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</o:shapelayout></xml><![endif]--></head><body bgcolor=white lang=EN-US link=blue vlink=purple><div class=WordSection1><p class=MsoNormal>Hi Albrecht, Wolf, Grahame<o:p></o:p></p><p class=MsoNormal><o:p> </o:p></p><p class=MsoNormal>So my study of the electron and electric charge, from the standpoint of energy being a displacement of space, has led to some interesting observations.<o:p></o:p></p><p class=MsoNormal><o:p> </o:p></p><p class=MsoNormal>At this point I will just present some of the math. Perhaps when there is a bit more time I can fill in with a description of each step in formulation of the relationships.<o:p></o:p></p><p class=MsoNormal><o:p> </o:p></p><p class=MsoNormal><!--[if gte msEquation 12]><m:oMathPara><m:oMath><i><span style='font-family:"Cambria Math",serif'><m:r>Ҡ</m:r><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><m:rad><m:radPr><m:degHide m:val="on"/><span style='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-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>2ћ</m:r><m:r>cϰ</m:r></span></i></m:num><m:den><i><span style='font-family:"Cambria Math",serif'><m:r>ϱ</m:r></span></i></m:den></m:f></m:e></m:rad></m:num><m:den><i><span style='font-family:"Cambria Math",serif'><m:r>4</m:r><m:r>π</m:r><m:r>ħ</m:r></span></i><m:sSup><m:sSupPr><span style='font-family:"Cambria Math",serif;font-style:italic'><m:ctrlPr></m:ctrlPr></span></m:sSupPr><m:e><i><span style='font-family:"Cambria Math",serif'><m:r>c</m:r></span></i></m:e><m:sup><i><span style='font-family:"Cambria Math",serif'><m:r>3</m:r></span></i></m:sup></m:sSup></m:den></m:f><i><span style='font-family:"Cambria Math",serif'><m:r>=4.58576946280331</m:r><m:r>E</m:r><m:r>-</m:r><m:r>06</m:r></span></i></m:oMath></m:oMathPara><![endif]--><![if !msEquation]><span style='font-size:12.0pt;font-family:"Times New Roman",serif;color:black;mso-fareast-language:EN-US'><img width=284 height=57 id="_x0000_i1025" src="cid:image001.png@01D2C111.23573BD0"></span><![endif]><o:p></o:p></p><p class=MsoNormal><!--[if gte msEquation 12]><m:oMathPara><m:oMath><i><span style='font-family:"Cambria Math",serif'><m:r>ϰ</m:r><m:r>=</m:r></span></i><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>E</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:rad><m:radPr><m:degHide m:val="on"/><span style='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-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>α</m:r></span></i></m:num><m:den><i><span style='font-family:"Cambria Math",serif'><m:r>ћ</m:r><m:r>c</m:r></span></i></m:den></m:f></m:e></m:rad><i><span style='font-family:"Cambria Math",serif'><m:r>=0.039333680453191</m:r></span></i></m:oMath></m:oMathPara><![endif]--><![if !msEquation]><span style='font-size:12.0pt;font-family:"Times New Roman",serif;color:black;mso-fareast-language:EN-US'><img width=241 height=39 id="_x0000_i1025" src="cid:image002.png@01D2C111.23573BD0"></span><![endif]><o:p></o:p></p><p class=MsoNormal><!--[if gte msEquation 12]><m:oMathPara><m:oMath><i><span style='font-family:"Cambria Math",serif'><m:r>ϱ</m:r><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><m:rad><m:radPr><m:degHide m:val="on"/><span style='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-family:"Cambria Math",serif'><m:r>α</m:r><m:r>ћ</m:r><m:r>c</m:r></span></i></m:e></m:rad></m:num><m:den><i><span style='font-family:"Cambria Math",serif'><m:r>2</m:r></span></i><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>E</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><i><span style='font-family:"Cambria Math",serif'><m:r>=0.092762137719152</m:r></span></i></m:oMath></m:oMathPara><![endif]--><![if !msEquation]><span style='font-size:12.0pt;font-family:"Times New Roman",serif;color:black;mso-fareast-language:EN-US'><img width=232 height=44 id="_x0000_i1025" src="cid:image003.png@01D2C111.23573BD0"></span><![endif]><o:p></o:p></p><p class=MsoNormal><!--[if gte msEquation 12]><m:oMathPara><m:oMath><i><span style='font-family:"Cambria Math",serif'><m:r>2</m:r><m:r>ϱϰ</m:r><m:r>=</m:r><m:r>α</m:r></span></i></m:oMath></m:oMathPara><![endif]--><![if !msEquation]><span style='font-size:12.0pt;font-family:"Times New Roman",serif;color:black;mso-fareast-language:EN-US'><img width=58 height=19 id="_x0000_i1025" src="cid:image005.png@01D2C111.23573BD0"></span><![endif]><o:p></o:p></p><p class=MsoNormal><!--[if gte msEquation 12]><m:oMathPara><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>ϰ</m:r><m:r><m:rPr><m:scr m:val="roman"/><m:sty m:val="p"/></m:rPr>= </m:r><m:r><m:rPr><m:scr m:val="roman"/><m:sty m:val="p"/></m:rPr>ϱ</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><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>c</m:r></span></i></m:sub></m:sSub></m:num><m:den><i><span style='font-family:"Cambria Math",serif'><m:r>2</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:f><m:fPr><span style='font-family:"Cambria Math",serif'><m:ctrlPr></m:ctrlPr></span></m:fPr><m:num><m:rad><m:radPr><m:degHide m:val="on"/><span style='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-family:"Cambria Math",serif'><m:r>α</m:r><m:r> </m:r></span></i><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>c</m:r></span></i></m:sub></m:sSub></m:e></m:rad></m:num><m:den><i><span style='font-family:"Cambria Math",serif'><m:r>2</m:r></span></i></m:den></m:f><i><span style='font-family:"Cambria Math",serif'><m:r>=</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: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>α</m:r></span></i></m:num><m:den><i><span style='font-family:"Cambria Math",serif'><m:r>2 </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>ϱ</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>=0.039333680453191</m:r></span></m:oMath></m:oMathPara><![endif]--><![if !msEquation]><span style='font-size:12.0pt;font-family:"Times New Roman",serif;color:black;mso-fareast-language:EN-US'><img width=332 height=45 id="_x0000_i1025" src="cid:image006.png@01D2C111.23573BD0"></span><![endif]><o:p></o:p></p><p class=MsoNormal><!