Similarly, Maxwell's Equations Revisited Beware of the Bull Comments to ivorcatt@live.co.uk 2010 The end of electric charge and current as we know them The Hidden Message in Maxwell’s Equations - Ivor Catt, Electronics and Wireless World, November 1985
Did Maxwell lodge with his
bank the answer to his mathematical bluff, Maxwell’s Equations, with
instructions to open and publish a century later? And did the bank lose the
envelope? http://www.ivorcatt.com/em_test04.htm Historically, the theory of electrodynamics grew out of the theory of
static fields, electric and magnetic. These static fields resulted from
steady electric currents and static electric charge. Maxwell wrestled with
the paradox of the capacitor^{1,2}, and this
led him to reassert Faraday’s idea of “the propagation of transverse
[electro]magnetic [waves]^{3}.” So the concepts of electric charge
and electric current preceded the concept of a transverse electromagnetic
wave^{4}, and it is generally agreed (but not by me) that the TEM
Wave follows from the prior postulation of electric charge and current^{1,2}. A strong case can be made for the view that the TEM Wave is a more
fundamental Primitive, or starting point, for electromagnetic theory than
electric charge and electric current. ·
When light and heat reach
us from the sun, it is by the mechanism of a TEM Wave, not electric charge
and electric current. ·
Kip^{5} says that
the energy dissipated in a resistor entered it sideways, and was transported into the resistor by the TEM
Wave ·
In Wireless World, May
1955, page 18, in a reply to G. Berzins, I showed
that the TEM Wave, not the electric current, must be the mechanism by which
energy is transferred. ·
We all adhere to the
underlying primitive ‘conservation of energy’. Now energy is transported by
the TEM Wave, not by electric charge and electric current. ·
We all adhere to the
underlying relativistic primitive, ‘no instantaneous action at a distance’.
While electric charge could be
argued to be located at only one point in space-time, this is not true of an
electric current, some of which is located at the same time at points which
in the language of Minkowski are ‘elsewhere’ to
itself. Catt’s Equations of motion for a tapering wooden
plank. [See diagram in German version at http://ourworld.compuserve.com/homepages/Ekkehard_Friebe/Catt-85a.htm ] Consider a plank of wood tapering to a
point at the front, travelling at velocity v. The aspect ratio of the wood’s
cross section is z. Height and width at any point are
denoted by h and w. Within the tapering section, the ratio of height to width
remains z.
The velocity of the plank is the factor
which relates the change of height with forward distance to the change of
height at a point with time, so from first principles, we can write
dh/dx = - (1/v) dh/dt (1) ^{7,8}^{ }[For explanation of the minus sign, see ^{9}]
Since
we have stated that at any point, h/w=z, we can substitute for h in equation
1: dh/dx = - (z/v) dw/dt (2) Again
from first principles, we can write dw/dx = - (1/v) dw/dt (3) In the same way as we substituted for h in equation (1) to get (2), now substitute for w, to get dw/dx = - (1/vz) dh/dt (4) Equations
(2) and (4) we define as Catt’s Equations
of Motion for a wooden plank. Note that they hold true for any type
of taper, and even a straight portion of the plank, when both sides of the
equation are equal to zero. The only imposed limitation is that h remain proportional to w. Catt’s Equations of Motion
for a thick warm plank
We
postulate that a thick plank of wood travels forward with velocity v. At
every point within the plank, we postulate that the temperature T is
proportional to the density of the wood r, so that T/r = z . (To picture this,
think of spontaneous combustion.) Catt’s
equations 2 and 4 now become dT/dx = - (z/v) dr/dt
(5) dr/dx =
- (1/vz) dT/dt (6) These
equations remain valid for two thick short planks moving forward side by
side. Maxwell’s Equations compared
with two thick short planks
Let
us first review two of the many extant versions of maxwell’s
Equations for a vacuum. dE/dx = - dB/dt (7) dh/dx = - dD/dt (8) The
version above has been obscured by the introduction of alternative symbols B
and D to denote magnetic and electric fields. Our purpose is more easily
served if we use another of the many versions that litter the text books^{2}: dE/dx = - m_{0} dH/dt (9) dH/dx = - e_{0}
dE/dt (10) Our
problem is that whereas the equations for planks have constants v for
velocity and z for ratio, Maxwell’s Equations have the obscure symbols m_{0} and e_{0}. However, this problem
becomes trivial because it is known from experiment that -
the velocity of light or a
TEM Wave is c = 1/ \/(m_{0}e_{0}), -
the ratio
between E and H at any point, described by the symbol Z_{0}, has been
found by experiment to be equal to the constant \/(m_{0}/e_{0}). By
algebra, we find that m_{0} = Z_{0}/c
and e_{0} = 1/c^{10}.
