em

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 forcefit 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 em 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 7923,) 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
singlevelocity 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 . 
