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Beware of the bull Praise of Academics The
New Scholasticism Throwing glasses at stone houses To
Kathy Symonds 20 April 1995 Dear Kathy, 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. Best wishes [signed] Neil McEwan (Dr.), Reader in
Electromagnetics [Copy typed by I Catt,
1oct95] |
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