We can now see that equations (9) and (10) are in fact (5) and (6), Catt’s Equations for Two Thick Short Planks,
and contain virtually no information about the
nature of electromagnetism. The Hidden Message in
Maxwell’s Equations
In
general, Maxwell’s Equations tell us only the obvious truisms about any body
or material moving through space. It is the obscurantism of the fancy maths in
which they are dressed that has for the last century caused scholars to think
that they contain significant information about the nature of
electromagnetism (but see ^{7} and ^{9}). Most versions are
far more messy and obscurantified than the two
comparatively clean versions (7) through (10) listed above. Other versions
tend to contain a mixture of integrals, divs,
curls, and much more, leading to a head-spinning brew, see for instance ^{1},
^{13}. (For the Inscrutable Ultimate, see panel for Chen-To Tai. [Missing from
this web page.]) Two
questions arise; -
Do Maxwell’s Equations
contain any information at all about the nature of electromganetism? -
Why do academics and
practitioners generally believe that Maxwell’s Equations are useful? The
answer to each of these turns out to be much the same at the answer to the
other. Returning
to equation (1), this is only valid if the constant in the equation equals
the velocity of propagation v. When we then mix together h and w to produce
the hybrid equations (2) and (4), they only remain true if h and w are always
in fixed proportion z. So we find that Maxwell’s Equations (9) and (10) are
only true if at every point in space E is proportional to H, and also if the
velocity of electromagnetism has a fixed value c. So the only information
about electromagnetism contained in the apparently sophisticated equations
(9) and (10) is about the two constants in electromagnetism: the fixed
velocity c, and that E, H at every point are in fixed proportion Z_{0}.
The remaining content of Maxwell’s Equations is hogwash. We
have to conclude, with respect, that what Maxwell and his sycophants do not
say about a tapering, disappearing plank of wood isn’t worth saying. Now
move on to the second question, “Why do academics and practitioners generally
believe that Maxwell’s Equations are useful?” The answer to this question,
deriving from the previous discussion, is extraordinary. We have already seen
that Z_{0} and c are the only items of information buried in
Maxwell’s Equations. We resolve the paradox by pointing out that Z_{0 }[377] is not
available as a concept to the whole of the fraternity called ‘Modern
Physics’. The only way they can use such a necessary constant in their work is by taking on board with it all the meaningless rubbish in Maxwell’s Equations which shrouds this valuable nugget. In September 1984, in a paper delivered to a
learned conference^{11} and in that month’s issue of Wireless World, I wrote: “It is
noteworthy that Einstein himself and also the whole post-Einstein community
who call themselves ‘Modern Physics’ never mention the impedance of free
space \/(m_{0}/e_{0}), although it is one of the
key primitives on which digital electronic engineering is based. The reader
is encouraged to look for reference to it in the literature of ‘Modern Physics’.”
