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<p class="MsoNormal"><span style="color:#1F497D">Dear John,<o:p></o:p></span></p>
<p class="MsoNormal"><span style="color:#1F497D">To put it into context, it would be good to refer to people who have considered these stability problems before. It is in fact one of the most important problems of all.<o:p></o:p></span></p>
<p class="MsoNormal"><span style="color:#1F497D">First of all Poincare’, who criticized the Abraham-Lorentz model for not being stable.<o:p></o:p></span></p>
<p class="MsoNormal"><span style="color:#1F497D">Second, Casimir, who suggested that the vacuum fluctuations could stabilize the electron. Not so, as proven by Timothy Boyer. Indeed the pressure in a sphere is higher than outside. This is different for an oblate
ellipsoid or a torus (private discussion between me, John W and Casimir).<o:p></o:p></span></p>
<p class="MsoNormal"><span style="color:#1F497D">Third Feynman, see for example chapter 28, Vol. II of the lectures.<o:p></o:p></span></p>
<p class="MsoNormal"><span style="color:#1F497D">Fourth, I once gave a key lecture for the Dutch Society of Plasma Physics in which I showed that all electrons in the universe could stabilize each other, but that was based on some questionable hypothesis. I
will look for the overhead slides, see if I can find them, just for a laugh.<o:p></o:p></span></p>
<p class="MsoNormal"><span style="color:#1F497D">There are many more, and some of us will actually talk about this at the conference (including me).<o:p></o:p></span></p>
<p class="MsoNormal"><span style="color:#1F497D">Take away message: important problem, difficult so not too many know how to cope with it. But fortunately it has not been ignored. Good that you think about it too.<o:p></o:p></span></p>
<p class="MsoNormal"><span style="color:#1F497D">Cheers, Martin<o:p></o:p></span></p>
<p class="MsoNormal"><span style="color:#1F497D"><o:p> </o:p></span></p>
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<span lang="DE" style="font-size:10.0pt;font-family:"Arial","sans-serif";color:navy">Dr. Martin B. van der Mark</span><span lang="DE" style="font-size:12.0pt;font-family:"Times New Roman","serif";color:navy"><o:p></o:p></span></p>
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<span style="font-size:10.0pt;font-family:"Arial","sans-serif";color:navy">Principal Scientist, Minimally Invasive Healthcare</span><span style="color:navy"><o:p></o:p></span></p>
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<span style="color:navy"> <o:p></o:p></span></p>
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<span style="font-size:10.0pt;font-family:"Arial","sans-serif";color:navy">Philips Research Europe - Eindhoven</span><span style="color:navy"><o:p></o:p></span></p>
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<span style="font-size:10.0pt;font-family:"Arial","sans-serif";color:navy">High Tech Campus, Building 34 (WB2.025)</span><span style="color:navy"><o:p></o:p></span></p>
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<span style="font-size:10.0pt;font-family:"Arial","sans-serif";color:navy">Prof. Holstlaan 4</span><span style="color:navy"><o:p></o:p></span></p>
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<span style="font-size:10.0pt;font-family:"Arial","sans-serif";color:navy">5656 AE Eindhoven, The Netherlands</span><span style="color:navy"><o:p></o:p></span></p>
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<span style="font-size:10.0pt;font-family:"Arial","sans-serif";color:navy">Tel: +31 40 2747548</span><span style="color:#1F497D"><o:p></o:p></span></p>
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<p class="MsoNormal"><span style="color:#1F497D"><o:p> </o:p></span></p>
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<b><span style="font-size:10.0pt;font-family:"Tahoma","sans-serif"">From:</span></b><span style="font-size:10.0pt;font-family:"Tahoma","sans-serif""> General [mailto:general-bounces+martin.van.der.mark=philips.com@lists.natureoflightandparticles.org]
<b>On Behalf Of </b>John Macken<br>
<b>Sent:</b> zondag 12 april 2015 9:05<br>
<b>To:</b> Nature of Light and Particles<br>
<b>Subject:</b> [General] Internal Pressure of an Electron<o:p></o:p></span></p>
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<p class="MsoNormal"><o:p> </o:p></p>
<p class="MsoNormal" style="margin-bottom:0cm;margin-bottom:.0001pt"><span style="font-size:14.0pt;line-height:105%;font-family:"Times New Roman","serif"">Hello everyone,<o:p></o:p></span></p>
<p class="MsoNormal" style="margin-bottom:0cm;margin-bottom:.0001pt"><span style="font-size:14.0pt;line-height:105%;font-family:"Times New Roman","serif""><o:p> </o:p></span></p>
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<span style="font-size:16.0pt;line-height:105%;font-family:"Times New Roman","serif"">Internal Pressure of an Electron</span><span style="font-size:14.0pt;line-height:105%;font-family:"Times New Roman","serif""><o:p></o:p></span></p>
<p class="MsoNormal" style="margin-bottom:0cm;margin-bottom:.0001pt"><span style="font-size:14.0pt;line-height:105%;font-family:"Times New Roman","serif""><o:p> </o:p></span></p>
<p class="MsoNormal" style="margin-bottom:0cm;margin-bottom:.0001pt"><span style="font-size:14.0pt;line-height:105%;font-family:"Times New Roman","serif"">Today I want to address an important consideration that has to be discussed when a quantifiable model
of an electron is proposed. When an electron model has energy propagating at the speed of light in a specific volume, then it is possible to calculate the implied energy density and the implied internal pressure. For example, energy density has units of J<b>/</b>m<sup>3</sup>
