Dear Frederick David Tombe

“Is the suggestion that the horn matches the transmission circuit impedance at the narrow end, but that it widens out to match the impedance of free space at the wide end?

Exactly, that is the implication.

Has anybody found a way to numerically measure 377 Ohms in isolation in one of these horn antennae?”

In my opinion the main point is that the ratio between E and H is 377Ohm. If that ratio is fulfilled the wave can propagate smoothly into free space.

For resonating antennas I’m with you, that the impedance to match is: R is integral of ExH over the surface of a sphere and X is the integral of stored energy in near field. However, the ratio between E and H for waves in free space is 377Ohm. Clearly, E and H has to be involved in the right ratio to propagate the wave.

Best regards

Jörn

Dr. Schliewe, As you already agree, the ratio of E and H in a wireless wave will always be 377 Ohms. Now, remember that an antenna is a transducer which converts electric current into wireless EM radiation. Will the E and H fields in the emission circuit refer to the same thing as the E and H fields in a wireless wave that has long since disconnected itself from its emission circuit?

The fact that in general, the ratio between E and H in the emission circuit is not 377 Ohms, is at least one reason for believing that we are looking at two different E fields and two different H fields on either side of the transducer.

We know what E and H refer to in the emission circuit, but few people ever ask what they refer to physically in a wireless wave in space when a wave pulse has disconnected from its emission source.

Dear Frederick David Tombe

it is your theory that there is a difference between the E of the guided wave and the E in free space.

State of the art is: it is the same E without connection to charges.

In my opinion it is the same E and we have a real polarisation (separation of charge densities) which corresponds to that E in space.

A wave is a transport of energy between coupled oscillators. The oscillators in the free wave are the separated charges (polarisation) against their attraction (E field) and the inertia (induction) against change of velocity (H field).

The plane waves as mathematical solutions to the wave equation are unphysical (unbounded) and just an oversimplification of the real process. The divergence free E field of state of the art view should be a curl field, but the curl is closed at infinity in the plane wave. There is no possibility to have a curlE around H and a curlH around E at the same time in a bounded wave without polarisation and magnetisation of space.

Best regards

Jörn

Dr. Schliewe, Let's first consider a wireless EM wave pulse in space that is already disconnected from its emission source. We are agreed that the ratio of E and H is 377 Ohms.

My point is that the E and the H are locally sourced at the point in space, whereas back at the emission circuit, E was sourced from an AC generator and H was the near magnetic field surrounding the circuit, and that the ratio of E and H was not necessarily 377 Ohms.

As regards any intermediary cable connecting the emission circuit to the antenna, we will also have had an electrostatic E at right angles to the propagation direction, sourced in the charge on the wires.

with this wording I can agree

Dr. Schliewe, Yes, because on the other thread about the Poynting vector, it was discussed how there are three different types of E field. But the issue above isn't about different types of E field. It's about differently sourced E fields within the system, irrespective of their type. For example, there will be the AC power source E field, which could have originated at the power station as either μv×H or −∂A/∂t. Then within the circuit, there will be a reactive E field due to capacitance which will be purely electrostatic, as in −∇φ, and we will have a self-inductance E field which will be −∂A/∂t. Then we will have the E field in the wireless radiation in space, which will be −∂A/∂t.

The interesting thing really, is where is the physical source for the latter. I’m not clear what your own view on the matter is, but you seem to allude to a dielectric background in space. There’s another question thread that I have just opened on the Dirac Sea which you may be interested in.

https://www.researchgate.net/post/How_did_the_Dirac_Sea_connect_with_the_Luminiferous_Aether_of_the_Nineteenth_Century

Frederick David Tombe , it does sound like you are getting into a realm of free-energy. Fundamentally, on a zero-point energy level, the condition of the permittivity and permeability of space exists as a baseline with zero-point energy. To say that the impedance of free space can be calibrated in an antenna horn to thence capture an EM field, then such would result in that antenna horn potentially absorbing an unlimited amount of EM energy as that energy is resourced by the antenna horn.

In saying that though, the impedance of free space has practical use in being evidence for zero-point energy for a pure spatial vacuum. In other words, its practicality can only really serve a better understanding, for physics, for how time and space and associated physical phenomena works. More than that, it serves as a "road map", as practical as road maps are for navigation, to better understand the concept of zero-point energy without falling into the trap of free energy.

Stephen Jarvis , I believe your second paragraph hits the nail on the head. The concept of impedance of free space is generally promoted by those who believe that space has physical characteristics, and it is generally played down by those who believe that space is a pure empty vacuum.

In this regard, I stand in between. I believe, that what is believed to be empty space, is not in fact empty. But I don't believe that this is proved simply by defining the impedance of space from the plane wave solutions of Maxwell's equations.

That's why I'm asking if anybody can provide evidence of 377 Ohms being deliberately calibrated into an EM wave emission circuit in order to match the impedance of free space.

Frederick David Tombe , I believe, that what is believed to be empty space, is not in fact empty. But I don't believe that this is proved simply by defining the impedance of space from the plane wave solutions of Maxwell's equations.

What else is there then in an empty vacuum, as you are thinking might be there? Where are you hedging? Would not that anything else "thing" also be a feature of how the impedance value for electric permittivity and magnetic permeability is/are arranged as it/they is/are, something that an underlying basis of permittivity and permeability underwrites in tandem with, like the idea of c (speed of light) itself?

If there is something else, the equations would show it, would they not?

"c" as a limiting value for any frame of moving reference for EM is core to what you need to be thinking about it seems, as the equations for electric and magnetic impedance propose. There, the question is, "why is EM limited at c for any relative motioning reference?". Why is the propagation of light in space impeded to c and does it have anything to do with electric permittivity and magnetic permeability with space, and if so, how?

The real idea there to focus on is how and why c as the speed of EM propagation is an impedance, is set, for any frame of reference for an object moving in space, filed electric or magnetic.

At least it is recognized that there can be no type of E that is not charge dependent, thereby making it necessary to invent a NEW state-of-the-art type of E “without connection to charges”. What is not correct is sticking to the old types of E, which are all charge dependent and still making them applicable in wireless propagation without first populating space with charges.

But Jörn Schliewe , what can this possibly mean and how can an “E without connection to charges” be connected to “real polarization”?

You are not obliged to answer that, but I will like to know if your “charge densities” are also mass densities?

And thanks for this reference on the other thread

https://www.researchgate.net/post/Is_there_an_aether_If_yes_then_what_are_its_implications

Akinbo Ojo , charge dependent?

At least it is recognized that there can be no type of E that is not charge dependent, thereby making it necessary to invent a NEW state-of-the-art type of E “without connection to charges”.

That statement is paradoxical.

The first part of the statement makes E righteous (At least it is recognized that there can be no type of E that is not charge dependent), yet the second part not so (thereby making it necessary to invent a NEW state-of-the-art type of E “without connection to charges).

How are you actually intending to present a case? The first part of your statement or the second part?

Although the first part of the statement swings for E being charge dependent, yet is that necessarily a mandate for E being independent of charge energy?

Dear Akinbo Ojo

I mentioned 3 different views.

A: David’s view

B: State of the Art: field without connection to charges

C: My view: E is always the Coulomb field of charges. Charge density and field are one and the same physical entity. So you need real separation of charges (polarisation) for wave propagation

Best regards

Jörn

Is there any clear result here with this forum question?

What does the forum questioner seek?

Stephen Jarvis , I was alluding to a dielectric medium. The permeability of space and the permittivity, and their connection to the speed of light are sufficient in this study without extending it to the 377 Ohms impedance of space. The latter has the effect of confusing the issue by making wireless radiation out to be like an electric current that would obey Ohm's law. The equations of electromagnetism will show this medium up when the physical justification for Maxwell's displacement current is established.

