"Veritasium" (YT) - "The Big Misconception About Electricity" ?

[adx]

See for yourself

https://aapt.scitation.org/doi/abs/10.1119/1.1286115

Surface charge accounts for the Electric field intensity at a conducting boundary.

https://eng.libretexts.org/Bookshelves/Electrical_Engineering/Electro-Optics/Book%3A_Electromagnetics_I_(Ellingson)/05%3A_Electrostatics/5.18%3A__Boundary_Conditions_on_the_Electric_Flux_Density_(D)

Well that was quick, thanks for the references (no access the first, but first hit of search pdf of Ellingson answered it straight away).

We conclude this section with a warning. Even
though the SI units for D are C/m², D describes an
electric field and not a surface charge density. It is
certainly true that one may describe the amount of
charge distributed over a surface using units of C/m².
However, D is not necessarily a description of actual
charge, and there is no implication that the source of
the electric field is a distribution of surface charge.
On the other hand, it is true that D can be interpreted
as an equivalent surface charge density that would
give rise to the observed electric field, and in some
cases, this equivalent charge density turns out to be
the actual charge density.

(I assume that last bit relates to electrostatic type charge carried on the surface on insulators.) It's just that a lot of references refer to surface charge as though it's obviously physical, without comment on the reasoning.

[Sredni]

Well, surface charge is exceedingly small in ordinary circuits. I have always wondered if there are instances where it would be required to have fraction of the charge of the electron, and how - if it is possible - to resolve that classically
The fields have been shown to be real. See for example jefimenko's 1962 paper ( or his book)

[EEVblog]

I've been gone for several weeks, can someone TLDR me what happened here in regards to the quantum field theory explanation? Thanks.

[EEVblog]

(after two weeks away I've just jumped back to random page, so I have no idea about any follow-ups to this post)

Yet, like it or not, QFT has provided a 'worldview' which assists in 'debunking' (intentionally being loose with that wording) Poynting's vector as a source of truth for power flow at DC, a situation which is not far off being untestestable. It would require the experimental capabilities of Henry Cavendish's Earth density determination squared.

Debunking? You got to be kidding me. QFT in fact confirms the Poynting vector at DC or at any frequency. The idea that nothing is happening at DC so the energy cannot flow through the fields is a misconception.

Not according to the quantum professor. Are you catagorically saying she's wrong and that no energy flows inside the wire?

At DC, AC, whatever, the electrons are exchanging virtual particles. That's why energy flows in the fields, even if the fields are not changing or moving.

What if those fields are inside the copper wire at DC?
Again, the fundamental question here is whether energy flows inside or outside the wire (or both). And it should be easiest to argue this for DC.

Dave thinks that the Poynting vector does not work at DC because he is a circuit-headed engineer. The only way he can think of the energy traveling through space is when you have AC or RF. At DC no worky, because capacitors, transformers, and antennas, which are the only devices he knows that allow the transmission of energy through space, block DC.

I have never said that Poynting vector math doesn't work at DC, I have in fact said that it does. What I was getting at is that they basically become of no practical relevance at DC.

[adx]

Well, surface charge is exceedingly small in ordinary circuits. I have always wondered if there are instances where it would be required to have fraction of the charge of the electron, and how - if it is possible - to resolve that classically
The fields have been shown to be real. See for example jefimenko's 1962 paper ( or his book)

I've also wondered about what a few electrons do to picovolt levels. I guess for the "balls in pipe" model, especially if they are 'hot', they can be part in the volume of interest. Only if cut off from the rest of the circuit would it become an electron counter (like a pixel in a CCD, or any high impedance node). I then start wondering about a nanostructure to fit 3 electrons side by side, to reduce the 'cogging' as they go past the metal ions, a 3 phase power delivery nano-system. Even pairs (2 phase). But only if very cold... Oh the blissful ignorance of only ever doing high school level physics. And I digress once (probably an underestimate) more. In any case, I assume the surface charge will quantize to fractions of an electron, because it represents charge inside a surface rather than on it. I had been wondering if a million volts is put across a gap in a vacuum (just under the field emission limit) what will happen - would there be a (numeric) point too many electrons crammed into a monolayer on the surface, if surface charge were physically real? And what would that do to the local field?!