--[if gte msEquation 12]><m:oMathPara><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>ϱ</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><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>F</m:r></span></m:e><m:sub><i><span style='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-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>c</m:r></span></i></m:sub></m:sSub></m:den></m:f><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><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>E</m:r></span></i></m:e><m:sub><i><span style='font-family:"Cambria Math",serif'><m:r>q</m:r></span></i></m:sub></m:sSub></m:num><m:den><i><span style='font-family:"Cambria Math",serif'><m:r>δ</m:r><m:r> </m:r></span></i><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>c</m:r></span></i></m:sub></m:sSub></m:den></m:f><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><m:rad><m:radPr><m:degHide m:val="on"/><span style='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-family:"Cambria Math",serif'><m:r>α</m:r></span></i></m:e></m:rad></m:num><m:den><m:rad><m:radPr><m:degHide m:val="on"/><span style='font-family:"Cambria Math",serif;font-style:italic'><m:ctrlPr></m:ctrlPr></span></m:radPr><m:deg></m:deg><m:e><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>c</m:r></span></i></m:sub></m:sSub></m:e></m:rad></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;font-style:italic'><m:ctrlPr></m:ctrlPr></span></m:fPr><m:num><i><span style='font-family:"Cambria Math",serif'><m:r>α</m:r></span></i></m:num><m:den><i><span style='font-family:"Cambria Math",serif'><m:r>2 </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>ϰ</m:r></span></m:den></m:f><i><span style='font-family:"Cambria Math",serif'><m:r>=</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>0.092762137719152</m:r></span></m:oMath></m:oMathPara><![endif]--><![if !msEquation]><span style='font-size:12.0pt;font-family:"Times New Roman",serif;color:black;mso-fareast-language:EN-US'><img width=344 height=48 id="_x0000_i1025" src="cid:image007.png@01D2C111.23573BD0"></span><![endif]><o:p></o:p></p><p class=MsoNormal><o:p> </o:p></p><p class=MsoNormal>The term Ҡ=4.585769462803310E-06 and yields a radius for the electron of:<o:p></o:p></p><p class=MsoNormal><!--[if gte msEquation 12]><m:oMathPara><m:oMath><i><span style='font-family:"Cambria Math",serif'><m:r>r</m:r><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>1</m:r></span></i></m:num><m:den><i><span style='font-family:"Cambria Math",serif'><m:r>4</m:r><m:r>π</m:r><m:r> </m:r></span></i><m:sSup><m:sSupPr><span style='font-family:"Cambria Math",serif;font-style:italic'><m:ctrlPr></m:ctrlPr></span></m:sSupPr><m:e><i><span style='font-family:"Cambria Math",serif'><m:r>c</m:r></span></i></m:e><m:sup><i><span style='font-family:"Cambria Math",serif'><m:r>2</m:r></span></i></m:sup></m:sSup><i><span style='font-family:"Cambria Math",serif'><m:r> Ҡ</m:r></span></i></m:den></m:f><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><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>ε</m:r></span></i></m:e><m:sub><i><span style='font-family:"Cambria Math",serif'><m:r>0</m:r></span></i></m:sub></m:sSub><i><span style='font-family:"Cambria Math",serif'><m:r> </m:r></span></i><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>μ</m:r></span></i></m:e><m:sub><i><span style='font-family:"Cambria Math",serif'><m:r>0</m:r></span></i></m:sub></m:sSub></m:num><m:den><i><span style='font-family:"Cambria Math",serif'><m:r>4</m:r><m:r>π</m:r><m:r> Ҡ</m:r></span></i></m:den></m:f></m:oMath></m:oMathPara><![endif]--><![if !msEquation]><span style='font-size:12.0pt;font-family:"Times New Roman",serif;color:black;mso-fareast-language:EN-US'><img width=142 height=36 id="_x0000_i1025" src="cid:image009.png@01D2C111.23573BD0"></span><![endif]><o:p></o:p></p><p class=MsoNormal>The term: §=1.44492000606359E-28<o:p></o:p></p><p class=MsoNormal><!--[if gte msEquation 12]><m:oMathPara><m:oMath><i><span style='font-family:"Cambria Math",serif'><m:r>h</m:r><m:r>=Ҡ §=6.62607004</m:r><m:r>E</m:r><m:r>-</m:r><m:r>34</m:r></span></i></m:oMath></m:oMathPara><![endif]--><![if !msEquation]><span style='font-size:12.0pt;font-family:"Times New Roman",serif;color:black;mso-fareast-language:EN-US'><img width=205 height=19 id="_x0000_i1025" src="cid:image010.png@01D2C111.23573BD0"></span><![endif]><o:p></o:p></p><p class=MsoNormal><!--[if gte msEquation 12]><m:oMathPara><m:oMath><i><span style='font-family:"Cambria Math",serif'><m:r>Ҡ</m:r><m:r>=4.58576946280331</m:r><m:r>E</m:r><m:r>-</m:r><m:r>06</m:r></span></i></m:oMath></m:oMathPara><![endif]--><![if !msEquation]><span style='font-size:12.0pt;font-family:"Times New Roman",serif;color:black;mso-fareast-language:EN-US'><img width=217 height=19 id="_x0000_i1025" src="cid:image011.png@01D2C111.23573BD0"></span><![endif]><o:p></o:p></p><p class=MsoNormal><!--[if gte msEquation 12]><m:oMathPara><m:oMath><i><span style='font-family:"Cambria Math",serif'><m:r>§=1.44492000606359</m:r><m:r>E</m:r><m:r>-</m:r><m:r>28</m:r></span></i></m:oMath></m:oMathPara><![endif]--><![if !msEquation]><span style='font-size:12.0pt;font-family:"Times New Roman",serif;color:black;mso-fareast-language:EN-US'><img width=212 height=19 id="_x0000_i1025" src="cid:image013.png@01D2C111.23573BD0"></span><![endif]><o:p></o:p></p><p class=MsoNormal><o:p> </o:p></p><p class=MsoNormal>So that, for the energy level of the electron:<o:p></o:p></p><p class=MsoNormal><!