# questions about energy current (ExH slab)

Mac Rynkiewicz from Australia, who has been exploring the problem of the existence of aether, and recommended to me to read papers by Vladimir Demjanov, a Russian physicist from Novorrossisk, has posed the following interesting questions:

(1) How exactly does an E by H slab (or em radiation or photons or photaenos) manage to follow say copper, including bends etc.

(2) How exactly does a change in impedance (or a termination) give partial (or full) reflexion.

(3) How is a good conductor a good obstructor? (there is a contradiction deep inside that, especially re heat losses).

Here is my answer sent to Mac today:

My view:

Imagine a messy fall of water – like rain falling in all directions (something like we see around Niagara Falls). That’s energy current ExH. The drops of rain can happily move where they can easily penetrate. In EM terms this means very low epsilon and mu. If you put some relatively porous material (i.e. epsilon still being lowish but not very low) around, the drops will still relatively easily penetrate but partly reflect back. Imagine you put a gutter made of hard water proof material (i.e. very high epsilon). Drops will start concentrating near and along the gutter because they can’t penetrate the gutter’s material. Most likely the density of rain around the gutter will be much higher than further away from the gutter.

Let’s now turn to Mac’s questions:

1) How exactly does an E by H slab (or em radiation or photons or photaenos) manage to follow say copper, including bends etc.

In the view of the above model, ExH slab will follow copper as its impenetrable gutter.

(2) How exactly does a change in impedance (or a termination) give partial (or full) reflexion.

In the view of the above model, change in impedance will give partial or full reflection. Low impedance means high epsilon and no penetration but following the gutter. Termination (high impedance) means no more good gutter to follow, hard to disperse near the terminator, reflect the energy stream back and inscrease pressure on the gutter (e.g. higher E). If the impedance is low (higher epsilon), part of the stream is reflected part is guttered.

(3) How is a good conductor a good obstructor? (there is a contradiction deep inside that, especially re heat losses).

In the view of the above model, we should actually “reverse” (cf. “We reverse this …” as per Heaviside) the terminology when we move from electric current to energy current. From the energy current point of view we must call highly permitting material (high epsilon) low permitting material (like copper). Sponge is should have higher permittivity than copper. Copper is a gutter. Every time part of the rain that hits the gutter it loses energy. When it hits the sponge it still penetrates.

What we have in EM now is a mess. Everything is defined from the point of view of imaginary ‘electric current’ being seen as a promoter of energy propagation. The notion of materials with respect to their names like permittivity is made to serve the  imaginary world rather than material world.

So, you are quite right:  here is a contradiction deep inside that

# Looking at various ‘paradoxes’ from the energy current standpoint

There are many puzzling questions around the relationship between Maxwell’s equations and elementary particles. Many of them form unresolved paradoxes. Perhaps, physicists can explain them in one or another way, but these explanations are often fairly complex and difficult to understand by a more practically minded person.

For example:

I saw the following paragraph in the paper “A derivation of Maxwell’s equations using the Heaviside notation” by Damian P. Hampshire in 376, Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences

https://doi.org/10.1098/rsta.2017.0447

“We suggest investigating an Einstein–Podolsky–Rosen experiment . Typically, an entangled electron–positron pair is mixed and prepared as a superposition of states with equal and opposite magnetic moments (or spins). The charges are separated and the magnetic moment or spin of the electron is measured. The well-known instantaneous collapse of the wavefunction occurs, so that the positron ends up with the opposite magnetic moment (or spin) to the electron. The appearance of the moment of the positron is triggered by entirely quantum mechanical effects—no direct electromagnetic communication occurs between the electron and positron. Indeed, one can think about the two charges as a single entity. However, one can argue that we do not really know how the information that leads to the positron producing a magnetic moment of opposite sign is instantaneously received— beyond asserting it is part of the fabric of quantum mechanics, or part of the nature of a macroscopic wavefunction. We suggest that while the moment of the positron is being created (rather than excited), the production of the B-field associated with its magnetic moment may not be coupled to the production of any E-field at all. So, one could measure (∂E/∂t)r and (∂B/∂t)r in the wavefront of the positron, hoping to find B-fields with E-fields that are inconsistent with
Maxwell’s equations.”

