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</o:shapelayout></xml><![endif]--></head><body lang=EN-US link=blue vlink=purple><div class=WordSection1><p class=MsoNormal style='background:white'><span style='color:#222222'>Chip, John D, Chandra – </span><span style='font-size:14.0pt;color:#222222'>Interaction of Waves</span><span style='color:#222222'><o:p></o:p></span></p><p class=MsoNormal style='background:white'><span style='color:#222222'><o:p> </o:p></span></p><p class=MsoNormal style='background:white'><span style='color:#222222'>I take the position that all waves propagating in a finite medium interact. The easiest to prove example of this is with sound waves propagating in a gas. When sound waves propagate in a gas, the compression part of a sound wave causes an increase in temperature and the expansion part of the sound wave produces a decrease in temperature. Since the speed of sound is temperature dependent, this means that a sound wave produces a modulation of the speed of sound in the propagating medium. Another frequency sound wave propagation in the same volume of gas and the same direction will encounter this modulation in the speed of sound and produce a second order effect which is new sound waves at the sum and difference frequency. I recall that there is experimental proof of the interaction of sound waves, but I have not attempted to find a reference.<o:p></o:p></span></p><p class=MsoNormal style='background:white'><span style='color:#222222'><o:p> </o:p></span></p><p class=MsoNormal style='background:white'><span style='color:#222222'>Water waves have also been mentioned as examples of the non-interaction of waves. If the depth of the water is infinite and the speed of sound in water is vastly larger than the speed of the water wave, then there appears to be no interaction between water waves. However, imagine an experiment where the water in in a shallow flat bottom pond. If the amplitude of the wave is on the order of half the depth of the pond, then nonlinearities become noticeable and there would be detectable interaction between waves. In the limit, there is a definable maximum amplitude of the water wave. This occurs when the wave minimum equals the depth of the pond. Similarly, when the sound wave produces a vacuum at its minimum, this is the limiting condition. <o:p></o:p></span></p><p class=MsoNormal style='background:white'><span style='color:#222222'> <o:p></o:p></span></p><p class=MsoNormal style='background:white'><span style='color:#222222'>Another clear example with a great deal of proof is the interaction of two beams of laser light interacting in a nonlinear medium. There is the optical Kerr effect which changes the index of refraction of the propagation medium. All transparent mediums including glass and even air exhibit the optical Kerr effect. Here is a quote from Wikipedia.<o:p></o:p></span></p><p class=MsoNormal style='background:white'><span style='color:#222222'> <o:p></o:p></span></p><p class=MsoNormal style='background:white'><span style='color:#660033'>"<span style='background:white'>The optical Kerr effect, or AC Kerr effect is the case in which the electric field is due to the light itself. This causes a variation in index of refraction which is proportional to the local </span><a href="https://en.wikipedia.org/wiki/Irradiance" title=Irradiance><span style='color:#660033;background:white;text-decoration:none'>irradiance</span></a><span style='background:white'> of the light.<sup><a href="https://en.wikipedia.org/wiki/Kerr_effect#cite_note-3"><span style='color:#660033;text-decoration:none'>[3]</span></a></sup> This refractive index variation is responsible for the </span><a href="https://en.wikipedia.org/wiki/Nonlinear_optics" title="Nonlinear optics"><span style='color:#660033;background:white;text-decoration:none'>nonlinear optical</span></a><span style='background:white'> effects of </span><a href="https://en.wikipedia.org/wiki/Self-focusing" title=Self-focusing><span style='color:#660033;background:white;text-decoration:none'>self-focusing</span></a><span style='background:white'>, </span><a href="https://en.wikipedia.org/wiki/Self-phase_modulation" title="Self-phase modulation"><span style='color:#660033;background:white;text-decoration:none'>self-phase modulation</span></a><span style='background:white'> and </span><a href="https://en.wikipedia.org/wiki/Modulational_instability" title="Modulational instability"><span style='color:#660033;background:white;text-decoration:none'>modulational instability</span></a><span style='background:white'>, and is the basis for </span><a href="https://en.wikipedia.org/wiki/Kerr-lens_modelocking" title="Kerr-lens modelocking"><span style='color:#660033;background:white;text-decoration:none'>Kerr-lens modelocking</span></a><span style='background:white'>. This effect only becomes significant with very intense beams such as those from </span><a href="https://en.wikipedia.org/wiki/Laser" title=Laser><span style='color:#660033;background:white;text-decoration:none'>lasers</span></a><span style='background:white'>."<o:p></o:p></span></span></p><p class=MsoNormal style='background:white'><span style='color:#222222'><o:p> </o:p></span></p><p class=MsoNormal style='background:white'><span style='color:#252525;background:white'>There is a long list of nonlinear effects using laser beams in nonlinear crystals including sum frequency generation, difference frequency generation and second harmonic generation. These examples of nonlinear effects in a transparent optical material illustrate an important point. The optical medium has a finite ability to transmit light. The optical material is made of atoms which are bonded together by finite electrostatic forces. When the intensity of one or more laser beams reaches a level that the electrostatic bonding force is noticeably approached, then we detect a nonlinear optical effect. However, even at undetectable levels the nonlinearity is still present because of the finite properties of the transparent medium set a boundary condition. For example, even sunlight passing through a glass window produces a slight change in the index of refraction of the window. <o:p></o:p></span></p><p class=MsoNormal style='background:white'><span style='color:#252525;background:white'><o:p> </o:p></span></p><p class=MsoNormal style='background:white'><span style='color:#252525;background:white'>These examples set the stage for the big question: Does the vacuum of spacetime have a limiting boundary condition which produces nonlinear effects on light as this limit is approached? We know that Planck force (c<sup>4</sup></span><span style='font-family:"Cambria Math",serif;color:#252525;background:white'>/</span><span style='color:#252525;background:white'>G = 1.2 x 10<sup>44</sup> N) is a maximum possible force. I once referenced a paper which showed that all of general relativity could be derived by assuming this boundary condition. The speed of light is another boundary condition. In fact, Planck length, Planck frequency, Planck energy etc. are also boundary conditions when properly applied. Therefore, I am setting the stage to make the claim that light waves interact when the intensity reaches the level that the boundary conditions (nonlinear conditions) of spacetime become detectable. <br><br></span><span style='color:#222222'><o:p></o:p></span></p><p class=MsoNormal><span style='color:#252525;background:white'>Chandra has written extensively on the non-interaction of waves. This is a very useful concept to understand optical effects at ordinary intensities. I have not said anything challenging this before because he is correct for all experiments which can currently be conducted with available technology. However, I maintain that he is not correct at the extreme limits of high intensity light which produce nonlinear effects in the vacuum. This statement is analogous to saying that Newton's gravitational equation is very useful for calculating ordinary gravitational interactions. However, there is a nonlinearity as the limiting properties of spacetime are approached.</span><span style='color:#252525;background:white'> General relativity is required when the nonlinear effects become important. </span><span style='color:#252525;background:white'><o:p></o:p></span></p><p class=MsoNormal><span style='color:#252525;background:white'><o:p> </o:p></span></p><p class=MsoNormal><span style='color:#252525;background:white'>To prove these points, it is necessary to have a model of an electrically charged particle, electric field and a photon. I have developed a model of these, but I want to tell a story about an experience I had during this process. I asked the question: What is the smallest volume that I can physically confine a photon? A circularly polarized photon can be confined in a cylindrical waveguide that is slightly more than ½ wavelength in diameter with flat reflecting end separated by ½ wavelength. I define this as “maximum confinement”. There are several more steps but I concluded that a single photon would produce a Planck length polarized distortion of spacetime that modulates the transverse distance across the waveguide diameter by plus and minus Planck length (designated <i>L<sub>p</sub></i>) at the frequency of the photon. Multiple coherent photons, designated as “n” photons, would increase this modulation by the square root of n (by</span><!--[if gte msEquation 12]><m:oMath><i><span style='font-family:"Cambria Math",serif;color:#252525;background:white'><m:r> </m:r><m:r>ΔL</m:r><m:r>= </m:r></span></i><m:rad><m:radPr><m:degHide m:val="on"/><span style='font-family:"Cambria Math",serif;color:#252525;background:white;font-style:italic'><m:ctrlPr></m:ctrlPr></span></m:radPr><m:deg></m:deg><m:e><i><span style='font-family:"Cambria Math",serif;color:#252525;background:white'><m:r>n</m:r></span></i></m:e></m:rad><m:sSub><m:sSubPr><span style='font-family:"Cambria Math",serif;color:#252525;background:white;font-style:italic'><m:ctrlPr></m:ctrlPr></span></m:sSubPr><m:e><i><span style='font-family:"Cambria Math",serif;color:#252525;background:white'><m:r>L</m:r></span></i></m:e><m:sub><i><span style='font-family:"Cambria Math",serif;color:#252525;background:white'><m:r>p</m:r></span></i></m:sub></m:sSub></m:oMath><![endif]--><![if !msEquation]><span style='font-size:12.0pt;font-family:"Times New Roman",serif;position:relative;top:4.5pt;mso-text-raise:-4.5pt;mso-fareast-language:EN-US'><img width=83 height=22 style='width:.8645in;height:.2291in' id="_x0000_i1025" src="cid:image002.png@01D27BC5.C004A7B0"></span><![endif]><span style='color:#252525;background:white'>). Then I was struck by a serious doubt because if this model of a photon was correct, it was predicting that there was a maximum number of photons which could be put into this maximum confinement waveguide. The limiting condition was when </span><span style='font-family:"Cambria Math",serif;color:#252525;background:white'>the modulating distance equaled ½ wavelength which is the diameter of the waveguide. This would be 100% modulation of the properties of spacetime at the frequency of the photon. A different frequency would achieve this limit at a different intensity, but in all cased the model was predicting a limit. This seemed impossible, but I quickly calculated the condition that would produce this limit. To my surprise, it exactly equaled the energy density of photons that would produce a black hole with the diameter of the waveguide. What I thought would be a proof that I was wrong turned out to be a proof supporting the model. An experiment with the intensity required to achieve a detectable modulation of distance is beyond our current technology, but it is not necessary to do an experiment. A simple calculation proves that the predicted limiting condition forma a black hole. If it was possible to arbitrarily increase the power of a focused laser beam, then there would be a limit where the modulation of spacetime at the focus reached the predicted 100% modulation condition. No more light would be transmitted through this volume because a black hole would form. No further transmission would be possible. <o:p></o:p></span></p><p class=MsoNormal><span style='font-family:"Cambria Math",serif;color:#252525;background:white'><o:p> </o:p></span></p><p class=MsoNormal><span style='font-family:"Cambria Math",serif;color:#252525;background:white'>The same model that achieved this success predicts that at a very high intensity approaching the formation of a black hole, the nonlinear properties of spacetime become obvious and there would be detectable “interaction of waves”.