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.

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 …

80th Anniversary of late Professor David Kinniment and my lecture on Research Leadership for Iraqi Researchers

Yesterday, 10th July, was a special day in the calendar – we celebrated the 80th Anniversary of late Professor David Kinniment. David was my closest mentor at Newcastle when I arrived here in 1991.

He was a pioneer of research in metastability , arbitration and
synchronization as well as VLSI design led Microelectronic Systems Design group at Newcastle for 20 years.

We generated many ideas for projects, PhD research, papers, design tools, conference and industrial presentations. Above all, we just enjoyed spending time in discussions about science, culture and genealogy. David and his wife Anne welcomed on many occasions the whole Newcastle MSD team in their wonderful Sike View house in Kirkwhelpington in the middle of Northumberland.

By lovely coincidence it wouldn’t have been a better occasion yesterday that I was kindly invited to give a lecture “Becoming a Researcher: from Follower to Leader” to the wonderful 100+ audience of Iraqi researchers – the invitation came from my PhD alumni Dr Ammar J M Karkar, Professor and Director of IT Research and Development at University of Kufa, Iraq.

The lecture is now available on YouTube https://youtu.be/JnfObxmTslc

All the best!

The Heaviside Prize

Last weekend I twitted on the following exciting challenge:

The Heaviside Prize:

https://youtube.com/watch?v=mr9-Nu5HvWM&feature=youtu.be…

$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!!!

Static vs Dynamic when referring to the electric field in capacitor

I wrote in my paper “Energy current and computing” (https://royalsocietypublishing.org/doi/10.1098/rsta.2017.0449 ):

“there is no such a thing as a static electric field in a capacitor. In other words, a capacitor is a form of TL in which a TEM wave moves with a single fixed velocity, which is the speed of light in the medium”.

This statement causes some controversy – Ivor Catt refers to it as “heresy”.

Here I would like to explain what is meant here by static/dynamic:

One of the important aspects of considering the distinction between ‘static’ and ‘dynamic’ is that of what we mean by dynamic/static in the first place.

I think that the notion of dynamic/static, first of all, concerns as to whether a particular value (say, electric field intensity E) changes in time or not, i.e. whether dE/dt is non-zero or not. Another notion of dynamic/static is about the movement of the value in space (and, necessarily in time because movement in space cannot be instantaneous!), so if we talk about the electric field E, we can be talking about dE/dx being non-zero, and here is the critical notion of the link between dE/dt and dE/dx, which MUST be mediated by dx/dt (speed of light in the medium!). The latter MUST BE ALREADY SET UP, ab initio, and that’s what Ivor Catt’s Heaviside signal is about. So, even if we have an impression that something is static – like electric field in a fully charged or fully discharged capacitor, this impression will be viewed in the form of contrapuntal dE/dt=0, we somehow need to retain the notion of c=dx/dt being constant and non-zero. But then the immediate question arises of: what is there that is moving in a longitudal direction at speed c? And the answer is the Heaviside signal! What else? So, my understanding is that THIS MOVING THING is what makes me state that that there is no such a thing as a static electric field in a capacitor!

“Contrapuntal superposition” of Heaviside signals unravelled as a lookalike state coding problem in asynchronous circuit design

This article http://www.ivorcatt.co.uk/x267.pdf by Ivor Catt – published (now more than) 40 years ago – proposed looking at transverse electromagnetic (TEM) wave by means of the so-called Heaviside signal. Heaviside signal is basically EM “energy current”, described by Poynting vector ExH (E and H are electric and magnetic field intensities, respectively), that travels and can only travel in space with a speed of light in the medium, fully determined by its fundamental parameters permittivity (epsilon) and permeability (mu) – i.e., c=1/sqrt(mu*epsilon). The key point here, I should again stress, is that ExH cannot stand still – it can only travel with speed of light. One might ask, where does it travel? It travels where the environment – i.e the combination of materials – leads it to, and in practice it predominantly goes where the effective impedance of the medium is smaller. The effective or characteristic impedance of the medium, Z0, is also fully determined by the permittivity (epsilon) and permeability (mu), i.e. Z0=sqrt(mu/epsilon). Moreover, Z0=E/H – this is sometimes called the constant of proportionality of the medium.

