On ohmic losses in caps and transmission lines

Some people object the idea of reciprocating ExH waves in a charged capacitor because they claim that then we should have ohmic losses. Why?

Why should we associate the emergence of ohmic losses with the basic ExH energy current propagation. At this level there is no point to talk about ohmic losses because at this level we have no idea about any charge movement, i.e. no electric current is defined here. It’s all about EM energy current.
Ohmic losses need only be considered at the level of the superposition of Electric and Magnetic fields, i.e. at the level of V and I values in a particular place in space and a particular point in time.
If we take any of Wakefield experiments, we can find in them an interval of time at a certain place where the odds of overlap of two reciprocating waves are such that they produce no current (i.e. the cumulative effect on magnetic field is zero), so there are ohmic losses here and then. This does not however preclude the two ExH waves to move in opposite directions.

Static fields are an illusion …

To my previous blog, proving that EM power can only exist in motion with a speed of light, one might react with a question: What about Static EM fields?

(cf. the Static Fields rubric on the wiki page about Poynting Vector: https://en.wikipedia.org/wiki/Poynting_vector)

The corollary of the proposition proven earlier is that there is NO static fields per se.

Of course we need to say what we mean by ‘static’ here. Well static means – Not moving! A common online English dictionary defines static (adjective) as follows: lacking in movement, action, or change, especially in an undesirable or uninteresting way.

So, I then have the full right to surmise that Static fields do not move with speed of light according to this definition. So, there is a contradiction with the proof. Therefore, the only way to resolve it is to conclude that Static Fields DO NOT have the right to exist!

Indeed, what is believed to be static is actually a superposition or contrapuntal effect of normally moving fields (Poynting vectors to be precise), where their stepping or pulsing effects are not visible. A normal illusion due to superposition.

One might ask but what about for example a cylindrical capacitor shown on //en.wikipedia.org/wiki/Poynting_vector ?

The answer is that – just the same thing – the are at least two power flows of ExH form there – like two conveyor belts of sheaths moving against one another, where the H (magnetic components are superposed and show the cumulative effect of H=0). Just short-circuit this cylinder from at least one edge, and you will see the effect of transition (redistribution) of the magnitudes of E and H so that the total amount of power ExH crossing the spatial cross-section will remain the same.

So Static Field (as being static in the sense of the above definition) is an illusion – just another H G Wells’ Invisible Man visiting us!

On the Necessity and Sufficiency of Poynting vector’s motion with speed of light …

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.


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.


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).


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 …

The real sense of energy conservation law is in permanent and omnipresent motion of energy

In my email exchange with Ivor Catt, a following idea came to my mind.

The law of energy conservation as it is being presented to students and understood is rather abstract as it begs for many interpretations, because energy exists in its permanent and omnipresent motion. Even if it is trapped in a fragment of space like a capacitor or an elementary particle it is in motion. 

So, what seems to be less convoluted is the law that energy can only exist in motion and it can only move at speed of light. That’s actually what conservation of energy is. This is true by Occam’s razor principle and does not need to be proven. So, it is necessarily so before or after the switch [between voltage source and a capacitor] is closed … and without this law we would not have had those prefect contrapuntal effects, including those that ’cause’ people to think we have stationary conditions in capacitors and transmission lines.

Static vs Dynamic and Charges vs Fields

There is a constant debate in Electromagnetism between the Charge-based views and Field-based views. I am of course over-simplifying the picture here, at least terminologically. But the main point is that you can talk about EM either from the point of view of; (i) objects that have mass, like electrons, protons, ions etc – I called them collectively charges or charge carriers, or (ii) entities that carry EM energy, like strength of electric and magnetic field, Poyinting vector etc – those are not associated with mass. Both views are often linked to some form of motion, or dynamics. For the world of objects people talk about moving charges, electric current, static charges etc. For the world of fields, people talk about EM waves, TE, TM and TEM, energy current, static field etc.

Often people talk about a mix of both views, and that’s where many paradoxes and contradictions happen. For example, there is an interesting ‘puzzle’ that has been posed to the world by Ivor Catt. It is sometimes called Catt’s question or Catt Anomaly.


