Dear Jarek
As I argue in my essay, the scientific value of a theory resides in the power to explain and reproduce the body of experimental evidence under consideration. One should distinguish between Lorentz invariance (LI) and Special Relativity (SR). LI can be derived (as Lorentz himself did in 1904, and many others even nowadays) from the assumption that there exists a medium for the propagation of light waves (what I called space itself but seen as a fluid not as geometry) which can be assumed to be the preferred system of reference (PSR). This means that the existence of the medium does not contradict LI (This is precisely the discussion of my essay). Let us called, Lorentz approach, Lorentz theory (LT).
On the other hand, SR makes no assumptions as to the medium for light. Actually, SR accepts LI but rejects per se the PSR. In other words, we have two theories that explain the same physical phenomena. However, each theory has its problems. The former has been forgotten because it has not been possible to detect the medium. This does not mean however that the medium does not exist. And the latter, as it is well known within the circles of the philosophy of physics, has logical inconsistencies (paradoxes) such as the Supple paradox, the clock paradox, etc. --unfortunately, most physicists do not even acknowledge them.
So, if both theories explain the same phenomena, in principle, it turns out to be irrelevant which one we chose to work out the calculations of a problem under consideration. Einstein considered the aether superfluous and moved on with his approach despite the paradoxes. These paradoxes could be ignored --as it is actually done-- since they do not interfere with the theory predictions. I have no problem with this.
Nowadays there are many problems in physics, in a certain sense, it is widely recognized that theoretical physics has been in a state of stagnation, no major breakthroughs have occurred for the last 30 years. As time goes by the experimental evidence piles up and adds more to the puzzle. So, some years ago I started to carefully analyze and study the history and the foundations of physics. I found that LT is still valid and that it could be still useful to solve many problems in physics if the medium is reintroduced (you may wish to see my discussion with Daryl Janzen in his entry and mine in relation to the physical interpretation of the redshift). So, in the present state of things, if I were asked what theory, i.e. LT or SR, I would chose to work out the calculations, I would chose LT. Why? because it has no paradoxes and the idea that there is a medium it is helpful to some our present problems. In 1951 Dirac and later in 1965 strongly suggested that the situation in physics in 1905 was quite different than the situation 50 or 60 years later and that the notion of aether could be reintroduced. The Cassimir effect, the Lamb shift and many other experiments strongly suggest that the vacuum has an internal structure.
Certainly, physics has changed since the sixties and we have to update some conceptions. During this investigation I come across with Christov's work in which I found some plausible results. First, based on the assumption that space is a fluid and applying the theory of fluid and wave mechanics, he succeeded in deriving Maxwell equations and Lorentz force formula as integral parts of a major formulation (Eq. 17). This is clearly of great significance. Keep in mind that in the present view Maxwell equations (the classical Lagrangian of the electromagnetic field was inferred from Maxwell equations but is not derived from a higher principle) and the Lorentz force are empirical constructs not derived from any physical principle. Moreover his formulation reproduces the relativistic effects, i.e., length contraction, time dilation, etc., and pave the way for the introduction of solitons as natural ingredients. And above all his proposal fulfills with the principle that the laws of physics should be the same in any system of reference. As he explains in section 6, there is one caveat. Experiments do not measure absolute magnitudes (he called them material variables) but only relative ones (this is why SR has been so successful) and for such reason he reformulates his model in Euler variables. Therefore, since his model explains physical phenomena --just as relativity does--, unifies electromagnetism (he went further and unified gravity and QM), fulfills the principle of covariance and is free from paradoxes I do not see any objection. Your comment "...he intends to violate Lorentz invariance by electromagnetism in simple few body systems..." causes me confusion, why do you argue that his experiment violates LI?
Likewise, I did not understand this part very well: PDE's are Lorentz invariant and so if one gets violation in their consequences, it means he has made a mistake somewhere, like forgetting that boosts add magnetic field to charges. I would appreciate if you could elaborate a little bit further. Do you mean that all equations in physics are PDE and that they should all be Lorentz invariant? How is he violating the fact that boost add magnetic field to charges? I do not clearly see the connection, since he is complying with LI.
With respect to your last paragraph, if you are interested in the detection of the medium I would suggest that you take a look at my reference 17, Eq. 3.14 shows that in principle an inertial observer can determine its absolute speed. I do not know what other concepts/experiments you mean.
Cheers
Israel