<o:p></o:p></span></p><p class=MsoNormal><span style='font-family:"Cambria Math",serif;color:#252525;background:white'><o:p> </o:p></span></p><p class=MsoNormal><span style='font-family:"Cambria Math",serif;color:#252525;background:white'>All of this is documented in technical papers and my book. For further reading I suggest first reading the paper I posted on January 21 titled “Gravitational waves indicate vacuum energy exists”. This paper has recently been submitted to a technical journal. It sets the stage defining the properties of spacetime. The paper titled “Spacetime based foundation of quantum mechanics and general relativity” gives the quantifiable model of particles and photons. It also describes in more detail the photon thought experiment just described. Pages 13 to 16 of this paper describe the quantifiable model of electrical charge, photons and the maximum confinement thought experiment. This paper is available at: <o:p></o:p></span></p><p class=MsoNormal><a href="https://www.researchgate.net/publication/264311427_Spacetime_Based_Foundation_of_Quantum_Mechanics_and_General_Relativity">https://www.researchgate.net/publication/264311427_Spacetime_Based_Foundation_of_Quantum_Mechanics_and_General_Relativity</a><span class=MsoHyperlink><o:p></o:p></span></p><p class=MsoNormal><span style='font-family:"Cambria Math",serif;color:#252525;background:white'> <o:p></o:p></span></p><p class=MsoNormal><span style='font-family:"Cambria Math",serif;color:#252525;background:white'>John Macken </span><span style='color:#252525;background:white'> </span><o:p></o:p></p><p class=MsoNormal><span style='color:#20188C'><o:p> </o:p></span></p><p class=MsoNormal><span style='color:#20188C'><o:p> </o:p></span></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'>From:</span></b><span style='font-size:11.0pt;font-family:"Calibri",sans-serif'> General [mailto:general-bounces+john=macken.com@lists.natureoflightandparticles.org] <b>On Behalf Of </b>Chip Akins<br><b>Sent:</b> Tuesday, January 31, 2017 10:35 AM<br><b>To:</b> 'Nature of Light and Particles - General Discussion' <general@lists.natureoflightandparticles.org><br><b>Subject:</b> Re: [General] On photon momentum<o:p></o:p></span></p></div></div><p class=MsoNormal><o:p> </o:p></p><p class=MsoNormal><span style='color:black'>Hi John D<o:p></o:p></span></p><p class=MsoNormal><span style='color:black'><o:p> </o:p></span></p><p class=MsoNormal><span style='color:black'>Thank you. Now I understand what you are saying, and the mechanics behind it. In your example, as the large ocean waves crest, the density is greater in the water, and less in the valleys, net zero, but still it causes temporary changes in direction of the small intersecting waves because any change in density causes the small wave to change directions (standard refraction).<o:p></o:p></span></p><p class=MsoNormal><span style='color:black'><o:p> </o:p></span></p><p class=MsoNormal><span style='color:black'>I can model (simulate) this effect. I will do that to see what the conditions would have to be to get a closed circular wave.<o:p></o:p></span></p><p class=MsoNormal><span style='color:black'><o:p> </o:p></span></p><p class=MsoNormal><span style='color:black'>Chip<o:p></o:p></span></p><p class=MsoNormal><span style='color:black'><o:p> </o:p></span></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'>From:</span></b><span style='font-size:11.0pt;font-family:"Calibri",sans-serif'> General [</span><a href="mailto:general-bounces+chipakins=gmail.com@lists.natureoflightandparticles.org"><span style='font-size:11.0pt;font-family:"Calibri",sans-serif'>mailto:general-bounces+chipakins=gmail.com@lists.natureoflightandparticles.org</span></a><span style='font-size:11.0pt;font-family:"Calibri",sans-serif'>] <b>On Behalf Of </b>John Duffield<br><b>Sent:</b> Tuesday, January 31, 2017 12:21 PM<br><b>To:</b> 'Nature of Light and Particles - General Discussion' <</span><a href="mailto:general@lists.natureoflightandparticles.org"><span style='font-size:11.0pt;font-family:"Calibri",sans-serif'>general@lists.natureoflightandparticles.org</span></a><span style='font-size:11.0pt;font-family:"Calibri",sans-serif'>><br><b>Subject:</b> Re: [General] On photon momentum<o:p></o:p></span></p></div></div><p class=MsoNormal><o:p> </o:p></p><p class=MsoNormal><span lang=EN-GB style='font-size:11.0pt;font-family:"Calibri",sans-serif;color:#1F497D'>Chip:<o:p></o:p></span></p><p class=MsoNormal><span lang=EN-GB style='font-size:11.0pt;font-family:"Calibri",sans-serif;color:#1F497D'><o:p> </o:p></span></p><p class=MsoNormal><span lang=EN-GB style='font-size:11.0pt;font-family:"Calibri",sans-serif;color:#1F497D'>Yes, you’re missing the simplicity of it. I didn’t actually say light refracts light. I said it causes a path change. This does occur in water. Think of an oceanic swell wave. I gazed at them a few years back when I was on a cruise. An oceanic swell wave is maybe 200m wide with a wavelength of maybe 100m, and maybe 3m high. Now imagine an ordinary little 1m wave intersecting it. The little wave goes up and over the big wave. Whilst it does so it changes path. Its path started straight and ended up straight, but whilst the little wave was going <i>over</i> the big wave, its path was curved. If this didn’t happen, and if waves just went straight through one another, you wouldn’t get “monster” waves. You can imagine a similar scenario with seismic waves and sound wave. If the ground is displaced to the North by 1 metre, this alters the path of a sound wave through the ground. <o:p></o:p></span></p><p class=MsoNormal><span lang=EN-GB style='font-size:11.0pt;font-family:"Calibri",sans-serif;color:#1F497D'><o:p> </o:p></span></p><p class=MsoNormal><span lang=EN-GB style='font-size:11.0pt;font-family:"Calibri",sans-serif;color:#1F497D'>Regards<o:p></o:p></span></p><p class=MsoNormal><span lang=EN-GB style='font-size:11.0pt;font-family:"Calibri",sans-serif;color:#1F497D'>JohnD <o:p></o:p></span></p><p class=MsoNormal><span lang=EN-GB style='font-size:11.0pt;font-family:"Calibri",sans-serif;color:#1F497D'><o:p> </o:p></span></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'>From:</span></b><span style='font-size:11.0pt;font-family:"Calibri",sans-serif'> General [</span><a href="mailto:general-bounces+johnduffield=btconnect.com@lists.natureoflightandparticles.org"><span style='font-size:11.0pt;font-family:"Calibri",sans-serif'>mailto:general-bounces+johnduffield=btconnect.com@lists.natureoflightandparticles.org</span></a><span style='font-size:11.0pt;font-family:"Calibri",sans-serif'>] <b>On Behalf Of </b>Chip Akins<br><b>Sent:</b> 31 January 2017 13:15<br><b>To:</b> 'Nature of Light and Particles - General Discussion' <</span><a href="mailto:general@lists.natureoflightandparticles.org"><span style='font-size:11.0pt;font-family:"Calibri",sans-serif'>general@lists.natureoflightandparticles.org</span></a><span style='font-size:11.0pt;font-family:"Calibri",sans-serif'>><br><b>Subject:</b> Re: [General] On photon momentum<o:p></o:p></span></p></div></div><p class=MsoNormal><span lang=EN-GB><o:p> </o:p></span></p><p class=MsoNormal><span style='color:black'>Hi John D<o:p></o:p></span></p><p class=MsoNormal><span style='color:black'><o:p> </o:p></span></p><p class=MsoNormal><span style='color:black'>You are saying that light refracts light. Is there any experimental evidence?