which in dimensional analysis terminology is: M/T<sup>2</sup>L (mass<b>/</b>time<sup>2</sup>length). Pressure has units of N/m<sup>2</sup> which also has the same dimensional analysis units of M/T<sup>2</sup>L. In other words, I believe that in all cases
energy density implies pressure. However, I will confine my comments to the implied pressure exerted by confining photons (or other spacetime waves) to a specific volume. This gives creates energy density and therefore implies pressure. For example, the reason
that stars do not undergo a gravitational collapse is that the photon pressure within the star is sufficient to oppose gravitational collapse and create the long life star structures that we know. For photons propagating in 3 dimensions, the relationship
between energy density <i>U</i> and pressure <i>P</i> is <i>U</i> = 3<i>P</i>. Now here is the problem. If you are making electrons out of a 511,000 eV photon confined to a spherical volume with a radius of 1.93x10<sup>-13</sup> m, then this is 8.19x10<sup>-14
</sup>Joule in a volume of 3x10<sup>‑38</sup> m<sup>3</sup>. This is an energy density of about 3x10<sup>24</sup> J/m<sup>3</sup> which is exerting a pressure of about 10<sup>24</sup> N/m<sup>2</sup>. What contains this tremendous pressure?<o:p></o:p></span></p>
<p class="MsoNormal" style="margin-bottom:0cm;margin-bottom:.0001pt"><span style="font-size:14.0pt;line-height:105%;font-family:"Times New Roman","serif""><o:p> </o:p></span></p>
<p class="MsoNormal" style="margin-bottom:0cm;margin-bottom:.0001pt"><span style="font-size:14.0pt;line-height:105%;font-family:"Times New Roman","serif"">This might seem like an argumentative type of question, but I believe that it is forcing people to go
beyond their comfort zone and confront questions which ultimately greatly improve the model.<o:p></o:p></span></p>
<p class="MsoNormal" style="margin-bottom:0cm;margin-bottom:.0001pt"><span style="font-size:14.0pt;line-height:105%;font-family:"Times New Roman","serif""><o:p> </o:p></span></p>
<p class="MsoNormal" style="margin-bottom:0cm;margin-bottom:.0001pt"><span style="font-size:14.0pt;line-height:105%;font-family:"Times New Roman","serif"">My model is not only a model of fundamental particles, but also a model of the energetic vacuum (the spacetime
field) and a model of forces. Since the spacetime field also has energy density, it also exerts pressure. The only particles that are stable or semi-stable are ones which achieve a type of resonance with the surrounding spacetime field and achieve an opposing
force (opposing pressure) which counteracts the particle’s internal pressure and stabilize the particle. This interaction creates a strain in the surrounding volume of spacetime. The linear portion of this strain we know as the particle’s electric/magnetic
field and the nonlinear portion of the strain is the particle’s gravitational field which we also call “curved spacetime”. For example, starting on page 8-11 of my book I calculate the gravitational force exerted on an electron in the earth’s gravity. The
calculation involves the internal pressure of the electron and the slight pressure difference exerted on opposite sides of the electron by the spacetime field. The rate of time gradient caused by the earth’s gravitational field is responsible for this slight
pressure difference. This calculation yields the correct gravitational force on an electron in the earth’s gravity with no analogy to acceleration.
<o:p></o:p></span></p>
<p class="MsoNormal" style="margin-bottom:0cm;margin-bottom:.0001pt"><span style="font-size:14.0pt;line-height:105%;font-family:"Times New Roman","serif""><o:p> </o:p></span></p>
<p class="MsoNormal"><span style="font-size:14.0pt;line-height:105%;font-family:"Times New Roman","serif"">For a long time I ignored the implied internal pressure of my particle model. Then I hit a problem that I could not solve. I was able to calculate the
correct gravitational force between my particles, but I finally realized that the implied force direction was repulsive rather than attractive. Initially I thought that this was a minor problem, but it grew worse when I realized that my calculation also implied
the continuous emission of energy from the particle. Finally I confronted the implied internal pressure. For example, my electron model has “dipole waves in spacetime” propagating at the speed of light in a limited volume. These waves are quantifiable energy
propagating at the speed of light in a single loop volume. This is similar to photons, and they also generate pressure in the range of 10<sup>24</sup> N/m<sup>2</sup>. Confronting this internal pressure allows a precise calculation of not only the electron’s
gravity, but also its inertia, and electrostatic force. In quarks the internal pressure also is a key component in the explanation of the strong force and even the explanation of asymptotic freedom of quarks in hadrons. In other words, incorporating this
internal pressure is key to explaining any of the forces exerted by fundamental particles.<o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-size:14.0pt;line-height:105%;font-family:"Times New Roman","serif""><o:p> </o:p></span></p>
<p class="MsoNormal"><span style="font-size:14.0pt;line-height:105%;font-family:"Times New Roman","serif"">John M.</span><span style="font-size:12.0pt;line-height:105%;font-family:"Times New Roman","serif""><o:p></o:p></span></p>
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