From Sir Andrew Huxley, OM, FRS
Dear Mr. Catt,
I much enjoyed our conversation at dessert in Trinity a week ago.
Thank you for your letter. Before I received it, I got your book [The Catt Anomaly] out of the library at Trinity. My reactions to the main point, as stated on your p. 3, are as follows.
It seems to me that an anomaly such as you describe might arise if the two-conductor waveguide were capable of transmitting a step function some orders of magnitude sharper than the one with a rise time of 1 ns as you discuss [I do not. IC]. For a given amplitude of step, the peak current will be inversely proportional to the rise time. [It is independent of the rise time. IC.] I am not familiar with quantitative aspects of conduction in metals but electrons might have to travel with the speed of propagation of the wavefront if the risetime were perhaps (10) -15 sec, [ten to the power -15, or 1 femtosecond - IC] involving Fourier components at frequencies comparable to those of visible light. However, such a wavefront cannot be conducted along a metallic waveguide for the reasons explained by Neil McEwan in the part of his letter that you quote on p. 8, middle, i.e. the wavefront becomes smoothed out because the high-frequency components are attenuated, and your original proposition is based on a situation that cannot exist. As I said, I am not familiar with the quantitative aspects of the relevant theory but I suppose that the immediate reason why the waveguide cannot transmit these very high frequencies is the finite resistance of the wires, but if this were negligible then transmission would fail precisely because it would require electrons to travel at speeds approaching the velocity of light and, as you point out, this is impossible because their energy would approach infinity.
With a risetime of the order of 1 ns such as you discuss [I do not. IC], the currents are several orders of magnitude smaller than what would be carried if all the electrons moved at the speed of light, and the situation is correctly described both by Prof. Pepper in the second paragraph of p. 5 of your book and by Neil McEwan on p. 8 of your book., i.e. the huge number of free electrons present in the metal need only to move at a small fraction of the speed of light to carry the current.
I confess that I find it unsatisfactory that you dismiss Pepper's discussion as "drivel" (p. 5, bottom) and make no attempt to explain what you think is wrong with it.
An analagous situation exists in nerve conduction, the field in which I worked for many years with Alan Hodgkin. The best-understood nerve fibre …..
St. Albans AL3 4JR,
+44 1727 864257
second copy sent 2july00; third copy sent 29july00
Sir Adrian Huxley, OM, FRS,
1 Vicarage Drive,
Dear Sir Andrew Huxley,
The Catt Anomaly
Thank you for your letter dated 14may00.
I quote from your letter;
"I confess that I find it unsatisfactory that you dismiss Pepper's discussion as 'drivel' (p. 5, bottom) and make no attempt to explain what you think is wrong with it."
I would refer you to page 11, bottom, of the same book The Catt Anomaly;
".... Pepper, (defying Gauss's Law by) producing charge from the south from inside the conductor like a rabbit from a hat.... The Westerner view could have been brazened out, .... but .... Pepper's ingenious but mad Southerner view could not."
According to Gauss's Law [see below], rearrangement of charge already in the relevant section of the conductor could not enable it to terminate more electric flux than heretofore. Movement of charge ".... at right angles to the direction of propagation of the wave .... " (Pepper, p5,) can have no bearing on the Catt Anomaly.
The growing scandal which is The Catt Anomaly has nothing to do with me. McEwan pontificated on it once only in apr1995, and then went incommunicado for five years. Pepper pontificated on it once only in 1993, and then went permanently incommuncado. I never communicated with either of them. I first commented on their behaviour in dec1996, in my book The Catt Anomaly.
Since, initially, Secker of the IEE backed Pepper the Southerner, the disagreement between these two men, who continue to earn salary for teaching this material, needs to be addressed. Nobody, including the IEE, has deigned to comment on the request written by Hockenjos on 25.11.95. (p55, The Catt Anomaly.) Why not? How does science advance?
Best wishes, Ivor
Please regard material to follow on Gauss's Law, as Appendices to this letter.
".... Gauss' theorem, which states that the outward flux of D from any closed surface is equal to the enclosed charge." - G W Carter, Professor of Electrical Engineering, Leeds Univ., The Electric Field in its Engineering Aspects, pub. Longmans 1954/59, p311.
"Gauss' law says that the net number of lines emerging through a closed surface depends only on the total charge surrounded by that surface ...." - A F Kip, Professor of Physics, Berkeley, Calif., Fundamentals of Electricity and Magnetism, pub. McGraw-Hill 1962, p32.
