambria Math",serif'><m:r>mc</m:r></span></i></m:num><m:den><i><span style='font-size:18.0pt;line-height:115%;font-family:"Cambria Math",serif'><m:r>ħ</m:r></span></i></m:den></m:f></m:e></m:d></m:e><m:sup><i><span style='font-size:18.0pt;line-height:115%;font-family:"Cambria Math",serif'><m:r>2</m:r></span></i></m:sup></m:sSup><m:d><m:dPr><span style='font-size:18.0pt;font-family:"Cambria Math",serif;font-style:italic'><m:ctrlPr></m:ctrlPr></span></m:dPr><m:e><m:f><m:fPr><span style='font-size:18.0pt;font-family:"Cambria Math",serif;font-style:italic'><m:ctrlPr></m:ctrlPr></span></m:fPr><m:num><i><span style='font-size:18.0pt;line-height:115%;font-family:"Cambria Math",serif'><m:r>G</m:r></span></i></m:num><m:den><m:sSup><m:sSupPr><span style='font-size:18.0pt;font-family:"Cambria Math",serif;font-style:italic'><m:ctrlPr></m:ctrlPr></span></m:sSupPr><m:e><i><span style='font-size:18.0pt;line-height:115%;font-family:"Cambria Math",serif'><m:r>c</m:r></span></i></m:e><m:sup><i><span style='font-size:18.0pt;line-height:115%;font-family:"Cambria Math",serif'><m:r>4</m:r></span></i></m:sup></m:sSup></m:den></m:f></m:e></m:d></m:oMath><![endif]--><![if !msEquation]><span style='font-size:11.0pt;line-height:106%;font-family:"Calibri",sans-serif;position:relative;top:11.5pt;mso-text-raise:-11.5pt;mso-fareast-language:EN-US'><img width=132 height=63 id="_x0000_i1025" src="cid:image018.png@01D07540.86973E80"></span><![endif]><span style='font-size:14.0pt;line-height:115%;font-family:"Cambria Math",serif'> = </span><!--[if gte msEquation 12]><m:oMath><m:f><m:fPr><span style='font-size:18.0pt;font-family:"Cambria Math",serif;font-style:italic'><m:ctrlPr></m:ctrlPr></span></m:fPr><m:num><i><span style='font-size:18.0pt;line-height:115%;font-family:"Cambria Math",serif'><m:r>G</m:r></span></i><m:sSup><m:sSupPr><span style='font-size:18.0pt;font-family:"Cambria Math",serif;font-style:italic'><m:ctrlPr></m:ctrlPr></span></m:sSupPr><m:e><i><span style='font-size:18.0pt;line-height:115%;font-family:"Cambria Math",serif'><m:r>m</m:r></span></i></m:e><m:sup><i><span style='font-size:18.0pt;line-height:115%;font-family:"Cambria Math",serif'><m:r>2</m:r></span></i></m:sup></m:sSup></m:num><m:den><i><span style='font-size:18.0pt;line-height:115%;font-family:"Cambria Math",serif'><m:r>ħ</m:r><m:r>c</m:r></span></i></m:den></m:f></m:oMath><![endif]--><![if !msEquation]><span style='font-size:11.0pt;line-height:106%;font-family:"Calibri",sans-serif;position:relative;top:11.0pt;mso-text-raise:-11.0pt;mso-fareast-language:EN-US'><img width=47 height=58 id="_x0000_i1025" src="cid:image020.png@01D07540.86973E80"></span><![endif]><span style='font-size:18.0pt;line-height:115%;font-family:"Cambria Math",serif'><o:p></o:p></span></p><p class=MsoNormal style='margin-bottom:0in;margin-bottom:.0001pt;text-align:justify;line-height:115%;background:white'><b><i><u><span style='font-size:14.0pt;line-height:115%'>E</span></u></i></b><sub><span style='font-size:14.0pt;line-height:115%'>i</span></sub><i><span style='font-size:12.0pt;line-height:115%;font-family:"Cambria Math",serif'> </span></i><span style='font-size:12.0pt;line-height:115%;font-family:"Cambria Math",serif'>=</span><!