<o:p></o:p></span></p><p class=MsoNormal><span style='color:black'><o:p> </o:p></span></p><p class=MsoNormal><span style='color:black'>I have not found any evidence that waves of any sort behave in this manner, including water waves.<o:p></o:p></span></p><p class=MsoNormal><span style='color:black'><o:p> </o:p></span></p><p class=MsoNormal><span style='color:black'>Do you have any supporting information?<o:p></o:p></span></p><p class=MsoNormal><span style='color:black'><o:p> </o:p></span></p><p class=MsoNormal><span style='color:black'>The refraction of water waves in the ocean, as I understand it, is generally due to the depth of the water changing near the shore, or due to an object, not due to other waves.<o:p></o:p></span></p><p class=MsoNormal><span style='color:black'><o:p> </o:p></span></p><p class=MsoNormal><span style='color:black'>When we use a ripple tank, we see interference, but not a change in direction of the waves when they interact.<o:p></o:p></span></p><p class=MsoNormal><span style='color:black'><o:p> </o:p></span></p><p class=MsoNormal><span style='color:black'>Am I missing something here?<o:p></o:p></span></p><p class=MsoNormal><span style='color:black'><o:p> </o:p></span></p><p class=MsoNormal><span style='color:black'>Chip<o:p></o:p></span></p><p class=MsoNormal><span style='color:black'><o:p> </o:p></span></p><p class=MsoNormal><span style='color:black'><o:p> </o:p></span></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'>From:</span></b><span style='font-size:11.0pt;font-family:"Calibri",sans-serif'> General [</span><a href="mailto:general-bounces+chipakins=gmail.com@lists.natureoflightandparticles.org"><span style='font-size:11.0pt;font-family:"Calibri",sans-serif'>mailto:general-bounces+chipakins=gmail.com@lists.natureoflightandparticles.org</span></a><span style='font-size:11.0pt;font-family:"Calibri",sans-serif'>] <b>On Behalf Of </b>John Duffield<br><b>Sent:</b> Monday, January 30, 2017 1:43 PM<br><b>To:</b> 'Nature of Light and Particles - General Discussion' <</span><a href="mailto:general@lists.natureoflightandparticles.org"><span style='font-size:11.0pt;font-family:"Calibri",sans-serif'>general@lists.natureoflightandparticles.org</span></a><span style='font-size:11.0pt;font-family:"Calibri",sans-serif'>><br><b>Subject:</b> Re: [General] On photon momentum<o:p></o:p></span></p></div></div><p class=MsoNormal><o:p> </o:p></p><p class=MsoNormal><span lang=EN-GB style='font-size:11.0pt;font-family:"Calibri",sans-serif;color:#1F497D'>Chip:<o:p></o:p></span></p><p class=MsoNormal><span lang=EN-GB style='font-size:11.0pt;font-family:"Calibri",sans-serif;color:#1F497D'><o:p> </o:p></span></p><p class=MsoNormal><span lang=EN-GB style='font-size:11.0pt;font-family:"Calibri",sans-serif;color:#1F497D'>When an ocean wave moves over another ocean wave, the curvature of the “up and over” path depends on the amplitude and wavelength of the other wave. If however all ocean waves were 1m high, the curvature of the path waves would depend only on the wavelength. Given what I said about h, when an electromagnetic wave moves through itself, the curvature of its path depends on the wavelength. So for the Dirac spinor, there’s only one wavelength where that curved path is a closed path: <o:p></o:p></span></p><p class=MsoNormal><span lang=EN-GB style='font-size:11.0pt;font-family:"Calibri",sans-serif;color:#1F497D'><o:p> </o:p></span></p><p class=MsoNormal><span style='font-size:11.0pt;font-family:"Calibri",sans-serif;color:#1F497D'><img border=0 width=279 height=267 style='width:2.9062in;height:2.7812in' id="_x0000_i1026" src="cid:image005.jpg@01D27BC5.57E1B830" alt="cid:image001.jpg@01D27BBE.171E7380"></span><span lang=EN-GB style='font-size:11.0pt;font-family:"Calibri",sans-serif;color:#1F497D'><o:p></o:p></span></p><p class=MsoNormal><span lang=EN-GB style='font-size:11.0pt;font-family:"Calibri",sans-serif;color:#1F497D'><o:p> </o:p></span></p><p class=MsoNormal><span lang=EN-GB style='font-size:11.0pt;font-family:"Calibri",sans-serif;color:#1F497D'>Regards<o:p></o:p></span></p><p class=MsoNormal><span lang=EN-GB style='font-size:11.0pt;font-family:"Calibri",sans-serif;color:#1F497D'>John D<o:p></o:p></span></p><p class=MsoNormal><span lang=EN-GB style='font-size:11.0pt;font-family:"Calibri",sans-serif;color:#1F497D'><o:p> </o:p></span></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'>From:</span></b><span style='font-size:11.0pt;font-family:"Calibri",sans-serif'> General [</span><a href="mailto:general-bounces+johnduffield=btconnect.com@lists.natureoflightandparticles.org"><span style='font-size:11.0pt;font-family:"Calibri",sans-serif'>mailto:general-bounces+johnduffield=btconnect.com@lists.natureoflightandparticles.org</span></a><span style='font-size:11.0pt;font-family:"Calibri",sans-serif'>] <b>On Behalf Of </b>Chip Akins<br><b>Sent:</b> 30 January 2017 14:31<br><b>To:</b> 'Nature of Light and Particles - General Discussion' <</span><a href="mailto:general@lists.natureoflightandparticles.org"><span style='font-size:11.0pt;font-family:"Calibri",sans-serif'>general@lists.natureoflightandparticles.org</span></a><span style='font-size:11.0pt;font-family:"Calibri",sans-serif'>><br><b>Subject:</b> Re: [General] On photon momentum<o:p></o:p></span></p></div></div><p class=MsoNormal><span lang=EN-GB><o:p> </o:p></span></p><p class=MsoNormal><span style='color:black'>Hi John D<o:p></o:p></span></p><p class=MsoNormal><span style='color:black'><o:p> </o:p></span></p><p class=MsoNormal><span style='color:black'>The amplitude of the wave not being the size of the wave makes sense in this context.