The seeds "strewn" on the circuit are neat. But it feeds into my schooled confusion - in reality there are no field lines etc. It's just the seeds lining up to create circuits of their own across the voltage difference (which is what an electric field is, admittedly), but as a high school student it is (or was for me) hard to know what is meant, especially if some teachers aren't really sure themselves. The field doesn't exist as an infinite continuum on its own, but is simply the sum of field emanating from every charged particle. Not even that - it is the combined interaction force between those particles, the field is an imaginary construct to represent those. I used to sort of wonder how a vacuum can have voltage at a point or between two points. Of course it doesn't - voltage is a property of matter, and is the excess charge density (number of extra or missing electrons from a state of absolute neutrality). When a metal, it represents the mechanical pressure of those electrons in the wire, a pressure that can't exist in a vacuum (unless a cleaner). But the mathematical field can - it predicts the force that would act on a charge if one were there.

[adx]

I've been gone for several weeks, can someone TLDR me what happened here in regards to the quantum field theory explanation? Thanks.

Not sure, but I think it's done at least one more cycle of spiralling in on zero or more answers!

Best I can see is it's down to semantic differences, which trigger different thought pathways in people's heads leading them to have no way to reasonably dispute what they are now thinking, or at least wondering about the conflict now centred in their minds rather than projected externally. I say, faux psychoanalytically.

I'm starting to wonder if classical theory is grossly misleading through no fault of its own, just that it has propagated through textbooks where the authors have struggled for teachable meaning, now just layers of history and interpretation. Should have prefaced that with an extreme cynicism warning, but seems too true.

[Kalvin]

<snip>

What if those fields are inside the copper wire at DC?
Again, the fundamental question here is whether energy flows inside or outside the wire (or both). And it should be easiest to argue this for DC.

<snip>

I have never said that Poynting vector math doesn't work at DC, I have in fact said that it does. What I was getting at is that they basically become of no practical relevance at DC.

You may find this simulation interesting regarding your questions about fields at DC:

Another cool simulation video.  Shows that energy outside the wires flows along parallel to the wire direction from source to load.  Ohmic losses flow in towards the center of the wire.  This one simulates at low frequency, close to DC.

[snarkysparky]

If that simulation is for DC why does he run it at 1 hz.   Why does he discuss skin depth so much.

Where in the video does he support dc power flowing outside the wires.

If DC power is flowing outside the wires shouldn't it be easy to prove without so much blah blah blah.....

[rfeecs]

If that simulation is for DC why does he run it at 1 hz.   Why does he discuss skin depth so much.

Where in the video does he support dc power flowing outside the wires.

If DC power is flowing outside the wires shouldn't it be easy to prove without so much blah blah blah.....

The math applies to DC just as much as AC.  It calculates the instantaneous power flow at any point in time.

His simulator is just a fancy calculator, showing the result of E cross H.  The E field in a good conductor is negligible.  So E cross H inside the wire is also negligible.

 ... blah blah blah.   

[adx]

...Of course it doesn't - voltage is a property of matter, and is the excess charge density (number of extra or missing electrons from a state of absolute neutrality). When a metal, it represents the mechanical pressure of those electrons in the wire, a pressure that can't exist in a vacuum (unless a cleaner). But the mathematical field can - it predicts the force that would act on a charge if one were there.

(About the field in wire thing.) Ok, how about assuming the field isn't real. It is always the interaction between charged particles. If there's only 1 particle in the local vicinity, there is no significant force. Then consider a circuit, with wires, and charges. Are the interactions that drive energy through the system primarily along the length of the wire, or between them?

[bdunham7]

Ok, how about assuming the field isn't real. It is always the interaction between charged particles.

That's essentially QFT and possibly a bit closer to "what is really going on", especially if you generalize that to eliminate 'charged'.  Which is why I kept croaking that you can't consider power to be 'in' the fields on their own without considering charges. 

[EEVblog]

I've been gone for several weeks, can someone TLDR me what happened here in regards to the quantum field theory explanation? Thanks.

Not sure, but I think it's done at least one more cycle of spiralling in on zero or more answers!
Best I can see is it's down to semantic differences, which trigger different thought pathways in people's heads leading them to have no way to reasonably dispute what they are now thinking, or at least wondering about the conflict now centred in their minds rather than projected externally. I say, faux psychoanalytically.

I'm starting to wonder if classical theory is grossly misleading through no fault of its own, just that it has propagated through textbooks where the authors have struggled for teachable meaning, now just layers of history and interpretation. Should have prefaced that with an extreme cynicism warning, but seems too true.

I like QTF in that it seems to predict that in all probability the majority of energy flow is inside the wire. This just makes sense to me at DC.
So my mind keeps going back to DC and say an example of a 50mm diameter HVDC undersea cable. You can't tell me there is no energy flowing inside the copper cable at DC? ZERO! That just seems nuts.
Extend it to 1m diameter if you want. All the energy is still outside the cable at DC? Really?

Usually it's the quantum world that doesn't make intuitive sense, but in this case QTF seems to make intuitive sense at DC.

[rfeecs]

I like QTF in that it seems to predict that in all probability the majority of energy flow is inside the wire.

But does QFT predict that?

Shouldn't QFT give the same results as the classical model?  The classical model agrees with measurements.  By the correspondence principle (https://en.wikipedia.org/wiki/Correspondence_principle), QFT should do the same.

Of course, if we can't actually measure "energy flow", then that could be a problem.  In that case, QFT's prediction would be just as useless as the classical model.

[EEVblog]

I like QTF in that it seems to predict that in all probability the majority of energy flow is inside the wire.

But does QFT predict that?

That's what the quantum professor says in her video. She says QFT essentially trumps Poynting theorm in understanding, which doesn't make Poynting obsolete.
it's just that if you want to understand whether or not the energy actually flows within the wire or outside the wire, QFT appears to say it's almost entirely inside the wire. I'm sure the maths still works either way, it's about understanding and answering the inside/outside question posed by Derek. He did not consider QTF at all and only looked to Poynting for the answer.
I did try to research some articles on it before I went on holidays but my head exploded.

[bdunham7]

Shouldn't QFT give the same results as the classical model?  The classical model agrees with measurements.
Of course, if we can't actually measure "energy flow", then that could be a problem.  In that case, QFT's prediction would be just as useless as the classical model.

You've neatly summarized the issue.  Both the QFT and classical model will agree as to the movement of the charges, the dissipation of energy in the load, the surface charges and fields, the magnetic fields and so on.  So both should agree with any actual physical measurements you can take, but they arrive at their results differently.  There's no reason to assume that the two models have to agree on intermediate constructs like probability, virtual particles, S-fields or other mathematical results.

[Sredni]

Lets have two slides with almost no friction and with the same slope. One is at one meter above ground level (plus the minimum height to get the minimum slope to compensate for friction), the other is at 100 meters above ground. We make two one ton stones slide for 1 km to their destination: a machine that will make the block fall and turn all gravitational potential energy into heat (eat your heart out, Carnot!).

The block falling one meter generates m g (1 meter) J of energy. The block falling 100 meters generates one hundred times that energy.
Has the energy travelled along the slide?
Both slides are identical, both stone blocks are identical, and the both moved at the same speed on the slide.

Has one slope really carried 100 times the energy of the other one? Or was the function only that to bring the mass where the gravitational potential field was allowed to make the conversion of energy to heat possible?
What if we dig a hole 100 meters in the ground with a Predator's starship beam, just microseconds before the stone reaches destination? Has the energy travelled along the slide before we decided to dig the hole?

EM adds a twist to this scenario in that the charges carry a significant field and so they set up the field that allows the conversion of energy into heat on the resistor. They are basically digging their own hole as they pile up and (what's the opposite of piling up?) decrease in density at the resistors interface, but not during their journey (which is still necessary to maintain a dynamical equilibrium).

[adx]

...Which is why I kept croaking that you can't consider power to be 'in' the fields on their own without considering charges.

I get that now. I kept thinking of it in a context of trying to 'fuse' the concepts of the classical field with an aspect of physical reality, because what I learned 'must be right' on some level, and so the sum of the parts (education) has to be a better starting point than rejecting part and moving forward with another. Which of course isn't rational. What I learned at school and uni might not be wrong, but that doesn't mean it is right. There is no need to hang on to some thing that isn't right as some pillar of truth. Letting go of the concept of "field" entirely is ok. It doesn't make it disappear.

That type of reasoning also leads to the possibility that the theory isn't right for RF. It's merely not wrong.

[EEVblog]

Shouldn't QFT give the same results as the classical model?  The classical model agrees with measurements.
Of course, if we can't actually measure "energy flow", then that could be a problem.  In that case, QFT's prediction would be just as useless as the classical model.

You've neatly summarized the issue.  Both the QFT and classical model will agree as to the movement of the charges, the dissipation of energy in the load, the surface charges and fields, the magnetic fields and so on.  So both should agree with any actual physical measurements you can take, but they arrive at their results differently.  There's no reason to assume that the two models have to agree on intermediate constructs like probability, virtual particles, S-fields or other mathematical results.

And therein lies the rub.
Many people have been screaming blue in the face at anyone who dares think that energy might actually flow inside the wire, particualy at DC. Yet along comes QTF that seems to imply exactly that with almost certain probability. In which case I doubt there is anyone on this forum with the qualifications or knowledge to actually talk on the topic of QTF. So they might have to ultimately eat humble pie and submit to the higher thoery. Because ultimately the question isn't about meadurement and transients etc, that's already conclusively modeled and answered with Ponyting or anything else classcial you want to throw at it. But does any of the energy actually flow inside the wire? Why stop at Maxwell and Poynting to expalin that?

[Naej]

In this post, I will explain the true (and surprising) physics behind "The biggest misconception about electricity".

tl;dr : energy flows in wires. Or in vacuum. Whatever.

First, what is energy? The modern "definition" is "energy is conserved", namely it is a mathematical invariant.
It goes this way:
1) you select the rules of physics you want to apply (the lagrangian)
2) you check that they are invariant by time-translation
3) if they are, Noether theorem will give you A corresponding invariant https://en.wikipedia.org/wiki/Noether%27s_theorem
A *crucial* point here is that an infinite number of quantities are time-translation invariants. The simplest examples are "multiplying energies by 10" or "adding 10J" or "changing the reference frame", but there are far more complicated ones.

Maxwell's equations: Maxwell defined electromagnetism with the electric potential field V, the magnetic potential field A, the electric/magnetic field E/B (and others; I'll talk only about vacuum here).
He found that E is the gradient of V corrected by dA/dt, and B the curl of A.
He found the electrical energy as being given by E^2/2 or qV/2, and magnetic is B^2/2 or qu dot A/2 with u the speed of the charge (in the correct units)
He also interpreted qA as being the 'potential momentum' of the charge.

Quickly it was realized that V,A are not uniquely defined, i.e. different V/A give the same physics, a fact now known as "gauge invariance".
The simplest example of this is that adding 420V to V does not change anything.
Which gauge you use is therefore up to you, so you use most convenient one, and often it is the Lorenz gauge (technically, almost-gauge).
The Lorenz gauge has the nice practical property that a potential difference is equal to what you measure with a voltmeter, as long as the voltmeter's wires are far from coils (this last condition is what you should learn from Lewin's KVL videos btw).
There are nice theoretical ones too: it's obvious that EM perturbations (or "light") propagate with the speed of light, i.e. it is obvious that it respects special relativity (it's covariant).

One good reason to use potentials is that you must do this if you consider a quantum mechanical electron in a field, as A contributes to its canonical momentum.
In fact it's pretty easy to derive the equation with the energy given above. ( https://en.wikipedia.org/wiki/Aharonov%E2%80%93Bohm_effect )

Are you disturbed by the gauge invariance? Well almost all fundamental physics were made with gauge invariance. https://en.wikipedia.org/wiki/Yang%E2%80%93Mills_theory

*Historical interlude* : The Maxwellians decided to "assassinate the potential", in their words, which is probably why it's usually barely mentioned in courses.
On a possibly related note, Victorian scientists believed that nature was the ether; sometimes that molecules were "vortices" of the ether.
Having an electromagnetic "proof" that energy was in the ether, and that you could stress the ether ( https://en.wikipedia.org/wiki/Electromagnetic_stress%E2%80%93energy_tensor ) was certainly a great "triumph" of the ether theory.
After Einstein's relativity, the ether was removed but the equations and concepts remained.

Heaviside-Poynting's energy flow was defined as ExB, and this is indeed correct.
Here's Poynting last sentence: "We can hardly hope, then, for any further proof of the law beyond its agreement with the experiments already known until some method is discovered of testing what goes on in the dielectric independently of the secondary circuit".
The modern take is that you apply Noether's theorem to the free-field lagrangian (so the EM equation in vacuum! or (E^2-B^2)/2), and you use a Belinfante relocation to get a symmetric stress-energy tensor.
Then you can read in it the energy, the energy flow and the symmetric stress. And you get the angular momentum flow in another tensor. https://webhome.phy.duke.edu/~rgb/Class/phy319/phy319/node143.html http://www.physics.rutgers.edu/~shapiro/613/615lects/maxwTmunu_2.pdf
The kicker is this: you *decided* that energy and energy flow have nothing to do with charge particles, and are a property of vacuum. You did not *prove* anything.
Applying it to the EM world you get the following:
- light has energy and momentum 
- a lightbulb is powered by light 
- an (imperfect) emitter antenna is also heated by the radio waves it absorbs 
- hundreds of GW are turning around every single classical electron
- you want to measure the power absorbed by a resistor? just measure E, B everywhere around it; and compute the average of ExB
- you want to compute the power radiated by a perfect antenna an AC generator? just compute E,B everywhere around it and add them

One century later, Carpenter arrives, in 1989.
If you know a bit of multivariate calculus, definitely read his papers: https://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.205.4488&rep=rep1&type=pdf  http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.205.4597&rep=rep1&type=pdf
Here is the thing: you can do the exact opposite choice, namely taking the interaction lagrangian, and use the same mathematical machinery.
From it, you deduce that the energy flow is JV with J the (vector) current.
The consequences are:
- light has no energy and no momentum (this is a lie you're taught in physics!). Ackchyually, electrons wiggling over there are losing energy/momentum, and electrons over here are gaining energy/momentum.
- a lightbulb is powered by its wires
- an emitter antenna is also heated by its wires
- there's no power associated with a single classical electron at rest
- you want to measure the power absorbed by a resistor? just measure the current and potential difference (currents* at high frequency)
- you want to compute the power consumed by an AC generator a perfect antenna? just compute V,i in the wires
Here is the fun part: it *depends on the gauge chosen*.
You may think it's a problem, if you don't know that energy is arbitrary; but now that you do, it's a way to remember the fact that energy is an arbitrary invariant.
Take Gibbs' gauge V=0, and there is no energy flow, just potential energy which varies.


Now for the other problems in the video.
1) The question.
It's possible to learn 3 things from the question/answer:
a) A capacitor is not always a plate. A description of the circuit is not always the right lumped-element model that you should use. Or "capacitive coupling".
b) Current seems to go through a capacitor
c) EM disturbances move at the speed of light; and this is the only thing you need for answering the question
I admire the way the question was asked: the circuit is given with the lumped-element symbols, and you're invited to assume the wires have no resistance, as in the lumped-element model.
The "otherwise it wouldn't work" is of course wrong, you would just have a current which eventually reaches a very low value.
But it shouldn't matter because the light turns out even with a minimal current… oops we shouldn't insist on this.

2) "electrons dissipate their energy in the device" "my claim is that it is false"
Resistance, at high temperature (above -200°C), is due in most metals by electron-phonon scattering.
That is, electrons transfer their energy to the metal ions. If Derek has a new theory, what is it?
http://large.stanford.edu/courses/2007/ap273/rogers1/

3) The animation at 6:17 of the transmission line is correct only if the battery has the same impedance as the lightbulb and transmission line.
Clearly, this is not a video about transmission lines.

4) "You might think this is just an academic discussion, but that is not the case, and people learned this the hard way"
Indeed, it is not an academic discussion. It's a choice of invariant you can make, and the consequence is the amount of time needed to do the computation/measure.
Everything else (what invariant is the "real" one, what is "merely a mathematical concept") is a philosophical statement.

5) At 8:20 we see no Poynting's vector coming out. But Poynting's vector is supposed to tell the direction of light!
It's not wrong if you assume the light bulb is a resistor, with a very low efficiency in emitting light. But it must be very confusing!

6) "Thomson thought signals moved like water in a tube"
Well… the analogy he made was with heat in a bar. The result is known as the famous "law of squares" because the time it takes for signal/heat to travel is proportional to the square of the length.
The problem is that he didn't account for inductance, nor the leakage.
Had he taken account of inductance and capacitance, then he… would have the same equations as water (pressure waves) going through a pipe… https://en.wikipedia.org/wiki/Acoustic_ohm

7) "Electrons in the power lines are just wiggling back and forth, they never actually go anywhere" "Note that this drift velocity is extremely slow, around 0.1mm/s" "How far do the electrons go? They barely move, they probably don't move at all."
Suppose you assume electricity is like water going through a pipe. Let's take water vapor, or air if you prefer.
If you turn a pump on then you will get a pressure wave through the pipe, going at the speed of sound.
Now the speed of sound in a gas is, more or less, the average speed of molecules.
So the question we should ask is: what's the average speed of electrons.
If you answer 0.1mm/s, then you are a distracted viewer, this is the norm of the average velocity, or drift velocity. The "electron wind speed" if you prefer.
The speed of electron in a metal is around 1000 km/s, so "wiggling back and forth" "don't move at all" is widely incorrect and the "argument" is void. https://duckduckgo.com/?t=ffab&q=fermi+velocity&ia=web
The difference with air, is the air molecules are not charged, so they need to "collide" to interact while EM disturbances go at the speed of light.

0.1 mm/s is (more or less) the amount of copper you would get in an electrolysis, or consume in a battery. That's the best way you can use this information.

8 ) "Others argued that the field around the wire was carrying the energy, and ultimately this view proved correct."
Lorenz, and then Heaviside derived the telegrapher's equations, which is what "proved correct" refers to.
The big controversy at the time with Heaviside was the following:
a) Heaviside remarked that when the isolation of cables was deteriorating, the signal was improving. He proposed to degrade the cables, and his idea was rejected.
b) Heaviside derived, and then used the equations, and showed that if you artificially increase inductance (Pupin coil) and degrade the cables, you would get less losses and no distortion.
He was right, but the editor Preece had already tried the inductance part with a very poor result. Taking Heaviside for a mathematician out of touch with reality, he decided to censor Heaviside everywhere he could, until a debate, which he lost and was then fired.
So what proved correct is Lorenz equations. Lorenz who didn't believe in "energy in vacuum", but he did believe in inductance.

9) "the light bulb is 1m away and that is the limiting factor" with Derek's hands showing the distance between the battery and the bulb
Well no. The limiting factor is the distance between the switch and the bulb.
Which led to a lot of confusion (can you communicate FTL with a switch far away? no).
But if you say that the distance between the switch and the bulb is the answer, how does it appear to prove that "energy moves through vacuum" between the battery and the bulb?
This is not a convincing argument, and for a good reason: there is no valid argument possible.



Overall:
a) Derek insisted you use a counterintuitive (but correct) understanding of energy flow in a context where it is poyntless, claiming other ones are wrong, without proving they are wrong.
b) everything else is incorrect, except possibly the engineering history of the first transatlantic cables/the existence of transformers in the grid.

PS: Feynman claimed that the energies given are only correct in statics, it's not the case. Of course, the amount of electric energy depends on the gauge, so you won't get the same one.
Feynman claimed you could know where is energy using general relativity. You don't.
Einstein-Hilbert's version is defined with respect to the Einstein-Hilbert stress-energy tensor, which is the one given above. But tetrad/vierbein's version can use any stress-energy tensor.
So there is no argument here.

[adx]

Has one slope really carried 100 times the energy of the other one? ...

I was going to say that the best I can come up with is that energy isn't real (in the sense of my previous post, being that it obviously exists in some form(s), but is not to be trusted), maybe something about what goes into a transmission line. But after Naej's great post, I might go off and think for a while. Maybe forever!

[bsfeechannel]

tl;dr : energy flows in wires. Or in vacuum. Whatever.

Is the earth the center of the universe? YES, at least for 1500 years. If you don't live under a rock, you'll see that the sun, the moon, the stars and the planets all traverse the skies every day and every night around us. The planets have that little loop they do in their orbits, but that's all perfectly predicted by the theory of the epicycles.

If that is so, why don't we use it anymore these days? It is because Galileo pointed his telescope to Jupiter and it became pretty clear that calculating the orbits of its recently discovered moons would be a nightmare.

Galileo then came with the Galileo's invariance, a.k.a. Galileo's relativity, where all inertial frames are equivalent to each other and their results can be converted from one to another using Galileo's transformation.

This principle underpins Newtonian mechanics.

One century later, Carpenter arrives, in 1989.
If you know a bit of multivariate calculus, definitely read his papers: https://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.205.4488&rep=rep1&type=pdf  http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.205.4597&rep=rep1&type=pdf

What the author is basically saying is that engineers are too dumb to understand energy in the fields (fields are counterintuitive, current as a fluid is not) so the author suggests that we embrace a concept abandoned by Maxwell and Heaviside because of its incompleteness.

As Maxwell himself pondered in his treatise below:

547.] He [Faraday] observes, however, that 'the first thought that arises in the mind is that the electricity circulates with something like momentum or inertia in the wire.' Indeed, when we consider one particular wire only, the phenomena are exactly analogous to those of a pipe full of water flowing in a continued stream. If while the stream is flowing we suddenly close the end of the tube, the momentum of the water produces a sudden pressure, which is much greater than that due to the head of water, and may be sufficient to burst the pipe.

If the water has the means of escaping through a narrow jet when the principal aperture is closed, it will be projected with a velocity much greater than that due to the head of water, and if it can escape through a valve into a chamber, it will do so, even when the pressure in the chamber is greater than that due to the head of water.

It is on this principle that the hydraulic ram is constructed, by which a small quantity of water may be raised to a great height by means of a large quantity flowing down from a much lower level.

548.] These effects of the inertia of the fluid in the tube depend solely on the quantity of fluid running through the tube, on its length, and on its section in different parts of its length. They do not depend on anything outside the tube, nor on the form into which the tube may be bent, provided its length remains the same.

In the case of the wire conveying a current this is not the case, for if a long wire is doubled on itself the effect is very small, if the two parts are separated from each other it is greater, if it is coiled up into a helix it is still greater, and greatest of all if, when so coiled, a piece of soft iron is placed inside the coil. Again, if a second wire is coiled up with the first, but insulated from it, then, if the second wire does not form a closed circuit, the phenomena are as before, but if the second wire forms a closed circuit, an induction current is formed in the second wire, and the effects of self-induction in the first wire are retarded.

549.] These results shew clearly that, if the phenomena are due to momentum, the momentum is certainly not that of the electricity in the wire, because the same wire, conveying the same current, exhibits effects which differ according to its form; and even when its form remains the same, the presence of other bodies, such as a piece of iron or a closed metallic circuit, affects the result.

550.] It is difficult, however, for the mind which has once recognised the analogy between the phenomena of self-induction and those of the motion of material bodies, to abandon altogether the help of this analogy, or to admit that it is entirely superficial and misleading.

A Treatise on Electricity and Magnetism, 3d edition, J.C. Maxwell, pp 195-196.

a) Derek insisted you use a counterintuitive (but correct) understanding of energy flow in a context where it is poyntless, claiming other ones are wrong, without proving they are wrong.
b) everything else is incorrect, except possibly the engineering history of the first transatlantic cables.

Well, we can go back to the epicycles. It is intuitive and we don't even have to learn the counterintuitive laws of Newton. But the scientific paradigm shifted long ago, so saying that the earth is the center of the universe may sound like a misconception these days. Kids don't even learn about epicycles in school.

[EEVblog]

Note 1: Regarding the transformations so slow as to be considered almost static so they would not lose energy to radiation, I have found comfort in

    Stratton,
    Electromagnetic Theory
    1941:

_{p. 131, italics mine}

"Poynting’s Theorem: In the preceding sections of this chapter it has been shown how the work done in bringing about small variations in the intensity or distribution of charge and current sources may be expressed in terms of integrals of the field vectors extended over all space.
The form of these integrals suggests, but does not prove, the hypothesis that electric and magnetic energies are distributed throughout the field with volume densities respectively

   fig densities formulae

"The derivation of these results was based on the assumption of reversible changes; the building up of the field was assumed to take place so slowly that it might be represented by a succession of stationary states".
"It is essential that we determine now whether or not such expressions for the energy density remain valid when the fields are varying at an arbitrary rate. It is apparent, furthermore, that if our hypothesis of an energy distribution throughout the field is at all tenable, a change of field intensity and energy density must be associated with a flow of energy from or toward the source."

On the arbitrariness of the assumptions relating Poynting's theorem Stratton has this to say:

_{p. 133}

"As a general integral of the field equations, the validity of Poynting's theorem is unimpeachable. Its physical interpretation, however, is open to some criticism. The remark has already been made that from a volume integral representing the total energy of a field no rigorous conclusion can be drawn with regard to its distribution. The energy of the electrostatic field was first expressed as the sum of two volume integrals.
Of these one was transformed by the divergence theorem into a surface integral which was made to vanish by allowing the surface to recede to the farther limits of the field. Inversely, the divergence of any vector function vanishing properly at infinity may be added to the conventional expression u = 1/2 E.D for the density of electrostatic energy without affecting its total value. A similar indefiniteness appears in the magnetostatic case."

But all in all

_{pp. 134-135, bold mine}

"The classical interpretation of Poynting’s theorem appears to rest to a considerable degree on hypothesis. Various alternative forms of the theorem have been offered from time to time,’ but none of these has the advantage of greater plausibility or greater simplicity to recommend it, and it is significant that thus far no other interpretation has contributed anything of value to the theory.
The hypothesis of an energy density in the electromagnetic field and a flow of intensity S = E x H has, on the other hand, proved extraordinarily fruitful. A theory is not an absolute truth but a self-consistent analytical formulation of the relations governing a group of natural phenomena. By this standard there is every reason to retain the Poynting-Heaviside viewpoint until a clash with new experimental evidence shall call for its revision."

Now, what experimental evidence have we?

Enlarged text mine.
You've found comfort in a text from 1941? Ok, whatever makes you sleep well at night!

[EEVblog]

tl;dr : energy flows in wires. Or in vacuum. Whatever.

I'm begining to think that Derek/Ponyting can no more correctly claim that the energy actually flows outside the wires than QFT says it flows mostly inside the wire.
Except that QFT makes more intuitive sense if you take it to the most simplistic case (but very realistically practical) of DC in a huge diameter conductor.

[SilverSolder]

For practical purposes such as sizing of wires, it is probably safer to stick with a working assumption that the energy flows inside the wires! 

[SiliconWizard]

A lot of the "debate" coming more from using different (or even vague) definitions and a philosophical approach of science rather than experimental, it can probably go on forever. =)
Just like with the KVL one.