Consider André-Marie Ampère's position two hundred years ago and compare it with modern quantum fluctuation.

In 1825, French physicist and mathematician André-Marie Ampère came up with two conceptions for the aether. In the first he speaks of an elastic fluid which extends throughout all space, whose vibrations produce the phenomenon of light. He said that this fluid or aether can “be no other than that which results from the combination of the two electricities.”. In his second conception, he has the interspaces between the metallic molecules of a current carrying wire occupied by a fluid composed of the two electricities. In this inter-molecular fluid, the opposite electricities are continually being dissociated and recombined.

An appropriate class of measures, the variational principle is to minimize integral expressions of an underlying nonnegativity on topological spaces [ free space not excluded ] turns out to be virtual bifurcative minimizers in the class of so-called strictly negative definite measures in the strong sense : Euler Lagrange equations in momentum space in the homogeneous setting are derived , both for the theory that HAS TO take the place of Relative electromagnetism AND for noncompact second-countable and\or locally compact Hausdorff spaces deemed special for inter-atomic and intra-atomic use . I think I am right that the assumption of Hausdorff-ness serves the purpose to avoid dealing with different notions of local compactness in case of non-Hausdorff spaces , too . Apparently : Almost necessary for how the late Tesla theorised that electricity could be transmitted wirelessly through the air at long distances .

Hi David,

You wrote: " That's why I'm asking if anybody can provide evidence of 377 Ohms being deliberately calibrated into an EM wave emission circuit in order to match the impedance of free space."

I have been following your so interesting mutual discussion off and on, and I don't really have time to partake in the discussion, but on this particular point, I can contribute this tidbit that may or may not be useful in context.

This value that seems at first glance to be 377 Ohms when calculated from the standard means (see Equation (15b) in the referred link), is in reality meters per second (m/s) when dimensional analysis is done to full extent (see Equation (32)):

Article Deriving Eps_0 and Mu_0 from First Principles and Defining t...

Best Regards, André

André Michaud ,

Hi André, I would have asked what you think the significance of the speed 377 m/s would have been. But when I checked it out, I began with Z = E/H = μc. So unless μ were dimensionless, I can't get Z having units of speed.

I'd be inclined to ignore impedance in this matter. The real issue is the 1856 Weber-Kohlrausch experiment which linked the speed of light to the ratio of two different units of charge. Maxwell was able to link this ratio further to the ratio of transverse elasticity and density, from where it was related to permittivity and permeability. Impedance only clouds the issue in my opinion, since we are not dealing with an electric current where Ohm's law would apply.

Frederick David Tombe , current models of physics are unable to answer your question, as current models of physics are based on motion and mass, as André Michaud also appears to be implying.

To answer your question properly, one needs to entertain the idea of zero-dimensional time and space, construct a model for an EM analogue equation from that basis, derive all the equations of physics from such, and then explain the relationship of the permittivity and permeability of space with the EM analogue equation and associated zero-point energy equation of space.

That's what my work does. I am wrapping up a paper on this with associated research and results on how charge works with space compared to a standard EM field, both on the sub-atomic particle scale and elementary particle scale.

Here is the recent paper forming the number-theory basis on this work:Preprint Zero-dimensional number theory

The physical-theory paper requires a bit of detail yet is entirely consistent with the number theory paper.

One thing to note, free-energy, free-energy machines, and so on, in relation to zero-point energy, have no basis. To relate the energy of the impedance of space to a temporal fluxing EM field per-se as a direct link, you are creating a phenomenal absurdity. The impedance as permittivity and permeability by space can only be based on a zero-dimensional level. Yet free space also contains a background EM value in sync with the known impedance, and this registers as the CMBR.

A paper of interest is paper 41, thence leading to paper 42 towards paper 49 (above link):Preprint A time-equation thought experiment deriving 3D space as time...

There, is explained how the temporal/quantum wave function is formed and thence how very more detailed the description of EM actually is from a zero-dimensional level basis compared to known/understood albeit limited models.

Technically, your question must answer why permittivity and permeability of free space exists in the first place. You can only do that in asking what zero-point energy is and what the baseline value for EM is in free space also. There, that baseline energy value for EM is calculated in the paper after 41, paper 42: Preprint The Temporal Mechanics XEMDIR field resolving zero-point ene...

You also need to consider the binding strength of the electric and magnetic components of an EM field, and thence derive the fine structure constant (paper 41).

Ultimately, in trying the standard physics route to answer your question, you may indeed learn much about contemporary physics, but your question will not be answered with having all of contemporary physics explained to you with no fine result. You're more than likely going to to be pointed to black hole singularities. A more complete number theory approach for a zero-dimensional scale of time and space is required.

Stephen Jarvis , I've always taken permittivity to be the reciprocal of the dielectric constant, which in turn relates to the elasticity of the wave propagation medium. And I've taken permeability to be related to the density of the same medium.

Frederick David Tombe , here's a new way of looking at the question you're asking:Deleted research item The research item mentioned here has been deleted

One asks themselves how mass and the motion of mass relates to the idea of charge, right, and how that then relates to the idea of EM.

Thanks Jörn Schliewe

Yes, I recognize the different views. I also understand your well-considered position that as long as E is to play a part in wave propagation, THERE MUST BE a field of charges. This has its own theoretical consequences that you must then be prepared to confront and explain.

This position that you have taken does not even need much debate, because, even if for argument sake, there are three types of E, (v×B, ∂A/∂t and ∇ψ), they are ALL “charge dependent”. That is, without charge, they cannot exert any force, as they are all given by F/q (force per unit charge).

More serious, we know that ALL ‘q’s have an electrostatic field. We can therefore not be mistaken by saying that ALL of the E’s (if we accept them) must represent force per unit electrostatic field, F/ES (just as force per unit charge). In other words, there is no way for any of the forces from an E to avoid acting on, interacting with, or doing work on an electrostatic field ES, even if it does other work in addition. And in my opinion, the work of Faraday’s law is done in the main on an electrostatic field.

Finally, if we accept that action-reaction must be present for force to manifest (going by Newton’s and Coulomb’s force laws), we must contemplate that as any of the forces, v×B, ∂A/∂t and ∇ψ, is acting on the electrostatic field of a charge q, that electrostatic field is reacting equally and oppositely in turn to those forces. We know this is surely the case with ∇ψ.

That is just what I am saying.

Stephen Jarvis , I was only asking if the 377 Ohms of impedance in free space has any practical use. For example, can we connect the number 377 with a horn antenna?

Akinbo Ojo , We've been over this before. An E field does not require the presence of a test charge in order for it to exist. But an E field propagating through space as a wave, does require the presence of test charges in order for the propagation mechanism to function.

Frederick David Tombe what were you opening a mention to though? Making static charge a formula to capture "what" exactly, EM?

A horn antenna is usually well matched to 377 ohms at is mouth, where the impedance of the horn will be close to 377 ohms, and the input can be from waveguide or from 50 ohm coaxial cable. Inside the horn, the horn is designed to give a good transformation between the impedance of the input and the output over the designed frequency range, so that there is no significant reflection from the horn, typically less than 1% (-20 dB).

Frederick David Tombe

Hi David,

Was there any part of my post that appeared to convey the impression that an E field requires the presence of a different test charge (other than its own source)?

I don’t think so I said so. It doesn't require a test charge to exist.

What I said was that none of v×B, ∂A/∂t and ∇ψ, can exert any force in chargeless space. Specifically, no electric field can be brought into being nor an electric current induced, because no electromotive force can happen in an environment where q∂A/∂t = 0.

