The
Mathematical Universe

*“ .... Dirac wasn’t
interested in interpretation because he believed that the truth lay in the
equations, and it was pointless to ask about their physical meaning.” – John Gribbin, “Erwin Schrödinger and the
Quantum Revolution”, pub. Bantam 2012, p154*

http://www.ivorcatt.co.uk/2_2.htm
Malcolm Davidson has pointed out that since a capacitor is a transmission line,
the model models a transmission line in terms of itself, which is absurd.

This is an interesting introduction to “The
Mathematical Universe”, which has supplanted a physical universe in science.
This can be seen by doing a Google search for “mathematics is the language of
science”, which produces 200,000 hits.

The LCLCLC model for that transmission line is
interesting because it illustrates the collision between these two universes.
It could be argued that it is not absurd because it models the transmission
line, which for this purpose is part of the physical universe, in terms of a
capacitor from the mathematical universe. Thus, it does not commit the
absurdity of modelling something in terms of itself. It is only a physical
capacitor which is a transmission line, not a mathematical capacitor.

Far from being a transmission line, a mathematical
capacitor has zero volume, and its capacitance is concentrated at a single
point in space, where the dielectric constant is, of course, infinite, so that
its capacitance can be more than zero.

A mathematical resistor also has zero volume. When a
charged mathematical capacitor is connected to a mathematical resistor, the
result is an exponential. In such a universe, the delay in the conductors
connecting capacitor to resistor is zero. Thus, there is instantaneous action
at a distance.

The question arises. Why, within the mathematical
universe, is the transmission line ever considered, since it appears to breach
a fundamental principle in the mathematical universe, that components have zero
volume. This, of course, explains the incompetence
shown by today’s professors and text book writers when addressing, or rather
not addressing, the transmission line. It is not properly part of their
mathematical world. http://www.electromagnetism.demon.co.uk/17136.htm

A mathematical capacitor (which has zero volume) has
a stationary electric field because it has nowhere else to travel.

http://www.ivorcatt.co.uk/x343.pdf

Ivor
Catt 3 June
2013

Thank goodness I have now found http://www.ivorcatt.co.uk/x363.htm

In conventional circuit theory, a
component has zero volume. There is instantaneous action at a distance along
the wires connecting the components. In a circuit connecting various components
in a loop, the electric current at every point is the same. This is the world
of the exponential when a resistor discharges a capacitor. In http://www.ivorcatt.co.uk/x363.htm I
call it “The Mathematical Universe”. The transmission line made up of two
parallel conductors cannot be part of that world. Interestingly, since a
capacitor has zero volume, its dielectric constant must be infinite.
“Displacement Current” derives from this world. In the last diagram in http://en.wikipedia.org/wiki/Displacement_current ,
the electric charge/current does not have to spread out across the capacitor
plate, because the plate has zero area, or perhaps the charge travels across
the plate at infinite velocity. http://www.ivorcatt.com/3613.htm Certainly
it instantaneously spreads out to be uniform in density across the plate. http://www.ivorcatt.org/icrwiworld78dec1.htm

Away from this Mathematical
Universe is the Physical Universe, where components do not have zero
volume. In this world we can have a transmission line. In the real, physical
world, a capacitor plate has area. Now we get to the next point. The
“electricity” does not enter the centre of a capacitor, as Wikipedia says. http://en.wikipedia.org/wiki/Displacement_current .
Rather, as Professor Kip says, it enters the capacitor (or resistor) *sideways*, entering at one end, travelling
at right angles to the direction indicated in Wikipedia.

http://www.gsjournal.net/h/papers_download.php?id=3750

Now let us consider a simple circuit
with

battery
and resistor. Two conductors

guide
the energy current from battery to

resistor.
It enters the resistor sideways

(Kip 1962)6. 'Electric current' is
merely the

side
of a wave of energy current.

Thus, once it enters a capacitor sideways,
and advances across the capacitor, we see that the capacitor is a transmission
line. But Displacement Current, invented to generate magnetic field in a
capacitor, must not do so in a transmission line. http://www.ivorcatt.co.uk/x22j.pdf .
The displacement current dD/dt
at the front face of a TEM step must not generate magnetic field. The
TEM wave travelling along in a transmission line is incompatible with displacement
current. They both survive – displacement current in a capacitor and the
TEM wave in a transmission line – so long as nobody notices that a
capacitor ** is**
a transmission line. An editor who published; “a capacitor is a transmission
line” will never again get a job as an editor, because he brings the whole
structure tumbling down. http://www.ivorcatt.co.uk/x0309.htm .
“A capacitor is a transmission line” does not appear in any peer reviewed
journals, and will probably not appear during the next thirty years.

Ivor
Catt. 20 June 2013