--[if gte msEquation 12]><m:oMathPara><m:oMath><i><span style='font-family:"Cambria Math",serif'><m:r>Ҡ</m:r><m:r>=</m:r></span></i><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><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>§ </m:r></span></i><m:sSup><m:sSupPr><span style='font-family:"Cambria Math",serif'><m:ctrlPr></m:ctrlPr></span></m:sSupPr><m:e><i><span style='font-family:"Cambria Math",serif'><m:r>c</m:r></span></i></m:e><m:sup><i><span style='font-family:"Cambria Math",serif'><m:r>3</m:r></span></i></m:sup></m:sSup></m:den></m:f></m:e></m:rad><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><m:rad><m:radPr><m:degHide m:val="on"/><span style='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-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>2 </m:r><m:r>c</m:r><m:r> ħ </m:r><m:r>ϰ</m:r></span></i></m:num><m:den><i><span style='font-family:"Cambria Math",serif'><m:r>ϱ</m:r></span></i></m:den></m:f></m:e></m:rad></m:num><m:den><i><span style='font-family:"Cambria Math",serif'><m:r>4</m:r><m:r><m:rPr><m:scr m:val="roman"/><m:sty m:val="bi"/></m:rPr><b>π</b></m:r><m:r><m:rPr><m:scr m:val="roman"/><m:sty m:val="bi"/></m:rPr><b> </b></m:r><m:r>ħ </m:r></span></i><m:sSup><m:sSupPr><span style='font-family:"Cambria Math",serif;font-style:italic'><m:ctrlPr></m:ctrlPr></span></m:sSupPr><m:e><i><span style='font-family:"Cambria Math",serif'><m:r>c</m:r></span></i></m:e><m:sup><i><span style='font-family:"Cambria Math",serif'><m:r>3</m:r></span></i></m:sup></m:sSup></m:den></m:f><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><m:rad><m:radPr><m:degHide m:val="on"/><span style='font-family:"Cambria Math",serif;font-style:italic'><m:ctrlPr></m:ctrlPr></span></m:radPr><m:deg></m:deg><m:e><m:sSup><m:sSupPr><span style='font-family:"Cambria Math",serif;font-style:italic'><m:ctrlPr></m:ctrlPr></span></m:sSupPr><m:e><i><span style='font-family:"Cambria Math",serif'><m:r>4 </m:r><m:r>E</m:r></span></i></m:e><m:sup><i><span style='font-family:"Cambria Math",serif'><m:r>2</m:r></span></i></m:sup></m:sSup></m:e></m:rad></m:num><m:den><i><span style='font-family:"Cambria Math",serif'><m:r>4</m:r><m:r><m:rPr><m:scr m:val="roman"/><m:sty m:val="bi"/></m:rPr><b>π</b></m:r><m:r><m:rPr><m:scr m:val="roman"/><m:sty m:val="bi"/></m:rPr><b> </b></m:r><m:r>ħ </m:r></span></i><m:sSup><m:sSupPr><span style='font-family:"Cambria Math",serif;font-style:italic'><m:ctrlPr></m:ctrlPr></span></m:sSupPr><m:e><i><span style='font-family:"Cambria Math",serif'><m:r>c</m:r></span></i></m:e><m:sup><i><span style='font-family:"Cambria Math",serif'><m:r>3</m:r></span></i></m:sup></m:sSup></m:den></m:f></m:oMath></m:oMathPara><![endif]--><![if !msEquation]><span style='font-size:12.0pt;font-family:"Times New Roman",serif;color:black;mso-fareast-language:EN-US'><img width=223 height=67 id="_x0000_i1025" src="cid:image015.png@01D2C111.23573BD0"></span><![endif]><o:p></o:p></p><p class=MsoNormal><!--[if gte msEquation 12]><m:oMathPara><m:oMath><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'><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><m:sSup><m:sSupPr><span style='font-family:"Cambria Math",serif'><m:ctrlPr></m:ctrlPr></span></m:sSupPr><m:e><i><span style='font-family:"Cambria Math",serif'><m:r>Ҡ</m:r></span></i></m:e><m:sup><i><span style='font-family:"Cambria Math",serif'><m:r>2</m:r></span></i></m:sup></m:sSup><m:sSup><m:sSupPr><span style='font-family:"Cambria Math",serif'><m:ctrlPr></m:ctrlPr></span></m:sSupPr><m:e><i><span style='font-family:"Cambria Math",serif'><m:r>c</m:r></span></i></m:e><m:sup><i><span style='font-family:"Cambria Math",serif'><m:r>3</m:r></span></i></m:sup></m:sSup></m:den></m:f><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>8</m:r></span></i><m:sSup><m:sSupPr><span style='font-family:"Cambria Math",serif;font-style:italic'><m:ctrlPr></m:ctrlPr></span></m:sSupPr><m:e><b><i><span style='font-family:"Cambria Math",serif'><m:r><m:rPr><m:scr m:val="roman"/><m:sty m:val="bi"/></m:rPr>π</m:r></span></i></b></m:e><m:sup><i><span style='font-family:"Cambria Math",serif'><m:r>2</m:r></span></i></m:sup></m:sSup><m:sSup><m:sSupPr><span style='font-family:"Cambria Math",serif;font-style:italic'><m:ctrlPr></m:ctrlPr></span></m:sSupPr><m:e><i><span style='font-family:"Cambria Math",serif'><m:r>ħ</m:r></span></i><span style='font-family:"Cambria Math",serif;font-weight:bold;font-style:italic'><m:ctrlPr></m:ctrlPr></span></m:e><m:sup><i><span style='font-family:"Cambria Math",serif'><m:r>2</m:r></span></i></m:sup></m:sSup><m:sSup><m:sSupPr><span style='font-family:"Cambria Math",serif;font-style:italic'><m:ctrlPr></m:ctrlPr></span></m:sSupPr><m:e><i><span style='font-family:"Cambria Math",serif'><m:r>c</m:r></span></i></m:e><m:sup><i><span style='font-family:"Cambria Math",serif'><m:r>3</m:r></span></i></m:sup></m:sSup></m:num><m:den><m:rad><m:radPr><m:degHide m:val="on"/><span style='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-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>2 </m:r><m:r>c</m:r><m:r> ħ </m:r><m:r>ϰ</m:r></span></i></m:num><m:den><i><span style='font-family:"Cambria Math",serif'><m:r>ϱ</m:r></span></i></m:den></m:f></m:e></m:rad></m:den></m:f><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>8</m:r></span></i><m:sSup><m:sSupPr><span style='font-family:"Cambria Math",serif;font-style:italic'><m:ctrlPr></m:ctrlPr></span></m:sSupPr><m:e><b><i><span style='font-family:"Cambria Math",serif'><m:r><m:rPr><m:scr m:val="roman"/><m:sty m:val="bi"/></m:rPr>π</m:r></span></i></b></m:e><m:sup><i><span style='font-family:"Cambria Math",serif'><m:r>2</m:r></span></i></m:sup></m:sSup><m:sSup><m:sSupPr><span style='font-family:"Cambria Math",serif;font-style:italic'><m:ctrlPr></m:ctrlPr></span></m:sSupPr><m:e><i><span style='font-family:"Cambria Math",serif'><m:r>ħ</m:r></span></i><span style='font-family:"Cambria Math",serif;font-weight:bold;font-style:italic'><m:ctrlPr></m:ctrlPr></span></m:e><m:sup><i><span style='font-family:"Cambria Math",serif'><m:r>2</m:r></span></i></m:sup></m:sSup><m:sSup><m:sSupPr><span style='font-family:"Cambria Math",serif;font-style:italic'><m:ctrlPr></m:ctrlPr></span></m:sSupPr><m:e><i><span style='font-family:"Cambria Math",serif'><m:r>c</m:r></span></i></m:e><m:sup><i><span style='font-family:"Cambria Math",serif'><m:r>3</m:r></span></i></m:sup></m:sSup></m:num><m:den><m:rad><m:radPr><m:degHide m:val="on"/><span style='font-family:"Cambria Math",serif;font-style:italic'><m:ctrlPr></m:ctrlPr></span></m:radPr><m:deg></m:deg><m:e><m:sSup><m:sSupPr><span style='font-family:"Cambria Math",serif;font-style:italic'><m:ctrlPr></m:ctrlPr></span></m:sSupPr><m:e><i><span style='font-family:"Cambria Math",serif'><m:r>4 </m:r><m:r>E</m:r></span></i></m:e><m:sup><i><span style='font-family:"Cambria Math",serif'><m:r>2</m:r></span></i></m:sup></m:sSup></m:e></m:rad></m:den></m:f></m:oMath></m:oMathPara><![endif]--><![if !msEquation]><span style='font-size:12.0pt;font-family:"Times New Roman",serif;color:black;mso-fareast-language:EN-US'><img width=223 height=62 id="_x0000_i1025" src="cid:image016.png@01D2C111.23573BD0"></span><![endif]><o:p></o:p></p><p class=MsoNormal>The mass of the electron is:<o:p></o:p></p><p class=MsoNormal><!