I hypothesise that if we consider the (only!) postulate of Energy current ExH captured in finite space – pretty much as we do it in a section of Tx line, we should be able to explain the above entanglement of electron-positron as a superposition of states. My previous blogs about Wakefield 4 experiment exactly talk about the effects of this vein. We trap EM energy into a cap (Tx line section) and then short-circuit it. We have the effect of the “two-faced Janus” – where the same object switches between electron and positron states.

# A two-faced Janus, this electron!

Let’s think a bit more about the Wakefield 4 experiment.

We have already observed how it can be that in some points of the same Tx like we experience different behaviour of essentially the same object.

The point near the shortened (ON state) switch has 0V potential, so basically the E component of the Poynting vector ExH is destroyed here, but we have a full H component all the time here.

In point B – in the middle of the Tx line, we have a full swing oscillation between +7V and -7V with equal intervals of time being in each of these two states. So here we don’t have H component active but only full E component swapping its positive state to negative and back.

In points A and C we have a mix of both E and H dominated intervals.

What sort of conclusions we may make out of this?

Well, one of such conclusions is that a Tx line, first charged and then short-circuited, is something that can appear in its different spatial sides, either like a swinging capacitor (only E field is visible), or inductor (only H field visible), or a bit of both – a time-division multiplexed cap-inductor.

My hypothesis is now, is electron a tiny Tx line that behaves like that two-faced Janus?

Why not?! The entire world, as I used to hypothesise in my “Energy current and computing” paper is discretised or granulated into Tx lines where we have substances (or lack of them)  with characteristic epsilon and mu, and these “cocktails of epsilon and mu of particular values” form our matter, and behave in EM fields accordingly, turning to us with their points A, B, C etc … depending where we touch them with our instruments!

# More comments on Wakefield 4 experiment – energy hides as magnetic near the switch!

Incidentally, I forgot to say in my comments to drawings for Wakefield 4 that wherever and whenever (spatially and temporally) we have a zero potential in the waveforms, it doesn’t mean the energy current drops to zero there and then. No! Energy current there is in magnetic H rather than electric E form. For example, when the switch is being connected short, the voltage drops from 7V to 0V. That’s where and when energy current changes it’s presence from E to H. But it carries on without loss (we assume lossless Tx line).

So, the above fact does only enhance the statement that the content of the capacitor is dynamic. We have spatio-temporal changes of the entire ExH content.
Here is a hopefully useful analogy:
Energy current is just like a rotating ribbon which in some points in time passes some points in space vertically but then turns to the horizontal plane and vice versa. When this cap (Tx line) was charged uniformly to 7V the entire ribbon was moving vertically. When we jammed it by short-circuiting the switch, it had to turn to horizontal in order to pass through our jam. In other points (A,B,C)  it began to vacillate from horizontal to vertical and back.
But in order to vacillate it had to move and rotate like a conveyor ribbon inside the cap. With the switch being turned ON, we don’t push the ribbon forward we only jam it! It doesn’t need to be pushed. It has its own drive at the speed of light in the medium!
An interesting experiment would be to modulate the switch with some ON/OFF duty cycle!

# Wakefield 4 experiment – causal picture in energy current

Ivor Catt reminded yesterday about the Wakefield 4 experiment, the description can be found here:

http://www.ivorcatt.co.uk/wak4.pdf

I have sketched the space-time cause-effect diagram for it: It can be seen that in the point next to the switch after we short-circuit the cable to ground, although the normal state of potential is 0V, we have transfer of energy vi the reflection of steps with a coefficient (-1). Energy comes to this point from both sides independently. This means that as soon as say a falling step of -7V arrives from the side of point A, it gets reflected into a rising step +7V and hence the overall level of potential is unchanged.

The mid-point B oscillates with the overall amplitude of 14V from +7V to -7V.

If you look at the experimental traces from the above link http://www.ivorcatt.co.uk/wak4.pdf

especially with the compressed time resolution, we have an interesting effect of sine-like wave oscillation at the level of steps (rather than conventional sine-wave as an envelope in condensed circuit-theoretic LC circuits) which takes place in the middle of the loop – point B, and this oscillation is totally ‘hidden’ from the view at say point of the switch, which ‘thinks’ that the cable is in static 0V state. This is a wonderful effect from the distributed-capacitor of the Tx line. The moving energy current is invisible to the outside world from the terminal point but it actually stays in the Tx line for a a fairly long time even with the unmitigated natural losses of the real-copper cable. The system has hidden memory to perform energy transfer!