--[if gte msEquation 12]><m:oMath><m:f><m:fPr><span style='font-size:18.0pt;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:18.0pt;font-family:"Cambria Math",serif;font-style:italic'><m:ctrlPr></m:ctrlPr></span></m:sSubPr><m:e><i><span style='font-size:18.0pt;line-height:115%;font-family:"Cambria Math",serif'><m:r>E</m:r></span></i></m:e><m:sub><i><span style='font-size:18.0pt;line-height:115%;font-family:"Cambria Math",serif'><m:r>i</m:r></span></i></m:sub></m:sSub></m:num><m:den><m:sSub><m:sSubPr><span style='font-size:18.0pt;font-family:"Cambria Math",serif;font-style:italic'><m:ctrlPr></m:ctrlPr></span></m:sSubPr><m:e><i><span style='font-size:18.0pt;line-height:115%;font-family:"Cambria Math",serif'><m:r>E</m:r></span></i></m:e><m:sub><i><span style='font-size:18.0pt;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:106%;font-family:"Calibri",sans-serif;position:relative;top:16.0pt;mso-text-raise:-16.0pt;mso-fareast-language:EN-US'><img width=26 height=61 id="_x0000_i1025" src="cid:image022.png@01D07540.86973E80"></span><![endif]><span style='font-size:14.0pt;line-height:115%;font-family:"Cambria Math",serif'> =</span><!--[if gte msEquation 12]><m:oMath><i><span style='font-size:14.0pt;line-height:115%;font-family:"Cambria Math",serif'> </span></i><m:d><m:dPr><span style='font-size:14.0pt;font-family:"Cambria Math",serif;font-style:italic'><m:ctrlPr></m:ctrlPr></span></m:dPr><m:e><i><span style='font-size:14.0pt;line-height:115%;font-family:"Cambria Math",serif'><m:r>m</m:r></span></i><m:sSup><m:sSupPr><span style='font-size:14.0pt;font-family:"Cambria Math",serif;font-style:italic'><m:ctrlPr></m:ctrlPr></span></m:sSupPr><m:e><i><span style='font-size:14.0pt;line-height:115%;font-family:"Cambria Math",serif'><m:r>c</m:r></span></i></m:e><m:sup><i><span style='font-size:14.0pt;line-height:115%;font-family:"Cambria Math",serif'><m:r>2</m:r></span></i></m:sup></m:sSup><span style='font-size:18.0pt;font-family:"Cambria Math",serif;font-style:italic'><m:ctrlPr></m:ctrlPr></span></m:e></m:d><m:rad><m:radPr><m:degHide m:val="on"/><span style='font-size:18.0pt;font-family:"Cambria Math",serif;font-style:italic'><m:ctrlPr></m:ctrlPr></span></m:radPr><m:deg></m:deg><m:e><m:f><m:fPr><span style='font-size:18.0pt;font-family:"Cambria Math",serif;font-style:italic'><m:ctrlPr></m:ctrlPr></span></m:fPr><m:num><i><span style='font-size:18.0pt;line-height:115%;font-family:"Cambria Math",serif'><m:r>G</m:r></span></i></m:num><m:den><i><span style='font-size:18.0pt;line-height:115%;font-family:"Cambria Math",serif'><m:r>ħ</m:r></span></i><m:sSup><m:sSupPr><span style='font-size:18.0pt;font-family:"Cambria Math",serif;font-style:italic'><m:ctrlPr></m:ctrlPr></span></m:sSupPr><m:e><i><span style='font-size:18.0pt;line-height:115%;font-family:"Cambria Math",serif'><m:r>c</m:r></span></i></m:e><m:sup><i><span style='font-size:18.0pt;line-height:115%;font-family:"Cambria Math",serif'><m:r>5</m:r></span></i></m:sup></m:sSup></m:den></m:f></m:e></m:rad></m:oMath><![endif]--><![if !msEquation]><span style='font-size:11.0pt;line-height:106%;font-family:"Calibri",sans-serif;position:relative;top:12.0pt;mso-text-raise:-12.0pt;mso-fareast-language:EN-US'><img width=117 height=59 id="_x0000_i1025" src="cid:image024.png@01D07540.86973E80"></span><![endif]><span style='font-size:14.0pt;line-height:115%;font-family:"Cambria Math",serif'> = </span><!--[if gte msEquation 12]><m:oMath><m:rad><m:radPr><m:degHide m:val="on"/><span style='font-size:18.0pt;font-family:"Cambria Math",serif;font-style:italic'><m:ctrlPr></m:ctrlPr></span></m:radPr><m:deg></m:deg><m:e><m:f><m:fPr><span style='font-size:18.0pt;font-family:"Cambria Math",serif;font-style:italic'><m:ctrlPr></m:ctrlPr></span></m:fPr><m:num><i><span style='font-size:18.0pt;line-height:115%;font-family:"Cambria Math",serif'><m:r>G</m:r></span></i><m:sSup><m:sSupPr><span style='font-size:18.0pt;font-family:"Cambria Math",serif;font-style:italic'><m:ctrlPr></m:ctrlPr></span></m:sSupPr><m:e><i><span style='font-size:18.0pt;line-height:115%;font-family:"Cambria Math",serif'><m:r>m</m:r></span></i></m:e><m:sup><i><span style='font-size:18.0pt;line-height:115%;font-family:"Cambria Math",serif'><m:r>2</m:r></span></i></m:sup></m:sSup></m:num><m:den><i><span style='font-size:20.0pt;line-height:115%;font-family:"Cambria