Are you talking about propagation of waves or propagation of the fields. EM waves are originated from the EM fields, not viceversa. It is not the same thing.

Maybe we have to reexpress everything with Quaternions, like Maxwell first did, if we want to model a better framework in which Electricity and Magnetism are phenomena working toghether.

Dear Stefano,

You are right, yet the problem is what is measurable - field of wave? - and what then we measure in reality? If we have equations for the EM potentials [1/c²∂²/∂t²-Δ]A^{μ}=J^{μ}, then the constant c means the velocity of what you think ??? If that of fields, so  what is the velocity of the waves?

Regards!

I think that for any solution the only propagation limit is your imagination. But what concerns electromagnetic waves there is no measured result showing their velocity above c limit.

Dear Adam,

could you be more  concrete having explained  "... the only propagation limit is your imagination. "? What do you mean? It is hard to catch this original thought, - so sorry for my stupidity...

Regards!

As the speed of light in a vacuum has an exact value (CODATA, Recommended Values of the Fundamental Physical Constants 2010 – http://arxiv.org/pdf/1203.5425.pdf) no solutions to the Maxwell equations propagating in a vacuum with velocities either greater or lower than the standard light velocity are allowed. Besides, I don't know how easy it is, when experimentally determining light speed, to take the response time of the instrument correctly into account.

Of course, the above recommendation doesn't solve any of the long-standing debates about the interpretation of the solutions, which arise on account of the difficulties in solving and visualizing the system of Maxwell equations. Therefore, I think that some criticisms are valuable. For example, in the article by Chubycalo & Smirnov-Rueda cited by Rodrigues Jr. & Maiorino there are two, which I would summarize as follows: (1) If the “potential” is understood as a latent, yet unrealized ability -- not just as a mathematical device -- , does the electromagnetic potential exist prior to the “actual” electromagnetic field? (2) Two of Maxwell equations are taken over from the theory of static fields. How do they comply with the two time-dependent ones?

Dear Sara,

thanks for your comment.-Yet, the question is  about the "solutions of the Maxwell eqautions with velocities different from that of light"  -  As it is written  in the above cited/attached  article by Maiorino and Rodrigues -  "„… instead we are going to show in the rest of this section that the free Maxwell equations have nonpurely transverse solutions which correspond in general to electromagnetic field configurations moving with velocity v ≠ 1 (again in units where c=1)…”  

So, we face the problem - is the  constant   light velocity c=1 the energy transportation velocity, or it is the velocity of propagating in space the electromagnetic field changing?

Cordial regrads!

pls read  h. f. harmuth articles and l. brillioun book.

Dear Anatolij,

a problem emerges when we talk about EM equations:

the fields surely respect the Lorentz Group of transformations, the waves I'm afraid though the present theory tries to  forced them to do,  they actually don't,  this is a serious issue.

As Fermi himself pointed out in the attached file, during matter radiation interaction, in the generation or in the absorption of radiation in reciprocally moving IRFs the phase of the waves is not preserved. Lorentz Transformations and Maxwell Equations impose that such phase is preserved, and sadly fail in their limited description.

I trust Fermi like nobody else because

1) he was like Planck a top theorist and top experimentalist together and had a grasp on problems like nobody else as Feynman, who met him, said.

2) his Fermi-Dirac statistics is over tested in the electronic circuits at the base of all our electronics and solid state theory.

3) He was the leader of one of the brigthest group of people in the world, including Majorana.

 Radiation is the epiphenomenon of the transitory of a field and by itself cannot be treated with fourirer series but with Fourier transform or Laplace transform math description suitable for system transitories.

In transitories like a scattering or dirac delta pulses, a set of higher frequencies appear (which have a cut off) to be carefully taken in consideration and this is something treatable with Laplace transform, FFT  or cauchy integrals.

Dear prof. Prykarpatski,

I wish to inform you of this article citing (and criticizing) an article by Giovannini et al. (http://de.arxiv.org/ftp/arxiv/papers/1504/1504.06059.pdf). The latter reports experiments where the light speed is measured to be different from c in a vacuum, after clarifying that on the inside of a hollow wave guide there is a vacuum.

Dear dr. Quattrini,

I agree that the solutions to the wave equation are not necessarily solutions of Maxwell's equations. It should be checked. A transient is a particular solution which takes initial and accessory conditions into account. To me it seems that, as soon as boundary conditions on a real reflecting, transmitting or absorbing surface are given, the shape of the latter is not Lorentz invariant.

When applying Green's theorem the surface enclosing the matter interacting with radiation is not an actual boundary. But, as the solution of a wave equation needs to have a second derivative while the normal component doesn't, the class of solutions satisfying that theorem is more general than that of twice derivable functions.

Dear Sara,

Interesting, a Bessel beam makes the photons travel slower because they take a longer path in vacuum...

You can see:A.LAKHTAKIA.Essays on the formal aspects of e.m theory.World Scientific.New York.1992.

Thanks!

Can you present a pdf-file of this edition to read it?

Sincerely,

A.

This is rather complex topic. First of all, type of velocity must be defined. There are some velocities in the literature such as propagation velocity, grup velocity, phase velocity, signal velocity and so on.  Pls check H. H. Harmuth papers in IEEE EMC and his book "Propagation of Electromagnetic Signals".

To: @Serkan Aksoy

Thanks! What kind of velocity is exploited in the Einstein "gedanken" experiments with light signals and what are their  real velocities? Do these experimets have a reasonable sense from a physical point of view?

Thanks in advance!

I do not know about their evaluations.

P.S. The Maxwell equations allow propagation of the electromagnetic  wave fronts with the constant light  velocity  c. Yet, this does not mean that these equations are not allowing other signal like solutions which can propagate in space with greater than c velocity, or less than c. It was before mention at the very beginning of my post. A question arises - does this signal solution is related with some EM energy and what is its real propagation velocity? I claim that it can not be greater than c...

There are always reference points that can be shown to have a different speed with respect to the wave and yet have no speed with relation to the observing body.  We see these situations all the time in astrophysics.

Say I am on a star that rotates at the same speed that a planet orbits the star.  In reference to the planet someone on the planet can send a signal in the AM band that circumnavigates the globe and they see the signal at c in all spaces and times. 

When the observer on the sun looks at the signal they see it differently.  As the signal comes around the globe towards them, it is traveling faster towards them and at the speed of c.  As it goes around the other side going away from the star it is traveling faster than c.  It must do this or there is no reality in Physics that can be measured.  It also means that if the star observer does not see this difference as his distance and speed from the planet observer is not changing that there is a paradox or that we are not correct in how we approach the information.  You can not have it both ways.

There are problems in how we look at Physics today.

Dear Anatolij,

since you are dealing with electrodynamics in deep, would it be possible for you to have a look at a paper of mine which has some insights on matter radiation interactions?

Best regards

Dear Stafano,

thanks for your touch - please,  send your  paper under regard at my email address. Sincerely,

A.