Lorentz's Force

It is not necessary to ponder into subatomic realms to notice the inconsistency of Maxwell's equations. It may be shown by an elementary experiment. The experiment needs just a bar magnet, a coil and a galvanometer.

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This is obviously inconsistent being that the two last cases are equivalent and they should be described by same equation. According to Hertz's equations, however, both cases are described by the same equation:

×E = -dB/dt,

and in both cases, it is the same electric field E that acts on free electrons of the coil.

 
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I was very surprised when I found (thanks to Andrija Radovic's page: THEORY OF RELATIVITY - ULTIMATE DISPROOF) almost the same remarks about Maxwell's equations in the introductory statements of the famous Einstein's paper Zur elektrodinamik bewegter Körper:

Scientists were aware of the flaws of Maxwell's equations at the beginning of the 20th century, however few of them dared to amend them. It was Hertz who proposed a variant of Maxwell's equations (H.R. Hertz, Electric Waves, translated by D.E. Jones (Teubner, Leipzig, 1892; Dover, NY, 1962).), that differed slightly from Maxwell's original form (partial derivatives were substituted by total ones), and that did not "lead to asymmetries" as mentioned by Einstein and are invariant to Galilean transformations.

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Moving truck

Let's now append a truck to the previous experiment. Let's take into consideration that part of the case when bar magnet SN moves toward the coil, say by the velocity v₁ = 3m/s. For the blue observer O₁ on the illustration, the galvanometer needle turns due to induced electric field that pushes electrons in the coil. Let's now take that this observer with all his gadgets is inside a truck that moves by the opposite velocity v₂ = -v₁ = -3m/s. For another observer O₂ outside the truck, the bar magnet is standing still, while the coil is moving toward the bar. For that observer, there is no electric field and the galvanometer needle turns due to Lorentz force. In other words, the same physical event is described by two different equations, i.e. by two different physical laws. Namely, in the first case by the low of electromagnetic induction, and in the second case by the low of Lorentz force. Thus, it is violated one of the fundamental postulate of physics:
The laws of physics are the same in all inertial frames!
Moreover, this experiment shows that Maxwellian electric field is not a physical quantity, but a mathematical construction, being that it exists for one observer and doesn't exist for another. In Hertzian electrodynamics, both observers use the same law to describe the phenomenon, and measure the same electric field.

Moving truck and relativity

Let's now analyze the above experiment in the light of the Special relativity. We'll start with green observer O₂, being that there is no electric field in the coil for him (E₂ = 0). let's now get the electric field in the coil inside the reference frame of the blue observer O₁. Applying relativity transformations (Stephenson G., Kilmister C.W., Special Relativity for Physicists, Dover Publications, Inc., Mineola, N.Y., 1987., expression 6.11 on pg. 14) on E₂, we get:

E₁ = E₂^* + βv₂×B/c,

where:

E₂^* = βE₂ −(β−1)v₂(v₂·E₂)/v₂²,
and
β = (1 − (v₂/c)²)^−1/2.

Being that:

(v₂/c)² = 10⁻¹⁶,
and
E₂ = 0,

we get, finally:

E₁ = v₂×B/c.

From the just obtained results we can deduce many conclusions.

1. The two fields E₁ and E₂ have two different values. However, nobody matters it for they are now covariant.
2. If the bar magnet moved by nonuniform velocity, it would be inappropriate to use special relativity for it is valid just for uniform transformations.
3. If we take a closer look at the expressions for relativistic transformation of electric and magnetic field:
   E₁ = E₂^* + βv₂×B/c,
   B₁ = B₂^* − βv₂×E/c,
   it may be seen that they comprise just those parts missing from Maxwell's equations that are included in Hertzian equations:
   
   V

   _
   ×E = - 
   dB

   ___

   dt
    = - 
   ∂B

   ___

   ∂t
    + 
   V

   _
   ×(v×B),

   .

   V

   _
   ×B =   μ_oj_r + 
   dE

   ____

   c²dt
    = μ_oj + 
   ∂E

   ____

   c²∂t
    - 
   V

   _
   ×(v×
   E

   __

   c²
   ).
4. It seems to me that this coincidence is the main reason why the relativity gives satisfactory results, even in quantum mechanics where the particles movings are far from uniform.

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A weird experiment that has changed the face of Physics

One may asks now: "Why all this fuss? Why did not Maxwell take total derivatives instead of partial ones?"

As I could discern, the answer is bizarre.

At the very beginning of his investigations, Michael Faraday stumbled upon a totally weird experiment, known as "homopolar generator". I will only mention that this experiment has been making headache to physicists since (if someone is interested on the subject, just google little bit with this expression, and you will reveal a heap of relevant materials). I am suggested (Andrija Radovic) that it was this experiment that led Maxwell to take partial derivatives instead of total ones.

It is unbelievable that such an experiment could have such tremendous impact on the science. The fact is that Hertzian form of Maxwell's equations does not need Einstein's relativity. On the other hand, Joseph A. Rybczyk (yet another heretic) proved that Lorentz transformations and other relativistic equations could be derived just from the independency of light speed from the velocity of its source.

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Some links to homopolar generators:
Wikipedia
THE ROTATION OF MAGNETIC FIELD
Andrija Radovic
THE WEIRD BUBBLE

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