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</o:shapelayout></xml><![endif]--></head><body lang=EN-US link="#0563C1" vlink="#954F72"><div class=WordSection1><p class=MsoNormal>Hi Everyone,<o:p></o:p></p><p class=MsoNormal><o:p> </o:p></p><p class=MsoNormal><b><span style='font-size:14.0pt;color:black'>Schwinger Limit</span></b><b><span style='font-size:14.0pt'><o:p></o:p></span></b></p><p class=MsoNormal>I have just had an insight which I thought that the group would find interesting. One of the questions Davis asked about the energy density of spacetime was: “<span style='color:black'>Is it subject to the Schwinger limit where results go from linear to non-linear?”</span><span style='font-size:16.0pt'> </span>I looked up the Schwinger limit and it is the electric field <!--[if gte msEquation 12]><m:oMath><m:sSub><m:sSubPr><span style='font-family:"Cambria Math",serif;color:#444444'><m:ctrlPr></m:ctrlPr></span></m:sSubPr><m:e><span style='font-family:"Cambria Math",serif;color:#444444'><m:r><m:rPr><m:scr m:val="double-struck"/><m:sty m:val="p"/></m:rPr>E</m:r></span></m:e><m:sub><span style='font-family:"Cambria Math",serif;color:#444444'><m:r><m:rPr><m:scr m:val="roman"/><m:sty m:val="p"/></m:rPr>s</m:r></span></m:sub></m:sSub></m:oMath><![endif]--><![if !msEquation]><span style='font-size:12.0pt;font-family:"Times New Roman",serif;position:relative;top:3.0pt;mso-text-raise:-3.0pt;mso-fareast-language:EN-US'><img width=20 height=23 id="_x0000_i1025" src="cid:image001.png@01D08695.776B3C70"></span><![endif]><span style='color:#444444'> </span>which would start to generate electrons and positrons from the vacuum. This limit is given below. The reason for writing again is that it is a quite reasonable that any model which has either a radius or diameter equal to the reduced Compton wavelength would be supported by the electrons and positrons being created by an electric field at the<span style='color:#444444'> Schwinger limit.</span> <span style='font-size:10.0pt'><o:p></o:p></span></p><p style='margin:0in;margin-bottom:.0001pt;line-height:13.5pt'><span style='color:#444444'><o:p> </o:p></span></p><p style='margin:0in;margin-bottom:.0001pt;line-height:13.5pt'><span style='font-family:"Cambria Math",serif;color:#444444'> </span><!--[if gte msEquation 12]><m:oMath><m:sSub><m:sSubPr><span style='font-size:16.0pt;font-family:"Cambria Math",serif;color:#444444'><m:ctrlPr></m:ctrlPr></span></m:sSubPr><m:e><span style='font-size:16.0pt;font-family:"Cambria Math",serif;color:#444444'><m:r><m:rPr><m:scr m:val="double-struck"/><m:sty m:val="p"/></m:rPr>E</m:r></span></m:e><m:sub><span style='font-size:16.0pt;font-family:"Cambria Math",serif;color:#444444'><m:r><m:rPr><m:scr m:val="roman"/><m:sty m:val="p"/></m:rPr>s</m:r></span></m:sub></m:sSub><i><span style='font-size:16.0pt;font-family:"Cambria Math",serif;color:#444444'><m:r>=</m:r></span></i><m:f><m:fPr><span style='font-size:16.0pt;font-family:"Cambria Math",serif;color:#444444;font-style:italic'><m:ctrlPr></m:ctrlPr></span></m:fPr><m:num><m:sSubSup><m:sSubSupPr><span style='font-size:16.0pt;font-family:"Cambria Math",serif;color:#444444;font-style:italic'><m:ctrlPr></m:ctrlPr></span></m:sSubSupPr><m:e><i><span style='font-size:16.0pt;font-family:"Cambria Math",serif;color:#444444'><m:r>m</m:r></span></i></m:e><m:sub><i><span style='font-size:16.0pt;font-family:"Cambria Math",serif;color:#444444'><m:r>e</m:r></span></i></m:sub><m:sup><i><span style='font-size:16.0pt;font-family:"Cambria Math",serif;color:#444444'><m:r>2 </m:r></span></i></m:sup></m:sSubSup><m:sSup><m:sSupPr><span style='font-size:16.0pt;font-family:"Cambria Math",serif;color:#444444;font-style:italic'><m:ctrlPr></m:ctrlPr></span></m:sSupPr><m:e><i><span style='font-size:16.0pt;font-family:"Cambria