--[if gte msEquation 12]><m:oMathPara><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>m</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:sSup><m:sSupPr><span style='font-family:"Cambria Math",serif'><m:ctrlPr></m:ctrlPr></span></m:sSupPr><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>Ҡ</m:r></span></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><span style='font-family:"Cambria Math",serif'><m:r><m:rPr><m:scr m:val="roman"/><m:sty m:val="p"/></m:rPr>§ c</m:r></span></m:oMath></m:oMathPara><![endif]--><![if !msEquation]><span style='font-size:12.0pt;font-family:"Times New Roman",serif;color:black;mso-fareast-language:EN-US'><img width=83 height=19 id="_x0000_i1025" src="cid:image017.png@01D2C111.23573BD0"></span><![endif]><o:p></o:p></p><p class=MsoNormal>The energy of the electron is of course:<o:p></o:p></p><p class=MsoNormal><!--[if gte msEquation 12]><m:oMathPara><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>E</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:sSup><m:sSupPr><span style='font-family:"Cambria Math",serif'><m:ctrlPr></m:ctrlPr></span></m:sSupPr><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>Ҡ</m:r></span></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><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:sSup><m:sSupPr><span style='font-family:"Cambria Math",serif'><m:ctrlPr></m:ctrlPr></span></m:sSupPr><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>c</m:r></span></m:e><m:sup><b><span style='font-family:"Cambria Math",serif'><m:r><m:rPr><m:scr m:val="roman"/><m:sty m:val="b"/></m:rPr>3</m:r></span></b></m:sup></m:sSup></m:oMath></m:oMathPara><![endif]--><![if !msEquation]><span style='font-size:12.0pt;font-family:"Times New Roman",serif;color:black;mso-fareast-language:EN-US'><img width=87 height=19 id="_x0000_i1025" src="cid:image019.png@01D2C111.23573BD0"></span><![endif]><o:p></o:p></p><p class=MsoNormal>The radius of the electron is:<o:p></o:p></p><p class=MsoNormal><!--[if gte msEquation 12]><m:oMathPara><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>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><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>1</m:r></span></i></m:num><m:den><i><span style='font-family:"Cambria Math",serif'><m:r>4</m:r><m:r>π</m:r></span></i><m:sSup><m:sSupPr><span style='font-family:"Cambria Math",serif'><m:ctrlPr></m:ctrlPr></span></m:sSupPr><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>Ҡ</m:r></span></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><i><span style='font-family:"Cambria Math",serif'><m:r>c</m:r></span></i></m:den></m:f></m:oMath></m:oMathPara><![endif]--><![if !msEquation]><span style='font-size:12.0pt;font-family:"Times New Roman",serif;color:black;mso-fareast-language:EN-US'><img width=79 height=36 id="_x0000_i1025" src="cid:image020.png@01D2C111.23573BD0"></span><![endif]><o:p></o:p></p><p class=MsoNormal><o:p> </o:p></p><p class=MsoNormal><o:p> </o:p></p><p class=MsoNormal>The gravitational constant related to energy is:<o:p></o:p></p><p class=MsoNormal><!--[if gte msEquation 12]><m:oMathPara><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>G</m:r></span></i></m:e><m:sub><i><span style='font-family:"Cambria Math",serif'><m:r>q</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>G</m:r></span></i></m:num><m:den><m:sSup><m:sSupPr><span style='font-family:"Cambria Math",serif;font-style:italic'><m:ctrlPr></m:ctrlPr></span></m:sSupPr><m:e><i><span style='font-family:"Cambria Math",serif'><m:r>c</m:r></span></i></m:e><m:sup><i><span style='font-family:"Cambria Math",serif'><m:r>4</m:r></span></i></m:sup></m:sSup></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>=8.262112922369050E-45</m:r></span></m:oMath></m:oMathPara><![endif]--><![if !msEquation]><span style='font-size:12.0pt;font-family:"Times New Roman",serif;color:black;mso-fareast-language:EN-US'><img width=265 height=36 id="_x0000_i1025" src="cid:image021.png@01D2C111.23573BD0"></span><![endif]><o:p></o:p></p><p class=MsoNormal><!--[if gte msEquation 12]><m:oMathPara><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>G</m:r></span></i></m:e><m:sub><span style='font-family:"Cambria Math",serif'><m:r><m:rPr><m:scr m:val="roman"/><m:sty m:val="p"/></m:rPr>q</m:r></span></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'><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><i><span style='font-family:"Cambria Math",serif'><m:r>α</m:r></span></i></m:e><m:sup><i><span style='font-family:"Cambria Math",serif'><m:r>2</m:r></span></i></m:sup></m:sSup><i><span style='font-family:"Cambria Math",serif'><m:r>ϱ</m:r><m:r> </m:r><m:r>c</m:r><m:r> ħ </m:r></span></i><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><m:f><m:fPr><span style='font-family:"Cambria Math",serif'><m:ctrlPr></m:ctrlPr></span></m:fPr><m:num><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><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>α</m:r></span></i></m:num><m:den><i><span style='font-family:"Cambria Math",serif'><m:r>ϱ</m:r></span></i></m:den></m:f></m:e></m:rad><i><span style='font-family:"Cambria Math",serif'><m:r>α</m:r><m:r> ħ </m:r><m:r>c</m:r></span></i></m:num><m:den><i><span style='font-family:"Cambria Math",serif'><m:r>1-</m:r></span></i><m:d><m:dPr><span style='font-family:"Cambria Math",serif;font-style:italic'><m:ctrlPr></m:ctrlPr></span></m:dPr><m:e><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>ϱ</m:r><m:r>+</m:r><m:r>ϰ</m:r></span></i></m:num><m:den><i><span style='font-family:"Cambria Math",serif'><m:r>2</m:r></span></i></m:den></m:f></m:e></m:d></m:den></m:f></m:e></m:rad></m:num><m:den><i><span style='font-family:"Cambria Math",serif'><m:r>4</m:r><m:r>ϰ</m:r></span></i></m:den></m:f></m:oMath></m:oMathPara><![endif]--><![if !msEquation]><span style='font-size:12.0pt;font-family:"Times New Roman",serif;color:black;mso-fareast-language:EN-US'><img width=185 height=93 id="_x0000_i1025" src="cid:image023.png@01D2C111.23573BD0"></span><![endif]><o:p></o:p></p><p class=MsoNormal><!