<html><head><meta http-equiv="Content-Type" content="text/html charset=windows-1252"></head><body style="word-wrap: break-word; -webkit-nbsp-mode: space; -webkit-line-break: after-white-space;" class=""><div class="">Hello Vivian,</div><div class=""><br class=""></div><div class=""> Thanks for your recent comments, and for resending your electron model article, which gave me an opportunity to take a second look at it. It is definitely a pioneering article, particularly since you were unaware of John and Martin’s 1997 article at the time.</div><div class=""><br class=""></div><div class=""> The last time I critiqued your article, I pointed out three significant errors, one of which (the error in calculating the electron’s magnetic moment) you acknowledged at the time. For the others, you said that experiment would be the best judge.</div><div class=""><br class=""></div><div class=""> But let me repeat the two other significant errors that I spotted, which affect other relativistic derivations in your article.</div><div class=""><br class=""></div><div class=""> The first error occurs when you derive the radius of the circular orbit of the double-looping photon of a moving electron, where the electron is moving in a direction perpendicular to the plane of the orbit. You called the time t as the time for the photon to move in the purely circular orbit, so 2 pi Ro = ct . Then you use the same value t in calculating the triangular distance relationships for a moving electron, which are (2 pi Rv)^2 = (vt)^ + (ct)^2 , where Rv is the radius of the particle when it it is moving at velocity v. In the first case, t is measured in the frame of the particle itself. In the second case, t is measured in the frame in which the particle is moving, as seen by a stationary observer. Your derivation is analogous to the standard derivation of relativistic time dilation for a moving “light clock” in which the light pulse is traveling up and down vertically (perpendicular to the direction of the horizontal movement of the light clock) in the frame of the stationary light-clock, but the reflecting light pulse follows a zig-zag trajectory for the horizontally-moving light clock (mounted on a moving train for example) as seen by a stationary observer. The point of the light-clock derivation is that since the speed of light c is accepted as constant as measured in both reference frames, the value of time elapsed between “tics" of the stationary clock and between “tics" of the moving light clock is not the same. But you called both of these times t in your derivation. Based on this, you calculated that the moving electron would have a transverse radius Rv = Ro/gamma . But by relativistic time dilation (which is what is actually derived in the light-clock thought experiment), the value of the second t in your derivation , as measured for the moving light-clock, should have been t’ = gamma t , due to relativistic time dilation for a moving electron as seen by a stationary observer. If you put t’ = t/gamma into your equation instead of putting the same t for both times, you will find that you get Rv= Ro instead of the value Rv=Ro/gamma that you found. In other words, the light clock (and your particle) does NOT contract in the direction perpendicular to the direction of motion of the particle. Special relativity predicts no relativistic length contraction perpendicular to the direction of motion of an object.</div><div class=""><br class=""></div><div class=""> You will see in my attached SPIE article “Electrons are spin-1/2 charged photons generation the de Broglie wavelength” that to get the change in the radius of the trajectory of the moving double-looping photon, you need to take into account that the moving electron is associated with a helically circulating photon whose frequency f is proportional to the total energy E=gamma mc^2 of the moving electron: hf = gamma mc^2 . The corresponding wavelength of this higher energy photon along its trajectory is easily found to be lambda = h/(gamma mc) . When this wavelength and frequency for the higher energy helically-moving photon are taken into account, the radius of the trajectory of the moving photon is found to decrease as Ro/gamma^2 as the speed of the electron increases. Now, the actual total radius of the helically circulating photon may decrease as Ro/gamma with increasing electron velocity, but this is a different story.</div><div class=""><br class=""></div><div class=""> The second significant error I pointed out to you before is that, near the end of your article, when using the relativistic energy-momentum equation (bottom of page 13), you add energies using the Pythagorean triangle: resting energy hFo + kinetic energy hFke = total electron energy hFv. But energies are scalar quantities and don’t add vectorially by the Pythagorean theorem. So the frequency Fke for your frequency corresponding to the kinetic energy of the moving electron has no physical meaning, and so to derive the de Broglie wavelength lambdaKE from this FrequencyKE has no physical meaning either.</div><div class=""><br class=""></div><div class=""> A better approach, as I show in my article, is to interpret the electron's relativistic energy-momentum equation E^2 = p^2 c^2 + m^2 c^4 as corresponding to the vector relationship of three MOMENTA: the transverse momentum of the circling photon mc in a resting electron, plus the longitudinal momentum of the linearly moving electron p=gamma mv, to give the total momentum P of these two momentum components, where P= E/c and E is the total energy of the helically moving charged photon forming the relativistically moving electron, which equals the total energy E of the moving relativistic electron. This momentum addition DOES corresponding to the Pythagorean theorem: P^2 = p^2 + (mc)^2 and to the relativistic energy-momentum equation. The de Broglie wavelength of the moving electron is derived from the wave vector K corresponding to the total momentum P of the helically-moving higher energy charged photon, since this wave vector K has a component k=K cos (theta)=K v/c along the longitudinal axis of the helical trajectory of the circulating charged photon. It is this longitudinal component of the higher energy helically moving photon that generates the relativistic de Broglie wavelength.</div><div class=""><br class=""></div><div class=""> with best regards,</div><div class=""> Richard</div><div class=""><br class=""></div><div class=""><br class=""></div><div class=""></div></body></html>