# Is energy current and speed of light vector or scalar?

Yesterday, Ivor Catt effectively questioned whether it matters at all whether energy current, and its velocity, is a vector or scalar:

” ExH: “ExH was the primitive … By definition, I think it is a scalar. It cannot be a vector because there is no directional information inherent in it. It is a single constant for the medium.” Malcolm Davidson

Perhaps Malcolm made a mistake here. None of us is perfect.
I prefer to not talk about vectors and scalars. In our book, we never mentioned them. http://www.ivorcatt.org/digital-hardware-design.htm . I have never mentioned them in any of my articles, including these; http://www.ivorcatt.co.uk/x18j1.htm
I wonder if anyone will venture that in that case, our writings (and seminars) are valueless. I suggest none of us three ever mentioned vectors and scalars in the seminars we gave for ten years. http://www.ivorcatt.co.uk/43.htm . We earned a lot of money for ten years not mentioning vectors or scalars.
Seminars called “Digital Electronic Design Seminars” and no mention of vectors or scalars! One of us is called Dr. David Walton! Earlier he worked in Dublin with Nobellist Walton (no relative).
I should finally mention that I do not object to anyone using the words. The above is just a smokescreen for my co-author Malcolm. The three of us spent decades designing digital electronics, and became quite sophisticated designing high speed digital systems.. None of the engineers I worked with in the UK and USA ever mentioned vectors or scalars.
When  I was Principal Lecturer in a college, I never mentioned vectors or scalars. Nobody else did either.
Ivor Catt
++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++

Today Malcolm Davidson wrote in response to Stephen Crothers:

Hi Stephen,
You stated;

ExH: “ExH was the primitive … By definition, I think it is a scalar. It cannot be a vector because there is no directional information inherent in it. It is a single constant for the medium.” Malcolm Davidson

If Malcolm means by ExH a cross product, the cross product only has meaning when operating on vectors. Both and H

are vectors. The cross-product of two vectors is a vector that is orthogonal to both vectors, such as and H, and, by the

right-hand rule, points in the direction of one’s thumb when one’s fingers curl from E to H. The magnitude of the cross

product of two vectors A and B is AB times sine of the angle between A and B, the angle between A and B being that which

is less than or equal to 90 degrees, A and B being the magnitudes of the vectors A and B respectively. Hence the magnitude

of the Poynting vector is EH, since and H are orthogonal to one another.

I agree with everything you state above, within the conventional way we were taught, however these days I look at it from a slightly different perspective. (and of course) for all these years we discussed energy current using the phrase “The Poynting Vector!

Because we can know only the value at any one point, the direction being defined by the inherent Tx Line itself isn’t the idea of a vector superfluous? Of course I immediately think of a microwave line of site Tx & Rx system. Given that the ExH “vector” is moving at speed c and  has it’s own coordinate system built in I cannot think of where we would apply the basic rules of vector algebra.

Any thoughts? Also is it useful ? If I take two microwave beams . at say 45o angle how do the E & H fields add up to the scalar value that could be measured. anyway thanks for keeping me honest!

Regards,

Malcolm

My response to that was:

Hi Malcolm,

I agree with you, likewise I agree with Stephen. The notions of scalar and vector are the the kind of mathematical quagmire which puts some pseudo-strictness on our way of thinking. Of course we can take the line of reasoning where we can say, well, a scalar value is a special case of vector value, where we don’t show the direction because the direction is given by an out-of-model assumption. In that way, your reasoning  about the Tx giving us such a direction removes from us the liability for (not) talking about the direction. All this is a mathematical maze in which we can be easily trapped. And here, I am on Ivor’s side – does it really matter if it is vector or scalar? The point is about the Occam – it just makes us see the everlasting ability of universe to transfer energy at c. One might ask, in what direction? the direction is defined by the way how the EM (or gravitational …) field is perturbed in some point in space and the materials (including vacuum) surrounding this point.

Kind regards

Alex

# Towards computing on energy current

My further discourse with Ed and Ivor last night has resulted in the following message from Ed.