--[if gte msEquation 12]><m:oMathPara><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>G</m:r><m:r>=</m:r><m:r>G</m:r></span></i></m:e><m:sub><i><span style='font-family:"Cambria Math",serif'><m:r>q</m:r></span></i></m:sub></m:sSub><m:sSup><m:sSupPr><span style='font-family:"Cambria Math",serif;font-style:italic'><m:ctrlPr></m:ctrlPr></span></m:sSupPr><m:e><i><span style='font-family:"Cambria Math",serif'><m:r>c</m:r></span></i></m:e><m:sup><i><span style='font-family:"Cambria Math",serif'><m:r>4</m:r></span></i></m:sup></m:sSup><i><span style='font-family:"Cambria Math",serif'><m:r>=</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>6.673811533003440E-11</m:r></span></m:oMath></m:oMathPara><![endif]--><![if !msEquation]><span style='font-size:12.0pt;font-family:"Times New Roman",serif;color:black;mso-fareast-language:EN-US'><img width=276 height=21 id="_x0000_i1025" src="cid:image024.png@01D2C111.23573BD0"></span><![endif]><o:p></o:p></p><p class=MsoNormal><!--[if gte msEquation 12]><m:oMathPara><m:oMath><i><span style='font-family:"Cambria Math",serif'><m:r>G</m:r><m:r>=</m:r></span></i><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><i><span style='font-family:"Cambria Math",serif'><m:r>α</m:r></span></i></m:e><m:sup><i><span style='font-family:"Cambria Math",serif'><m:r>2</m:r></span></i></m:sup></m:sSup><i><span style='font-family:"Cambria Math",serif'><m:r>ϱ</m:r><m:r> </m:r></span></i><m:sSup><m:sSupPr><span style='font-family:"Cambria Math",serif;font-style:italic'><m:ctrlPr></m:ctrlPr></span></m:sSupPr><m:e><i><span style='font-family:"Cambria Math",serif'><m:r>c</m:r></span></i></m:e><m:sup><i><span style='font-family:"Cambria Math",serif'><m:r>5</m:r></span></i></m:sup></m:sSup><i><span style='font-family:"Cambria Math",serif'><m:r> ħ </m:r></span></i><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><m:f><m:fPr><span style='font-family:"Cambria Math",serif'><m:ctrlPr></m:ctrlPr></span></m:fPr><m:num><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><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>α</m:r></span></i></m:num><m:den><i><span style='font-family:"Cambria Math",serif'><m:r>ϱ</m:r></span></i></m:den></m:f></m:e></m:rad><i><span style='font-family:"Cambria Math",serif'><m:r>α</m:r><m:r> ħ </m:r><m:r>c</m:r></span></i></m:num><m:den><i><span style='font-family:"Cambria Math",serif'><m:r>1-</m:r></span></i><m:d><m:dPr><span style='font-family:"Cambria Math",serif;font-style:italic'><m:ctrlPr></m:ctrlPr></span></m:dPr><m:e><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>ϱ</m:r><m:r>+</m:r><m:r>ϰ</m:r></span></i></m:num><m:den><i><span style='font-family:"Cambria Math",serif'><m:r>2</m:r></span></i></m:den></m:f></m:e></m:d></m:den></m:f></m:e></m:rad></m:num><m:den><i><span style='font-family:"Cambria Math",serif'><m:r>4</m:r><m:r>ϰ</m:r></span></i></m:den></m:f></m:oMath></m:oMathPara><![endif]--><![if !msEquation]><span style='font-size:12.0pt;font-family:"Times New Roman",serif;color:black;mso-fareast-language:EN-US'><img width=186 height=93 id="_x0000_i1025" src="cid:image025.png@01D2C111.23573BD0"></span><![endif]><o:p></o:p></p><p class=MsoNormal><o:p> </o:p></p><p class=MsoNormal>Let us use the distance <!--[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><span style='font-family:"Cambria Math",serif'><m:r><m:rPr><m:scr m:val="roman"/><m:sty m:val="p"/></m:rPr>ħ </m:r><m:r><i>c</i></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>2 </m:r></span><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>E</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>=1.93079632559013E-13 m, </m:r></span></m:oMath><![endif]--><![if !msEquation]><span style='font-size:12.0pt;font-family:"Times New Roman",serif;color:black;position:relative;top:8.5pt;mso-text-raise:-8.5pt;mso-fareast-language:EN-US'><img width=248 height=30 id="_x0000_i1025" src="cid:image026.png@01D2C111.23573BD0"></span><![endif]>and compute the force of gravity between two electrons.<o:p></o:p></p><p class=MsoNormal>So the force of gravity under these conditions is:<o:p></o:p></p><p class=MsoNormal><!--[if gte msEquation 12]><m:oMathPara><m:oMath><i><span style='font-family:"Cambria Math",serif'><m:r>F</m:r><m:r>=</m:r></span></i><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>G</m:r></span></i></m:e><m:sub><i><span style='font-family:"Cambria Math",serif'><m:r>q</m:r></span></i></m:sub></m:sSub><m:f><m:fPr><span style='font-family:"Cambria Math",serif;font-style:italic'><m:ctrlPr></m:ctrlPr></span></m:fPr><m:num><m:sSup><m:sSupPr><span style='font-family:"Cambria Math",serif;font-style:italic'><m:ctrlPr></m:ctrlPr></span></m:sSupPr><m:e><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>E</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><i><span style='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-family:"Cambria Math",serif;font-style:italic'><m:ctrlPr></m:ctrlPr></span></m:sSupPr><m:e><i><span style='font-family:"Cambria Math",serif'><m:r>r</m:r></span></i></m:e><m:sup><i><span style='font-family:"Cambria Math",serif'><m:r>2</m:r></span></i></m:sup></m:sSup></m:den></m:f><i><span style='font-family:"Cambria Math",serif'><m:r>=</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>1.48552768342978E-45</m:r></span></m:oMath></m:oMathPara><![endif]--><![if !msEquation]><span style='font-size:12.0pt;font-family:"Times New Roman",serif;color:black;mso-fareast-language:EN-US'><img width=277 height=39 id="_x0000_i1025" src="cid:image027.png@01D2C111.23573BD0"></span><![endif]><o:p></o:p></p><p class=MsoNormal>Then when we compare that result to the conventional gravitational equation for the electron’s mass:<o:p></o:p></p><p class=MsoNormal><!