Why is this look at the TEM wave more advantageous than some other looks, such as for example, the so called “rolling wave” of the alternating concentrations of magnetic energy 1/2*mu*H^2 and electric energy 1/2*epsilon*E^2 in the direction of propagation? As Catt shows in the above article, this more conventional way is actually meta-physical, because it is based on the assumption of causality between the electric field and magnetic field and vice versa. The latter is a form of tautology because it creates a non-physical, but rather, mathematical or equation-based “feedback mechanism”, which does not make sense in physics.

Another important issue that calls for the use of Heaviside signal is that it retains the notion of the travelling EM “ExH slab” in each direction where it can travel, and hence its change-inducing geometric causality between points in space. As exemplified by the effects of travelling TEM waves in transmission lines (TLs), this look, for example, naturally separates the incident wave from the reflected (of the interface with another medium) wave, or from another wave that may travel in the opposite direction. As a result, the analysis of the behaviour of the TL becomes fuller and can explain the phenomena such as superposition of independent waves in cases such as cross-talk between TLs. Here is another paper by Ivor Catt – published more than 50 years ago – http://www.ivorcatt.co.uk/x147.pdf and subsequent clarifications – http://www.ivorcatt.co.uk/x0305.htm of the superposition of the even and odd modes (modes of TEM travelling with different speeds of light in the medium due to different epsilon and mu conditions arising between adjacent pairs of metal lines).

As shown in these papers, the view provided by the conventional theory is necessarily contrapuntal – it looks at the combined EM field in every point in space and in time. As a result it simply overlays the travelling ExH signals. And that’s what one can see by measuring voltage and current in points of interest on the TL. Or, equally, what one could see on the oscilloscope’s waveforms at points in space. Interestingly that looking at the same time at a number of points, in a spatially orderly way, leads to a conjecture that there is an interplay of several travelling TEM waves, but the conventional rolling wave approach would not explain the physics behind them properly!

What is remarkable in this for me is that this reminds me the difference between two types of models in asynchronous control circuits and how one of them obscures the information revealed by the other. One type of model that is based on recording purely binary encoded states of the circuit (akin to the contrapuntal notion). The other is based on a truly causal model (say Signal Transition Graph – or STG – called Signal Graph or Signal Petri Net in my early publications: https://www.staff.ncl.ac.uk/alex.yakovlev/home.formal/LR-AY-TPN85.pdf or https://www.staff.ncl.ac.uk/alex.yakovlev/home.formal/AY-AP-PN90.pdf), where we have the explicit control flow of signal transitions or events running in the circuit. The difference between these two looks is often manifested in the so-called Complete State Coding problem (cf https://www.researchgate.net/publication/2951782_Detecting_State_Coding_Conflicts_in_STGs ). If we only look at the contrapuntal notion of the state without knowing the pre-history of the event order we cannot distinguish the semantically different states that map onto the same binary code provided by the signals. To distinguish between such states one needs additional information or memory that should be either provided in the underlying event-based model (the marking of the STG) or by introducing additional (aka internal or invisible) signals (in the process of solving the CSC problem).

I am not claiming that the above-noted analogy leads to a fundamental phenomenon, but it reflects the important epistemic aspect of modelling physical world so that important relationships and knowledge are retained, yet in a minimalist (cf. Occam’s razor) way. Some more investigation into this analogy is needed.

Correction on my previous blog and some interesting implications …

Andrey Mokhov spotted that to satisfy the actual inverse Pythagorean we need to have alpha=1/2 rather than 2. That’s right. Indeed, what happens is that if we have alpha = 1/2 we would have (1/a)^2=(1/a1)^2+(1/a2)^2. This is what the inverse Pythagorean requires. In that case, for instance if a1=a2=2, then a must be sqrt(2). So the ratio between the individual decay a1=a2 and the collective decay is sqrt(2). For our stack decay under alpha = 2, we would have for a1=a2=2, a=1/2, so the ratio between individual decay and collective decay is 4.

It’s actually quite interesting to look at these relations a bit deeper, and see how the “Pythagorean” (geometric) relationship evolves as we change alpha from something like alpha<=1/2 to alpha>=2.

