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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:12.0pt;line-height:106%;font-family:"Cambria Math",serif'>Vivian and All,<o:p></o:p></span></p><p class=MsoNormal style='margin-bottom:0in;margin-bottom:.0001pt'><span style='font-size:12.0pt;line-height:106%;font-family:"Cambria Math",serif'><o:p> </o:p></span></p><p class=MsoNormal><span style='font-size:12.0pt;line-height:106%;font-family:"Cambria Math",serif'>We all agree that collision experiments indicate that the size of an electron is smaller than the resolution of the collision experiment. Since some experiments have been done at about 50 GeV, this means that the electron appears to be smaller than about 10<sup>-18</sup> m. We have different models of an electron and they have different explanations for how an electron can appear to be a point particle. In a previous post you say, “</span><span style='font-size:12.0pt;line-height:106%;font-family:"Times New Roman",serif;color:#A50021'>I prefer the answers given by John W, Richard G, myself and others that the radius of an electron decreases with its energy, giving it a point like property as it travels at sufficiently high velocity.</span><span style='font-size:12.0pt;line-height:106%;font-family:"Times New Roman",serif'>” I will address this point. You seem to be saying that a fundamental particle </span><span style='font-size:12.0pt;line-height:106%;font-family:"Cambria Math",serif'>changes its radius in X, Y and Z dimensions as it propagates. As I recall, the radius decreases with 1/ã in one model and 1/ã<sup>2</sup> in another model. Also as I recall the decrease in radius is accompanied by an increase in the electron’s Compton frequency in some models. Perhaps I do not understand this concept correctly, but the change in radius and frequency appears to violate the covariance of physical laws. All frames of reference should have the same physical laws. Here is the problem. In order for the laws of physics to be the same in all frames of reference, Lorentz transformations have to hold between different frames of reference. The changes you propose do not correspond to Lorentz transformations. <o:p></o:p></span></p><p class=MsoNormal><span style='font-size:12.0pt;line-height:106%;font-family:"Cambria Math",serif'>Suppose that we designate the Z axis as the direction of propagation between two frames of reference. Then the expectation is that an observer in frame A would perceive that an electron in frame B retains its original radius in the X and Y dimensions while the Z axis dimension decreases by r = r<sub>o</sub>/ã. Also, the rate of time in frame B appears to slows down by 1/ã as seen from frame A. The Compton frequency can be considered a clock beat. Therefore the observer in frame A should perceive that the electron’s Compton frequency in frame B has slowed down rather than speed up. If the changes you propose take place, then an observer in frame B would perceive that an electron has different properties than the properties observed in frame A. This would be a violation of the basic assumption of invariance in spacial relativity.<o:p></o:p></span></p><p class=MsoNormal><span style='font-size:12.0pt;line-height:106%;font-family:"Cambria Math",serif'>Perhaps, the most important point is that the changes that you propose do not even achieve the goal of making the electron appear to be a point particle in a collision. Here is the reasoning. Suppose that we have two electrons accelerated to 50 GeV and propagating in opposite directions in an accelerator. I am in the acceleration frame of reference and the electrons will collide in front of me. If the collision is head-on, both electrons momentarily are stopped in my frame of reference at the moment of closest approach. Therefore at that moment neither electron is moving relative to me. They might have been small when they were moving, but when they have stopped in the collision, in your model they should have their original radius equal which you believe to be ½ the reduced Compton wavelength. Since the scattering is taking place in my frame of reference, the scattering should indicate this full size.<o:p></o:p></span></p><p class=MsoNormal><span style='font-size:12.0pt;line-height:106%;font-family:"Cambria Math",serif'>Contrast that to my model. I say that the electron appears to be the same size and have the same Compton frequency when viewed as a “stationary” electron in any frame of reference. This means that Lorentz transformations hold between frames. An electron in frame B retains the same radius in the X and Y dimensions but appears to shrink in the Z direction. Also the Compton frequency appears slower when observed from frame A. <o:p></o:p></span></p><p class=MsoNormal><span style='font-size:12.0pt;line-height:106%;font-family:"Cambria Math",serif'>However, the important point is not the size during propagation, but the size during collision. In my model, the size of each electron physically decreases when the two electrons collide and momentarily are stopped in my frame of reference. The kinetic energy carried by each electron has been converted to the internal energy of the waves that make up the two electrons. At the moment of collision, the wave amplitude increases and wave frequency increases. The Compton wavelength decreases, therefore <b>the radius decreases</b> when the colliding electrons are momentarily stopped. If the collision is at 50 GeV then ã = 100,000 and the radius decreases by this factor. The calculations are done in the “foundation” paper, in section 4.5, titled Point Particle Test. This section of the paper concludes that the reason that electrons appear to be point particles is that “It is a classic case of the experiment distorting the property being measured and invalidating the measurement”. <o:p></o:p></span></p><p class=MsoNormal><span style='font-size:12.0pt;line-height:106%;font-family:"Cambria Math",serif'>I also have other arguments supporting my electron size and characteristics, but this is enough for one post.<o:p></o:p></span></p><p class=MsoNormal><span style='font-size:12.0pt;line-height:106%;font-family:"Cambria Math",serif'><o:p> </o:p></span></p><p class=MsoNormal><span style='font-size:12.0pt;line-height:106%;font-family:"Cambria Math",serif'>John M.</span><span style='font-size:12.0pt;line-height:106%;font-family:"Times New Roman",serif'><o:p></o:p></span></p></div></body></html>