Math",serif'><m:r>ħ</m:r><m:r>c</m:r></span></i></m:den></m:f></m:e></m:rad></m:oMath><![endif]--><![if !msEquation]><span style='font-size:11.0pt;line-height:106%;font-family:"Calibri",sans-serif;position:relative;top:14.5pt;mso-text-raise:-14.5pt;mso-fareast-language:EN-US'><img width=70 height=76 id="_x0000_i1025" src="cid:image026.png@01D07540.86973E80"></span><![endif]><span style='font-size:18.0pt;line-height:115%;font-family:"Cambria Math",serif'> <o:p></o:p></span></p><p class=MsoNormal style='margin-bottom:0in;margin-bottom:.0001pt;text-align:justify;line-height:115%;background:white'><span style='font-size:14.0pt;line-height:115%;font-family:"Cambria Math",serif'>Therefore:</span><span style='font-size:14.0pt;line-height:115%;font-family:"Cambria Math",serif'><o:p></o:p></span></p><p class=MsoNormal style='margin-bottom:0in;margin-bottom:.0001pt;text-align:justify;line-height:115%'><b><i><u><span style='font-size:18.0pt;line-height:115%'>F</span></u></i></b><sub><span style='font-size:18.0pt;line-height:115%'>g</span></sub><span style='font-size:16.0pt;line-height:115%;font-family:"Cambria Math",serif'> </span><span style='font-size:14.0pt;line-height:115%;font-family:"Cambria Math",serif'>=</span><b><i><u><span style='font-size:18.0pt;line-height:115%'> F</span></u></i></b><i><sub><span style='font-size:16.0pt;line-height:115%'>E</span></sub></i><sup><span style='font-size:16.0pt;line-height:115%'>2</span></sup><span style='font-size:18.0pt;line-height:115%;font-family:"Cambria Math",serif'> </span><span style='font-size:14.0pt;line-height:115%;font-family:"Cambria Math",serif'>=</span><b><i><u><span style='font-size:18.0pt;line-height:115%'> E</span></u></i></b><sub><span style='font-size:18.0pt;line-height:115%'>i</span></sub><i><sup><span style='font-size:16.0pt;line-height:115%'>4</span></sup></i><span style='font-size:18.0pt;line-height:115%;font-family:"Cambria Math",serif'> </span><span style='font-size:14.0pt;line-height:115%;font-family:"Cambria Math",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:"Cambria Math",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:"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. <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:"Cambria Math",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:"Cambria Math",serif'>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:18.0pt;line-height:115%'>F</span></u></i></b><sub><span style='font-size:18.0pt;line-height:115%'>g</span></sub><span style='font-size:16.0pt;line-height:115%;font-family:"Cambria Math",serif'> </span><span style='font-size:14.0pt;line-height:115%;font-family:"Cambria Math",serif'>= </span><b><i><u><span style='font-size:18.0pt;line-height:115%'>F</span></u></i></b><i><sub><span style='font-size:16.0pt;line-height:115%'>E</span></sub></i><sup><span style='font-size:16.0pt;line-height:115%'>2</span></sup><span style='font-size:16.0pt;line-height:115%'>/</span><span style='font-size:16.0pt;line-height:115%;font-family:"Cambria Math",serif'>4</span><span style='font-size:18.0pt;line-height:115%;font-family:"Cambria Math",serif'> </span><span style='font-size:14.0pt;line-height:115%;font-family:"Cambria Math",serif'>= </span><span style='font-size:16.0pt;line-height:115%;font-family:"Cambria Math",serif'>4</span><b><i><u><span style='font-size:18.0pt;line-height:115%'>E</span></u></i></b><sub><span style='font-size:18.0pt;line-height:115%'>i</span></sub><i><sup><span style='font-size:16.0pt;line-height:115%'>4</span></sup></i><span style='font-size:16.0pt;line-height:115%'>. </span><span style='font-size:14.0pt;line-height:115%;font-family:"Cambria Math",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:"Cambria Math",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:"Cambria Math",serif'>Next we will express the force relationship for the conditions stated without using dimensionless Planck units (no underline).