I don’t see how E (along with B) can propagate as a wave without using Faraday mechanism, and I don’t know how propagation requiring Faraday’s mechanism in transit can take place, if the medium is devoid of test charges q. If you do, show me.

The options I see include 1) provide test charges in the medium so that E can propagate (together with B, by mutual induction of Faraday and Ampere mechanism) and damn the theoretical consequences of that choice; 2) take propagating E wave as implying the propagation of test charges along with their electrostatic fields E, since in Jörn’s view “E is always the Coulomb field of charges”. Therefore, possibly when E is propagating I think the source charges too are propagating along at the same speed. This is novel and allows the propagating electric fields to retain their roots in q; 3) excuse E from wireless propagation and let B alone do the job.

Note from above, that populating space with charges is equivalent to populating space with electrostatic fields. It will be impossible for any force from Faraday’s law not to carry out its action on a curl-free electrostatic field ES, as these will be ubiquitous.

I suspect you prefer option 1) but don’t want to commit yourself openly yet. You are treading carefully because you are wary of the consequence.

Imagine you have some fast magnetic field sensor and electric field sensor. You want to compare the amplitude of electromagnetic wave observed by them. The ratio of observed V/m and A/m should correspond to 377 ohm.

Also, the impedance of balanced line refers to that impedance divided by pi and some logarithmic dependence on ratio of spacing to conductor diameter.

https://wikimedia.org/api/rest_v1/media/math/render/svg/503ee5519ea9c8074d4814dc729cc574e88a31e8

Malcolm White , Thanks. You have addressed the question exactly. The horn is what we might call a smooth transducer. At the cable end its impedance is matched to the feeder cable while at the open end, you are saying that it is matched to the 377 Ohms of free space.

But how do we measure that in isolation?

Nikolay Pavlov , Thank you. Yes, that's the theory. But is it used in practice? And on a side note, if we go into space, at a point where a wireless EM wave is passing through, where do you see the source of the oscillating E field?

Frederick David Tombe , Perhaps you can look at so called cardiod direction finding antenna which sums both electrical and magnetic component of the incoming wave ( whip antenna + small loop) . That allows to resolve front-back ( just whip or dipole are ambiguous on that ).

Hi Akinbo, If space is empty, I can't see how we can apply the EM wave equations in it. That's why so many people are suggesting the presence of some kind of dielectric medium. And that goes back at least to Ampère in 1825.

At the moment I'm trying to establish exactly when, and by whom, the idea arose in quantum mechanics, that space is filled with particles and anti-particles that keep popping in and out of existence. I don't subscribe to this idea, but it is close enough to my own idea from me to take an interest in the reasoning behind it. And I'd like to know why those people who support this modern QFT idea are so adamant that it has got nothing whatsoever to do with the EM wave propagation mechanism, despite the fact that the whole theory is tied up with the electrodynamics of these particle-anti-particle pairs.

In the coaxial feeder to a microwave horn, the voltage and current, or alternatively electric field and magnetic field can be measured at the connector or in the cable. The ratio will be 50 ohms.

The same can be done in the walls of the horn. The ratio of transverse electric field to transverse magnetic field in the horn will be close to 377 ohms most of the way to the aperture. As these vary sinusoidally across the width for a rectangular horn, but are constant across the height, the transmitted power P=Area*EmaxHmax/2. Then Emax = 2P/(HMaxArea) Measurement of the transverse magnetic field beside the centre of the top wall will give a value for the electric and magnetic fields which can then be used to get the impedance. Or the electric field can be measured - perhaps using something that happens at a particular field strength and increasing the power until that happens.

Malcolm White , You may well be right. I'm having great difficulty trying to imagine the shape of the magnetic field line pattern in the context, not that it matters as such what I can or can't imagine.

When we are inside the horn, we are obviously in a transition zone between cable and wireless transmission. We will have an electrostatic ES field crossing between the walls of the horn and the central wire in the coaxial cable, and we will have electric fields of the Faraday EK kind radiating into space. And we will only be able to measure the ES field, which will be the voltage in practice. I don't think anybody has ever physically measured the EK or the H of an EM wave in space. As we approach the open end of the horn, ES and H will both be reducing to zero. And you are saying that the ES to H ratio, where H is the near magnetic field, will be approaching 377 Ohms?

If what you say is correct, the impedance of the horn must rise gradually from 50 Ohms at the neck to 377 Ohms at the open end. How then would the cable pulse actually reach the open end without some of it being reflected, since the impedance of the middle part of the horn will no longer be matched with the power source?

In my mind, the antenna as a whole, whether dipole, loop, or horn shaped, has to have an impedance that matches that of the transmission circuit.

I can see how a horn antenna smoothens the transduction, but I can't see how it differs in principle from any other antenna, and they don't concern themselves with the number 377.

Conventional field theoretic notion of free space has gotten its own defaults because the natural variables of holographic space-time for such a system, are the degrees of freedom of massless superparticles. The GRUND holographic field which , even if only asymptotically , lies as energy backdrop to hypothetical Lorentz transformations , has in fact different solutions of the same low energy gravitational field equations corresponding to different quantum systems, rather than different states in the same electron-negativity system. A nonperturbative, Lagrangian formulation appears/emanates only when much of confusion caused by misinterpretation and misunderstanding of what the theory was supposed to do, and too little appreciation of how important it is to take the large N limit in order to calculate amplitudes of interest to a Lorentz invariant theory , might be removed . As a matter of fact , e- holographic spacetime as quasi-local quantum mechanical SubManifold based on the holographic principle cannot work , at least for negativity charge , unless the related formalism leads to a non-singular NON_Big Bang cosmology, the emerging dimension of which is time rather than space in asymptotically spacetimes.

Reza Sanaye , Do you have a physical context for which we could relate to what you are saying.

Frederick David Tombe

Yes

Sir , , ,, ,, ,

In the framework of the proposed theory the physical context of the meaning of metric tensors lying as "hidden" in free space variables within pseudo-Euclidian may provide almost all all the exact connotations of GR with the said 377 Ohms even though somewhat in violation of the law of conservation of energy_momentum which were actually eliminated, as well as other difficulties have been overcome.

There will be a transition from coaxial cable at 50 ohms to waveguide at slightly above 377 ohms, which is a transformer. In the coaxial cable the electric current runs along the outside of the inner wire, and on the inside of the earth sheath. The electric field is radial between the inner and the sheath, and the magnetic field is circular in loops around the centre conductor, inside the sheath. There is an alternating voltage between the inner and the sheath.

Often the end of the coaxial cable will radiate into the waveguide in a similar way to an electric monopole antenna, or a magnetic loop antenna. This is the transformer, and can be designed to work well over perhaps 50% bandwidth or more.

In the waveguide the electric field is parallel to the short wall, and is largest in the centre and zero at the edges. It has a sinusoidal profile. There is an alternating voltage between the centre of the top wall and the centre of the bottom wall, but not between the edges of the top and bottom walls. Current flows along the centre-line of the top and bottom walls, and also sideways and down the side walls, between the centres of the top and bottom walls. The magnetic field is in loops just over half a wavelength long (this is half the guide wavelength) that are parallel to the top and bottom walls. The ends of the loops cross the guide where the electric field is strongest, and at this point the magnetic field varies sinusoidally across the guide. In between these points, the magnetic field runs partly or completely parallel to the walls, in the direction of the wave, and is strongest at the walls. This is called a TE mode because the electric field is transverse to the direction of the wave, but the magnetic field is partly transverse and partly in the direction of travel.