If we take alpha going to 2 and above, we have the effect of much slower collective decay than 4x compared to the individual decay. Physically this corresponds to the situation when the delay of an inverter in the ring becomes strongly inversely proportional to voltage. Geometrically, this is like contracting the height of the triangle in which sides go further apart than 90 degrees – say the triangle is isosceles for simplicity, and say its angle is say 100 degrees.

The case of alpha = 1/2 corresponds to the case where delay is proportional to the square root of Voltage, and here the stack makes the decay rate to follow the inverse Pythagorean! So this is the case of a triangle with sides being at 90 degrees.

But if alpha goes below 1/2, we have the  effect of the collective decay being closer to individual decays, and geometrically the height of the triangle where sides close up to less than 90 degrees!

Incidentally, Andrey Mokhov suggested we may consider a different physical interpretation for inverse Pythagorean. Instead of looking at lengths a, b and h, one can consider volumes Va, Vb and Vh of 4-D cubes with such side lengths. Then these volumes would relate exactly as in our case of alpha=2, i.e. 1/sqrt (Vh)=1/sqrt(Va)+1/sqrt(Vb).

Cool!


Charge decay in a stack of two digital circuits follows inverse Pythagorean Law!

My last blog about my talk at HDT 2019 on Stacking Asynchronous Circuits contained a link to my slides. I recommend you having a particular look at slide #21. It talks about an interesting fact that a series (stack) discharge rate follows the law of the inverse Pythagorean!

It looks like mother nature caters for a geometric law of the most economic common between two individual sides.

My Talk on Stacked Asynchronous Circuits at HDT 2019

I just attended a Second Workshop on Hardware Design Theory, held in Budapest, collocated with 33rd International Symposium on Distributed Computing http://www.disc-conference.org/wp/disc2019/

The HDT’19 workshop was organised by Moti Medina and Andrey Mokhov. It had a number of invited talks, and here is the programme: https://sites.google.com/view/motimedina/hdt-2019

I gave a talk on Stacked Asynchronous circuits.

Here is the abstract: In this talk we will look at digital circuits from the viewpoint of electrical circuit theory, i.e. as loads to power sources. Such circuits, especially when they are asynchronous can be seen as voltage controlled oscillators. Their switching behaviour, including their operating frequency is modulated by the supply voltage. Interestingly, in the reverse direction if they are driven by external event sources, their switching frequency determines their inherent impedance which itself makes them ideal potentiometers or voltage dividers. Such circuits can be stacked like non-linear resistors in series and parallel, and lend themselves to interesting theoretical and practical results, such as RC circuits with hyperbolic capacitor discharges and designs of dynamic frequency mirrors.

Here is the PDF of my slides: https://www.staff.ncl.ac.uk/alex.yakovlev/home.formal/stacked-async-budapest-2019.171019.pdf

New book on Carl Adam Petri and my chapter “Living Lattices” in it

A very nice new book “Carl Adam Petri: Ideas, Personality, Impact“, edited by Wolfgang Reisig and Grzegorz Rozenberg, has just been published by Springer:

https://link.springer.com/book/10.1007/978-3-319-96154-5

Newcastle professors, Brian Randell, Maciej Koutny and myself contributed articles for it.

An important aspect of those and other authors’ articles is that they mostly talk about WHY certain models and methods related to Petri nets have been investigated rather than describing the formalisms themselves. Basically, some 30-40 years of history are laid out on 4-5 pages of text and pictures.

My paper  “Living Lattices” provides a personal view of how Petri’s research inspired my own research, including comments on related topics such as lattices, Muller diagrams, complexity, concurrency, and persistence.

The chapter can be downloaded from here:

https://link.springer.com/chapter/10.1007/978-3-319-96154-5_28

There is also an interesting chapter by Jordi Cortadella “From Nets to Circuits and from Circuits to Nets”, which reviews the impact of Petri nets in one of the domains in which they have played a predominant role: asynchronous circuits. Jordi also discusses challenges and topics of interest for the future. This chapter can be downloaded from here:

https://link.springer.com/chapter/10.1007/978-3-319-96154-5_27