<o:p></o:p></span></p><p class=MsoNormal><span style='color:black'><o:p> </o:p></span></p><p class=MsoNormal><span style='color:black'>But if the electron’s mass is somehow dependent on the amplitude always being the same, then how does that relate to…<o:p></o:p></span></p><p class=MsoNormal><span lang=EN-GB style='color:#2E75B6'>If you’re going to “wrap up” a wave into a spin ½ spinor to make a stable standing-wave standing-field particle, only one wavelength will do. <o:p></o:p></span></p><p class=MsoNormal><span lang=EN-GB style='color:#2E75B6'><o:p> </o:p></span></p><p class=MsoNormal><span lang=EN-GB>Wavelength is size. <o:p></o:p></span></p><p class=MsoNormal><span lang=EN-GB><o:p> </o:p></span></p><p class=MsoNormal><span lang=EN-GB>So how do we equate amplitude and wavelength to make this electron with the size and mass it has in nature?<o:p></o:p></span></p><p class=MsoNormal><span lang=EN-GB>How do we show that only one wavelength will work?<o:p></o:p></span></p><p class=MsoNormal><span lang=EN-GB><o:p> </o:p></span></p><p class=MsoNormal><span lang=EN-GB>Chip<o:p></o:p></span></p><p class=MsoNormal><span style='color:black'><o:p> </o:p></span></p><p class=MsoNormal><span style='color:black'><o:p> </o:p></span></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'>From:</span></b><span style='font-size:11.0pt;font-family:"Calibri",sans-serif'> General [</span><a href="mailto:general-bounces+chipakins=gmail.com@lists.natureoflightandparticles.org"><span style='font-size:11.0pt;font-family:"Calibri",sans-serif'>mailto:general-bounces+chipakins=gmail.com@lists.natureoflightandparticles.org</span></a><span style='font-size:11.0pt;font-family:"Calibri",sans-serif'>] <b>On Behalf Of </b>John Duffield<br><b>Sent:</b> Sunday, January 29, 2017 5:16 PM<br><b>To:</b> 'Nature of Light and Particles - General Discussion' <</span><a href="mailto:general@lists.natureoflightandparticles.org"><span style='font-size:11.0pt;font-family:"Calibri",sans-serif'>general@lists.natureoflightandparticles.org</span></a><span style='font-size:11.0pt;font-family:"Calibri",sans-serif'>><br><b>Subject:</b> Re: [General] On photon momentum<o:p></o:p></span></p></div></div><p class=MsoNormal><o:p> </o:p></p><p class=MsoNormal><span lang=EN-GB style='font-size:14.0pt;font-family:"Calibri",sans-serif;color:#1F497D'>Chip:<o:p></o:p></span></p><p class=MsoNormal><span lang=EN-GB style='font-size:14.0pt;font-family:"Calibri",sans-serif;color:#1F497D'><o:p> </o:p></span></p><p class=MsoNormal><span lang=EN-GB style='font-size:14.0pt;font-family:"Calibri",sans-serif;color:#1F497D'>My thoughts? The amplitude of a wave isn’t the size of the wave.<o:p></o:p></span></p><p class=MsoNormal><span lang=EN-GB style='font-size:14.0pt;font-family:"Calibri",sans-serif;color:#1F497D'><o:p> </o:p></span></p><p class=MsoNormal><span lang=EN-GB style='font-size:14.0pt;font-family:"Calibri",sans-serif;color:#1F497D'>Think of a seismic wave with an amplitude of 1 metre. It moves from West to East. As it does, your house shakes 1 metre to the North, then 1 metre to the South. At the same time a house 10km North shakes 10cm to the North, then 10cm to the South. A house 100 km North shakes 1cm to the North then 1cm to the South. Et cetera. <o:p></o:p></span></p><p class=MsoNormal><span lang=EN-GB style='font-size:14.0pt;font-family:"Calibri",sans-serif;color:#1F497D'><o:p> </o:p></span></p><p class=MsoNormal><span lang=EN-GB style='font-size:14.0pt;font-family:"Calibri",sans-serif;color:#1F497D'>Regards<o:p></o:p></span></p><p class=MsoNormal><span lang=EN-GB style='font-size:14.0pt;font-family:"Calibri",sans-serif;color:#1F497D'>JohnD<o:p></o:p></span></p><p class=MsoNormal><span lang=EN-GB style='font-size:11.0pt;font-family:"Calibri",sans-serif;color:#1F497D'><o:p> </o:p></span></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'>From:</span></b><span style='font-size:11.0pt;font-family:"Calibri",sans-serif'> General [</span><a href="mailto:general-bounces+johnduffield=btconnect.com@lists.natureoflightandparticles.org"><span style='font-size:11.0pt;font-family:"Calibri",sans-serif'>mailto:general-bounces+johnduffield=btconnect.com@lists.natureoflightandparticles.org</span></a><span style='font-size:11.0pt;font-family:"Calibri",sans-serif'>] <b>On Behalf Of </b>Chip Akins<br><b>Sent:</b> 29 January 2017 22:58<br><b>To:</b> 'Nature of Light and Particles - General Discussion' <</span><a href="mailto:general@lists.natureoflightandparticles.org"><span style='font-size:11.0pt;font-family:"Calibri",sans-serif'>general@lists.natureoflightandparticles.org</span></a><span style='font-size:11.0pt;font-family:"Calibri",sans-serif'>><br><b>Subject:</b> Re: [General] On photon momentum<o:p></o:p></span></p></div></div><p class=MsoNormal><span lang=EN-GB><o:p> </o:p></span></p><p class=MsoNormal><span style='color:black'>Hi John D<o:p></o:p></span></p><p class=MsoNormal><span style='color:black'><o:p> </o:p></span></p><p class=MsoNormal><span style='color:black'>Yes Planck’s constant applies to all wavelengths. However experimental evidence and experience tell us that the transverse physical size of a wave gets smaller as the longitudinal wavelength gets smaller with energy. <o:p></o:p></span></p><p class=MsoNormal><span style='color:black'><o:p> </o:p></span></p><p class=MsoNormal><span style='color:black'>An opening which will allow a high frequency wave to pass through, will also completely block a significantly lower wavelength from passing.<o:p></o:p></span></p><p class=MsoNormal><span style='color:black'><o:p> </o:p></span></p><p class=MsoNormal><span style='color:black'>So it seems that all wavelengths do not have the same physical transverse extents.<o:p></o:p></span></p><p class=MsoNormal><span style='color:black'>(My thoughts are that the wave extents are the wavelength / 2 pi. This seems to match the evidence and works well in the RF spectrum for system design considerations. Openings in Faraday shielding, unshielded trace lengths etc. need to be kept within a prescribed limit (fraction of a wavelength) based on the expected interfering frequency and the attenuation required.)<o:p></o:p></span></p><p class=MsoNormal><span style='color:black'><o:p> </o:p></span></p><p class=MsoNormal><span style='color:black'>Your thoughts?