Over the length of the horn, as the waveguide gets bigger, the wavelength gets closer to the free-space wavelength, and the impedance falls towards 377 ohms, so that at the mouth of the horn the fields are very similar to the wave in free space. This means that the wave is transmitted with very small reflection and that most of it goes in the right direction.

In free space the electric field and the magnetic field continue, and are at right angles to the direction of travel, and to each other. The pattern can be complicated near the mouth of the horn, but a short distance away the wave-fronts are spherical or elliptical, and the electric and magnetic fields are strongest in the middle and fall off in strength towards the edges. The field strength of both falls off as 1/distance.

Malcolm White , Thank you very much for this very informative reply, most of which concerned the activities inside the horn. By the way, did you really mean "transducer" where you said "transformer"?

Now, I want to go back to the very beginning again to the AC emission circuit. Let's suppose that the circuit has a capacitor with an impedance of 50 Ohms at the resonant frequency, when wireless EM waves will radiate off the side of the circuit wire.

We now replace the capacitor with a transmission line of indefinite length, and this transmission line of course has to have an impedance of 50 Ohms for the resonant condition to be maintained.

The transmission line actually has two separate functions. It not only performs the function of a capacitor in relation to the primary circuit, but if the AC frequency is high enough, it will siphon the EM energy out of the circuit and along the line. In order to maintain the 50 Ohms resonant condition, we must prevent the transmitted energy from reflecting back again at the open end, and for this purpose we use an antenna (transducer) which ushers the energy on out into space in a different physical form.

To me, the concept of impedance relates exclusively to the current flow in the primary circuit, and I see in this case, 50 Ohms, as being the impedance of the entire transmission line and antenna in their combined capacity as a capacitor. However, in their capacity as a transmission line and transducer, I see absolutely no relevance to the concept of impedance at all.

I really don't see where the 377 Ohms comes into the picture in relation to the apparatus. The 377 relates to the new kind of energy that emerges from the antenna, i.e. wireless EM waves.

But, you mentioned about measuring voltage and current at various points on the horn wall. Have you ever directly witnessed this yourself and seen the results being recorded, leading to the number 377?

Frederick David Tombe

Hi David,

You have mentioned your current area of interest so I will allow you focus on that here and engage you elsewhere. But your first paragraph is loaded with implications. I will modify it to: if space is a physical field that IS NOT made up of charged particles (dielectric medium), then the current model of wave propagation in it as fields of E and H cannot apply.

Having said that, we know that even if not a dielectric medium, fields can be disturbed.

For example, a scalar field, e.g. a map of temperature or pressure (see some illustrations here https://en.wikipedia.org/wiki/Field_(physics)), can have a spot on it disturbed by a wild fire in the temperature field or an atomic bomb exploding in the pressure field. In many cases, there is attempt to restore equilibrium, with the hot spot cooling and returning to an isothermal state or the high pressure returning to an isobaric situation. In a way, we can say “forces” were evoked to normalize the hotness or high pressure. Such forces, unlike v×B, ∂A/∂t and ∇ψ, will not be charge-dependent in order to carry out their restoration.

Vector field A is your preference for discussion, so I will use that. You accept that it is a field and that it can undergo circuital disturbance, which disturbance shows up as magnetism, i.e. ∇×A= B. You also accept that this magnetism can travel as wave, i.e. ∇2(∇×A) = 1/c2(∂2(∇×A)/∂t2), which can also be written ∇2B = 1/c2(∂2B/∂t2.

From the preamble, it is clear that the forces that will act to restore equilibrium in vector field A ARE NOT charge-dependent forces, yet a wave of B has propagated. It is therefore not compulsory for a field to be dielectric before a wave of B can travel in it.

I will stop here for now.

I meant transformer. It transforms the impedance, as well as transforming the field patters from radial/circular to vertical/horizontal.

A capacitor does not have an impedance of 50 ohms. A capacitor has a capacitance, or at a particular frequency it has an impedance that can be represented as 1/(jwC) or 1/wc with -90 degrees phase factor.

A capacitor can only be replaced by a transmission line with some exact lengths, not indefinite lengths. The lengths at which it has the correct capacitance increase in steps of half a wavelength from and exact shortest length that can be calculated. Sort lengths are usually chose because losses in the line make it look like there is a resistor in series with or across the capacitor.

The transmission line does not have to have an impedance of 50 ohms to do this.

It can't siphon off energy because it must end in an open or short to look like a capacitor, with no energy coming out of the other end. If energy comes out of the other end it will look like a capacitor with a resistor in series or parallel. If all the energy comes out of the other end it will look like a 50 ohm resistor, and not like a capacitor at all, and it can play no part in a resonance.

A horn antenna is not a capacitor. It is a tapered transmission line, with a deliberately chosen impedance profile along its length to result in transmission of all the energy from the end without reflection.

I have seen sparks caused by these fields in waveguide. They have also been measured/observed using fluorescent tubes in waveguide, which glow when they are in the high electric fields. I have measured them using wire probes introduced into waveguide. Antennas I have designed and which work use slots in the walls of waveguides that depend on exact knowledge of the directions and strengths of the currents in each position of the waveguide. The magnetic fields next to the walls of the waveguide have to be exactly equal in strength to the current density in the wall at each point, and perpendicular to it.

Akinbo Ojo , What is your point?

Malcolm White , I don't doubt what you say. But there is no doubt that a transmission line in a resonant emission circuit is playing a dual function. And in my opinion, the (reactive) impedance is only a relevant quantity in its role as a capacitor. As regards its role in siphoning energy out of the circuit in the form of guided waves, which are then transduced into wireless waves at the antenna, I don't see the concept of impedance as having any physical significance.

Have you ever actually witnessed the number 377 being measured in practice in a horn antenna?

No. I feel that until you have a great deal more experience of making and using microwave and transmission line components, and building and operating microwave radars, and working out the mathematics necessary for these to work, as I have done for 45 years, you will not believe any of the things that I have found to be true, including the impedance of free space, its relationship to refractive index and reflection at interfaces, and free space as an extension of a transmission line. Nor what a transmission line does or what it really is.

Mr Tombe, strongly suggest you switch to receive mode (radar analogy) and pay attention to those around you who understand the subject matter more than you appear to at the moment. You have some good subject matter experts on your thread that can help resolve your confusion.

Philip James Baldwin , All I was asking is whether or not anybody has physically measured the number 377 in a horn antenna.

It's my opinion that the combined transmission line and antenna serve two separate functions simultaneously and that the concept of impedance only has meaning in its capacity as a capacitor in the emission circuit.

Take for example a single DC transmission line pulse. How would we relate the concept of impedance to this phenomenon?

I don't know where to start. I have sympathy with your confusion, it is a very complex subject which is why it took me a working lifetime to understand. All I can say is others on your thread are pointing you in the right direction. Good luck.

Philip James Baldwin , It's not a matter of being confused. It's a matter of realizing that the situation is too complex to be treated as simply as it is. And by that, I am referring to the carrying of the concept of impedance from the capacitance in the emission circuit into the radiation escaping from a coaxial cable.

A textbook will explain the resonant condition in an LCR emission circuit, and it is assumed that the circuit has a capacitance which contributes to the reactive impedance.

But if we replace a simple parallel plate capacitor with a transmission line and horn antenna, then other factors come into play, such as the leaking of the energy out through the transmission line.

It's questionable then whether or not we can continue to apply the same simple mathematical analysis.

All we know is that we need the right kind of antenna for the purpose to ensure minimal reflection of the energy back into the circuit again. But I can't see where the concept of impedance is now relevant. The transmission line and the antenna as a whole will have an impedance, but I can't see how anybody can be talking about it having a different impedance at different points within it.