Ed:

Alex,

your yesterday message to Ivor makes me consider once again the mathematical equations Ivor introduces in his paper “The Heaviside Signal”. I concentrate on the equation c(dE/dx) = dE/dt in Appendix 1 (ignoring the ” – ” on the right side). This formula is constructed by interpreting the propagation of a voltage step in space (first diagram) and in time (second diagram) as a velocity v of motion in the direction of time, v = dx/dt, that is, a vector quantity. In the diagrams, this velocity v is symbolized by the letter c. With dx/dt = v the equation c(dE/dx) = dE/dt results in c = dx/dt = v. This asserted equality of c and v then insinuates that the voltage step would really “travel” in space and time with a vector velocity v = c in the direction of time. As I see things, the equation v = c is mistaken, since v is a vector quantity, which c is not. c is a scalar, as is proven by the Poynting vector E when put over p, resulting in c: E/p = c. Vector E over vector p = mv; v is a vector, c is a scalar quantity. Q.e.d. So c does not symbolize some velocity of some motion in the direction of time. What else does this factor mean, as it is  undoubtedly a quotient of a quantity of space, L, over a quantity of time, T, c [L/T] ? If you draw a diagram of Cartesian coordinates, space L in the vertical axis, time T in the horizontal, and you put the elements of space, L, over the elements of time, T, you get the constant quotient [L/T] to characterize the diagram as its parameter, or “grating constant”. Evidently this constant is not a vector, but a scalar. This shows that not every quotient dx/dt [L/T] represents a velocity of propagation in time, as the vector v does it. Rather it may be the case that such a quotient, the more if it is a constant (!), just represents the parameter of the space-time frame of reference wherein an observed phenomenon like the above-mentioned voltage step takes place. And this takes us into the middle of our finding that Poynting’s energy vector E = pxc differs from the classical scalar energy E = mv^2/2. This difference, as we can see now, is a consequence of not distinguishing between velocity v (vector, and variale), and the scalar constant c. Do you agree?

Ed.

To which I have replied the following:

Ed,

I am afraid I disagree with your conclusion that c coming out of the analysis of c(dE/dx) = dE/dt in Appendix 1  is a vector!

You raise a metaphysical story around it I am afraid.

This c is a constant coefficient. c is not a vector – its scalar.We have vectors around it dE/dt and dE/dx. These are vectors – one is force (or power in modern terms) and the other is momentum (as we agreed with you before).

Full stop here!

Then, we should acknowledge the fact that there is a physical element behind this c – and this is energy current, which emanates in the universe from its Big Bang!

This is the carrier of interactions in Nature. This wasn’t known to Artistotle, Galileo, Newton, Maxwell … Ivor was and is the first to give this carrier the appropriate place.

If you had known a bit of the physics of communication (I recommend you to read Hans Schantz papers and book for that) you’d realise that its completely natural for communication (or interaction for that matter) to have a carrier – and this carrier for ExH does not need massed matter – it can perfectly well live in vaccuum.

That’s my take on this. You played an important role in this discourse. We have identified what momentum is in Catt’s theory and Heaviside Signal. Eureka!

What I have also discovered thanks to Ivor is the potential way for future computing – which is based NOT on envelope characteristics – such as exponentials and sines, but on discretised steps – this can potentially give way to improving the speed of computations by 2-3 orders of magnitude – we just need appropriate devices to support this speed and react to changes transmitted in energy current. I am already working on this!!!

Alex

# Momentum in energy current

This is what Ed Dellian has just written to Ivor Catt:

Dear Ivor,

this discussion on the phone today was not useless, as I see it. I learned that we agree that in the phenomenon which you call “energy current” there is nothing which actually, as an individual something, changes place in time, from now to then, and in space, from here to there: no electron, no photon, no wave packet, etc. So I would say there is no “current” of anything, using the term “current” in its everyday meaning.

What then is your “energy current”? You say, it is “just energy”. But you are not ready to tell me whether or not it is a material substance, say a flow of something material or not material, even though it cannot be such a flowing something according to what we just have agreed on. You are not able to say whether it is “scalar energy” or “vector energy”, even though these are very different things, according to their very different measures. So to say that it is “just energy” makes no sense. While you remain silent about the meaning of “energy current”, I can tell you what it is: It is what science calls “momentum”, symbolized by the letter p. It is true that this letter doesn’t appear in your papers, but it is also true that this concept does indeed appear there, since it can be mathematically identified for instance in your “The Heaviside Signal”, where you call it “energy density”. The fact that it actually is not “energy” and not “energy density” but “momentum” can be demonstrated by dimensional analysis, which is the only means that allows to identify a scientific term independently of its name.