<o:p></o:p></span></p><p class=MsoNormal><span style='color:black'><o:p> </o:p></span></p><p class=MsoNormal><span style='color:black'>Chip<o:p></o:p></span></p><p class=MsoNormal><span style='color:black'><o:p> </o:p></span></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'>From:</span></b><span style='font-size:11.0pt;font-family:"Calibri",sans-serif'> General [</span><a href="mailto:general-bounces+chipakins=gmail.com@lists.natureoflightandparticles.org"><span style='font-size:11.0pt;font-family:"Calibri",sans-serif'>mailto:general-bounces+chipakins=gmail.com@lists.natureoflightandparticles.org</span></a><span style='font-size:11.0pt;font-family:"Calibri",sans-serif'>] <b>On Behalf Of </b>John Duffield<br><b>Sent:</b> Sunday, January 29, 2017 2:37 PM<br><b>To:</b> 'Nature of Light and Particles - General Discussion' <</span><a href="mailto:general@lists.natureoflightandparticles.org"><span style='font-size:11.0pt;font-family:"Calibri",sans-serif'>general@lists.natureoflightandparticles.org</span></a><span style='font-size:11.0pt;font-family:"Calibri",sans-serif'>><br><b>Subject:</b> Re: [General] On photon momentum<o:p></o:p></span></p></div></div><p class=MsoNormal><o:p> </o:p></p><p class=MsoNormal><span lang=EN-GB style='font-size:11.0pt;font-family:"Calibri",sans-serif;color:#1F497D'>Chip:<o:p></o:p></span></p><p class=MsoNormal><span lang=EN-GB style='font-size:11.0pt;font-family:"Calibri",sans-serif;color:#1F497D'><o:p> </o:p></span></p><p class=MsoNormal><span lang=EN-GB style='font-size:11.0pt;font-family:"Calibri",sans-serif;color:#1F497D'>Planck’s constant h is common to all photons regardless of wavelength. Look at those pictures of the electromagnetic spectrum. Irrespective of wavelength, the depicted amplitude is always the same. <o:p></o:p></span></p><p class=MsoNormal><span lang=EN-GB style='font-size:11.0pt;font-family:"Calibri",sans-serif;color:#1F497D'>If you’re going to “wrap up” a wave into a spin ½ spinor to make a stable standing-wave standing-field particle, only one wavelength will do. <o:p></o:p></span></p><p class=MsoNormal><span lang=EN-GB style='font-size:11.0pt;font-family:"Calibri",sans-serif;color:#1F497D'><o:p> </o:p></span></p><p class=MsoNormal><span lang=EN-GB style='font-size:11.0pt;font-family:"Calibri",sans-serif;color:#1F497D'>As for which characteristic of space, I’m not sure. Perhaps it’s something like an elastic limit. <o:p></o:p></span></p><p class=MsoNormal><span lang=EN-GB style='font-size:11.0pt;font-family:"Calibri",sans-serif;color:#1F497D'><o:p> </o:p></span></p><p class=MsoNormal><span lang=EN-GB style='font-size:11.0pt;font-family:"Calibri",sans-serif;color:#1F497D'>Regards<o:p></o:p></span></p><p class=MsoNormal><span lang=EN-GB style='font-size:11.0pt;font-family:"Calibri",sans-serif;color:#1F497D'>JohnD<o:p></o:p></span></p><p class=MsoNormal><span lang=EN-GB style='font-size:11.0pt;font-family:"Calibri",sans-serif;color:#1F497D'><o:p> </o:p></span></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'>From:</span></b><span style='font-size:11.0pt;font-family:"Calibri",sans-serif'> General [</span><a href="mailto:general-bounces+johnduffield=btconnect.com@lists.natureoflightandparticles.org"><span style='font-size:11.0pt;font-family:"Calibri",sans-serif'>mailto:general-bounces+johnduffield=btconnect.com@lists.natureoflightandparticles.org</span></a><span style='font-size:11.0pt;font-family:"Calibri",sans-serif'>] <b>On Behalf Of </b>Chip Akins<br><b>Sent:</b> 29 January 2017 14:36<br><b>To:</b> 'Nature of Light and Particles - General Discussion' <</span><a href="mailto:general@lists.natureoflightandparticles.org"><span style='font-size:11.0pt;font-family:"Calibri",sans-serif'>general@lists.natureoflightandparticles.org</span></a><span style='font-size:11.0pt;font-family:"Calibri",sans-serif'>><br><b>Subject:</b> Re: [General] On photon momentum<o:p></o:p></span></p></div></div><p class=MsoNormal><span lang=EN-GB><o:p> </o:p></span></p><p class=MsoNormal><span style='color:black'>Hi John D<o:p></o:p></span></p><p class=MsoNormal><span style='color:black'><o:p> </o:p></span></p><p class=MsoNormal><span style='color:black'>I am not understanding your idea. Can you explain how you feel that h contributes to the specific rest mass of the electron and not some other mass value? To which characteristic of space are you referring?<o:p></o:p></span></p><p class=MsoNormal><span style='color:black'><o:p> </o:p></span></p><p class=MsoNormal><span style='color:black'>Chip<o:p></o:p></span></p><p class=MsoNormal><span style='color:black'><o:p> </o:p></span></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'>From:</span></b><span style='font-size:11.0pt;font-family:"Calibri",sans-serif'> General [</span><a href="mailto:general-bounces+chipakins=gmail.com@lists.natureoflightandparticles.org"><span style='font-size:11.0pt;font-family:"Calibri",sans-serif'>mailto:general-bounces+chipakins=gmail.com@lists.natureoflightandparticles.org</span></a><span style='font-size:11.0pt;font-family:"Calibri",sans-serif'>] <b>On Behalf Of </b>John Duffield<br><b>Sent:</b> Sunday, January 29, 2017 8:25 AM<br><b>To:</b> 'Nature of Light and Particles - General Discussion' <</span><a href="mailto:general@lists.natureoflightandparticles.org"><span style='font-size:11.0pt;font-family:"Calibri",sans-serif'>general@lists.natureoflightandparticles.org</span></a><span style='font-size:11.0pt;font-family:"Calibri",sans-serif'>>; 'Hodge John' <</span><a href="mailto:jchodge@frontier.com"><span style='font-size:11.0pt;font-family:"Calibri",sans-serif'>jchodge@frontier.com</span></a><span style='font-size:11.0pt;font-family:"Calibri",sans-serif'>><br><b>Subject:</b> Re: [General] On photon momentum<o:p></o:p></span></p></div></div><p class=MsoNormal><o:p> </o:p></p><p class=MsoNormal><span lang=EN-GB style='font-size:11.0pt;font-family:"Calibri",sans-serif;color:#1F497D'>Chip:<o:p></o:p></span></p><p class=MsoNormal><span lang=EN-GB style='font-size:11.0pt;font-family:"Calibri",sans-serif;color:#1F497D'><o:p> </o:p></span></p><p class=MsoNormal><span lang=EN-GB style='font-size:11.0pt;font-family:"Calibri",sans-serif;color:#1F497D'>I think the electron has the mass that it has because h is what it is, because space has a particular characteristic: <o:p></o:p></span></p><p class=MsoNormal><span lang=EN-GB style='font-size:11.0pt;font-family:"Calibri",sans-serif;color:#1F497D'><o:p> </o:p></span></p><p class=MsoNormal><span style='font-size:11.0pt;font-family:"Calibri",sans-serif;color:#1F497D'><img border=0 width=664 height=266 style='width:6.9166in;height:2.7708in' id="Picture_x0020_1" src="cid:image006.jpg@01D27BC5.57E1B830" alt="cid:image002.jpg@01D27BBE.171E7380"></span><span lang=EN-GB style='font-size:11.0pt;font-family:"Calibri",sans-serif;color:#1F497D'><o:p></o:p></span></p><p class=MsoNormal><span lang=EN-GB