--[if gte msEquation 12]><m:oMathPara><m:oMath><i><span style='font-family:"Cambria Math",serif'><m:r>F</m:r><m:r>=</m:r><m:r>G</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><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>m</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><i><span style='font-family:"Cambria Math",serif'><m:r> </m:r></span></i><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>m</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:num><m:den><m:sSup><m:sSupPr><span style='font-family:"Cambria Math",serif;font-style:italic'><m:ctrlPr></m:ctrlPr></span></m:sSupPr><m:e><i><span style='font-family:"Cambria Math",serif'><m:r>r</m:r></span></i></m:e><m:sup><i><span style='font-family:"Cambria Math",serif'><m:r>2</m:r></span></i></m:sup></m:sSup></m:den></m:f><i><span style='font-family:"Cambria Math",serif'><m:r>=</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>1.48552768342978E-45</m:r></span></m:oMath></m:oMathPara><![endif]--><![if !msEquation]><span style='font-size:12.0pt;font-family:"Times New Roman",serif;color:black;mso-fareast-language:EN-US'><img width=292 height=33 id="_x0000_i1025" src="cid:image028.png@01D2C111.23573BD0"></span><![endif]><o:p></o:p></p><p class=MsoNormal><o:p> </o:p></p><p class=MsoNormal>This approach unifies the forces, including gravity. And gravity is somewhat as Grahame has described, and has the “almost instantaneous” quality that Wolf and Grahame have mentioned.<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><div><div style='border:none;border-top:solid #E1E1E1 1.0pt;padding:3.0pt 0in 0in 0in'><p class=MsoNormal><b><span style='font-size:11.0pt;font-family:"Calibri",sans-serif;color:windowtext'>From:</span></b><span style='font-size:11.0pt;font-family:"Calibri",sans-serif;color:windowtext'> General [mailto:general-bounces+chipakins=gmail.com@lists.natureoflightandparticles.org] <b>On Behalf Of </b>Dr Grahame Blackwell<br><b>Sent:</b> Saturday, April 29, 2017 4:15 PM<br><b>To:</b> phys@a-giese.de; Nature of Light and Particles - General Discussion <general@lists.natureoflightandparticles.org>; wolf@nascentinc.com; af.kracklauer@web.de<br><b>Subject:</b> Re: [General] HA: Gravity<o:p></o:p></span></p></div></div><p class=MsoNormal><o:p> </o:p></p><div><p class=MsoNormal><span style='font-size:10.0pt;font-family:"Arial",sans-serif;color:navy'>Hi Albrecht,</span><o:p></o:p></p></div><div><p class=MsoNormal> <o:p></o:p></p></div><div><p class=MsoNormal><span style='font-size:10.0pt;font-family:"Arial",sans-serif;color:navy'>I'm not sure how you figure that your two cases in any way discount my proposal. If the 'gravitational effects' of a massive body are in fact just the extended electromagnetic manifestation of that body (i.e. of all its constituent particles) then that extended manifestation will move synchronously with the part of that body that we register with our senses. It follows that, whilst that extended manifestation is at all times present throughout the cosmos, the 'intensity distribution' of that manifestation at any point (to use a limited analogy) will also move in perfect time with the perceived part of that body (in simple terms, subject to the inverse square law in respect of perceived position of that object) - in other words the 'gravitational field' will vary in (space)time exactly as one would expect of a gravitational field with zero latency.</span><o:p></o:p></p></div><div><p class=MsoNormal> <o:p></o:p></p></div><div><p class=MsoNormal><span style='font-size:10.0pt;font-family:"Arial",sans-serif;color:navy'>I believe that's fully consistent with observations regarding the two examples you cite - if they in turn are consistent with the possibility of 'propagation of gravitational effects being instantaneous'. To me the whole picture ties together seamlessly. The composite of all of those extended manifestations, varying in position in spacetime as their perceived 'cores' move, constitute the texture of spacetime that "tells matter how to move" (to quote Wheeler) - the 'curvature' of spacetime, as it's generally termed.</span><o:p></o:p></p></div><div><p class=MsoNormal> <o:p></o:p></p></div><div><p class=MsoNormal><span style='font-size:10.0pt;font-family:"Arial",sans-serif;color:navy'>I hope that helps.</span><o:p></o:p></p></div><div><p class=MsoNormal> <o:p></o:p></p></div><div><p class=MsoNormal><span style='font-size:10.0pt;font-family:"Arial",sans-serif;color:navy'>Best regards,</span><o:p></o:p></p></div><div><p class=MsoNormal><span style='font-size:10.0pt;font-family:"Arial",sans-serif;color:navy'>Grahame</span><o:p></o:p></p></div><blockquote style='border:none;border-left:solid navy 1.5pt;padding:0in 0in 0in 4.0pt;margin-left:3.75pt;margin-top:5.0pt;margin-right:0in;margin-bottom:5.0pt'><div><p class=MsoNormal><span style='font-size:10.0pt;font-family:"Arial",sans-serif'>----- Original Message ----- <o:p></o:p></span></p></div><div><p class=MsoNormal style='background:#E4E4E4'><b><span style='font-size:10.0pt;font-family:"Arial",sans-serif'>From:</span></b><span style='font-size:10.0pt;font-family:"Arial",sans-serif'> <a href="mailto:genmail@a-giese.de" title="genmail@a-giese.de">Albrecht Giese</a> <o:p></o:p></span></p></div><div><p class=MsoNormal><b><span style='font-size:10.0pt;font-family:"Arial",sans-serif'>To:</span></b><span style='font-size:10.0pt;font-family:"Arial",sans-serif'> <a href="mailto:general@lists.natureoflightandparticles.org" title="general@lists.natureoflightandparticles.org">general@lists..natureoflightandparticles.org</a> ; <a href="mailto:wolf@nascentinc.com" title="wolf@nascentinc.com">wolf@nascentinc.com</a> ; <a href="mailto:af.kracklauer@web.de" title="af.kracklauer@web.de">af.kracklauer@web.de</a> ; <a href="mailto:phys@a-giese.de" title="phys@a-giese.de">phys@a-giese.de</a> <o:p></o:p></span></p></div><div><p class=MsoNormal><b><span style='font-size:10.0pt;font-family:"Arial",sans-serif'>Sent:</span></b><span style='font-size:10.0pt;font-family:"Arial",sans-serif'> Saturday, April 