Please note that by this identification I just want to harmonize your finding with the basic elements and principles of theoretical physics in order to make it a homogeneous element of the mathematical language used in this field. By the way, to speak of an “energy current” that “continues to move because that is what energy currents do” is a tautological unscientific phrase, so long as science consists in indentifying the natural causes of natural effects. Sorry. Also note that to insist on identifying your “energy current” as not “energy” but “momentum” in the context of the principles and concepts, that is, of the language you call the “framework of modern physics”, certainly does not mean to call that framework of language into question. Rather it means to use terms unequivocally, as the indispensable basis of understanding. You are confusing “cause” and “effect”, if you insist on “energy current”, and you are blocking the progress of em science that is at hand so soon as we now understand the true meaning of Poynting’s vector, misleadingly symbolized by the letter E, as via E/p = c = constant representing the natural law of cause and effect, that is, the law of generation and propagation of momentum, c (scalar!) being not  velocity (vector!) of translation from A to B, but the “velocity of generation” here and now. This law is the most basic law of local interaction, in mechanics as well as in electromechanics, in thermodynamics, in special relativity, and in quantum mechanics. And, to reveal this common basis is one reason why I, trying to do what you call “saving science”, have been doing now for nearly 40 years what I am still doing, and quite successfully, as I see things. I’m glad to see that your finding, correctly identified as an effect of some generating cause, perfectly harmonizes with what I have found myself.

Best regards,

Ed.

+++++++++++++++++++++++++++++++++++++++++++++++

And this is what I wrote to Ivor:

My summary:

From my email to Ed last week:

It (viz. Figure from The Heaviside Signal) shows the relationship: that is equivalent (Right?) to your definition of c as the constant geometric proportionality coefficient,  as long as we agree that dE/dx (spatial energy density) is equivalent to momentum p and dE/dt is equivalent to your E (temporal energy intensity, aka power).

# The debate continues and moves on to what Momentum is in Electromagnetics – first signs of agreement …

The debate continued – it has moved to the notion of momentum.

And we seem to start to find agreement on some points.

Alex:

Thank you. I can accept your reasoning for the sake of Natural Philosophy and possibly application to Newtonian Mechanics.

(there is an expression in English “for the birds” – what I don’t want is that all this is useless for what we can see in transmission lines and Catt Theory)

So, let’s try to find some common ground. In fact I made my first attempt in my Royal Society paper, where I talked about your reasoning (I hope it wasn’t in contradiction with you) and how it may be applied to Electromag (note that I wasn’t specific about applying it to Catt Theory).

Basically, I am struggling in defining what momentum p is in terms of Catt. And I think this is what Ivor asked you his last email.

For example, if you say that E and p are in the same place and at the same time in the transmission line, and they are in proportion of c, we can argue that, since c is sqrt of 1/mu*eps (where mu and eps are the characteristics of the space where we are interested in the presence of E and p), then, basically E and p are the characteristics of the Poynting vector value ExH in that place in space and time. Right?

I suppose that, then since Ivor used to say “Energy density = EH/c”  (where he wrote the vector product in shorthand, but basically he meant Energy density=ExH/c)

it looks like in your terms of E/c=p, we effectively say that p (momentum) is Energy density. Right?

So, this momentum propagates in transmission line together with ExH.

Now a more interesting stage of discourse:

You state that this momentum p (i.e. the “effect” of the Energy being “cause”) if it affects some finite mass it may ‘hit’ it with the effect of mv, right?

So, we can have the mechanical (or material ?) consequent of this effect in particles, (if) located next to the point of contact with them, so that these particles move (possibly, tangential to the plane of ExH?)  with velocity v. Right?

Let first agree on the above “Right’s?”, before we move further, OK?

Ed:

natural philosophy began in the 17th century with Galileo and Newton as a geometrical theory of motion (description) and its generating cause (explanation).The aim was to understand how Nature really works. The basic insight was that the observable processes in Nature were generally such of motion, its generation, and its destruction. The common conviction was that “he who hasn’t understood motion, has not understood Nature” (Henry Oldenbourg, first secretary of the Royal Society, founded 1660). Galileo laid the foundation in his “Discorsi” (1638), beginning with a description of unresisted uniform straightline motion in space and time. He found that the motion of a body covering some space in consuming some time proceeded according to the geometrical law of equal integer multiples (Euclid),  the steps of space, ∆L, being proportional to the steps of time, ∆T, so that the relation of space to time was constant [L/T]. Here is Galileo’s diagram. JK is the standard of “time”, GH is the standard of “space”. Note that every increment of space is proportional to the corresponding increment of time (AB/DE, BC/EF, etc.), so that the relation “space over time”, [L/T], is always constant, independently of the measure (length) of the increments. This constant parameter [L/T] characterizes the natural “space-time frame of reference” of motion given through the standards of time, JK, and space, GH. Space, time, and motion are discrete or quantized, being scaled standards, according to the Ancient “atomistic” view held by Galileo and Newton.