style='font-size:11.0pt;font-family:"Calibri",sans-serif;color:#1F497D'><o:p> </o:p></span></p><p class=MsoNormal><span lang=EN-GB style='font-size:11.0pt;font-family:"Calibri",sans-serif;color:#1F497D'>Some people liken it to a crystal. <o:p></o:p></span></p><p class=MsoNormal><span lang=EN-GB style='font-size:11.0pt;font-family:"Calibri",sans-serif;color:#1F497D'><o:p> </o:p></span></p><p class=MsoNormal><span lang=EN-GB style='font-size:11.0pt;font-family:"Calibri",sans-serif;color:#1F497D'>Regards<o:p></o:p></span></p><p class=MsoNormal><span lang=EN-GB style='font-size:11.0pt;font-family:"Calibri",sans-serif;color:#1F497D'>JohnD<o:p></o:p></span></p><p class=MsoNormal><span lang=EN-GB style='font-size:11.0pt;font-family:"Calibri",sans-serif;color:#1F497D'><o:p> </o:p></span></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'>From:</span></b><span style='font-size:11.0pt;font-family:"Calibri",sans-serif'> General [</span><a href="mailto:general-bounces+johnduffield=btconnect.com@lists.natureoflightandparticles.org"><span style='font-size:11.0pt;font-family:"Calibri",sans-serif'>mailto:general-bounces+johnduffield=btconnect.com@lists.natureoflightandparticles.org</span></a><span style='font-size:11.0pt;font-family:"Calibri",sans-serif'>] <b>On Behalf Of </b>Chip Akins<br><b>Sent:</b> 29 January 2017 13:45<br><b>To:</b> 'Hodge John' <</span><a href="mailto:jchodge@frontier.com"><span style='font-size:11.0pt;font-family:"Calibri",sans-serif'>jchodge@frontier.com</span></a><span style='font-size:11.0pt;font-family:"Calibri",sans-serif'>>; 'Nature of Light and Particles - General Discussion' <</span><a href="mailto:general@lists.natureoflightandparticles.org"><span style='font-size:11.0pt;font-family:"Calibri",sans-serif'>general@lists.natureoflightandparticles.org</span></a><span style='font-size:11.0pt;font-family:"Calibri",sans-serif'>><br><b>Subject:</b> Re: [General] On photon momentum<o:p></o:p></span></p></div></div><p class=MsoNormal><span lang=EN-GB><o:p> </o:p></span></p><p class=MsoNormal><span style='color:black'>Hi John Hodge<o:p></o:p></span></p><p class=MsoNormal><span style='color:black'><o:p> </o:p></span></p><p class=MsoNormal><span style='color:black'>Thank you. I think you have made a good point here. For diffraction to work the way it does it seems the “photon” must have momentum.<o:p></o:p></span></p><p class=MsoNormal><span style='color:black'><o:p> </o:p></span></p><p class=MsoNormal><span style='color:black'>Hi Chandra. <o:p></o:p></span></p><p class=MsoNormal><span style='color:black'><o:p> </o:p></span></p><p class=MsoNormal><span style='color:black'>It seems to me that the simplest explanation of all we observe is to suspect that momentum is inherent in the motion of energy in space, and the cause for inertia. This approach allows us to derive E=mc^2 from the circulating energy in a particle. This would keep the particle stationary until it is acted on by an outside force. It would then also explain the property of inertia. It helps us to understand why light wants to travel a straight line unless deflected (diffracted).<o:p></o:p></span></p><p class=MsoNormal><span style='color:black'><o:p> </o:p></span></p><p class=MsoNormal><span style='color:black'>Like John D I feel space waves as energy propagates. However unlike a water wave, which is a simple displacement of particles of mass, a wave in space is a differential displacement of a transverse wave, with one part moving one way and the other part moving in the opposite direction. This differential displacement is what can give us part of the Chandra CTF type behavior of space. It yields things like electric charge naturally. It also causes things like the type of confinement in elementary fermions which Albrecht talks about.<o:p></o:p></span></p><p class=MsoNormal><span style='color:black'><o:p> </o:p></span></p><p class=MsoNormal><span style='color:black'>But in all this discussion I think we, and physics in general, have missed something important. <i>Space cannot be a linear medium.</i> Our equations generally describe space in “linear” relationships, like E=hf. But this ignores the resonant conditions which cause the specific masses of stable particles. It seems that resonances must be included in our physics before we really understand why the electron at rest is the specific mass and energy level which it possesses. I also think that once we identify and quantify the non-linear resonances of space, and their causes, we will be able to see better how all the pieces fit.<o:p></o:p></span></p><p class=MsoNormal><span style='color:black'><o:p> </o:p></span></p><p class=MsoNormal><span style='color:black'>Hi Andrew<o:p></o:p></span></p><p class=MsoNormal><span style='color:black'><o:p> </o:p></span></p><p class=MsoNormal><span style='color:black'>I have been able to detect EM radiation which is slower than 1Hz, so I am having a bit of trouble accepting the integer approach to the solution of quantization of waves. But I understand your example and appreciate its simplicity, and the smallest value of n could be whatever nature has chosen.<o:p></o:p></span></p><p class=MsoNormal><span style='color:black'><o:p> </o:p></span></p><p class=MsoNormal><span style='color:black'>Chip<o:p></o:p></span></p><p class=MsoNormal><span style='color:black'><o:p> </o:p></span></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'>From:</span></b><span style='font-size:11.0pt;font-family:"Calibri",sans-serif'> General [</span><a href="mailto:general-bounces+chipakins=gmail.com@lists.natureoflightandparticles.org"><span style='font-size:11.0pt;font-family:"Calibri",sans-serif'>mailto:general-bounces+chipakins=gmail.com@lists.natureoflightandparticles.org</span></a><span style='font-size:11.0pt;font-family:"Calibri",sans-serif'>] <b>On Behalf Of </b>Hodge John<br><b>Sent:</b> Saturday, January 28, 2017 10:10 PM<br><b>To:</b> Nature of Light and Particles - General Discussion <</span><a href="mailto:general@lists.natureoflightandparticles.org"><span style='font-size:11.0pt;font-family:"Calibri",sans-serif'>general@lists.natureoflightandparticles.org</span></a><span style='font-size:11.0pt;font-family:"Calibri",sans-serif'>><br><b>Subject:</b> Re: [General] On photon momentum<o:p></o:p></span></p></div></div><p class=MsoNormal><o:p> </o:p></p><div><div id="yui_3_16_0_ym19_1_1485662868797_2946"><p class=MsoNormal style='background:white'><span style='font-family:"Helvetica",sans-serif;color:black'>I do. And it explains diffraction.