Hi David,

re: “What is your point?”

The point seems clear to Jörn and sometimes also to you, at least as far as I can understand from some of your responses, such as “If space is empty (devoid of charges), I can't see how we can apply the EM wave equations in it” and “An E field does not require the presence of a test charge in order for it to exist. But an E field propagating through space as a wave, does require the presence of test charges in order for the propagation mechanism to function”.

The bottomline then, which Jörn also recommended, is that no matter the different views expressed here, “as long as E is to play a part in wave propagation, THERE MUST BE a field of charges”.

The point, then is that the job cannot be done, either in wave transmission or as Poynting vector, without the involvement of test charges and their electrostatic fields ES. I am yet to hear of test charges that don’t have electrostatic fields.

Repeat ES cannot be ruled out entirely from the proceedings by bringing in an EK, as should now be clear to you.

The corollary to this then, which you must now admit, is that if space is devoid of charges, an entirely different scheme for the propagation of light waves is unavoidable. Is this accepted?

Hi Akinbo, The E field that is involved in wireless EM waves in space is the EK field induced by a time-varying magnetic field. I simply use the subscripted version of the symbol, EK, for clarification in order to distinguish it from the electrostatic field ES.

Remember, the total non-convective E field is,

Etotal = −∇ψ − ∂A/∂t

or,

Etotal = ES + EK

What exactly is your problem?

Dear Frederick David Tombe

one problem for me is that you stated that Ek has no electric energy. However, a wave has to be equal electric and magnetic energy to propagate. This is directly linked to the E to H ratio and wave impedance.

Best regards

Jörn

Siphoning of of energy in cases of ohm transversality onto measurement tube is an instance of the current in a conductor between two points being proportional to the free space dipolarity tessellation between these points. It might be demonstrated that the voltage for each wave in a line topos is proportional to the current of that wave and that the constant of proportionality is just the characteristic impedance. At a much much smaller scale , Protons and neutrons are the lowest-energy bound states of quarks and gluons. When we put two or more of these particles together, they interact, scatter and sometimes form bound states due to the strong interactions. Let us ask ourselves how much space one ampere occupies under such circumstances . .. . .... .. . ..............

Jörn Schliewe , Yes, EK supplies electric energy in an EM wave. I don't recall ever saying otherwise. Here's my take on the relationship between EK and ES. I'll explain it in the context of an electric dipole. I've attached a diagram of the irrotational field line pattern surrounding an electric dipole. If the dipole is static, those field lines represent both A and E, and the curl of each of these fields is zero.

If, however, we rotate the dipole on an axis into the page, so that the negative and positive particles are orbiting each other, the E field pattern will rotate too, while still retaining its shape and remaining irrotational. The curl of E will still be zero.

As regards A, though, the rotation will cause the field line pattern to curl, and we will have ∇×A = B. The field lines for A will now spiral into one particle and out of the other.

And if we now angularly accelerate the dipole, whether in the same plane, or by a precession, then this time, the E field lines will also curl. The E field line pattern will spiral and we will now have a transverse component of E. We'll call the radial component, ES, and the transverse component, EK. The radial component is the electrostatic field, ES = −∇ψ, while the transverse component is that which arises due to a time-varying magnetic field, such that EK = −∂AK/∂t, ∇·AK = 0, and ∇×EK = −∂B/∂t. AK is the transverse component of A. A time-varying magnetic field in space is due to the presence of angularly accelerating dipoles.

So in order to have an EM wave propagating in space, space needs to be filled with electric dipoles, and there will be both an electric field energy and a magnetic field energy involved.

EM waves are transverse waves in the Coulomb gauge, where ∇·AK = 0.

Dear Frederick David Tombe

Just to recall:

Tombe 1: “Now I admit that I have never seen the energy expression, ½[εE∙E], actually derived in the textbooks for the electromagnetically induced E field that I call EK.”

Tombe 2: “Both H and EK have an associated magnetic energy, where EK is the electric field of time-varying EM induction, embedded within the fabric of the time-varying H field.”

Tombe 3: “Ultimately it's just a single magnetic wave. The vectors A, EK, and H, are simply different aspects of the same magnetic displacement mechanism. Electrostatics doesn't come into it.”

Best regards

Jörn

Jörn Schliewe , Yes. I did say all of those things. I have never seen the energy expression for EK derived in a textbook. It's always derived for ES. But I do believe that it holds equally for both. It's usually derived in connection with a capacitor, or in Maxwell's 1861 paper, in connection with a dielectric.

The energy associated with EK could be described equally as electric or magnetic energy. It is sourced in a time-varying magnetic field.

That's why I said an EM wave is ultimately a magnetic wave with no electrostatic component. The electric field which is involved in it is magnetically sourced and closely tied up with A and H.

But the message I sent last night gives my opinion on the close association that also exists between EK and ES, emphasizing the electric nature of EK. The facts regarding the magnetic nature of EK are textbook facts. The facts regarding the connection between EK and ES are only my own opinion.

Jörn Schliewe

Now that you and David have finally succeeded in populating the whole of space with charged particles, I assume your charges have mass. How bodies will be able to move in such a choked up space is one age old consequence. What is your mechanism for resolving that? I believe I know David’s.

Frederick David Tombe

re: "What exactly is your problem?"

I don't have a problem. It is you that has one accepting that B is a circuital disturbance in a vector field (which you prefer to label A). And that this circuital disturbance B can propagate through the vector field as a wave of that field.

Hi Akinbo, ∇×A = B is a standard textbook equation and one of Maxwell's original equations. It has no implications relating to wave theory. More input is required, principally Maxwell's displacement current, J = ε∂EK/∂t, before we are ready to derive a wave equation.

Frederick David Tombe is not the problem you are seeking to resolve describing how a fluxing EM field may or may not relate with a non-fluxing charge and magnetic field? Am I right in saying that you're asking, "is there a relationship there, and maybe a loose wire that can be tapped into?"

Hi David,

Yes, ∇×A = B is a standard textbook equation telling us that B is a circuital disturbance in a vector field. When we add that to what can be read from Heaviside in his 1893 book, Electromagnetic Theory, vol.1, The Electrician, p. 220/221, we should be in no doubt, or at least should entertain the idea that B can propagate through the vector field as a wave.

If vector field A does not represent a field of charged particles, it will not need the involvement of charge-dependent forces such as EK, ES or a displacement current for a wave to propagate in it. It will only need those superfluous things, if indeed it is a fact that space or the field IS populated by charged particles.

So we have two scenarios.

1) Space populated by charged particles is a fact: ES, EK, displacement current, etc are necessary for wave propagation;

2) Space populated by charged particles IS NOT a fact: Wave propagation will not need the involvement of charges, charge-dependent forces such as EK, or a displacement current in order for B to propagate. In scenario 2, we do not need charged particles, ad hoc concepts or a multiplicity of fields in order to write out the wave equation for B as ∇2(∇×A) = 1/c2(∂2(∇×A)/∂t2), or ∇2B = 1/c2(∂2B/∂t2).

So, it is only those who are fanatical about scenario 1, as if there can be no other possibility, that will insist that they would need more inputs before they can derive or write out a wave equation, not for those in the second group, where I belong.

Stephen Jarvis , That was actually a side issue. The main issue as per the title question is whether or not there is any physical significance to the definition of the impedance of free space as being 377 Ohms. It is a definition that is played up by those who wish to view space as being dielectric. But although I am in the category of people who view space as being dielectric, I nevertheless believe that the 377 Ohms of impedance argument is a red herring which confuses the issue unnecessarily.

However, if somebody could have confirmed that we do actually measure the number 377 in a horn antenna, I would have taken a deeper look into the matter to see if I could figure out why.