29, 2017 8:38 PM<o:p></o:p></span></p></div><div><p class=MsoNormal><b><span style='font-size:10.0pt;font-family:"Arial",sans-serif'>Subject:</span></b><span style='font-size:10.0pt;font-family:"Arial",sans-serif'> Re: [General] HA: Gravity<o:p></o:p></span></p></div><div><p class=MsoNormal><o:p> </o:p></p></div><p><u>Grahame,</u><o:p></o:p></p><p>you say: " ... <span style='font-size:10.0pt;font-family:"Arial",sans-serif;color:navy'> the 'effects of gravity' are in fact the consequences of those distributed entities ALREADY being present to some degree at every point in the cosmos</span> ... "<o:p></o:p></p><p>But look at the following cases: 1.) There may be two twin stars which orbit each other. Their distance is rapidly changing during an orbit. So the gravitational influences to their environment will change. And for this change I see the question justified which the propagation speed of this influence is. I think that your statement above does not cover this case, true? 2.) An even less regular case: I know a colleague (professor) who has built and performs an experiment to determine again the gravitational constant. In doing this he has two massive objects which he moves towards each other or apart from each other and measures the force between them. This process depends on his momentary decisions, so it is completely irregular compared to other physical processes. So, also in this case, nothing is constant or even predetermined.<o:p></o:p></p><p><u>Wolf,</u><o:p></o:p></p><p>there was an interesting development in our understanding of the physics of gravity. About a hundred years ago it was the general opinion that gravity is the simplest and most fundamental force in physics. This may also have been the reason that gravity is a fundamental parameter in the definition of the Planck units. At present, however, the representatives of the German Einstein Institute say that gravity is the least understood and perhaps most complicated force. <o:p></o:p></p><p>The idea to connect gravity in some way to the electric force comes up again and again. The reason is most probably that both follow the dependence of range of 1/r<sup>2</sup>. (But this dependence can be explained geometrically if we assume that forces are generally mediated by exchange particles.) The idea of Jefimenko that there is a cogravitation as a kind of different charge sign to make it compatible with electricity is a new and severe assumption. I find it better not to permanently introduce new - an unobserved - phenomena than to try to live with the existing ones (= Occam's razor). <o:p></o:p></p><p>Einstein has described gravity as a geometrical phenomenon, changing the understanding of space and time. On the other hand Theodor Kaluza has irritated Einstein with his hint that any force in physics can be explained by a specific geometry of space and time. (Einstein has accepted that but was not happy with it.) So, why not go back to physics and to forces in gravity rather than using space-time.<o:p></o:p></p><p>Regarding the instantaneous propagation of gravity: To my knowledge this was carefully investigated in past decades with the result that also gravity is limited to c. I do not go back to the details. Should there be new arguments which are not covered by the past discussions then this would be a good reason to investigate this case again. But are there new arguments? <o:p></o:p></p><p>If we want progress in the realm of gravitation, I expect an answer to at least one question: what is the cause of the weak equivalence principle, i.e. the fact that all objects are having the same gravitational acceleration independent of their inertial mass. Newton's theory of gravity does not answer this, Einstein's does not answer it as well. Gravity has to answer it!<o:p></o:p></p><p>Albrecht<o:p></o:p></p><p class=MsoNormal><o:p> </o:p></p><div><p class=MsoNormal>Am 29.04.2017 um 00:28 schrieb Dr Grahame Blackwell:<o:p></o:p></p></div><blockquote style='margin-top:5.0pt;margin-bottom:5.0pt'><div><p class=MsoNormal><span style='font-size:10.0pt;font-family:"Arial",sans-serif;color:navy'>Wolf et al,</span><o:p></o:p></p></div><div><p class=MsoNormal> <o:p></o:p></p></div><div><p class=MsoNormal><span style='font-size:10.0pt;font-family:"Arial",sans-serif;color:navy'>You will note that my proposal re gravity in my recently-circulated paper, as the 'extended being' of spatially distributed entities that we (with our limited senses) perceive as localised 'particles', implicitly proposes that the 'propagation speed of gravity' is in fact infinite - since there is in actuality NO propagation involved, the 'effects of gravity' are in fact the consequences of those distributed entities ALREADY being present to some degree at every point in the cosmos. I.e. 'everything is everywhere', to put it in simple terms; as a 'physical massive object' moves (again, a simplistic term), the WHOLE of its extended being moves with it and is immediately in a position to manifest 'gravitational' effects of that object consistent with its changed position, no matter how far spatially removed (more simplistic concepts!) from what we perceive as the 'massive object' itself.</span><o:p></o:p></p></div><div><p class=MsoNormal> <o:p></o:p></p></div><div><p class=MsoNormal><span style='font-size:10.0pt;font-family:"Arial",sans-serif;color:navy'>This points to a far deeper truth - that 'locality' and 'time' are both over-simplifications of deeper concepts, foisted on us by an evolutionary process that's more interested that we (a) breed, (b) find lunch and (c) don't become lunch - than it is in us fathoming the underlying principles of cosmic structure.