<o:p></o:p></span></p></div><div id="yui_3_16_0_ym19_1_1485662868797_2946"><p class=MsoNormal style='background:white'><span style='font-family:"Helvetica",sans-serif;color:black'>Hodge<o:p></o:p></span></p></div><div><p class=MsoNormal style='margin-bottom:12.0pt;background:white'><span style='font-family:"Helvetica",sans-serif;color:black'><o:p> </o:p></span></p></div><div><div><div><div><p class=MsoNormal style='background:white'><span style='font-size:10.0pt;font-family:"Arial",sans-serif;color:black'>On Saturday, January 28, 2017 7:12 PM, Dr Grahame Blackwell <</span><a href="mailto:grahame@starweave.com"><span style='font-size:10.0pt;font-family:"Arial",sans-serif'>grahame@starweave.com</span></a><span style='font-size:10.0pt;font-family:"Arial",sans-serif;color:black'>> wrote:</span><span style='font-family:"Helvetica",sans-serif;color:black'><o:p></o:p></span></p></div><p class=MsoNormal style='margin-bottom:12.0pt;background:white'><span style='font-family:"Helvetica",sans-serif;color:black'><o:p> </o:p></span></p><div><div id=yiv6089736424><div><div><p class=MsoNormal style='background:white'><span style='font-size:10.0pt;font-family:"Arial",sans-serif;color:navy'>Dear All,</span><span style='font-family:"Helvetica",sans-serif;color:black'><o:p></o:p></span></p></div><div><p class=MsoNormal style='background:white'><span style='font-size:10.0pt;font-family:"Arial",sans-serif;color:navy'>[Notably Chandra & Chip],</span><span style='font-family:"Helvetica",sans-serif;color:black'><o:p></o:p></span></p></div><div><p class=MsoNormal style='background:white'><span style='font-family:"Helvetica",sans-serif;color:black'> <o:p></o:p></span></p></div><div><p class=MsoNormal style='background:white'><span style='font-size:10.0pt;font-family:"Arial",sans-serif;color:navy'>I'm having a bit of a problem over this question of: 'How does a photon carry momentum'? (or similar words.)</span><span style='font-family:"Helvetica",sans-serif;color:black'><o:p></o:p></span></p></div><div><p class=MsoNormal style='background:white'><span style='font-size:10.0pt;font-family:"Arial",sans-serif;color:navy'>It seems to me that in order to even beginning to address this question, one needs a clear definition of 'momentum' that's applicable to the momentum carried by a photon.</span><span style='font-family:"Helvetica",sans-serif;color:black'><o:p></o:p></span></p></div><div><p class=MsoNormal style='background:white'><span style='font-size:10.0pt;font-family:"Arial",sans-serif;color:navy'>I may be looking in the wrong places (if so please advise), but the only definitions of momentum that I can find either refer to 'mass' or refer to some other phenomenon which in turn refers to momentum - i.e. circular references.</span><span style='font-family:"Helvetica",sans-serif;color:black'><o:p></o:p></span></p></div><div><p class=MsoNormal style='background:white'><span style='font-size:10.0pt;font-family:"Arial",sans-serif;color:navy'>If I'm going to figure, or be persuaded, how a photon carries momentum I first need to know what momentum IS in respect of a photon (yes, I know it's E/c, that's a measure it's not a definition).</span><span style='font-family:"Helvetica",sans-serif;color:black'><o:p></o:p></span></p></div><div><p class=MsoNormal style='background:white'><span style='font-size:10.0pt;font-family:"Arial",sans-serif;color:navy'>Of course I'm aware of the paper "Light is heavy", but I don't feel it's appropriate just to extract from that some sort of mass-equivalence of a photon. If we do, we get the result that 'm'=E/c^2, so 'm'c = E/c - gives the right result, but appears to be some sort of convoluted self-confirmation (i.e. a circular argument dressed up in fancy clothes). It certainly doesn't DEFINE a photon's momentum, just evaluates it.</span><span style='font-family:"Helvetica",sans-serif;color:black'><o:p></o:p></span></p></div><div><p class=MsoNormal style='background:white'><span style='font-family:"Helvetica",sans-serif;color:black'> <o:p></o:p></span></p></div><div><p class=MsoNormal style='background:white'><span style='font-size:10.0pt;font-family:"Arial",sans-serif;color:navy'>Does anyone have a convincing definition of momentum that's applicable to a photon? One that can be used as a firm basis for theorising?</span><span style='font-family:"Helvetica",sans-serif;color:black'><o:p></o:p></span></p></div><div><p class=MsoNormal style='background:white'><span style='font-size:10.0pt;font-family:"Arial",sans-serif;color:navy'>(I'd be glad if colleagues didn't use this as an excuse to yet again present their own personal theory/model - I'm looking for a definition that would be agreed by all, or at least most, physicists.)</span><span style='font-family:"Helvetica",sans-serif;color:black'><o:p></o:p></span></p></div><div><p class=MsoNormal style='background:white'><span style='font-family:"Helvetica",sans-serif;color:black'> <o:p></o:p></span></p></div><div><p class=MsoNormal style='background:white'><span style='font-size:10.0pt;font-family:"Arial",sans-serif;color:navy'>Thanks in anticipation,</span><span style='font-family:"Helvetica",sans-serif;color:black'><o:p></o:p></span></p></div><div><p class=MsoNormal style='background:white'><span style='font-size:10.0pt;font-family:"Arial",sans-serif;color:navy'>Grahame</span><span style='font-family:"Helvetica",sans-serif;color:black'><o:p></o:p></span></p></div></div></div><p class=MsoNormal style='margin-bottom:12.0pt;background:white'><span style='font-family:"Helvetica",sans-serif;color:black'><br>_______________________________________________<br>If you no longer wish to receive communication from the Nature of Light and Particles General Discussion List at </span><a href="mailto:jchodge@frontier.com"><span style='font-family:"Helvetica",sans-serif'>jchodge@frontier.com</span></a><span style='font-family:"Helvetica",sans-serif;color:black'><br><a href="</span><a href="http://lists.natureoflightandparticles.org/options.cgi/general-natureoflightandparticles.org/jchodge%40frontier.com?unsub=1&unsubconfirm=1" target="_blank"><span style='font-family:"Helvetica",sans-serif'>http://lists.natureoflightandparticles.org/options.cgi/general-natureoflightandparticles.org/jchodge%40frontier.com?unsub=1&unsubconfirm=1</span></a><span style='font-family:"Helvetica",sans-serif;color:black'>"><br>Click here to unsubscribe<br></a><o:p></o:p></span></p></div></div></div></div></div></div></body></html>