Kathy Symonds 20 April 1995
John Gardiner has passed this on to me - I think I can claim to be reasonably competent to discuss it.
To deal first with the problem raised in "Catt's Anomaly", there is definitely a correct answer, and it is just that the new charge required in the one foot of cable DOES flow from somewhere to the left! The charges DON'T have to travel at anywhere near the speed of light to do this!
The sentence that begins "Not from somewhere to the left ....." is fallacious ... such charge would NOT have to travel at the speed of light in a vacuum! The reason that the sentence cannot be grasped by those "disciplined in the art" is because it happens not to be true!!! It may be obvious to the untutored mind because they haven't had the theoretical training to see why it is wrong. It is exactly at the point where the assertion seems really obvious that you need to think most clearly to see where the logical deduction is unsound - and perhaps this is where the lesson for educators lies. The heart of the fallacy is as follows:
(a) If the voltage step originally at a transverse plane "A" on the conductors moves one foot to the right to a plane "B" (indeed about one nanosecond later) then it is true that a certain amount of charge must have entered the portion of the conductors between A and B. What is not true, however, is that any of the electrons that were in the neighbourhood of A actually had to travel to B to keep up the wave!
(b) The charge that appears between A and B is required to be uniformly distributed along the length between A and B. This charge really does enter at plane A - so how is it possible that the electrons didn't have to rush to the right at the speed of light? - I will now explain:-
(c) When the wires are electrically neutral, they are actually composed of vast numbers of positive charges and negatively charged electrons in equal densities - the total charge balances out. The thing we call the "charge on the line", which is required to account for the voltage wave is actually the unbalance between the two sets of charges.
(d) Imagine that, between A and B, you have 100 electrons and 100 positively charged nuclei arranged uniformly in pairs along one foot distance. There is no net charge.
(e) Now imagine that you push in one extra electron in at the left hand side A, and you squash the electrons up a bit so that they remain evenly spaced but now 101 electrons fill the distance that was previously occupied by 100. There is now a total of one unit of "charge on the line" between A and B, and, rather surprisingly, this unbalanced charge actually appears to be fairly uniformly distributed between A and B. The electron originally at A would only move about 1/100 of a foot as you squeezed the electrons closer together, and it would have to move this distance in the one nanosecond it took for the voltage wave to move from A to B. The electrons further to the right would move even less.
(f) If you imagine that you did this again with a larger number of positive and negative charge pairs - say 1000 becoming 1001, then as you squeezed in the extra electron the one next to it would only have to move up about 1/1000 of a foot in the one nanosecond - and so on.
If you go on increasing the density of available charges, you can easily see that the velocities required of the electrons to produce one unit of unbalance becomes smaller and smaller. (Also, the one unit of unbalance appears to be more and more uniformly distributed across the one foot of distance.)
It turns out that when you "put the numbers in" that the real number of free electrons in the one foot wire is colossal, and that consequently they only need to move at walking pace or less!
You can summarise all this by saying that the "charge" that is required to account for the voltage across the line is not produced simply by a small number of charges moving in to the section of line but by a very slight redistribution of a vastly larger number of charges that were already in that section! Putting it in still another way again, there has been a confusion over the identity of the charges that account for the voltage across the line.
You can go on describing this problem at deeper and deeper levels and it will go on revealing more and more interesting physics - which soon gets very hard. For example, there is a quite noticeable effect because you do need some force to keep the electrons moving against the collisions with the stationary atoms. This appears as resistance in the line and it can cause the advancing voltage step to become distorted, ie it smears out into a more gradual step.
At a higher level of precision there is even a very small effect from the finite acceleration of the electrons. As the voltage step passes over them, the local electrons in the conductor are accelerated (very rapidly!!!) to the very small speed that is needed. There is no paradox about the rapid acceleration of the particles, they are very light. This produces an extremely small effect on the velocity of the wave travelling down the line, but you would not be able to detect it at the frequencies used in ordinary electronics.
I hope this has helped and given you something to think about. The "anomaly" is very instructive educationally, it is a real challenge for the teacher to explain clearly, and a very good example of how fruitful it can be to be wrong about something!
Turning more generally to your 2 - day event, I am extremely intrigued about how "Catt's anomaly" came into the discussion. I do realise that progress has often been made by challenging orthodoxies, but in the case of Catt's problem I happen to think that the accepted theory gives a pretty good account, but you can learn a lot if you are really made to set out how. I would be very interested to hear what you make of my comments, and how they have been used in your event.
[signed] Neil McEwan (Dr.), Reader in
[Copy typed by I Catt, 1oct95]