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e=mc2

Ivor Catt. 6 February 2010. ***** below was written in 2001. I had always been doubtful of my derivation of e=mc2 from classical electromagnetic theory. What I did was to deliver a TEM pulse down a two conductor transmission line into a dead short. While the pulse reflected, there was an electric current in the short. That meant that to the left of the short was a certain magnetic field, “caused by the electric current”, and so a force resulted on the short Bil , using the usual formula for the force for a current carrying conductor in a magnetic field – magnetic field, electric current and length of conductor. (The flaw was that the magnetic field was on only one side, the left hand side, of the shorting conductor.) This led to the idea of a force for a period of time – the time taken for the pulse to reflect. Thus we had an impulse, (Force) x (Time). An impulse gives a change of momentum. Thus the change in momentum of the TEM Pulse could be calculated. But we know the velocity of the pulse, c. So we can deduce its mass. But right at the start, we had the energy in the pulse, (watts) x (time). Now, having mass end energy for the pulse, we could deduce e=mc2, purely from classical electromagnetic theory. I remained dubious about this procedure, because the magnetic field did not envelop the conductor shorting the end of the transmission line. It was only at the left side of the conductor. Today I have at last realised an even deeper flaw in the procedure, which is to deliver a TEM Pulse down a transmission line into an open circuit rather than into a short circuit. Again, the pulse reflects, but there is no force causing it to reflect, because there is nothing there, only vacuum. It seems that the original, dubious procedure for deducing e=mc2 purely from classical electromagnetic theory was actually merely some sort of dimensional analysis. If a TEM pulse travelling down a transmission line reflects at an open circuit, is there a (force) x (time) to deliver the necessary impulse to change the velocity of the pulse with mass m? Or does a TEM pulse have no mass? But see below; “Dave Walton told me long ago that light hitting an absorbing surface puts a pressure on the surface.” And light is a TEM Wave. When a TEM pulse travelling down a uniform two conductor transmission line with vacuum dielectric collides with a change in dielectric constant – going from vacuum to glass, say, some of the TEM pulse reflects. Does it deliver a force to the front face of the glass? If a TEM pulse travelling through glass down a transmission line collides with a change from glass to vacuum, some of it reflects. Does it deliver a force to the front face of the vacuum? What’s going on? There is no electric current across the face of the discontinuity. Yet momentum changes. [Addition on 13 February 2010. Dave told me that I could find informatio0n of “radiation pressure” by doing a Google search for “radiation pressure”. Sure enough, there is the evidence that it is generally agreed that when light falls on a surface, it exerts a pressure.] @@@@@@@@@@@@@@@@ 13 February 2010. I now realise that we should regard the short at the end of the transmission as merely an extreme kind of dielectric, where Zo is zero and propagation velocity is zero (see my book) . The laws of reflection (see my book again) tell us that there will be total reflection. So the dead short becomes merely one extreme case of a TEM pulse colliding with a change in Zo in a transmission line. Now in the general case of a change in the medium in a transmission line, there is no resulting electric current in the surface between the two mediums. This presents no problem in the case of "Theory C" , since under that theory electric current does not exist. However, in the case of "Theory N" , this may present problems. Unfortunately, if it does, it will attract no interest among The Establishment, who already ignore the implications of the contradictory answers to "The Catt Question" . @@@@@@@@@@@@@@@@ ***** Copied from http://www.electromagnetism.demon.co.uk/11120.htm Dave Walton told me long ago that light hitting an absorbing surface puts a pressure on the surface. Yesterday I phoned Dave about the two views; the TEM wave sidling between the crystals, and the TEM wave treating the other crystal as somewhat of a short in its path. I said we did not know what was the mass of the TEM wave. Dave said e=mc2. I had never thought of this formula in the context of TEM waves. That set the scene for my rumination for some hours. Last night, because of an error in a footnote of my Wireless World sep84 article, wrongly giving energy density as B.D, when it is