S Ramo, J R Whinnery, J van Duzer, Fields and Waves in Communication Electronics, 3rd Edn., pub. Wiley 1994.
p6 ".... electric flux out of a closed surface = charge enclosed (3)
This is Gauss's law .......... It is thus a most general and important law."
p129 "Maxwell's Equations in Large-Scale Form
[circular integral] D.ds = [volume integral] [rho] dV (1)
"Equation (1) is .... Gauss's law .... the electric flux out of a closed surface at a given instant is equal to the charge enclosed by the surface at that instant."
S R H Hoole and P R P Hoole, A Modern Short Course in Engineering Electromagnetics, pub. OUP 1996
xx p80 "The Divergence Theorem or Gauss's Theorem
[triple integral] V.AdR = [double integral] A.dS
The divergence theorem is intuitively obvious."
p118 "Gauss's Theorem
Gauss's Theorem for electric fields is one of the most fundamental in the study of electricity .... [p119] The advantages of working with such a theorem are readily apparent ...."
I Catt, Electromagnetism 1, pub. Westfields Press 1994, p1
Battery and resistor. Steady state.
We start with a conventional view of a battery with voltage V connected via two uniform perfect conductors to a resistor R (Fig.1). A steady current flows round the circuit, through battery, conductors and resistors. Ohm's Law tells us that the voltage equals the current multiplied by the resistance. Therefore the current is I = V/R. Every point on the surface of the upper conductor is at potential V, and every point on the surface of the lower conductor is at a zero potential.
The space between the two conductors, shown in cross section (Fig. 2), is filled by tubes of electric displacement D. Each tube of electric displacement terminates on unit positive charge on the upper conductor and unit negative charge on the lower conductor
This is Gauss's Law, which later became one of Maxwell's Equations.
A Einstein writing in a book by Schilpp, P. A.; Albert Einstein, Philosopher-Scientist, pub. Library of Living Philosophers, 1949, p62.
"The special theory of relativity owes its origin to Maxwell's equations of the electromagnetic field."
From Sir Andrew Huxley, O.M., F.R.S. 28 July 2000
Ivor Catt Esq., etc. , etc.
Dear Mr. Catt,
Thank you for your letter of 27 May. Unfortunately I was ill for much of last month, which is the reason for my delay in replying.
I now see another place where you have made a mistake, as well as the assumption that individual electrons move with a speed comparable to the speed of the wave that is passing along the waveguide. You say "According to Gauss's law, rearrangement of charge already in the relevant section of the conductor could not enable it to terminate more electric flux than heretofore". This is true for the total flux from a segment of the conductor long enough to include the whole of the wave you are considering, but it is not true for all points within that length. At any point where the current varies along the length of the conductor,
dq/dt = - di/dx [sic. See Note 1.]
where x is the distance along the conductor, q is the charge on the conductor per unit length, and i is the current in the conductor in the positive direction x. di/dx must have finite values at the beginning of the rising phase of a pulse, around its peak and where the pulse terminates; hence there will be charge accumulation at these regions with corresponding tubes of electric displacement originating and terminating on the conductor within the segment occupied by the pulse. It is these and their variation with time that give rise to Maxwell's equations.
I shall be interested to know whether you have any objections to this argument.
I am sending copies of this letter to the people whom you stimulated to write to me after my first letter.
[signed] Andrew Huxley
2aug00. Dear Ivor,. ….. I do not think you have retyped it right because you quote Huxley proposing the absurd equation: dq/dt = - di/dx which is wrong dimensionally. dq/dt = i. Hence, dq/dt does not equal -di/dx. Perhaps you had better correct your internet site before Sir Huxley complains that you are ridiculing him - MB.
Dear Mr. Catt,
Thank you for sending me (2 August) your website with our correspondence, including the note by "MB" claiming that the dimensions were wrong in my equation. I take it that you will have noticed that the mistake is his, not mine: q was explicitly defined as "the charge on the conductor per unit length", not simply as charge, so the dimensions of both sides of my equation are (charge) X (distance) -1 X (time) -1.
[i.e. (charge) / (distance x time)]
I am sorry not to have replied sooner: I was abroad most of August and have been very busy since returning.
Yours sincerely [signed] Andrew Huxley. 5sep00