Since then, no one has pointed out any case where it is mentioned in the
literature. It follows that The only purpose served by
Maxwell’s Equations is as a package to deliver the constant Z_{0} [377 ohms] to the theorist
and to the practitioner. [A bit like burning down your house to get roast
pig.] If they lacked another source for it, c [velocity of light,
300,000km/s] could also be accessed via Maxwell’s Equations,
but I think that to some extent c is available via other routes, although
university lecturers remain muddled and vague about the velocity of a TEM
Wave. Curiously, they are much more sure that the
velocity of light equals the constant c. Did Maxwell lodge with his bank manager the answer
to his mathematical bluff, Maxwell’s Equations, with instructions to open and
publish a century later? Should we say to Maxwell now, as he sits laughing,
or perhaps smarting, on Cloud Nine, “Now pull the other leg”? No. I am sure
that Maxwell was sincere, and did not knowingly shroud the very heart and
soul of science, Electromagnetism, in confusion and nonsense for over a
century. "From a
long view of the history of mankind – seen from, say, ten thousand years from
now – there can be little doubt that the most significant event of the 19th
century will be judged as Maxwell’s discovery of the laws of electrodynamics.
The American Civil War will pale into provincial insignificance in comparison
with this important scientific event of the same decade." – R.P. Feynman,
R.B. Leighton, and M. Sands, Feynman
Lectures on Physics, vol. 2, Addison-Wesley, London, 1964, c. 1,
p. 11. Oops! – Ivor apr03 It gets worse; “The special theory of relativity owes its
origin to Maxwell’s equations of the electromagnetic field.” Einstein quoted
in Schilpp, P A, “Albert Einstein, Philosopher –
Scientist,” Library of Living Philosophers, 1949, p62. - Ivor may03 [Perhaps we should look for some
different people to drool over. Ivor Catt 17may03] Appendix [to
nov85 paper] It is worth repeating here from ref. 7 that the
following two source equations, from which Maxwell’s Equations are derived,
have never been mentioned in the literature: dE/dx = - Z_{0}e_{0} dE/dt [So the E field causes the
E field! I Catt apr02] dH/dx = - m_{0}/Z_{0 }dH/dt [So the H field causes the H field! So much for the minus sign
implying causality! I Catt apr02] http://www.ivorcatt.com/em_test04.htm …… …… The cross-linkage of electric and magnetic fields E and H in Maxwell’s Equations only obscures the issue. There is no interaction between E and H. (Similarly, the width of a brick does not interact with its length.) They are co-existent, co-substantial, co-eternal (refs. 12, 14). To be continued. (Nearly all typed in.) Ivor Catt 24apr02_{} References: 1.
Carter, G. W., The Electromagnetic Field in its Engineering Aspects.
Longman, 1954, p. 313 |
The
deeper hidden message in Maxwell’s Equations |
A Mathematical Rake’s Progress. www.ivorcatt.com/2809.htm http://www.ivorcatt.com/em_test04.htm The Conquest of Science. http://www.electromagnetism.demon.co.uk/wbdanbk8.htm History of Maxwell’s
Equations
Scandals in Electromagnetic
Theory
http://www.ivorcatt.com/28scan.htm The Conquest of Truth
Includes, “Maxwell, Einstein and the Aether”
http://www.electromagnetism.demon.co.uk/Conquest%20of%20Truth.htm @@@@@@@@@@@@@@@@@ To Greg Volk, 2 May 2011. "I
was also intrigued by your “frame transformation” equations dH/dx * dx/dt = dH/dt
in the 1980 paper, where dx/dt certainly has dimensions of velocity." - Greg
Volk The
interesting point is that "they" write something like dE/dx = -dB/dt,
or dH/dx = -dB/dt However,
remember that we have two other terms, D and B. The link between them is µ and €. We
also have c and Zo. But velocity is c = 1/√ µ€ and Zo =
√µ/€ So judicious choice (particularly if you
don't know what you are doing) between D, E, B, H makes "them" able
to conceal c and Zo. However, there is no subterfuge. "They"
just don't know what they are doing. By "they" I mean everyone in
the 20th century. If the only possible field is ExH travelling at c,
as I believe, then anyone not believing this, or even (which includes
everyone) not having heard of it, can brew up silly stuff like dE/dx
= -dB/dt, or dH/dx = -dB/dt . If you don't know
that fields cannot be stationary, and that any E "field" is
inextricably attached to an H "field", you can brew up silly maths.
If you add DIVs and DELs, and integrals and differentials, you can drive away
any earnest young student in confusion, convinced that he is not bright anough to master electromagnetic theory. What a hilarious tragedy! Ivor. |