Article by Ivor Catt in Wireless World, March 1980
Maxwell’s Equations revisited
A critique of orthodox electromagnetic theory.
“It was once told as a good joke upon a mathematician that the poor man went mad and mistook his symbols for realities; as M for the moon and S for the sun.”
- Oliver Heaviside, Electromagnetic Theory, 1893, volume 1, page 133.
“… the universe appears to have been designed by a pure mathematician.”
- Sir James Jeans, The Mysterious Universe, 1931, page 115
Faraday’s Law of Induction, v = -d(phi)/dt, seems to imply:
1.A causality relationship; the rate of change of magnetic flux through a surface causes a voltage around the circumference of the surface.
2.A reluctance, or resistance to the change of magnetic flux indicated by the minus sign.
A careful analysis of this one equation will give an insight into the bogus nature of contemporary mathematical operations in electromagnetic theory. First let us discuss the minus sign, which leads us to the idea of a Lenz’s Law reluctance, or resistance, to the change d(phi)/dt. We shall see that a minus sign can occur in an equation when no causality can be involved.
Consider a high speed (125) railway train with sloping front passing an observer. As the front face passes, the observer will see a negative slope dh/dx as shown below. [Insert first diagram.] However, if the observer had watched the event through a narrow slit in a fence, he would have seen a rising edge dh/dt, as shown below. [Insert second diagram]
It would be absurd to suggest that there was a causality relationship between dh/dx and dh/dt. They are both descriptions associated with the passage of the train. Since Newton, it is accepted that a body continues in its state of uniform motion without a continuing cause, or push. (However, this principle is taking a long time to be applied to electromagnetic waves.) (refs. 1, 2)
Now we regard the velocity of the train dx/dt as positive. This creates an anomaly when we want to write the equation
dh/dx . dx/dt = dh/dt (1)
because the left hand side product is negative when the right hand side is positive, as in the case of the leading face of the train.
This kind of absurdity, or anomaly, is ignored when Newton’s Laws are considered. It is reasonable to do so, because Newton’s Laws are close to common sense and the obvious. Common sense will prevent absurd conclusions from creeping into a Newtonian theoretical framework, even though the mathematical formulation of Netwon’s Laws has always been slovenly in this respect. (Even the brilliant philosopher Ernst Mach frailed to notice this anomaly.) (Another perhaps permissible slovenly aspect is the use of the = sign for numerous different, mutually contradictory meanings.)
Maxwell’s Equations are not in the same class. Common sense will not save us from absurdity and nonsense if our initial formulations are ambiguous or wrong.
Let us consider an electromagnetic wave front advancing at the speed of light. When a step (or more accurately ramp) passes, as shown here, [Insert third diagram] dH/dx is negative. However, dH/dt is positive. To get the algebra right, we are forced to conclude that
dH/dx . dx/dt = - dH/dt (2)
However, no one would propose that the minus sign indicated a causality relationship between dH/dx and dH/dt.
The last equations never appears in the text books. One of the terms is first converted into a function of E according to the formula
E/H = sq.rt.(mu/epsilon)
The result is either
dE/dx = - dB/dt (3)
dH/dx = - dD/dt (4)
The text books say the “solution” to this pair of equations is a sine wave!See references 3 to 7. (In fact, almost anything is a solution to these equations.)
At this stage, the whole subject starts to look sophisticated and profound. Really it is neither. The minus signs have no significance, as we have seen. B and D are introduced on the r.h.s. merely to suppress mu and epsilon using the formula
E/H = sq.rt.(mu/epsilon)
In fact, the last two equations (3), (4) are meaningless. If the front end of the high speed train were pointed, sloping out sideways as well as upwards, and w were the term given to width (as H stands for height), exactly the same pair of equations could be constructed.
dw/dx = -(mu)dH/dt
dH/dx = - (epsilon)dw/dt
As with e-m theory, we could conclude with equal validity that a train’s height (and width) must vary sinusoidally along its length, making out trains look like a row of short sausages, as shown here. [insert fourth diagram.]
It is shocking that this nonsense has survived for a century at the core of a subject as crucial as electromagnetic theory. We see now that mathematical formulation of e-m theory, far from making the subject more rigorous, has made it ludicrous and false. We see that the mathematicians are incompetent where physical reality is concerned and hide their incompetence and confuse others by conjuring up nonsensical, interrelated formulae.
When Hertz established that electromagnetic waves existed, Maxwell’s equations should have been re-examined, and the large rubbish element removed. Instead physically ignorant mathematicians took over, piling garbage on garbage, frightening away those with real insight into the subject – the latter-day Faradays.
Those who try to build extensions, or additions to, the House of Newton should not assume that since the foundations were good enough for Newton’s simpler theory, they are strong enough to support their own more complex constructions. Minkowski’s failure to re-examine the foundations of Newton, in particular his assumption that velocity is positive and the passage of time is positive, makes his constructions useless in the same way as Maxwell’s equations are useless.
In the Minkowski sense [ref. 8] time really flows from (+ infinity) to (- infinity), not, as he thought (and our clock faces, with their ascending sequence of numbers, think), from (- infinity) to (+ infinity). Velocity, being the gaining of distance in return for the loss of time, is negative. This points to a fundamental difference between space and time, and means that the “space-time continuum” as Minkowski formulated it is bogus. At best, we see his pronouncements as oracular, similar to the answer that Delphos gave when asked about the sex of an unborn child, “Girlnoboy”. This remark could well be interpreted as true, but really it has no content.
Einstein failed to consider the problem of the sign of time and of velocity. Also [ref. 9], he never succeeded in fighting his way through the mass of mathematical garbage surrounding electromagnetic theory.
1. Wireless World, July 1979, page 72.
2. I. Catt et. Al., Digital Electronic Design vol2, Westfields Press, 1979, pp248, 319
3. G W Carter, The Electromagnetic Field in its Engineering Aspects, pub. Longmans 1954, p268, eqns. 12.5.1, 12.5.2
4. A F Kip, Fundamentals of Electricity and Magnetism, pub. McGraw-Hill 1962, p321, eqns. 12.19, 12.20
5. E G Cullwick, Electromagnetism and Relativity, pub. Longmans 1959, p81, eqn. 6(2)
6. S A Schelkunoff, Electromagnetic Waves, pub. D van Nostrand 1943, p39, eqn. 10-1
7. Wireless World, August 1979, p44, eqns. (i) and (ii)
8. A Einstein, Principles of Relativity, pub. Dover, p76
9. ed. P A Schilpp, Albert Einstein, Philosopher-Scientist, pub. Library of Living Philosophers 1949, page 17, „.... the approach to more profound knowledge ….”
10. ibid, p63
11. I Catt, Computer Worship, pub. Pitman 1973, p71
12. I Catt, The rise and fall of bodies of knowledge, The Information Scientist, 12(4), dec 1978, pp137-144