Math",serif;color:#444444'><m:r>c</m:r></span></i></m:e><m:sup><i><span style='font-size:16.0pt;font-family:"Cambria Math",serif;color:#444444'><m:r>3</m:r></span></i></m:sup></m:sSup></m:num><m:den><i><span style='font-size:16.0pt;font-family:"Cambria Math",serif;color:#444444'><m:r>ħ</m:r><m:r>e</m:r></span></i></m:den></m:f><i><span style='font-size:16.0pt;font-family:"Cambria Math",serif;color:#444444'><m:r>=1.323×</m:r></span></i><m:sSup><m:sSupPr><span style='font-size:16.0pt;font-family:"Cambria Math",serif;color:#444444;font-style:italic'><m:ctrlPr></m:ctrlPr></span></m:sSupPr><m:e><i><span style='font-size:16.0pt;font-family:"Cambria Math",serif;color:#444444'><m:r>10</m:r></span></i></m:e><m:sup><i><span style='font-size:16.0pt;font-family:"Cambria Math",serif;color:#444444'><m:r>18</m:r></span></i></m:sup></m:sSup></m:oMath><![endif]--><![if !msEquation]><span style='font-size:12.0pt;font-family:"Times New Roman",serif;position:relative;top:22.5pt;mso-text-raise:-22.5pt;mso-fareast-language:EN-US'><img width=298 height=73 id="_x0000_i1025" src="cid:image002.png@01D08695.776B3C70"></span><![endif]><span style='font-size:16.0pt;font-family:"Cambria Math",serif;color:#444444'> </span><span style='font-family:"Cambria Math",serif;color:#444444'>V/m </span><span style='color:#444444'>Schwinger limit<o:p></o:p></span></p><p style='margin:0in;margin-bottom:.0001pt;mso-line-height-alt:13.5pt'><span style='font-size:16.0pt;font-family:"Cambria Math",serif;color:#444444'> </span><!--[if gte msEquation 12]><m:oMath><m:sSub><m:sSubPr><span style='font-size:16.0pt;font-family:"Cambria Math",serif;color:#444444;font-style:italic'><m:ctrlPr></m:ctrlPr></span></m:sSubPr><m:e><i><s><span style='font-size:16.0pt;font-family:"Cambria Math",serif;color:#444444'><m:r>λ</m:r></span></s></i></m:e><m:sub><i><span style='font-size:16.0pt;font-family:"Cambria Math",serif;color:#444444'><m:r>c</m:r></span></i></m:sub></m:sSub><i><span style='font-size:16.0pt;font-family:"Cambria Math",serif;color:#444444'><m:r>= </m:r></span></i><m:f><m:fPr><span style='font-size:16.0pt;font-family:"Cambria Math",serif;color:#444444;font-style:italic'><m:ctrlPr></m:ctrlPr></span></m:fPr><m:num><i><span style='font-size:16.0pt;font-family:"Cambria Math",serif;color:#444444'><m:r>ħ</m:r></span></i></m:num><m:den><m:sSub><m:sSubPr><span style='font-size:16.0pt;font-family:"Cambria Math",serif;color:#444444;font-style:italic'><m:ctrlPr></m:ctrlPr></span></m:sSubPr><m:e><i><span style='font-size:16.0pt;font-family:"Cambria Math",serif;color:#444444'><m:r>m</m:r></span></i></m:e><m:sub><i><span style='font-size:16.0pt;font-family:"Cambria Math",serif;color:#444444'><m:r>e</m:r></span></i></m:sub></m:sSub><i><span style='font-size:16.0pt;font-family:"Cambria Math",serif;color:#444444'><m:r>c</m:r></span></i></m:den></m:f></m:oMath><![endif]--><![if !msEquation]><span style='font-size:12.0pt;font-family:"Times New Roman",serif;position:relative;top:25.0pt;mso-text-raise:-25.0pt;mso-fareast-language:EN-US'><img width=104 height=74 id="_x0000_i1025" src="cid:image004.png@01D08695.776B3C70"></span><![endif]><span style='font-size:16.0pt;font-family:"Cambria Math",serif;color:#444444'> </span><span style='color:#444444'>Reduced Compton wavelength for an electron<o:p></o:p></span></p><p style='margin:0in;margin-bottom:.0001pt;line-height:13.5pt'><span style='font-family:"Cambria Math",serif;color:#444444'><o:p> </o:p></span></p><p style='margin:0in;margin-bottom:.0001pt;line-height:13.5pt'><span style='color:#444444'>If a particle has a radius (or diameter) equal to its reduced Compton wavelength, then it is reasonable that the particle/antiparticle pair could be extracted from the virtual particles present in the spacetime field if the electric field times the particle’s radius (or diameter) is equal to the energy of the particle divided by charge. Here is the calculation.