Galileo also investigated the “cause” of motion, starting with “change of” motion in the case of “acceleration” to be observed in the phenomena of free fall, using the “preferred” absolute space-time frame of reference just described. The result was that motion is generated stepwise by addition of finite increments ∆L, ∆T of space and time, and that the generating cause thereof is as a quantity preserved when a moving body’s direction changed from the vertical to the horizontal, the body, now moving uniformly, remaining able to ascend to the same height decelerating as the one which it had left accelerating vertically. The cause of the body’s power to continue moving, and to ascend again, was called “impetus” by Galileo, using an old term of “cause”, or “force”. But Galileo also used other terms for it, such as for example “vis impressa”, the impressed force. The underlying view was that natural entities were characterized not by their names but by their “measures”, since everything in Nature should have a specific “measure” according to an old wisdom. Consequently, natural science had to be a quantitative science, investigating the individual “measures” or quantities of the natural entities inquired, such as “motion”, “change of motion”, and “force” as its cause. Finite “spaces” and “times” of motion were measured relatively to the natural or “absolute” infinite standards of “time”, JK, and “space”, GH, as in the above diagram, that is, relatively to the absolute space-time frame of reference of motion.

On this background arouse in the second half of the 17th century the problem of “the true measure of force”. This problem leads immediately to the centre of our discussion about what it is that in electromagnetic theory “proceeds” through a transmission line at the constant velocity c. However, in order to understand what’s going on we must add another short reflection on the “history” of science.

In the wake of René Descartes’s natural philosophy it had become a common view in the middle of the 17th century that “force” as a cause of motion had to be measured through its effect, the generated motion; in symbols, with F for force, and p for mot-ion: F = p, or differently, as the geometers put it, F ~ p, or F/p = c = constant, with c as “proportionality constant”. But in 1686, one year before Newton’s Principia appeared in London, the German mathematician Gottfried Wilhelm Leibniz published  in the German journal “Acta eruditorum” a paper entitled “Short demonstration of a remark-able error of Descartes and others related to a natural law according to which God should always maintain one and the same quantity of motion, and how they misuse it in mechanics”. In this paper, Leibniz criticized the F = mv = p concept of “force”, developing a different law by calculating the “force” (cause of fall) of a falling body by  the distance fallen. Of course, Leibniz’s measure of “force”, later baptized “vis viva”, the living force, resulted in the “squared” relation F = mv^2, which became later on the “concept of energy”, E = mv^2/2.

Newton, however, held the view that the “force” F as cause of motion must be measured in proportion to its effect, which is motion, so that a quantity of force would generate and maintain a proportional quantity of motion: F/p = F/mv = c = constant. This is the background of Newton’s theory of force and motion, as it emerges from the Principia (def. 2 of “quantity of motion”, def. 3 of “quantity of inertial force or impetus”; def. 4 of “impressed force” to generate changes of motion, as described in Newton’s  second law of motion). The formula F/p = c relates to Newton’s concept of “force innate in matter” or “impetus” which is the force that maintains uniform straightline motion. Note that the constant c to connect force (cause) and motion (change of) as its proportional effect is the same as in Galileo’s basic law of motion described above. The different Leibnizian concept of force, or “energy”, was rejected by Newton, because Leibniz, when he derived it, had committed a “wonderfully philosophical error” (Samuel Clarke). The error was to measure the force in proportion to distance (space). Galileo had demonstrated in his “Discorsi” that in this case the falling body would occupy different places in space at the same time which is absurd and impossible. Therefore, the only realistic measure was “force proportional to time”, leading to the well-known Galilean term of acceleration [L/T^2] of free fall.

With Leibniz’s paper of 1686 there arouse a serious controversy among scientists and philosophers concerning the problem of the true measure of “force”, the so-called “vis-viva controversy”. Was the true measure of force given by mv^2, or was it given by mv? The controversy lasted over 60 years until 1746. In this year, the French philosopher Jean d’Alembert published a book in which he proposed to measure the basic “force” according to the measure of mass-acceleration, d(mv)/dt, and to gain on this basis by integrating over space (i.e. by the line integral of d(mv)/dt) the measure mv^2, and by integrating over time the measure mv. Thus the term d(mv)/dt seemed to be the common “root of” the controversial concepts, which view finally settled the vis-viva controversy.

