One more time: the greatest signal speed by which information can be transmitted is very close to c, if not c. For this reason, it is assumed that the greatest signal speed is the speed of light in vacuum. If, for some reason someone finds out a signal that goes faster than light in vacuum, the greatest signal speed will become that. But according to the current understanding, if this was to happen, the difference would be very small so it is quite safe to say the maximal achievable speed is c.
In a wave packet what represents an optical pulse (pulse is actually open to interpretation), there are gazillions of different propagating monochromatic waves included. Because each of these waves have always existed and will always exist (by definition of the monochromaticity), the waves add-up destructively in most space, but because we are talking about a pulse, there is also a single location in spacetime where the add-up is constructive, and a peak is formed exactly there.
As you move the observation aperture along the pulse peak, you will see that there are fluctuations propagating in the pulse, and the propagation speed of these fluctuations might exceed c. However, you are only observing the sum of the monochromatic waves at each moment of time. This is perfectly reasonable explanation for me, and according to my understanding it is also the officially correct one. But unfortunately I cannot write it any way better.
But Fourier Maths is great and the above is based on my interpretation on that, so don't skip your lectures there as you might never know where you meet it again (hint: in surprisingly many places)! And quite surprisingly, its justification is that it simply works (for a physicist at least). Then model the same thing with the particle model... and talk about X-rays with the index of refraction below you-know-what. Some wise guy once said that if lambda gets below UV, congratulations, you (are screwed and) have chosen exactly the wrong career
The quantum mechanical teleportation stuff is something beyond me and I cannot comment on those experiments where the two particles supposedly always turn to face each other or something.
By the way Doc, feel free to abrupt this if I'm saying something totally incorrect/incoherent so that I apply self-censoring on it before too many people see it. I usually think more of MTFs and spot sizes than wavepackets.
I digged up some old material regarding relativity, the whole problem in the beginning of 1900's was the aether which got some unphysical properties, as it must have been everywhere and extremely heavy and on the same time have no mass at all. Einstein found a problem by examining Maxwell's equations (I don't bother to repeat it here) and concluded that the speed of light must be c in free space in order to have any sense in anywhere. At that time he was unaware of the experiments conducted by Michelson and Morley, however nowadays the above mentioned experiment is mentioned first as it is an indisputable measurement result and makes sense as such.
So special relativity rests on two assumptions:
1. Speed of light in free space is a constant c.
2. All coordinate systems are equal.
And then all we need is a magnificant idea of mixing time and space together! Einstein himself wrote that the idea dawned to him when he was discussing about the difficulties in Electromagnetic theory with his friend Michele Besso. He only mentioned that that day was specially beautiful spring day for him, he never mentioned anything else about the origins of the idea.
The normal Galilean transformation equations (that you should use in normal life) between coordinate systems along the movement of one axis are:
x' = x-vt
t' = t
Now, mixing time and space together gives:
x' = A_1*x+B_1*t
t' = A_2*t+B_2*x
Here A1, B1, A2 and B2 are the unknown constants to be solved.
Now working with the two basic assumptions of special relativity using two coordinate systems moving along each other at speed v and taking notice that the speed of light should be c when viewed from another coordinate system, and noticing the invariance of light cone in any coordinate system, the transformation equations become:
x ' = (x - vt) / sqrt(1 - v^2/c^2)
t' = (t - vx/c^2) / sqrt( 1 - v^2/c^2)
The details can be found in-depth Physics book and so I skip them
These are called Lorentz transformation equations, and by using these the time dilatation and the length contraction can be derived in another way.
If anyone is interested, here is a nice site for visualisation of relativistic Optics:
http://www.anu.edu.au/physics/Searle/Please explain yourself the disformations in the train when it is passing by you.
Mika