<o:p></o:p></span></p><p style='margin:0in;margin-bottom:.0001pt;line-height:13.5pt'><span style='font-family:"Cambria Math",serif;color:#444444'> <o:p></o:p></span></p><p style='margin:0in;margin-bottom:.0001pt;mso-line-height-alt:13.5pt'><span style='font-size:16.0pt;font-family:"Cambria Math",serif;color:#444444'> </span><!--[if gte msEquation 12]><m:oMath><span style='font-family:"Cambria Math",serif;color:#444444'><m:r><m:rPr><m:scr m:val="roman"/><m:sty m:val="p"/></m:rPr> </m:r></span><m:sSub><m:sSubPr><span style='font-size:16.0pt;font-family:"Cambria Math",serif;color:#444444'><m:ctrlPr></m:ctrlPr></span></m:sSubPr><m:e><span style='font-size:16.0pt;font-family:"Cambria Math",serif;color:#444444'><m:r><m:rPr><m:scr m:val="double-struck"/><m:sty m:val="p"/></m:rPr>E</m:r></span></m:e><m:sub><span style='font-size:16.0pt;font-family:"Cambria Math",serif;color:#444444'><m:r><m:rPr><m:scr m:val="roman"/><m:sty m:val="p"/></m:rPr>s</m:r></span></m:sub></m:sSub><m:sSub><m:sSubPr><span style='font-size:16.0pt;font-family:"Cambria Math",serif;color:#444444;font-style:italic'><m:ctrlPr></m:ctrlPr></span></m:sSubPr><m:e><i><s><span style='font-size:16.0pt;font-family:"Cambria Math",serif;color:#444444'><m:r>λ</m:r></span></s></i></m:e><m:sub><i><span style='font-size:16.0pt;font-family:"Cambria Math",serif;color:#444444'><m:r>c</m:r></span></i></m:sub></m:sSub><i><span style='font-size:16.0pt;font-family:"Cambria Math",serif;color:#444444'><m:r>= </m:r></span></i><m:f><m:fPr><span style='font-size:16.0pt;font-family:"Cambria Math",serif;color:#444444;font-style:italic'><m:ctrlPr></m:ctrlPr></span></m:fPr><m:num><m:sSubSup><m:sSubSupPr><span style='font-size:16.0pt;font-family:"Cambria Math",serif;color:#444444;font-style:italic'><m:ctrlPr></m:ctrlPr></span></m:sSubSupPr><m:e><i><span style='font-size:16.0pt;font-family:"Cambria Math",serif;color:#444444'><m:r>m</m:r></span></i></m:e><m:sub><i><span style='font-size:16.0pt;font-family:"Cambria Math",serif;color:#444444'><m:r>e</m:r></span></i></m:sub><m:sup><i><span style='font-size:16.0pt;font-family:"Cambria Math",serif;color:#444444'><m:r>2 </m:r></span></i></m:sup></m:sSubSup><m:sSup><m:sSupPr><span style='font-size:16.0pt;font-family:"Cambria Math",serif;color:#444444;font-style:italic'><m:ctrlPr></m:ctrlPr></span></m:sSupPr><m:e><i><span style='font-size:16.0pt;font-family:"Cambria Math",serif;color:#444444'><m:r>c</m:r></span></i></m:e><m:sup><i><span style='font-size:16.0pt;font-family:"Cambria Math",serif;color:#444444'><m:r>3</m:r></span></i></m:sup></m:sSup></m:num><m:den><i><span style='font-size:16.0pt;font-family:"Cambria Math",serif;color:#444444'><m:r>ħ</m:r><m:r>e</m:r></span></i></m:den></m:f><m:f><m:fPr><span style='font-size:16.0pt;font-family:"Cambria Math",serif;color:#444444;font-style:italic'><m:ctrlPr></m:ctrlPr></span></m:fPr><m:num><i><span style='font-size:16.0pt;font-family:"Cambria Math",serif;color:#444444'><m:r>ħ</m:r></span></i></m:num><m:den><m:sSub><m:sSubPr><span style='font-size:16.0pt;font-family:"Cambria Math",serif;color:#444444;font-style:italic'><m:ctrlPr></m:ctrlPr></span></m:sSubPr><m:e><i><span style='font-size:16.0pt;font-family:"Cambria Math",serif;color:#444444'><m:r>m</m:r></span></i></m:e><m:sub><i><span style='font-size:16.0pt;font-family:"Cambria Math",serif;color:#444444'><m:r>e</m:r></span></i></m:sub></m:sSub><i><span style='font-size:16.0pt;font-family:"Cambria Math",serif;color:#444444'><m:r>c</m:r></span></i></m:den></m:f><i><span style='font-size:16.0pt;font-family:"Cambria Math",serif;color:#444444'><m:r>=</m:r></span></i><m:f><m:fPr><span style='font-size:16.0pt;font-family:"Cambria