Basically, the question is about: when a step in voltage is transmitted in a transmission line from a source to the end, according to the classical EM theory charge appears on both wires (+ on the leading wire, and – on the grounded wire): Where does this new charge come from?

Surprisingly, there has not been a convincing answer from anyone that would not violate one or another aspect of the classical EM theory.

Similar to this, there is a challenge posed by Malcolm Davidson, called Heaviside Challenge https://www.oliver-heaviside.com/ that hasn’t also been given a consistent response even though the challenge has been posed with a 5 thousand USD prize!

So it seems that there is a fundamental problem in reconciling the two worlds, in a consistent theory based on physical principles and laws, rather than mathematical abstractions.

However, there is a hope that with the way to understand and explain EM phenomena, especially in high-speed electronic circuits, is through the notion of a Heaviside signal and the principle of energy-current (Poyinting vector) that never ceases from travelling with the speed of light in the medium. In terms of energy current perfect dielectrics are perfect conductors of energy, whereas perfect charge conductors are perfect insulators for EM energy current.

So, while those who prefer the charge based view of the world may continue to talk about static and dynamic charges, those who see the world via energy current live in the world where there is no such a thing as static electric or magnetic field, because TEM signal can only exist in motion with a speed of light in the medium. Medium is characterised by its permittivity and permissibility and gives rise to two principal parameters – speed of light and characteristic impedance. The inherent necessity of the TEM signal to move is stipulated by Galileo/Newton’s principles of geometric proportionality, which effectively define the relations between any change of the field parameter in time with its change in space. Those two changes are linked fundamentally, hence we have the coefficient of proportionality delta_x/delta_t, also known as speed of light, which gives rise to causality between the propagation of energy or information and momenta of force acting on objects with mass.

Another consequence of the ever-moving energy current is its ability to be trapped in a segment of space, pretty much what we can have in a so called capacitor, and thus form an energized fragment of space, that gives rise to an object with mass, e.g. a charged particle such as an electron. So, this corollary of the first principle of energy current paves the way to the view of EM that is based on charged particles.

Potential rise of interest in STEM subjects in society

I predict that during and following this period of COVID pandemics, we will witness a significant rise in of interest and some kind of renaissance of mathematics and other STEM subjects. You might ask, why?

Well, let’s look back into history. The development of many mathematical ideas and forms such as mathematical series like geometric series, Fibonacci series, theory of probability etc. were the result of people observing various processes in time or frequency domains during those epidemics like plague, cholera and so on, that took place in the past centuries.

Now, you can see how many smart people are doing home schooling and teach their kids to look at the geometric series and exponential and power laws of the proliferation of virus. A 7-8 year ol kid can have a good grasp of the series based models because he or she could witness its manifestation (sadly, but) in vivo.

So, being an academic in Engineering and curious in anything natural, I hope there will be more students doing Maths, Sciences and Engineering after that ….

The Heaviside Prize

Last weekend I twitted on the following exciting challenge:

The Heaviside Prize:


$5000 for someone who will explain the physical reality (without using maths!) of the electric current when a digital step propagates in USB-like transmission line. Students, engineers, academics, tackle this challenge!!!

On Hall Effect from the Energy Current viewpoint

People often talk about Hall effect as being an artefact of the interaction of the flow of electrons (aka electric current) in a metal plate with an external magnetic field, which causes (as an effect of Lorentz force) a potential difference created between the longitidal sides of the plate.

See for example, this site for the description of the Hall Effect:


I have had a look at the Hall effect and tried to scribble some rough picture in terms of Energy Current.

The story requires 3 dimensions x-y-z, and it is clear that the superposition of energy currents caused by the battery (where we don’t see the H aspect), and magnet (where we don’t see E) aspect, ends up in the cumulative energy current moving in the direction xy, while H is pointed in yz and E in xz, so no wonder that its projection on z is non-zero (this is the potential difference that is measured between plates 2).

The same effect is when the boat is moving from the wind, part of which is tangential, or plane lifts up despite the initial equilibrium between its weight and the counteraction of the ground.