As regards the side issue, I have believed since 1982 that the electric field induced by a time-varying magnetic field, is actually due to the presence of an all-pervading electron-positron sea, and that this electromagnetic force arises when this elastic sea is subjected to stress, and that of course it is all tied up with displacement current. I viewed the induced electromagnetic E field as being ultimately an electrostatic field at a deeper level in the electron-positron sea.

But since 2006, I have realized that while this is broadly true, we cannot actually rely on the radial electrostatic force field surrounding these particles, but that we must rely on a tangential extension of this E field, which arises when the rotating dipoles that make up the electron-positron sea are rendered into a state of angular acceleration, as in when ∇×EK = −∂B/∂t, where ∇×A = B.

Akinbo Ojo , You will never be able to derive an EM wave equation in either A or H, without the involvement of either the Maxwell-Faraday equation, ∇×EK = −∂B/∂t, or the electromotive force equation of time-varying EM induction, EK = −∂A/∂t.

If you are trying to say that wireless EM waves don't have an E component, then you are wrong. You are completely wrong.

Frederick David Tombe But although I am in the category of people who view space as being dielectric, I nevertheless believe that the 377 Ohms of impedance argument is a red herring which confuses the issue unnecessarily.

Can you explain further, the red herring? Do you have supporting evidence for your red herring find, or is this a new conjecture?

Stephen Jarvis , Are you referring to my own theory, as in the E field that is induced by a time-varying H field is ultimately the transverse extension of the radial electrostatic field that arises within a rotating dipole when the dipole is caused to angularly accelerate?

I don't know what you would accept as evidence, but you won't find any evidence in the textbooks.

So, in the meantime, we just have to accept the textbook position which is that an electrostatic field is a radial force field centred on a charge, and described by Coulomb's law, or ES = −∇ψ, where ψ is the scalar potential, while the E field that is induced by a time-varying magnetic field is described by, EK = −∂A/∂t, where ∇×A = B. And meanwhile we must continue to remain ignorant as to any possible physical connection between ES and EK.

Frederick David Tombe Evidence is anything new not accounted for by current textbooks, provided it is structured and repeatable. The "meantime" is no mans land, technically, for you. For everyone else it is certainty. The energy dynamics for a fluctuating EM are different to that of a static charge and magnetic field, as a mass-gravity route is required: Deleted research item The research item mentioned here has been deleted

Frederick David Tombe

Hi David,

You cannot eat your cake and have it on this matter. For EK to exist, space MUST be populated by charges, dipoles, vortices and fluids, otherwise EK must evaporate from physics. It is as simple as that.

Akinbo Ojo , OK, so how do you account for the E field in wireless EM waves in space if those things aren't there?

Frederick David Tombe , electric and magnetic features are recognized in EM by "relative motion of mass with static charge". Are you asking how the impedance of static charge in free space can ride the EM waterslide it is based on? Does physics know that waterslide though, how a fluctuating EM field has properties for charge and magnetism? Is that your question? You are therefore asking a question that can't be answered by physics by its approach, namely its sole approach of mass and motion of mass, not understanding electric and magnetic effects featured in an EM field. Is there a bounty there by that failure? Is that your question?

Stephen Jarvis , It's not me who is asking those questions. Akinbo is asking me those questions.

I'm asking whether or not the 377 Ohms of impedance that is defined for free space ever plays an active role in laboratory apparatus that transmits wireless EM waves.

Frederick David Tombe you're trying to pump a fluctuating EM impedance with what is calculated for free space for non-fluctuating electric magnetic fields, right?

The only "impedance" idea I am aware of as a fluctuating EM field is that EM has is a fluctuating field (important to note), and that such is constrained by the fine structure constant. That's related to particle phenomena of the atom, already. Are you trying to hop that with what is registered as the vacuum permittivity and magnetic permeability, already? Are you looking for holes in the system to connect the already-already ideas?

Dear Frederick David Tombe

Dear Akinbo Ojo

Tombe: “The facts regarding the magnetic nature of EK are textbook facts. The facts regarding the connection between EK and ES are only my own opinion.”

That sounds rather close to my position.

State of the art: We derive from the combination of Ampere’s and Faraday’s laws to wave equations for H, E, A and phi. The most convenient approach is to say phi=0 without charges and A is retarded. E and H can be calculated from A. The solution is the plane wave with everlasting straight E and H lines, which forms a Poynting vector for power transport. Then we use the plane wave solution to combine the effect from all source points to all points in space to come up with more sophisticated solutions like spherical harmonics or radiation patterns etc.. This neglect the lateral extension of the plane wave, which might be motivated by a cancellation of energy broadside. In my opinion this is an approximation and strong simplification of reality, but useful for far field analysis.

My view: phi can not be zero if E is involved, neither can rho be zero. I found a bounded wave solution to Maxwells equations which allows the same point to point transport of energy simplification in far field but with realistic E, H, A and phi fields and potentials. The basic idea is the polarisation and magnetisation of space by creation and separation and rotation of charge densities. Details are in my paper linked below.

Best regards

Jörn

Article Electrodynamics in Euclidean Space Time Geometries

Dear Akinbo Ojo

”Now that you and David have finally succeeded in populating the whole of space with charged particles, I assume your charges have mass. How bodies will be able to move in such a choked up space is one age old consequence. What is your mechanism for resolving that? I believe I know David’s.”

In my view: Bodies are made from incredibly many created and separated and rotated charge densities. Mass is the electromagnetic energy they contain. Gravity is a force on EM energy due to a gradient in polarisability and magnetisability.

Best regards

Jörn

Stephen Jarvis , OK, imagine an emission circuit at resonance in the microwave range, with a parallel plate capacitor of 50 Ohms. Microwaves will radiate off the side of the circuit wires. But then replace the 50 Ohm capacitor with a length of coaxial cable that has a horn antenna at the end.

The situation will now change. The cable serves as a kind of sink. It becomes the path of least resistance and so most of the energy leaves the circuit along the cable in the form of a guided wave.

Does the combined cable and horn have an impedance of 50 Ohms at resonance?

We have now introduced an extra process, and so one question is whether or not we are still free to use the initial circuit analysis of the situation.

My own opinion is that even if the cable and antenna can still be treated like a capacitor in the emission circuit, that it will still have a single value as regards the reactive impedance. I can't see how we can be talking about 50 Ohms at the neck of the horn and 377 Ohms at the open end.

The horn is a transducer that coverts guided waves into wireless waves, but once we get into the realm of wireless radiation, then the concept of impedance no longer has any meaning.

But if somebody can report having witnessed otherwise, I'm open to look into the matter.

Jörn Schliewe , Well basically, as regards the analysis of EM waves, you are going with the textbook analysis but suggesting that it doesn't tell us enough, and that perhaps some of the wave solutions have been over-extrapolated in the more complex situations. Is that correct? Is that your position?

If so, that's more or less my opinion too.

Frederick David Tombe

Hi David,

Now that once again, you seem to get the central message, go and preach it everywhere and don’t get distracted or involve yourself in secondary debates over different types of E.

Central message: There can be, and there should be no E field of any sort involved in light wave propagation, IF space is not populated with charges.

If the message can get to the great Maxwell himself, take it there. That would also be nice because he started the confusion by removing charges from his medium (calling it non-conducting [1], [2]), but yet holding on to E, even if in some of his conclusions, he emphatically referred to light as a magnetic disturbance [2].