Math",serif;color:#444444;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;color:#444444;font-style:italic'><m:ctrlPr></m:ctrlPr></span></m:sSubPr><m:e><i><span style='font-size:16.0pt;font-family:"Cambria Math",serif;color:#444444'><m:r>m</m:r></span></i></m:e><m:sub><i><span style='font-size:16.0pt;font-family:"Cambria Math",serif;color:#444444'><m:r>e</m:r></span></i></m:sub></m:sSub><m:sSup><m:sSupPr><span style='font-size:16.0pt;font-family:"Cambria Math",serif;color:#444444;font-style:italic'><m:ctrlPr></m:ctrlPr></span></m:sSupPr><m:e><i><span style='font-size:16.0pt;font-family:"Cambria Math",serif;color:#444444'><m:r>c</m:r></span></i></m:e><m:sup><i><span style='font-size:16.0pt;font-family:"Cambria Math",serif;color:#444444'><m:r>2</m:r></span></i></m:sup></m:sSup></m:num><m:den><i><span style='font-size:16.0pt;font-family:"Cambria Math",serif;color:#444444'><m:r>e</m:r></span></i></m:den></m:f><i><span style='font-size:16.0pt;font-family:"Cambria Math",serif;color:#444444'><m:r>=511,000 </m:r><m:r>eV</m:r></span></i></m:oMath><![endif]--><![if !msEquation]><span style='font-size:12.0pt;font-family:"Times New Roman",serif;position:relative;top:22.5pt;mso-text-raise:-22.5pt;mso-fareast-language:EN-US'><img width=409 height=68 id="_x0000_i1025" src="cid:image006.png@01D08695.776B3C70"></span><![endif]><span style='color:#444444'><o:p></o:p></span></p><p style='margin:0in;margin-bottom:.0001pt;line-height:13.5pt'><span style='color:#444444'><o:p> </o:p></span></p><p style='margin:0in;margin-bottom:.0001pt;line-height:13.5pt'><span style='color:#444444'>I am not intending to have a discussion about the virtues of either single loop or double loop, so I have acknowledged that my observation can be used to support either model because the proponent can claim that either the radius of diameter supports their model. The important point is that the Schwinger limit supports any model which is a fraction of the Compton wavelength.<o:p></o:p></span></p><p style='margin:0in;margin-bottom:.0001pt;line-height:13.5pt'><span style='color:#444444'><o:p> </o:p></span></p><p style='margin:0in;margin-bottom:.0001pt;mso-line-height-alt:13.5pt'><b><span style='font-size:16.0pt;color:#444444'>Frame Dragging <o:p></o:p></span></b></p><p style='margin:0in;margin-bottom:.0001pt;line-height:13.5pt'><span style='color:#444444'><o:p> </o:p></span></p><p style='margin:0in;margin-bottom:.0001pt;line-height:13.5pt'><span style='color:#444444'>David also asked a question about frame dragging. I have recently worked out another part of my model which implies that it should produce frame dragging. However, I have not quantified the magnitude of the effect yet. The attached Word document is one short section of my revised chapter 10. I am not sure that you will be able to understand all the symbols because I have not gone back and made sure that this section can be read independently of the rest of the book. However, for anyone interested in this concept, here is the section that mentions frame dragging.<o:p></o:p></span></p><p style='margin:0in;margin-bottom:.0001pt;line-height:13.5pt'><span style='color:#444444'><o:p> </o:p></span></p><p style='margin:0in;margin-bottom:.0001pt;line-height:13.5pt'><span style='color:#444444'>I am nearly finished with my revised draft of the book. If anyone wants to read the revised chapters rather than the chapters written 18 months ago, I will be happy to send them to you.<o:p></o:p></span></p><p style='margin:0in;margin-bottom:.0001pt;line-height:13.5pt'><span style='color:#444444'><o:p> </o:p></span></p><p style='margin:0in;margin-bottom:.0001pt;line-height:13.5pt'><span style='color:#444444'>John M.<o:p></o:p></span></p><p class=MsoNormal><o:p> </o:p></p></div></body></html>