<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:"Cambria Math",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:"Cambria Math",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: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></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>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:106%;font-family:"Calibri",sans-serif;position:relative;top:14.0pt;mso-text-raise:-14.0pt;mso-fareast-language:EN-US'><img width=88 height=56 id="_x0000_i1025" src="cid:image028.png@01D07540.86973E80"></span><![endif]><span style='font-size:14.0pt;line-height:115%;font-family:"Cambria Math",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:"Cambria Math",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:"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.<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:"Cambria Math",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:"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:16.0pt;line-height:115%'> F</span></u></i></b><sub><span style='font-size:16.0pt;line-height:115%'>g</span></sub><span style='font-size:14.0pt;line-height:115%;font-family:"Cambria Math",serif'> </span><span style='font-size:12.0pt;line-height:115%;font-family:"Cambria Math",serif'>=</span><b><i><u><span style='font-size:16.0pt;line-height:115%'> F</span></u></i></b><i><sub><span style='font-size:14.0pt;line-height:115%'>E</span></sub></i><sup><span style='font-size:14.0pt;line-height:115%'>2</span></sup><span style='font-size:16.0pt;line-height:115%;font-family:"Cambria Math",serif'> </span><span style='font-size:12.0pt;line-height:115%;font-family:"Cambria Math",serif'>=</span><b><i><u><span style='font-size:16.0pt;line-height:115%'> E</span></u></i></b><sub><span style='font-size:16.0pt;line-height:115%'>i</span></sub><i><sup><span style='font-size:14.0pt;line-height:115%'>4</span></sup></i><span style='font-size:12.0pt;line-height:115%;font-family:"Cambria Math",serif'> </span><span style='font-size:14.0pt;line-height:115%;font-family:"Cambria Math",serif'>becomes:<o:p></o:p></span></p><p class=MsoNormal style='margin-bottom:0in;margin-bottom:.0001pt;text-align:justify;line-height:115%'><b><i><u><span style='font-size:18.0pt;line-height:115%'>F</span></u></i></b><sub><span style='font-size:18.0pt;line-height:115%'>g</span></sub><i><span style='font-size:16.0pt;line-height:115%'>N</span></i><sup><span style='font-size:16.0pt;line-height:115%'>2</span></sup><span style='font-size:16.0pt;line-height:115%;font-family:"Cambria Math",serif'> </span><span style='font-size:14.0pt;line-height:115%;font-family:"Cambria Math",serif'>= (</span><b><i><u><span style='font-size:18.0pt;line-height:115%'>F</span></u></i></b><i><sub><span style='font-size:16.0pt;line-height:115%'>E</span></sub></i><i><span style='font-size:16.0pt;line-height:115%'>N<sup>2</sup></span></i><span style='font-size:16.0pt;line-height:115%'>)<sup>2</sup></span><span style='font-size:18.0pt;line-height:115%;font-family:"Cambria Math",serif'> </span><span style='font-size:14.0pt;line-height:115%;font-family:"Cambria Math",serif'>=</span><b><i><u><span style='font-size:18.0pt;line-height:115%'> E</span></u></i></b><sub><span style='font-size:18.0pt;line-height:115%'>i</span></sub><i><sup><span style='font-size:16.0pt;line-height:115%'>4</span></sup></i><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:"Cambria Math",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:"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:<o:p></o:p></span></p><p