[1] “If the medium is a non-conductor, conductivity = 0”, “we may therefore leave J and ∇ψ out of account in considering periodic disturbances”, [783], “Relation between Electric Conductivity and Opacity” [798] - Maxwell, J.C. (1873), https://en.wikisource.org/wiki/A_Treatise_on_Electricity_and_Magnetism/Part_IV/Chapter_XX

[2] “This wave consists entirely of magnetic disturbances…” [95], “The agreement of the results seems to show that light and magnetism are affections of the same substance” [97] - Maxwell, J.C. (1865),

https://en.wikisource.org/wiki/A_Dynamical_Theory_of_the_Electromagnetic_Field/Part_VI

Whatever you believe, hold on to the central message ALWAYS, and never let go of it again. The corollary is clear and may not need stating again to avoid distraction.

And I like this from Jörn Schliewe , "phi (ψ) can not be zero if E is involved, neither can rho (conductivity) be zero"

Hi Jörn Schliewe

I went through your paper again. I want to be clear how you eliminate div E from your derivation, in view of your statement, “phi (ψ) can not be zero if E is involved, neither can rho (conductivity) be zero”?

I don’t want to pre-empt your answer, but could this be the reason behind your introduction of virtual charges? Do you mean to imply that virtual charges will not be involved in definition of Gauss’s law (the first of the four Maxwell equations)?

On your view, “Bodies are made from incredibly many created and separated and rotated charge densities. Mass is the electromagnetic energy they contain. Gravity is a force on EM energy due to a gradient in polarisability and magnetisability”.

Happy to interrogate that later. I wonder if the charges interact with each other in the manner of like charges repel, unlike charges attract, etc

Akinbo Ojo , Maxwell used EK = −∂A/∂t when deriving the EM wave equation. He never removed charge. He just didn't use Coulomb's law in the derivation.

Hi Frederick David Tombe

Well, so that you don’t get yourself mixed up again, just hold on to the central message, which I believe you are in agreement with.

Also don’t forget you have said the following:

- “If space is empty, I can't see how we can apply the EM wave equations in it”

- “But an E field propagating through space as a wave, does require the presence of test charges in order for the propagation mechanism to function”

- “The facts regarding the connection between EK and ES are only my own opinion (for mainstream E is E)”

Yes, Maxwell used EK = −∂A/∂t when deriving the EM wave equation but it is a lie that “He never removed charge”.

What did he mean by “If the medium is a non-conductor, conductivity = 0”, “we may therefore leave J and ∇ψ out of account in considering periodic disturbances”?

When you remove electrostatic potential out of account, have you not removed charge?

Your E may be different. But to mainstream, the stated reason why ∇∙E = 0 in the derivation is from Coulomb's/Gauss’s law, ∇∙E = ρ/ε, where ρ is charge density.

Hi Akinbo,

Yes, I did said,

“If space is empty, I can't see how we can apply the EM wave equations in it”.

But why don't you get to your point? You don't believe that space is populated with charges, and you think that you have solved the problem by removing the E field from the electromagnetic wave, leaving it as a purely H wave.

Well you are wrong. There may be a conundrum, but you have not solved the conundrum. You have simply departed from Maxwell's equations in order to accommodate your own continuous aether theory.

At the end of the day, no matter what else, there is an E field involved in wireless EM waves, and it is involved in the power density (Poynting vector S = ExH). Any physical interpretation of EM waves will have to take account of this reality.

The absence of E in your theory of wireless waves means that it fails from the outset.

Dear Frederick David Tombe

agreed. But focusing on text book equations for field in materials, including M and P fields.

Best regards

Jörn

Dear Akinbo Ojo

“I went through your paper again. I want to be clear how you eliminate div E from your derivation, in view of your statement, “phi (ψ) can not be zero if E is involved, neither can rho (conductivity) be zero”?”

DivE is not zero but divD=O like at boundaries of polarisable materials. You have a divP which has same amplitude like divE. In materials the virtual charges are called bound charges.

“I wonder if the charges interact with each other in the manner of like charges repel, unlike charges attract, etc”

Sure. I think this is included in Maxwells equations. The force is directed to minimise the electrical energy.

Best regards

Jörn

Frederick David Tombe

Hi David,

OUR agreed central message is,

Central message: There can be, and there should be no E field of any sort involved in light wave propagation, IF space is not populated with charges.

Go and preach this, instead of focusing on existence or non-existence of E.

In wireless EM waves, where EK travels with B, what is their respective function at a receiving antenna? Which of the two induces current at a receiving antenna, or do they do it jointly?

Jörn Schliewe , Here’s a clue for you. A rotating electric dipole gives rise to a magnetic moment. But it’s not until the dipole angularly accelerates that the electric field lines curl. The transverse extension to the radial electrostatic ES field lines, which is induced by the angular acceleration, is the Faraday EK field. See the appendix in this article after the reference section, which illustrates the connection between Faraday’s law and an angularly accelerating electric dipole.

Article The Dirac Sea and the Aether

Fill space with these and you will have the basis for the displacement mechanism for wireless EM waves, with a power density expressed by EKxH.

This is in answer to your assertion that the radial electrostatic ES field remains present in the vicinity of a wireless EM wave. Yes, it is present, but it plays no part in the displacement or propagation mechanisms. Wireless EM waves are not about charge separation or polarization. There is no radial compression involved, as in the electric particles changing their separation distance. In that respect, the medium could be said to be incompressible. As regards wireless EM waves, we are in the Coulomb gauge where ∇·AK = 0.

The electric field lines in the attached diagram have zero curl if the dipole is either static or undergoing a steady rotation. But if the dipole angularly accelerates, then the E field lines will curl.

Jörn Schliewe

Hi Jorn,

Can you elaborate a bit on that. Are you interpreting the constitutive relations in an alternative way? If D = εE, and thus if DivD = εDivE, how can DivD be zero, and DivE will not be zero? Or is my math or physics wrong?

On the interaction between charges, is this via an intervening medium separating the charges; action-at-a-distance without an intervening medium; or by means of virtual particles/photons fired at each other; or other methods?

I note in your model that as a wave propagates, the distance between the bound charges oscillates elastically. Is this correct?

Frederick David Tombe

Hi David,

I have abandoned the topic, but decided to just take note, after seeing this, “The electric field lines in the attached diagram have zero curl if the dipole is either static or undergoing a steady rotation. But if the dipole angularly accelerates, then the E field lines will curl”.

So, the curl or curl-free nature of an electrostatic field is not eternal after all, and can be induced to suffer distortion/deformation by events, e.g. "angular dipole acceleration"? Yes or No?

Akinbo Ojo , I would say so. If an electric dipole angularly accelerates, a new transverse component of the electric field is induced which is not covered by Coulomb's law of electrostatics. It's the Faraday EK field (time-varying). But that's only my opinion. It's not a textbook fact.

Frederick David Tombe

Hi David,

When, in mimicking Faraday, a bar magnet is brought near a conductor in a time-varying way (∂B/∂t) in order to induce a current, where is the dipole that undergoes this angular acceleration located? In the conducting wire or in the space surrounding it?

Akinbo Ojo , The tiny angularly accelerating dipoles within a time-varying magnetic field are constituent components of the all pervading dielectric medium. But that's only within the context my own theory, and so it is irrelevant in this thread.

The only thing you need to know here, is that a time-varying magnetic field induces an electric field, and that this electric field is of the transverse kind, EK = −∂A/∂t, that is involved in a wireless EM wave, where, ∇·A = 0. That is, EM waves operate in the Coulomb gauge.

And by the way, my guess is that in the case of a moving magnet, we actually use the convective component, EC = vxB, and not EK = −∂A/∂t. But that is a side issue.