This Leibnizian method became the foundation of “classical mechanics”, as is well-known. In this context, however, the Leibnizian concept of “energy” advanced to be the only practically relevant “measure of force”, so that it, symbolized by H, even became the basic concept of the Hamilton-Jacobi form of mechanics, or “dynamics”, as the new science was called, following (not only) the terminology of Leibniz (cf. his “Specimen Dynamicum” of 1695). Note that Newton never used neither the terms nor the concepts of “energy” and “dynamics”. Note also, however, that nobody ever has noticed, much less corrected the “wonderfully philosophical error” which the Leibnizian energy concept is based on, even though Samuel Clarke had made the error public in a published correspondence he entertained, as Newton’s amanuensis, with Leibniz during the years 1715/1716 (the famous “Leibniz-Clarke –Correspondence”).

In the first half of the 19th century scientists (engineers) learned by experience and experiment that neither the time-reversible concept of “force”, d(mv)dt, nor the scalar concept of “energy”, mv^2/2, was able to describe the natural process of generation of motion in the direction of time as required according to natural experience (the “time-arrow”). As a consequence they developed the new science of thermodynamics” on a partly different foundation.

In the second half of the 19th century James Clerk Maxwell developed his mathematical theory of electromagnetism, based on Michael Faraday’s mainly experimental discoveries. Maxwell, as he says it in the Preface to the First Edition of his 1873 “Treatise”, endeavoured “to place in as clear a light as I can the relations between the mathematical form of this theory and that of the fundamental science of Dynamics”. This, however, meant to uncritically apply the basic principles of Leibnizian “dynamics” unconscious of their implicit deficiencies as outlined above. The result was the electromagnetic theory the principles of which we are now discussing, inconsistent as they are due to Maxwell uncritically presupposing as granted the principles of Lei-nizian “dynamics”.

In your email of yesterday, which I received at 14.29 h local time, you write:

Basically, I am struggling in defining what momentum p is in terms of Catt.”

As I see things, we should at first see what momentum p is in terms of Maxwell. Did he take the term p = mv for “electromagnetic momentum”?

– And here I must stop today. What I will do next is to disentangle the confusion of concepts that characterizes Maxwell’s theory and Ivor Catt’s as well. This has first required –inevitably from my point of view – to show where the Non-Newtonian concept of scalar “energy” (uncritically used by both Maxwell and Catt) stems from, and what its deficiency is; you find the analysis and the result above.

In my next mail I wrote:

Alex:

While I am waiting for your comments, here is the crucial diagram from Ivor’s paper: The Heaviside Signal It shows the relationship: that is equivalent (Right?) to your definition of c as the constant geometric proportionality coefficient,

as long as we agree that dE/dx (spatial energy density) is equivalent to momentum p and dE/dt is equivalent to your E (temporal energy intensity, aka power).

What do you think about all this (together with my earlier points)?

To which Ed agrees:

Ed:

In addition to what I just have sent you I agree that this diagram and your explanation results exactly in E/p = c = constant,

E representing a vector quantity in linear relation to p, and therefore different from the scalar E proportional to p^2 of classical mechanics and Maxwell’s theory.

As we now can see, momentum (dE/dx in your example, identical with Catt’s paper, Appendix 1) plays a central role in this context.

And that’s what he just sent to me prior to that:

Ed:

in my first reply I outlined the history of concepts of “cause” and “effect” in the theory of motion to show the confusion about the concepts of “force” and “energy” as “cause”. But the overview also shows that the concept of “effect”, that is, the concept of “momentum” p = mv, dimensions [ML/T], has not changed since the time of Galileo and Newton. As my last proposal was to look what p means in Maxwell’s theory, I want to point to his “Treatise”, vol. I, paragraph 6 “Derived Units”. Here he introduces “momentum” as “unit of mass moving with unit of velocity”, the dimensions of p being [ML/T] accordingly. So we see Maxwell’s concept of momentum to be identical withGalileo’s and Newton’s.