</span><o:p></o:p></p></div><div><p class=MsoNormal> <o:p></o:p></p></div><div><p class=MsoNormal><span style='font-size:10.0pt;font-family:"Arial",sans-serif;color:navy'>Best,</span><o:p></o:p></p></div><div><p class=MsoNormal><span style='font-size:10.0pt;font-family:"Arial",sans-serif;color:navy'>Grahame</span><o:p></o:p></p></div><blockquote style='border:none;border-left:solid navy 1.5pt;padding:0in 0in 0in 4.0pt;margin-left:3.75pt;margin-top:5.0pt;margin-right:0in;margin-bottom:5.0pt'><div><p class=MsoNormal><span style='font-size:10.0pt;font-family:"Arial",sans-serif'>----- Original Message ----- <o:p></o:p></span></p></div><div><p class=MsoNormal style='background:#E4E4E4'><b><span style='font-size:10.0pt;font-family:"Arial",sans-serif'>From:</span></b><span style='font-size:10.0pt;font-family:"Arial",sans-serif'> <a href="mailto:wolf@nascentinc.com" title="wolf@nascentinc.com">Wolfgang Baer</a> <o:p></o:p></span></p></div><div><p class=MsoNormal><b><span style='font-size:10.0pt;font-family:"Arial",sans-serif'>To:</span></b><span style='font-size:10.0pt;font-family:"Arial",sans-serif'> <a href="mailto:af.kracklauer@web.de" title="af.kracklauer@web.de">af.kracklauer@web.de</a> ; <a href="mailto:phys@a-giese.de" title="phys@a-giese.de">phys@a-giese.de</a> ; <a href="mailto:general@lists.natureoflightandparticles.org" title="general@lists.natureoflightandparticles.org">general@lists..natureoflightandparticles.org</a> <o:p></o:p></span></p></div><div><p class=MsoNormal><b><span style='font-size:10.0pt;font-family:"Arial",sans-serif'>Sent:</span></b><span style='font-size:10.0pt;font-family:"Arial",sans-serif'> Friday, April 28, 2017 11:11 PM<o:p></o:p></span></p></div><div><p class=MsoNormal><b><span style='font-size:10.0pt;font-family:"Arial",sans-serif'>Subject:</span></b><span style='font-size:10.0pt;font-family:"Arial",sans-serif'> Re: [General] HA: Gravity<o:p></o:p></span></p></div><div><p class=MsoNormal><o:p> </o:p></p></div><p>Al:<o:p></o:p></p><p>I'm too concerned with gravity and charge as the fundamental characteristics of mater in classic physics to appreciate deeper explanations until the discrepancies or simpler questions have been answered.<o:p></o:p></p><p>Is not Einstein's connection between gravity and space time based on the use of EM wave phase measurements that define space time? In other words masses interact with charges and EM propagation so that the definition of a meter and a second with which we measure space and time are the cause of the warping.<o:p></o:p></p><p>Even more important for me right now is the question of the speed of gravity. I now had more of a chance to read Jefimenko's Gravitation and Cogravitation which Al recommended, where he expands on the idea that the equations correcting Newton's look more like EM with a gravitational scalar and vector potential and a Lorenz like force replacing newtons. In his chapter 20 he points out that the 43 seconds of arc precession of Mercury rather than being a proof of Einstein's theory is actually a cause for questioning the validity of Einstein's equations, Because Gerber's formula for the 43secnds was based upon planetary calculations based upon Newton's Action at a distance i.e. gravity goes the speed of infinity. Jefimenko points out that if Newton's theory was wrong and gravity is not instantaneous than if Einstein's theory explaning somthing wrong (the 43sec precession) is wrong and Einstein's theory coming up with 43 seconds actually proves Einstein's theory is wrong. Jefimenko calculates the value of the precession from his theory is 14 arc sec. <o:p></o:p></p><p>If gravity propagates instantly we are talking about a completely different beast than Einstein's theory, and trying to explain an error that is assumed correct just leads to more errors although the errors may be self consistent.<o:p></o:p></p><p>Wolf<o:p></o:p></p><p> <o:p></o:p></p></blockquote><p class=MsoNormal><br><br><br><o:p></o:p></p><pre>_______________________________________________<o:p></o:p></pre><pre>If you no longer wish to receive communication from the Nature of Light and Particles General Discussion List at <a href="mailto:phys@a-giese.de">phys@a-giese.de</a><o:p></o:p></pre><pre><a href=<a href="http://lists.natureoflightandparticles.org/options.cgi/general-natureoflightandparticles.org/phys%40a-giese.de?unsub=1&unsubconfirm=1">"http://lists.natureoflightandparticles.org/options.cgi/general-natureoflightandparticles.org/phys%40a-giese.de?unsub=1&unsubconfirm=1"</a>><o:p></o:p></pre><pre>Click here to unsubscribe<o:p></o:p></pre><pre></a><o:p></o:p></pre></blockquote><p class=MsoNormal><o:p> </o:p></p><div id=DAB4FAD8-2DD7-40BB-A1B8-4E2AA1F9FDF2><p class=MsoNormal><o:p> </o:p></p><table class=MsoNormalTable border=1 cellpadding=0 style='border:none;border-top:solid #D3D4DE 1.0pt'><tr><td width=55 style='width:41.25pt;border:none;padding:13.5pt .75pt .75pt .75pt'><p class=MsoNormal><a href="https://www.avast.com/sig-email?utm_medium=email&utm_source=link&utm_campaign=sig-email&utm_content=emailclient" target="_blank"><span style='text-decoration:none'><img border=0 width=46 height=29 id="_x0000_i1025" src="https://ipmcdn.avast.com/images/icons/icon-envelope-tick-round-orange-animated-no-repeat-v1.gif"></span></a><o:p></o:p></p></td><td width=470 style='width:352.5pt;border:none;padding:12.75pt .75pt .75pt .75pt'><p class=MsoNormal style='line-height:13.5pt'><span style='font-size:10.0pt;font-family:"Arial",sans-serif;color:#41424E'>Virenfrei. <a href="https://www.avast.com/sig-email?utm_medium=email&utm_source=link&utm_campaign=sig-email&utm_content=emailclient" target="_blank"><span style='color:#4453EA'>www.avast.com</span></a> <o:p></o:p></span></p></td></tr></table></div><div class=MsoNormal align=center style='text-align:center'><hr size=2 width="100%" align=center></div><p class=MsoNormal>_______________________________________________<br>If you no longer wish to receive communication from the Nature of Light and Particles General Discussion List at <a href="mailto:grahame@starweave.com">grahame@starweave.com</a><br><a href="<a href="http://lists.natureoflightandparticles.org/options.cgi/general-natureoflightandparticles.org/grahame%40starweave.com?unsub=1&unsubconfirm=1">http://lists.natureoflightandparticles.org/options.cgi/general-natureoflightandparticles.org/grahame%40starweave.com?unsub=1&unsubconfirm=1</a>"><br>Click here to unsubscribe<br></a><o:p></o:p></p></blockquote></div></body></html>