"Do you play chess by any chance. If you do, then you know that even a couple of pawns in the right positions can checkmate a king. Modern physics seems to be mainly based on Einstein's theories. So, if the Special Relativity Theory falls, the General Relativity Theory will come down too.
All in all, it will be a disaster of biblical proportions for main stream science. "
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Reasoning too fast, without enough information and critical sense, and on the basis of wobbly analogies, cannot lead you anywhere.
I explained you quite honestly why your observation is (probably) true and your conclusion is (certainly) wrong.
If you are insensible to any logic, then let's wait until you try a FTL communication with mars!
Otherwise, I can only repeat myself, as I have not found the time yet to simulate your experience.
I have just bought the Mathematica Home version and I still need to evaluate how much time it would take me to make a convincing simulation of what you did. If time permits, I will simulate a small oscillating charge in vacuum above a dielectric ground. From what I have read, the conductivity can be neglected in your system and only the permittivity of the ground should play a role. I expect the (oscillating) charge build up to be an interesting feature (2). Before I go for this calculation, I will anyway refresh my skills on the simple dipolar antenna and observe phase and group velocity in the near field.
But I would like to stress one point before I even consider this question instead of other interesting topics. All these calculations I am considering are not more than a colorful illustration. The principles themselves do not depend on the fact that sound or radio waves or deep water waves or shallow water waves or earthquakes or anything are considered.
What is really important is to understand how observations like yours can be obtained when individual waves propagate STL and even much slower than light. Group and phase velocities faster than light have been observed even in acoustics with a less than 1000$ experiment!
I assume you will accept easily that a shadow on a very distant screen can move faster than light and that this does not contradict the principle of relativity: no communication from a part of the screen to the other is involved. This looks like a very stupid example, yet all parts of this system are moving STL and the shadow can move FTL. This illustrates that the words "FTL" are a qualifier and have no meaning without another word before. This word is for example a "signal". And the word "signal" itself needs more explanation. This word implies that a change (the signal) in the emitter will induce a change in the receiver.
In your experiment you have not show a FTL signal transmission.
(considering erdman.pdf only as I could not understand erdman2.pdf clearly enough)
You have only shown that the oscillations were in phase at different places.
No FTL communication to Mars on this basis!!!
It is not difficult to understand why this can happen even though the "individual waves" propagate STL (or ETL). You can find many applets on the web to illustrate that point. The question of group (wavepacket) velocity is a bit more complicated to discuss for the obvious reason that wave packets are usually not only displaced but also distorted which make the velocity undefined except in extreme situations (large packet in a weakly dispersive media).
I found the applet in ref (1) very illustrative: observe how a FTL signal arises from the sum of STL signals.
Therefore, Mr Erdman, your fears about modern physics are irrational and unfounded.
You have only observed a FTL artifact very similar to a shadow "propagating" on a distant screen.
To really prove a FTL signal, you will need a clear-cut experiment.
Pushing a button in one place (at a random time) should trigger a reaction faster than light at a distant place.
Till today nobody has ever been able to do that.
(quantum entanglement experiments do show quite amazing FTL effects, but no FTL signal either)
If you think that you can emit FTL signals (to Mars), you need a much better proof than what you have explained so far.
My guess: you will never ever succeed.
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(1)
http://gregegan.customer.netspace.net.au/APPLETS/20/20.html
(2) I feel that a delicate point is that the permittivity could not be simply assumed constant as this could imply FTL response of the dielectric. In short, the so-called "Kramer-Kronig relations" should be taken into account to take causality into account. This implies also that the medium should also be absorbent for some frequency range. Performing a constant-permittivity calculation can then be valid only if it can be checked that the calculation does not imply FTL response within the dielectric. If this cannot be proven, then the big calculation is just meaningless for our discussion. Today, I do not see clearly how to this verification can be done.