The trick is to create a superposition and turn the direction of the field by ‘blowing’ perpendicular energy current.

All these effects like Hall’s are just special cases of contrapuntal effects on the field from superposition of different energy currents.

As usual Occam’s razor wins!

Origins of sine waves

There is a lot of resistance amongst engineers and scientists to believing that the physics of electromagnetic signals and dynamic processes involving such signals is NOT based on sine waves. There is so much in engineering that has been and is still being invested into the mathematics and tools supporting harmonics based analytics and design activities of thousands of engineers. Equally, thousands of academics are teaching hundreds of thousands of electrical engineering students all this on and on.

But let’s think what we can learn from nature that communicates signals from one point in space to another point and does it in a most frugal and at the same time prodigal way.

Imagine that we need to send a signalling event from point A to point B in space. This clearly involves some sort of motion. What kinds of motions we know. Well, at least two. One directional – that would be, for our example, moving along a straight line between A and B. Another type of motion we know rotational. This latter one should go if there is a point in the circle or sphere around which the notion can revolve. So, if the signal event involves the change in say electric field E and magnetic field H, we know that their vector product ExH forms Poynting vector, which shows the direction of the signal propagation. This propagation can only happen at speed of light in the medium (as there has been no evidence of otherwise!). If the direction of the vectors E and H is not changing in time at point A, our signal, defined by the Poynting vector ExH, will travel from point A to point B directly, albeit, this direction may not be straight line as it may be determined by the surrounding environment’s properties of epsilon and mu. So, for example if that environment is a transmission line (TL) formed by two metallic plates, then the Poynting vector will travel in the direction defined by the TL.

Now, if E and H elements of the vector are steps, then clearly these steps will form pulses, both in time and space. Now if for example these components of the vector are themselves in the rotational motion, and this rotation of E and H happens with a particular frequency omega, then the phase of the rotation omega*time will form an instantaneous value of the angle whose sine and cosine will determine the value of the potential produced, say, by the E component, between the plates of the TL. Unfold this rotation of vector E in space in the direction of the propagation of the Poyning vector, and you get a spiral – which is a superposition of the rotational and directional motions. The projection of this spiral on the normal plane along the Poynting vector’s direction will give us a sine-wave for E, likewise a cosine-wave for H. Hence rotational shift of 90 degrees will manifest itself as a longitudal phase shift of 90 degrees.

So, to summarise, the sine-wave is a product of a combined effect of a rotational motion and longitudal motion. But what’s important is that this sine-wave has a clear point of the start and end, and it’s not being there as a fundamental element. It is a mathematical trace of the superposition of fundamental elements of motion.

Another possible source of sine-waves is a successive oscillation of step-wise process in the longitudal direction, between two points. This is something that we have already discussed in earlier blogs, where we talked about the physical processes of propagation of energy current in transmission lines. Indeed if we connect a TL which has an open circuit end with the TL which is short circuited end, we have the effect of C and L combined, and the process of reflection of the energy current in this system, will form a series of steps which can be approximated by a sine-wave. Again, the sin-wave is a mathematical product of more primitive physical process.

In my recent email exchange with a group of people arguing with Ivor Catt about the primal nature of sine-waves, I wrote:

“Mechanics tells us there are two basic motion types. Direct and rotation around a point. If we assume that ExH can follow both, the latter for example, under the influence of another force (gravity?), can help us the express the effect of “corkscrew propagation”, and hence spatio temporal sinewaves. Actually a corkscrew or spiral is a good explanation of an AC shaped energy current around a wire. Light can propagate from its source in myriads of corkscrews by the way! ”

“By the way a corkscrew-like propagation of signal (hence, information) via a medium with natural resistance or friction (usual epsilon and mu properties) would be most effective, again from mechanical analogy point of view. Nature, again, following Occam’s razor principle, would do it the same way we penetrate into a cork or a wall, and that’s what nature would always do if it needs to pass information from one point to another! Energy current screws up everything! Ha-ha!”

I also recommend to someone who wishes to visualise these corkscrew processes to have a look at these wonderful videos on youtube: