Electromagnetic Archimedes' screw

[Verpies]

Such a case is that of a rotating charged ring. We therefore have a circular current. If the rotation alternates in one direction and then the other, then Maxwell-Faraday tells us that the magnetic field created is variable and should therefore induce a current in a coupled loop.  The experiment is difficult to carry out in practice, but I maintain that no induction will be possible in this diagram, because nothing is rotating. Admittedly, the charged ring rotates, but since all the charges are at the same speed, the field is invariant under rotation. A snapshot of the charges shows no variation in charge density along the ring, so there is no field that could cause the charges in an induced circuit to rotate.

But when Henry Rowland spun a charged ring then he was able to detect a magnetic field from it with a compass ( here is an AI slop description of this experiment for truck drivers ).

Later, Wilhelm Roentgen and Alfred Eichenwald refined this experiment using different setups with charged spheres or cylinders.
They also detected a magnetic field caused by the motion of electric charges on the surfaces of these spinning objects.

Are you claiming that spinning charged objects do generate a magnetic field but this field is somehow different so when its magnitude is made to vary (by varying the angular velocity of the electrically charged object that generates it) then this time-variant field is unable to induce EMF or current in a detector coil ?
... or do you disagree with Rowland, et al, that spinning charged objects generate magnetic field at all ?

[F6FLT]

F6FLT
I used to windsurf as well. The last couple years I got into designing and building my own hydrofoil boards including mono-foils. A good high aspect hydrofoil can surf swells as small as 24" with little problem. It's interesting to consider the length of a sail board in relation to the length and height of the swell. Then consider the chord of my hydrofoil is only 9" and the width 36". The drop in the height of the swell were riding could be less than 2" across the chord of the foil. It's even more cool being 30" above the water and looking down to see an bright aqua marine colored foil slicing through the water only a few inches under the surface.

https://www.youtube.com/watch?v=PVyTAqUMd0k&t=160s
Hydrofoil | Wake Foil Slingshot Hover Glide (2020)

If we could apply this principal to electric circuits who knows what would be possible?...

Hydrofoils are cool. This is a great demonstration of what DC induction could be: the creation of this mini wave.
However, there is one important difference in the case of induction: the speed of the wave. In the case of a variable current, it moves forward (and backward) at a speed v close to c, of the order of 0.8c, the speed of signal propagation in the circuit, and not at the considerably slower speed of the charges.

I am still perplexed on this point. The wave, a potential difference, travels much faster than the charge, but even if the wave overtakes the charge, statistically the charges are carried along. A first idea is that the wave is not spatially symmetrical, probably compressed at the front, precisely because of a speed close to c.

[F6FLT]

But when Henry Rowland spun a charged ring then he was able to detect a magnetic field with a compass ( here is an AI slop description of this experiment for truck drivers ).

Later, Wilhelm Roentgen and Alfred Eichenwald refined this experiment using different setups with charged spheres or cylinders.
They also detected a magnetic field caused by the motion of electric charges on the surfaces of these spinning objects.

Are you claiming that spinning charged objects do generate a magnetic field but this field is somehow different so that when it is made to vary (by varying the angular velocity of the electrically charged object that generates it) then this time-variant field is unable to induce EMF or current in a detector coil ?
... or do you disagree with Rowland, et al, that spinning charged objects generate magnetic field at all ?

Read what I wrote more carefully:
"I've just concluded that a rotating charged ring, which we know creates a magnetic field because it's a rotating current, cannot produce induction in a coupled circuit when its rotation oscillates around the axis, even though there's a variable magnetic field (B) and a change in flux"

I agree with you that a charged ring does indeed produce a magnetic field; this has been verified experimentally.

However, if its angular velocity varies, it will not create induction despite the fact that the magnetic field is variable. This implies limiting the validity of Maxwell-Faraday's equation to currents from a generator. Only currents with spatial variation along the circuit can induce a current in a coupled circuit, so not the current from a charged ring. This is my thesis.
A snapshot of a charged ring rotating at variable speed shows no variation in current along the ring, while a snapshot of a circuit powered by generator current does show variation, due to the finite propagation time of the signal in the circuit.

The only way to invalidate this idea is to produce an experiment demonstrating a current induced by a charged ring at variable angular velocity, not to invoke the theory that the idea challenges.

This experiment is difficult to carry out. It is much more interesting to use the idea to produce effects not expected by Maxwell-Faraday's equation, which will validate or invalidate the idea depending on the results. That is what I am working on, and one of the effects is the possibility of inducing a direct current. I have the mathematics that allows us to move from a propagating current gradient (the case of an ordinary current in a circuit, not that of the charged ring) to a charge density gradient, to its electrical dipole field, and to the influence of this field on the induced charges.

As for the magnetic carousel, I answered the question with my method. If one thing is legitimate, it is to grant everyone the freedom to use their own method to solve a problem. The choice of the reference frame in which the analysis is carried out is part of this.
If it is not the solution to the problem that interests you, but a difficulty or a possible paradox in a particular framework of the analysis, you will need to rephrase the question.

One final remark: the subject of Archimedes' screw that I raised earlier, as we will have understood, concerns this missing link in the induction of a direct current. The posts I have just made here, following a recent insight triggered by the question of the charged ring, even if they do not respond to other posts that may have been made recently, are along these lines and are perfectly relevant to the subject.

[Verpies]

...cannot produce induction in a coupled circuit when its rotation oscillates around the axis,even though there's a variable magnetic field (B) and a change in flux
...
However, if its angular velocity varies, it will not create induction despite the fact that the magnetic field is variable.

It is nothing unusual when non-zero dB/dt does not induce anything in a sensor coil, but when non-zero dΦ/dt does not induce anything in a sensor coil, then this is big news.

This implies limiting the validity of Maxwell-Faraday's equation to currents from a generator.

Yeah, this needs to be tested empirically.  It would mean a new type of field that affects a compass needle but does not affect a sensor coil.  What about Hall effect sensors ?

[F6FLT]

It is nothing unusual when non-zero dB/dt does not induce anything in a sensor coil, but when non-zero dΦ/dt does not induce anything in a sensor coil, then this is big news.
...

A dΦ/dt does not induce any current, since a magnetic field cannot perform work.

Variable current => dΦ/dt
Variable current => induction
But dΦ/dt =/=> induction

Two effects with a common cause do not imply a causal relationship between the two effects; it is simply a matter of formal logic.

It is the nature of the current that makes the difference, depending on whether it propagates along the circuit at a finite speed or not. That is the "big news" to be verified.

[Verpies]

Two effects with a common cause do not imply a causal relationship between the two effects; it is simply a matter of formal logic.

That is true but they are not incompatible with the causal relationship between the two effects, either.

It is the nature of the current that makes the difference, depending on whether it propagates along the circuit at a finite speed or not. That is the "big news" to be verified.

Oh yeah!

[F6FLT]

That is true but they are not incompatible with the causal relationship between the two effects, either.

They are incompatible. I have given one reason for this: a magnetic field does not produce work, so its flux cannot set a charge in motion.
A second reason is that this would be a non-local effect. The flux variation can occur at a distance from the induced charges.

There are much stronger objections to my thesis. I raise them myself. For example:
-------------------
Let us bring a cylindrical magnet close to a conductor loop, both being coaxial.
Since the cylindrical magnet is equivalent to a current loop with no propagation effect, there should be no induction. However, there is induction => rejection of my thesis.
-------------------
(Perhaps, even though I have an idea for responding  ).

[Verpies]

I have given one reason for this: a magnetic field does not produce work.

That's true only for time-invariant fields.  You are overextending this property to time-variant fields so I am ignoring the extension.

A second reason is that this would be a non-local effect. The flux variation can occur at a distance from the induced charges.

I think you are conflating Maxwell's third law with the integral form of Faraday's law of induction ℰ = ∮E⋅dl according to which the EMF induced in a closed circuit does not depend on the distance between the source of the changing magnetic flux and that circuit.

This apparent non-locality is resolved by the local, differential form of the same Maxwell's law:
∇×E = -∂B/∂t
Which demonstrates that the electric field is produced locally - only where and when the magnetic field (B) is actually changing.
The integral form integrates this local effect over the entire surface spanned by the circuit Φ=∫∫B⋅dA, which is why the total EMF depends only on the net change of the flux threading that circuit ...and seems insensitive to distance.

P.S.
Although you have not mentioned anything about it, I'd like to add that the current induced in a shorted loop cannot be calculated from the Ohm's law, i.e.: just dividing the EMF by the resistance of the loop i=ℰ/R,  This is because such operation completely ignores the internal back-flux that opposes the change attempted by the external flux and fails arithmetically for superconducting shorted loops where it causes division by zero or infinite induced current at the limit.

[F6FLT]

That's true only for time-invariant fields.  You are overextending this property to time-variant fields so I am ignoring the extension.

That's always true. See below.

I think you are conflating Maxwell's third law with the integral form of Faraday's law of induction ℰ = ∮E⋅dl according to which the EMF induced in a closed circuit does not depend on the distance between the source of the changing magnetic flux and that circuit.

This apparent non-locality is resolved by the local, differential form of the same Maxwell's law:
∇×E = -∂B/∂t
Which demonstrates that the electric field is produced locally - only where and when the magnetic field (B) is actually changing.
The integral form integrates this local effect over the entire surface spanned by the circuit Φ=∫∫B⋅dA, which is why the total EMF depends only on the net change of the flux threading that circuit ...and seems insensitive to distance.

∇×E = -∂B/∂t : I agree, it is local. But this equality does not prove that ∂B/∂t is the cause of E; it could just as easily be ∇×E that is the cause of dB/dt. This equality, by definition, simply tells us that they are the same thing. ∂B/∂t IS an electric field per unit length. Indeed, the dimensional equation for an electric field is M L T⁻³ I⁻¹. For ∇×E and for ∂B/∂t, it is M T⁻³ I⁻¹, both are equivalent to electric fields per unit length. The same reality expressed in two different ways.

This is a consequence of the displacement of charges, and that magnetic and electric fields are mutually derived by Lorentz transformation. The electric field, when variable, is such that its curl is equal to -∂B/∂t. Same reality

However apart from a mechanical force, the only force capable of doing work on a charge is F=q.E. And this is clear when we write E=vxB: the displacement being orthogonal to B, W provided by B is 0.

See : https://en.wikipedia.org/wiki/Relativistic_electromagnetism
"The requirement that the equations remain consistent when viewed from various moving observers led to special relativity [...] The Coulomb force was generalized to the Lorentz force. [...] In other words, the electric field in the other frame does not depend on the particular distribution of the source charges, only on the local value of the electric field in the first frame at that point. Thus, the electric field is a complete representation of the influence of the far-away charges."
and : https://en.wikipedia.org/wiki/Classical_electromagnetism_and_special_relativity
Everything I say follows from this (except the question of the charged ring at a variable angular speed).

P.S.
Although you have not mentioned anything about it, I'd like to add that the current induced in a shorted loop cannot be calculated from the Ohm's law, i.e.: just dividing the EMF by the resistance of the loop i=ℰ/R,  This is because such operation completely ignores the internal back-flux that opposes the change attempted by the external flux and fails arithmetically for superconducting shorted loops where it causes division by zero or infinite induced current at the limit.

I agree.

[F6FLT]

Following my reflections on inducing a direct current, I began to wonder about forces derived from potential, such as the action of a generator on charges in a circuit, and those that are not, or are not supposed to be, such as the effect of induction.
Apart from forces where loss issues are involved, particularly through friction, and quantum mechanics, such cases are rare.
In this context, I asked Gemini about the Lorentz force. Here is his answer:

Could the Lorentz force  be a fictitious force like Coriolis?

--------------------------
The short answer is: **Yes, absolutely.**

Within the framework of **General Relativity** and **gauge theories**, the Lorentz force can be interpreted exactly like the Coriolis force: a force that appears because we are not using the "correct" coordinate system or the "correct" geometry to describe motion.

Here is how we bridge the gap between the two:

1. The Striking Mathematical Analogy

If you compare the two formulas, the structure is identical:

* Coriolis: Fc = 2m(vxΩ)
* Lorentz: Fm=q(vxB)

In both cases, the force is perpendicular to the velocity and does no work. In classical mechanics, we say Coriolis is "fictitious" (due to the rotation of the frame) and Lorentz is "real" (due to a field). However, this distinction fades in advanced physics.

2. The Lorentz Force as "Curvature"
[...]
[I skipped answer 2, which was too 'science fiction', a positive answer but not within the framework of relativity, only introducing a 5th dimension.]

3. Gauge Forces: "Connection" Forces

In modern physics, forces (electromagnetic, weak, strong) are called **gauge forces**. They appear to maintain the invariance of physical laws during a change of "internal reference frame" (the phase of the wave function).

*Coriolis* appears when we change our spatial reference frame (rotation).
*Lorentz* appears when we change our phase reference frame ( gauge).

From this perspective, the Lorentz force is a "correction force" necessary to keep the equations consistent, just as the Coriolis force is a necessary correction in a rotating carousel.

4. The Crucial Difference (Why we distinguish them)

Despite this theoretical kinship, a major practical difference remains:

1. **Universality:** The Coriolis force (and gravity) acts on **mass**. It accelerates all bodies in the same way (the equivalence principle).
2. **Selectivity:** The Lorentz force only acts on bodies possessing a **charge **. A neutron does not feel it.

It is this difference that prevents us from saying that electromagnetism is *purely* a property of classical 4-dimensional spacetime. One must "add" something to space (an internal space or an extra dimension) for it to become "fictitious."
--------------------------------------------------

His conclusion is less radical than his premises, but in any case we can conclude that the Lorentz force is a fictitious force linked to the reference frame we take, which is not 'inertial' in the electromagnetic sense.  Indeed, the Lorentz force is only visible in a reference frame immersed in a magnetic field, in the same way that the Coriolis force is only visible in a reference frame immersed in a gravitational field.
All of this reinforces my belief that, for any description of an electromagnetic effect, we should use a reference frame that is outside any magnetic field. This is the only way to obtain a description that does not depend on the observer.

[Smudge]

...... the Coriolis force is only visible in a reference frame immersed in a gravitational field.

Why do you say that?  The Coreolis force is in no way connected to a gravitational field.

Smudge

[F6FLT]

Why do you say that?  The Coreolis force is in no way connected to a gravitational field.

Smudge

I was thinking about the Coriolis force on Earth.
For it to exist, the object must be moving at a certain speed on the surface of the rotating system. Without a force to keep it moving on the surface, there would be no Coriolis force, and the moving object would travel in a straight line.
But you're right, it's true that gravity is not theoretically essential; all that is needed is a vertical force to keep the object on the surface. All the models we see implicitly assume that objects are subject to gravity (objects on a rotating disc, for example). I would be curious to see a model of Coriolis force that does not implicitly include gravity.

[Verpies]

It is this difference that prevents us from saying that electromagnetism is *purely* a property of classical 4-dimensional spacetime. One must "add" something to space (an internal space or an extra dimension) for it to become "fictitious."

Why limit the addition to space ?
Why keep the space privileged and multidimensional while keeping time as one-dimensional ?  Is it only because you can't see it with your material eyes or wrap your mind around it ?

[F6FLT]

Why limit the addition to space ?
Why keep the space privileged and multidimensional while keeping time as one-dimensional ?  Is it only because you can't see it with your material eyes or wrap your mind around it ?

Unclear question. I did not mention separate space or time, but rather a 4D spacetime.
Currently, the state of knowledge is that our universe has four dimensions. No definitive theory has established that there are other dimensions; there are only hypotheses to that effect. I am sticking to what we know. In a 4D universe, the Lorentz force cannot be expressed as a curvature similar to that used in relation to gravity. This would require an additional dimension, which is what Gemini said, and I am convinced that he is right.

[F6FLT]

When we say that a force "does not derive from a potential," such as induced electromotive force, we forget to mention that this concept depends on the frame of reference. A force may derive from a potential in one frame of reference but not in another.

Faraday came to the conclusion that ∇xE=-∂B/∂t based on his observation of the current in a macroscopic circuit. The frame of reference is that of the observer who sees the circuit at rest.
But if the frame of reference is taken on each charge in the induced circuit, each charge may well see locally a force derived from a potential such as a rotating PD, with the corollary that ∇xE=0.
The two points of view are compatible, but since it is what the charges are subjected to, from their point of view, that interests us, the second is more relevant and opens up interesting perspectives, such as the induction of direct current.

[Verpies]

Unclear question. I did not mention separate space or time, but rather a 4D spacetime.

So what?   You still mentioned adding something to space but not time.  That's not treating them on par.
Spacetime is a conflation of space and time into one reference system.
When space and time are given their separate reference systems, then motion's degrees of freedom are increased to give rise to what you call fictitious forces, ...or fields of forces.

Currently, the state of knowledge is that our universe has four dimensions.

It is a state of current dogma.
A gravitating material observer is unable to distinguish a pseudoscalar from a scalar.
The normalization of any deviation from a pseudoscalar temporal aspect of motion manifests itself as a distortion of the spatial aspect of motion and a fictitious force.

[F6FLT]

Gemini and I know the definition of spacetime, which is given by relativity. To take relativity, which is knowledge, as a "dogma" is to misunderstand the difference between a scientific theory and a religion. See Karl Popper and the notion of falsiability. Playing with words, especially excessive or derogatory ones, does not lead to any serious contradiction.

An observer in gravity knows that he is in gravity. This knowledge means that he does not confuse a fictitious force with a real force, and that is why physics makes a difference. However, it is interesting, particularly because we live on a rotating and massive object, to express the effects we see from our own point of view, from an inertial reference frame, because then they become the same for all inertial observers, and conversely to do this 'normalisation' that you mention.
The question is, 'can we perform this "normalisation" for the Lorentz force?'

Genimini replies:
"1. **Universality:** The Coriolis force (and gravity) acts on **mass**. It accelerates all bodies in the same way (the equivalence principle).
2. **Selectivity:** The Lorentz force only acts on bodies possessing a **charge **. A neutron does not feel it.
It is this difference that prevents us from saying that electromagnetism is *purely* a property of classical 4-dimensional spacetime. One must "add" something to space (an internal space or an extra dimension) for it to become 'fictitious.'"

Gemini only says that the Coriolis force (and gravity) can be 'coded' into spacetime as a fictitious force, but not the Lorentz force. To code it, why add a dimension to space rather than time, you'll have to ask him, but it doesn't really matter since we can view spacetime as four spatial dimensions because ct is a spatial dimension and we can always transform t into ct since c is a constant. This seems entirely secondary to me, the important point being that we must add an extra dimension if we want to be able to talk about curvature in relation to the Lorentz force. Gemini says no more than that, and neither will I.

[Verpies]

Gemini and I know the definition of spacetime, which is given by relativity. To take relativity, which is knowledge, as a "dogma" is to misunderstand the difference between a scientific theory and a religion. 

I agree with special relativity, but not with general relativity.  The phrase "fabric of space and time" is totally abhorrent to me as it objectifies reference systems.
I consider the Maxwell's equations (including the Lorentz forces) as 4 solutions to ∇F=J.
I consider space an illusion created by multidimensional motion at c as defined by the division of two trivectors in PGA.
The same goes for time that I consider totally symmetric to space, possessing the same amount of dimensions. This does not mean that these two aspects of motion share the same coordinate system, as the word "spacetime" implies.
Because of this I have come to the conclusion that 4D spacetime is myopic dogma exclusive to our material gravitating point of view.

Conversely, an antimatter version of you would lecture me on the difference between science and religion while gravitating inward in multidimensional time and expanding outward pseudoscalarly in our space and being being absolutely convinced and relishing in the "knowledge" that our space is devoid of directions (and thus scalar), while our time is multidimensional. Because of this he would call our space his time, and our time his space ...and most likely he would join these two reference systems into his own version of "timespace".

Oh, I can still argue with you within the confines of the mainstream "spacetime" dogma, but I have been down this road and I know exactly where it leads - i.e.: the place we find ourselves in now.  I find the entire paradigm of space as an object in which we swim as fish in an aquarium, myopic, boring and limited - which is the reason why don't engage with your ideas intensively within that limited conceptual framework.

[F6FLT]

@Verpies

There is nothing to prevent us from having an alternative theory, and you know that I question Maxwell-Faraday's equation. But whatever new theory is presented, it must:

• explain at least what current theories or the theory it claims to replace explain.
• be as general or more general than the theory it replaces.
• be compatible with it on observational results, within the margins of uncertainty (e.g. the attraction of massive bodies in 1/r² and not 1/r3).
• explains facts not explained by current theories and/or predicts new experimentally verifiable facts and/or predicts divergences in results from known theories, i.e. be innovative but only in the context of the last point:
• be capable of producing calculations that can be compared with measurements, demonstrating that it is indeed innovative.

In all other cases, a theory is useless, even harmful (except for personal convenience, or temporarily as a stepping stone to another theory as described).

Theories such as Maxwell's electromagnetism or relativity have proven themselves by giving rise to remarkable technologies. We use these theories to our advantage, but we can also question them, precisely because they are not dogmas; they are falsifiable. The dogma is to label them as dogma, as this label is not falsifiable. Questioning them requires much more than fiction, as in the Bible, where strings of words appeal to the imagination but have no operational meaning, such as talking about the value of prayer without ever being able to measure its effects.

That is why, in my Maxwell-Faraday challenge, I am looking for an experimental way to induce a direct current in a coil, which I believe is possible and would prove the limitations of classical theories.

I invite everyone to use this same method. Until I have produced a coherent model that meets these criteria, or at least an experiment that cannot be explained by classical theories, which requires understanding them, I would find it ridiculous to denigrate classical theories, which have proven themselves, and indecent to criticise the great minds that conceived them. I would feel like a yapping dog pissing at the foot of a cathedral, incapable of building one myself.

[F6FLT]

I agree with special relativity, but not with general relativity.
...

On the one hand, general relativity is a set of tensors that allows special relativity to be applied locally in an accelerated medium. Accepting SR implies accepting this part of GR, which is simply a correction for the applicability of SR in this medium.
On the other hand, GR is also a model in which gravity is interpreted as a geometric property of space-time. I suppose this is what you are contesting. It is indeed surprising that the physical process by which this deformation would occur is not defined.

But we must realise that the same is true for SR. I also looked for a physical cause for the slowing down of travelling clocks. And it was silly. After I returned to physics, it took me 10 years to understand why. It is simply a logical consequence of a 4-dimensional universe with a speed limit. These two criteria alone imply the shifting of clocks, without any need to invoke other physical causes.
With GR, we can also deal with the half-turn made by a clock. This implies an acceleration/deceleration phase whose effects must be compatible with the round trip handled without acceleration by SR. And of course this is the case: the clock shift effect linked to the acceleration of the U-turn is the same whether calculated in RR or GR, with similar equations.  In other words, acceleration modelled in 4D space implies this shift by pure logic and not by physical effect. Since acceleration is acceleration and no effect has ever been found to distinguish between gravitational acceleration and the acceleration experienced by the clock in its half-turn, the consequence of this principle of equivalence is that, similarly, gravitational acceleration is indeed a geometric property, hence the notion of 'spacetime fabric'. All this is pure logic implied by a 4D universe with a speed limit.

Now we know that GR is incompatible with QM, and also that it does not allow us to model everything in distant space, so obviously it will have to be questioned, and QM probably too.
However, a model should not be criticised on the points where it correctly models what we observe, as long as we have no better alternative. The adequacy of the model to the observations is all that is required, and challenging it when its limitations are already known is pointless, especially when no better, scientific and therefore falsifiable alternative is proposed.
We can imagine other dimensions, unlimited speed, gravity that is not identifiable with acceleration, a physical cause for the effect of masses on time or quantum vacuum or anything else, blah, blah, blah, as long as we have not produced anything better than GR in operational terms, i.e. in terms of predicting effects qualitatively and quantitatively, it remains at the level of a theory of transubstantiation.