**On the Necessity and Sufficiency of Poynting vector’s motion with speed of light for the existence of contrapuntal states observed in Wakefield experiments**

(see my earlier post: https://blogs.ncl.ac.uk/alexyakovlev/2019/09/14/wakefield-4-experiment-causal-picture-in-energy-current/ and Ivor Catt’s original paper on Wakefield 1: http://www.ivorcatt.co.uk/x343.pdf)

**Alex
Yakovlev**

**13 August
2020**

**The main
hypothesis is:**

H: EM
energy current in the form of ExH (aka Poynting vector) can only exist in
motion with a speed of light.

**Experiment:**

Consider a
Wakefield experiment with a Tx Line that is initially discharged.

At time
t=0, the TL is connected at point A (left-hand side) to a source 10V, where it
is terminated with an open circuit. Point B is in the middle. Point C is at the
right-hand side and is short-circuited.

Wakefield
shows that:

At point A
we have a square shape oscillation between +10V (half-time) and -10V
(half-time).

At point C
we see no changes – completely discharged line at 0V.

At point B
we have the following cyclically repeated sequence of phases: (a) 0V (quarter
time), (b) +10 (quarter time), (c) 0V (quarter time), (d) -10V (quarter time).

A similar
analysis can be carried out with an initially charged TL which is
short-circuited at point A and is open-circuited at point C.

**Experimental
fact:**

W: We
observe contrapuntal effects in Wakefield, such as in Point B we have phases
(a) and (c) where the cumulative effect of ExH field waves makes them look
observationally equivalent – at 0V, yet leading to different subsequent
behaviour, i.e. from (a) it goes to (b), and from (c) it goes to (d).

**The
proposition:**

P: The contrapuntal
effects that we observe in Wakefield hold if and only if ExH can only exist in
motion with a speed of light.

In other
words, we state that W is true if and only if H holds, i.e. H is a necessary
and sufficient condition for W.

**Proof:**

Sufficiency
(H->W):

Suppose H
is true. We can then easily deduce that at every point in space A, B and C, the
the observed waveform will be as demonstrated by Wakefield.

(Ivor’s website contains my prediction for Wakefield 3 with contrapuntal behaviour – the analysis was based on Ivor’s theory – i.e. hypothesis H, and it was correctly confirmed by the experiment. For details see: http://www.ivorcatt.co.uk/x91cw34.htm and http://www.ivorcatt.co.uk/x842short.pdf)

Necessity
(W->H, which is equivalent to not H -> not W):

Suppose H
does not hold, i.e. at some point in space and/or in time, ExH is stationary or
does not travel with speed of light. Let’s first look, say at point C. We see a
“discharged state” – it corresponds to what we may call stationary
state electric field, i.e. E=0 – a discharged piece of TL. Here we can possibly
say that the voltage across it is constantly equal to 0 because at C it is
short-circuited.

Next, we
look at point B at the time when the voltage level is equal to 0V, say in phase
(c). We think it is a static E=0. Using the same argument as we did for point C.
One might argue that the point B is not short-circuited, but this does not
matter from the point of view of our observation – it’s just 0V.

How can we
predict that after a specific and well-defined time interval, voltage at B will
go down to -10V and not up to +10V as it would have gone had we been in phase
(a)? In other words, how can we distinguish the states in those two phases
using classical theory, where phase (a) is observationally equivalent to phase
(c).

The only
way we could predict the real behaviour in W with classical theory if we had
some ADDITIONAL memory that would store information, in another object, that
although we were stationary here in that place and time interval, we were
actually being in transit between phases (b) and (d) rather than being in
transit between (d) and (b).

The fact
that we need ADDITIONAL memory (another TL) is something that is outside the
scope of our original model, because we did not have it organised in the first
place. So, there is no knowledge in the original model that will make us
certain that from phase (c) we will eventually and deterministically go to
phase (d).

**Q.E.D.**

**Note:** The above fact of having phases (a), (b), (c) and (d) is the result of the contrapuntal effect of the superposition of the partial actions performed by the steps moving in the right and left directions. And unless that motion was always (in time and in space) with a well-defined speed (speed of light), we would not be able to predict that from phase (c) we will definitely and only transition to phase (d) and not to phase (b) and how quickly that transition will happen. The case of a fully charged or fully discharged capacitor, with seemingly stationary E field, that is a contrapuntal effect of superposed motion of ExH in all directions, is just a special case of the TL.

**Remark from David Walton:**

The only way we could predict the real behaviour in W with classical theory if we had some ADDITIONAL memory that would store information, in another object, that although we were stationary here in that place and time interval, we were actually being in transit between phases (b) and (d) rather than being in transit between (d) and (b).

is the key point.

Another way to state the same thing in different context and less formally (I think) is to point out that when two pulses travelling in opposite directions pass through each other either the B or E fields will cancel, hence demonstrating that the field cannot be the cause of the onward propagation of the em pulse.

**My response:**

That’s a great point you make. Indeed the absence of either B or E in the contrapuntal state disables us from the ability to talk about further propagation of the pulses.

Yes, the key point is the absence of memory about the dynamical process in the classical field model.

In summary:

**Illusions … How many we have every day because we don’t really know they are happening around us (not enough sensors or memory to track things). **

The contrapuntal effects are those that H G Wells probably had in mind in the shape of the Invisible Man. They blind us from reality …