But we also see here confusion arise as Maxwell next introduces “force which produces unit of momentum” with units [ML/T^2]. This alleged “force” to produce “momentum” then works by integrating the force over time, which is certainly mathematically possible, but mathematically only (applying the calculus). It has nothing to do with reality, that is, generation of an effect by a cause in space and time. Therefore Maxwell’s “force” [ML/T^2], identical with the “force” of classical Non-Newtonian mechanics, is certainly not the real generating cause of motion (momentum). Note that this “force” of dimensions [ML/T^2] “is” nothing other but “the rate of change of momentum in time”, d(mv)/dt, so it is qualitatively (“genetically”) identical with “momentum”, and cannot therefore stand for the heterogeneous “cause” to “produce” momentum.

Now, to answer your question “what momentum p is in terms of Catt” I refer to Catt’s paper “The Heaviside Signal” as well as you. Here Catt says that the Heaviside signal “always contains one kind of energy only, which is equal to the product of E and H at that point”. This product ExH, divided by c he calls “energy density” here, but somewhat later only ExH is called “density”, and next he calls ExH the “Poynting vector”, and then the “energy current”. Nowhere does the term “momentum” appear in this paper. In a mail of 6 Sept. Catt even asserted that momentum p has no place in his “universe of discourse”.

The fact  is, however, that Catt’s ExH must be understood as simply the “cause” of momentum p, since divided by the constant c it just produces p. Catt writes “ExH/c = Energy density” but is not aware that this “energy density” is just momentum p. Of course, Catt’s term ExH must represent what we (you and me) have identified as “vector energy”, because only this vector energy, not the scalar energy of classical mechanics, can, devided by c, produce p. Here we meet with the difference between scalar energy and vector energy for the first time, which Maxwell did not realize, so far as I can see, nor does Ivor Catt. Therefore, as far as momentum p is concerned, I agree: Momentum p is exactly what Catt calls “energy density”. It is also true that this momentum “propagates in transmission line together with ExH”, as you put it.

Next stage: You infer that this momentum p “may hit some finite mass with the effect of mv” so that this mass moves with velocity v”.

This I doubt. Momentum p is not “mass” and not “velocity”, and not necessarily a material something. It is a natural entity in its own right, only the measure of which is dimensionally equal to the measure “mass times velocity”. So, if some finite mass is hit with momentum p = mv, for example an elementary particle, m, which is at rest, and is fixed in a compound so that it cannot leave its place (move, that is), the hit particle will somehow oscillate, and respond to the hit according to the rules of perfect elastic collision.This means that the particle will take the momentum, react by oscillating proportionally, and will pass this vector effect to its neighbour without moving itself, and so it happens with the neighbour particle, and so on, as can be seen in the case of “Newton’s cradle”. The process of “passing” will certainly not happen “instantaneously” but in time and space, even though very, very swift, (not at velocity v!), according to observation. Provided the pendulum line is long enough, so that one can measure the time it takes to propagate the momentum through the resting pendulums over a certain distance, dividing the distance by the time will yield the “velocity of momentum transfer”, which in the ideal case should equal c. Right?

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To this I can state that, in the Wakefield experiment quoted in my paper “Energy current and computing” https://royalsocietypublishing.org/doi/full/10.1098/rsta.2017.0449

I am putting that effectively dE/dt (power or Poynting vector) causes momentum p (in our terms now dE/dx – energy density), which can be observed via the oscilloscope connected to a point in the coax cable transmission line – it’s a measurement, and it can only be seen thanks to some effect in the matter – so I continue to be convinced that we have some form of energy conversion from energy current ExH to momentum p=mv, which is what is customarily called electric current!

I later wrote to Fei Xia the following:

I think my recent discussion with Catt/Dellian hasn’t shaken my position regarding Fundamentals expressed in my paper on Energy Current and Computing.In fact it probably has enhanced it by providing better understanding of what momentum p is in terms of Heaviside signal. Some disagreement with Ed Dellian remains as to how we pass the momentum to the organs that measure it. I state that it can only be done via action on matter (with mass – hence I formulate it as ‘hit’ the matter with mv)

Dellian seems to see it immediately as moving into the world of oscillating pendulums – which then removes the effect of the propagating ExH.

But we are gradually getting to some form of convergence.

My position is closer to Catt than to established views about passing energy (only via Newton cradle), which doesn’t necessarily imply that we have a speed of light c.

Catt’s view is that EM energy can and can ONLY move with speed of  light in the medium – without any matter involved (so Newton’s cradle ain’t obvious!).

So, seeking truth on what momentum is continues …