A vacuum is a place that is devoid of all matter. In the Solar System, there are typically five atoms per cm3 of space. In the interstellar space between stars, there are around one atom per 1 cm3, while there are 100 times less in the intergalactic region between galaxies. Because energy fluctuations known as "virtual particles" are constantly bursting into existence, even in "empty" space, a perfect vacuum is ultimately unachievable. however , this due to assumptions AND presumptions of QFT . We have two ways ahead of us :

Deeming QFT to be "correct" and , as a result , regarding vacuum space as the quantum vacuum state (also called the quantum vacuum or vacuum state) with the lowest possible quantum energy. The existence of a vacuum state cannot be derived from or refuted by the field equations and commutation relations that make up a local quantum field theory that describes zero-mass particles. It is a stand-alone postulate that may be included or withdrawn as needed without modifying the theory's fundamental physical tenets. According to present-day understanding of what is called the vacuum state or the quantum vacuum, it is by no means a simple empty space. Quantum corrections to Maxwell's equations are expected to result in a tiny nonlinear electric polarization term in the vacuum, resulting in a field-dependent electrical permittivity ε deviating from the nominal value ε0 of vacuum permittivity.

The theory of quantum electrodynamics predicts that the QED vacuum should exhibit a slight nonlinearity so that in the presence of a very strong electric field, the permitivity is increased by a tiny amount with respect to ε0. Subject to ongoing experimental efforts is the effect that a strong electric field would modify the effective permeability of free space, becoming anisotropic with a value slightly below μ0 in the direction of the electric field and slightly exceeding μ0 in the perpendicular direction. The quantum vacuum exposed to an electric field thereby exhibits birefringence for an electromagnetic wave travelling in a direction other than that of the electric field. The effect is similar to the Kerr effect but without matter being present. This tiny nonlinearity can be interpreted in terms of virtual pair production A characteristic electric field strength for which the nonlinearities become sizable is predicted to be enormous, about 1.32\times 10^18 , known as the Schwinger limit; the equivalent Kerr constant has been estimated, being about 1020 times smaller than the Kerr constant of water. Explanations for dichroism from particle physics, outside quantum electrodynamics, also have been proposed. Experimentally measuring such an effect is very difficult, and has not yet been successful.

The very non-linearity discussed above is a signifier of dipolarity "hidden" within Vacuum giving rise to a magnetic moment. Such a magnetic moment could , thence , be interpreted to be the minimum eigenvalue of the Hamiltonian of the system. The Hamiltonian is the operator which corresponds to the total energy of the system, so it is the sum of the kinetic and potential energy. This is often also referred to as the ground state energy of the system. Heuristically, the ground state energy is the energy which the system has simply by existing. Normally, this doesn't make any sense: If I just make the system do nothing, just sit there, then it would have zero energy. We wouldn't need the fancy name. Because the energy is quantized you usually find several possible values for the energy that are given by an integer number n called the Principal Quantum Number. The lowest value of En, normally when n=0n=0 or n=1n=1, is the Groud-State. This means that the energy of the Vacuum State is the lowest and it is a combination of the potential energy and the kinetic energy. The system must have some momentum, to satisfy the above-mentioned non-linearity. In turn, it will also have some energy. This is why we can never reach absolute zero , no matter how hard we try, there always remains the jiggling of the ground state.

Bear in mind that these are all in case we deem QFT to be "correct" and , as a result , regarding vacuum space as the quantum vacuum state (also called the quantum vacuum or vacuum state) with the lowest possible quantum energy. NOW , THE SECOND WAY OPEN IN FRONT OF US IS PUSHING QFT ASIDE [ WITH ALL ITS ASSUMPTIONS AND PRESUMPTIONS ] AND TAKING A MORE "TRADITIONAL" PATH . I shall talk about this one in a later post . Simply cannot bring in the whole elucidation here as in continuation .......................

Dear Akinbo Ojo

D=eps0*E+eps0*P

Rhov=eps0*divE=-eps0*divP

All standard treatment of polarisable materials. Please refer to:

Lehner G, Electromagnetic field theory for engineers and physicists, Springer-Verlag, Berlin Heidelberg, 2010

I recommend Lehner’s book because he discusses the limitations of the mathematical assumptions and limitations.

The physical question is: why is space polarisable and not empty? The answer is that if energy is around the space is not empty. So the wave energy makes the polarisation possible.

Best regards

Jörn

Reza Sanaye , With your knowledge about the quantum vacuum, It would be more appropriate if you took this knowledge over to this other question and answered as to why the quantum vacuum isn't also the medium for the propagation of light.

https://www.researchgate.net/post/How_did_the_Dirac_Sea_connect_with_the_Luminiferous_Aether_of_the_Nineteenth_Century

Yes, Jörn Schliewe

I am aware that there are several derivations of the wave equations, including in polarizable materials. Some can be found also on the easily accessible Wikipedia page, https://en.wikipedia.org/wiki/Maxwell%27s_equations. In most derivations, after taking the curl of the two curl equations, and substituting, we arrive at

∇(∇∙E) - ∇2E = - µε∂2E/∂t2

in many textbooks. David gets rid of ∇∙E by making E to be EK. Mainstream finds other ways.

My question is how do you get rid of ∇∙E to obtain a final wave equation in E?

What mathematical assumptions or limitations do you apply in your own method of derivation of the wave equation for E?

All, is there an actual theory linking how charge and magnetism as non-fluctuating field effects relate with fluctuation field effects other than the idea of a mass-charge moving relative to another object in question, thence phenomenally supporting all the EM induction field effects carried by a fluctuating "non-static" EM field? How hard is it to see what's going on there?

Frederick David Tombe

Hi David,

Are there dipoles also in the conducting wire and can these also be set into angular acceleration?

Can the ES of a dipole be converted into EK of a dipole by a magnetic action?

Akinbo Ojo , You need to get to your point, and I already know what it is. You are trying to sell a theory in which space is not dielectric and in which there is no E field involved in wireless EM waves.

Well, in my opinion you are wrong on both counts, and the textbooks will certainly back me up on the second count.

And besides, this is all totally irrelevant as regards the title question of the thread.

Stephen Jarvis , Are you asking if there is a physical connection between the electrostatic force field that surrounds a charged particle, on the one hand, and the electric force field that is induced in a time-varying magnetic field, on the other hand?

Is that your question?

In other words, are you asking if there is any physical connection between the two components on the right-hand-side of the equation,

E = −∇ψ − ∂A/∂t

where −∇ψ is the electrostatic field and −∂A/∂t is the Faraday electric field of time-varying EM induction?

Is that your question?

Frederick David Tombe Are you asking if there is a physical connection between the electrostatic force field that surrounds a charged particle, on the one hand, and the electric force field that is induced in a time-varying magnetic field, on the other hand?

Is that your question?

No, that's not my question.

I'm suggesting that static charge is as much related to EM as a car is to a road. It is a very poor analogy though.

How exactly are you trying to tap how zero-point energy is shoving mass with charge and then relating that with an EM field?

Stephen Jarvis , I see. So are you suggesting that electrostatics and EM induction are not related to each other?

Frederick David Tombe Electrostatics is a condition of mass. EM has a carrier effect there. How therefore does one say a static charge enforces impedance with EM? What you're suggesting, its like mass as mass-charge affects an EM code. You're talking about relating EM with mass and motion of mass as its, mass's, charge quality. Why not talk about quantum gravity in the meantime?

Stephen Jarvis , I don't associate impedance with either electrostatics or EM radiation. I associate impedance with the resistance to the flow of electric current in a conducting circuit.

Frederick David Tombe , so, this is now how an event can temporally affect another electrically using the logic of impedance despite if it is an EM or static charge field?

Frederick, how can't you understand how an EM field is not a static field?