properly EH/c, I could not get e=mc2 to come out of my calculations (below). However, today, I found the correct formula by deducing it from Cullwick p231. This difficulty; the fact that I did not force-fit the results like the prince's shoe, gives more credence to the validity of my work next day. First of all it would not come right because of faulty informational input, but next day it came right when I found the error in my factual input. (The error in my article is repeated as a footnote on p137 of my jan87 book "Death of Electric Current".) Everything that follows is classical theory - Theory N. First consider Approach !. If a transformer develops a shorted turn, it explodes outwards. If electric current is sent round a wire circle, there is an outwards force. If electric current is sent down one wire, causing magnetic field in the region of another, parallel wire, then if that wire carries current, a force Bil results, where; B = magnetic field i = electric current l = length of wire. Now send a TEM ExH wave step (slab of energy current) down a two wire transmission line. The line is perfectly terminated, and the termination absorbs the energy current. The Zo and r, the termination, are 377 ohms. From Ohm's Law, The electric current in the 377 ohms is E/r = E/377 The B field (= uH) is given by the H of the TEM wave. (B=uH) The force F resulting is Bil = uH,(E/377).l Length l = 1, so the force F = EHu/377 = EH u/ (sqrt u/e) = EH u (sqrt e/u) = EH (sqrt ue) = EH/c (since c=sqrt ue) We conclude that F = EH/c {1} Approach 2 A TEM wave step 300,000 Km long approaches a short down a transmission line. Energy density e is EH/c [Note 1]. The total energy W in the 1 sec (or 300,000 km) long step is ExH. W = EH From Approach 1, the force F required during one second to bring energy EH to rest is F = EH/c {1}). Now consider a mass m (density m/v) travelling at velocity v, brought to rest by this same force lasting for one second. Let us calculate the mass. From Newton's Second Law, F x t = m x v. t=1, v=c, so F = mc. So (using the result {1} from Approach 1,) EH/c = mc, or W/c = mc. It follows that energy W = mc2. This formula, usually written e=mc2, is claimed for Poincare and later for Einstein. Here it is derived from the TEM wave in a transmission line, using only classical electromagnetic theory (Theory N). Note 1. My 1984 Wireless World paper footnote wrongly gives energy density as ExH. The correct figure EH/c can be derived from E G Cullwick, "Electromagnetism and Relativity", pub. Longmans 1957/61 p231. "Energy Density[W] in an e-m wave is ED or HB." Take ED. We know that E/H = sqrt u/e, so E = H (sqrtu/e). Put W = ED = EeE = E e H (sqrt u/e) = EH (sqrtue) = EH/c The above shows that e=mc2 can be derived from the TEM wave solely using classical electromagnetism. Today (1.1.01) Dave told me that that was (well) known. However, I did not know it. Dave mentioned that Maxwell said so. The Cullwick book that I cite above, p231, says, in a section entitled "Electromagnetic momentum"; "It was first shown by Maxwell(Treatise, vol 2, pp 792-3,) that this pressure, according to the electromagnetic theory of light, should be equal to the energy per unit volume of the incident wave." I have not yet (1.1.01) looked this up in Maxwell, although I have bought the 2 Maxwell volumes 2 months ago. I hope to add the relevant Cullwick and Maxwell sections to this orphan site. Ivor Catt 2.1.01 01.00 In WW jan88 p54 I wrote that one could have a system containing velocity and momentum but lacking mass, which could sidle around hidden in the maths. The system could be made to function, produce results, and correlate with reality. The necessary parameter m, like the rabbit in the hat, could go about its business, the hat being in this case momentum and a fog of mathematics. The present discussion is different. I think that the TEM is a necessary primitive, and so also is the force. However, when a TEM wave runs into obstruction, a force results. Thus, we have as primitives energy, e, TEM, and also force. Perhaps we need a third primitive, momentum, although I think that in a single-velocity universe we do not. We certainly do not need mass as a primitive. Note that when I side with wave and against particle, mass is very much on the side of particle. So the move away from mass towards TEM/energy and force as primitive comes very much in the wake of favouring wave against particle in wave/particle duality. I ought to add Cullwick to this website, and the bit in Maxwell's Treatise. I have now (2.1.01) added Maxwell, Einstein and the Ether, the last part of Conquest of Truth. WWjan88, on p54, which is important. Ivor 2001 @@@@@@@@@@@@@@@@ 16 August 2007. More thoughts .