class=MsoNormal style='margin-bottom:0in;margin-bottom:.0001pt;text-align:justify;line-height:115%'><i><span style='font-size:14.0pt;line-height:115%;font-family:"Cambria Math",serif'>F</span></i><sub><span style='font-size:14.0pt;line-height:115%;font-family:"Cambria Math",serif'>g</span></sub><i><span style='font-size:14.0pt;line-height:115%;font-family:"Cambria Math",serif'>F</span></i><sub><span style='font-size:14.0pt;line-height:115%;font-family:"Cambria Math",serif'>p</span></sub><span style='font-size:14.0pt;line-height:115%;font-family:"Cambria Math",serif'> = (<i>F</i><sub>e</sub></span><i><span style='font-size:14.0pt;line-height:115%;font-family:"Times New Roman",serif'>N<sup>2</sup></span></i><span style='font-size:14.0pt;line-height:115%;font-family:"Cambria Math",serif'>/α)<sup>2</sup><o:p></o:p></span></p><p class=MsoNormal style='margin-bottom:0in;margin-bottom:.0001pt'><span style='font-size:14.0pt;line-height:106%;font-family:"Times New Roman",serif'><o:p> </o:p></span></p><p class=MsoNormal style='margin-bottom:0in;margin-bottom:.0001pt'><span style='font-size:14.0pt;line-height:106%;font-family:"Times New Roman",serif'>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.<o:p></o:p></span></p><p class=MsoNormal style='margin-bottom:0in;margin-bottom:.0001pt'><span style='font-size:14.0pt;line-height:106%;font-family:"Times New Roman",serif'><o:p> </o:p></span></p><p class=MsoNormal style='margin-bottom:0in;margin-bottom:.0001pt'><span style='font-size:14.0pt;line-height:106%;font-family:"Times New Roman",serif'>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. <o:p></o:p></span></p><p class=MsoListParagraph style='text-indent:-.25in;mso-list:l0 level1 lfo1'><![if !supportLists]><span style='font-size:14.0pt'><span style='mso-list:Ignore'>1)<span style='font:7.0pt "Times New Roman"'> </span></span></span><![endif]><span style='font-size:14.0pt'>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:14.0pt;font-family:"Cambria Math",serif'>Δ</span><span style='font-size:14.0pt'>E</span><span style='font-size:14.0pt;font-family:"Cambria Math",serif'>Δ</span><span style='font-size:14.0pt'>t = ½ </span><span style='font-size:14.0pt;font-family:"Cambria Math",serif'>ħ</span><span style='font-size:14.0pt'>). In other words, virtual photons can never produce measurable energy. <o:p></o:p></span></p><p class=MsoListParagraph style='text-indent:-.25in;mso-list:l0 level1 lfo1'><![if !supportLists]><span style='font-size:14.0pt'><span style='mso-list:Ignore'>2)<span style='font:7.0pt "Times New Roman"'> </span></span></span><![endif]><span style='font-size:14.0pt'>Electric fields have energy density which can be experimentally measured. <o:p></o:p></span></p><p class=MsoListParagraph style='text-indent:-.25in;mso-list:l0 level1 lfo1'><![if !supportLists]><span style='font-size:14.0pt'><span style='mso-list:Ignore'>3)<span style='font:7.0pt "Times New Roman"'> </span></span></span><![endif]><span style='font-size:14.0pt'>Therefore, electric fields cannot be created by a cloud of virtual photons.<o:p></o:p></span></p><p class=MsoNormal><span style='font-size:14.0pt;line-height:106%;font-family:"Times New Roman",serif'><o:p> </o:p></span></p><p class=MsoNormal><span style='font-size:14.0pt;line-height:106%;font-family:"Times New Roman",serif'>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. <o:p></o:p></span></p><p class=MsoNormal><span style='font-size:14.0pt;line-height:106%;font-family:"Times New Roman",serif'><o:p> </o:p></span></p><p class=MsoNormal><span style='font-size:14.0pt;line-height:106%;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:106%;font-family:"Times New Roman",serif'><o:p> </o:p></span></p></div></body></html>