geordief said:
...Or even based on logic?
Actually, even thinking in these terms is rather archaic. Start with the idea that you have a standard euclidean space, x,y,z. Now draw 2 (or more) lines in different directions and find the distances using the pythagorean theorem. How well does that work if you measure the x direction in feet, the y direction in meters and the z direction in fathoms? Not very well, so you have to have a conversion factor. Furthermore, to use the pythagorean theorm you have to define your space as a metric space, so that you know what a right angle is. So, just to do what seems like common sense, you need a lot more than common sense to understand what you are measuring. Euclidean geometry is a space equipped with a metric: ##ds^2 = dx^2 + dy^2 +dz^2##. You could extend that to as many dimensions as you wish. In a Gailean universe, time also plays a role but somewhat different. I'll get to that later.
Also, a rotation in the x-y plane for example is given by:
$$dx' = dx \cos\theta - dy \sin\theta$$
$$dy' = dx \sin\theta + dy \cos\theta$$
The angle of rotation is just ##\theta## and ##\theta## can be any value between 0 and ##2\pi##.
Relativity is just the same, except the "pythagorean theorm" (i.e., the metric) contains a minus sign:
$$ds^2 = dt^2 - (dx^2 + dy^2 =dz^2)$$
There is speed of light constant 'c' because like the previous example, we want to measure all quantities using the same units, so here, time is measured in meters. The constant 'c' just converts seconds to meters in the same way that the constant 2.54 converts centimeters to inches. What is really different the minus sign in the "pythagorean theorm" (i.e. metric). If we now rotate in the x-t plane (similarly to the example above for the x-y plane, because of the minus sign we get:
$$dx = dx\cosh\phi - dt\sinh\phi$$
$$dt' = dt\cosh\phi - dx\sinh\phi$$
Due to the minus sign, the trransformation uses hyperbolic functions, not circular functions. However, this means we really aren't talking about a "finite velocity," because the hyperbolic angle ##\phi## corresponding to a hyperbolic rotation in the x-t plane ranges from ##-\infty\ to\ \infty##. The hyperbolic tangent of ##\phi##, however ranges from ##-1\ to\ 1## and if we are using minutes or seconds instead, then we have the more familiar form:
$$(v/c) = tanh\phi$$
So, to say there is an "ultimate speed" and wonder why, is sort of like asking why there is a "maximum rotation" of ##2\pi## to make a complete circle. The answer to both is that it's just the choice of geometry you use to describe physics. Either choice is valid philosophically and logically, but physics discriminates between them by which one agrees with experiments and experiments favor einstein's version of relativity.
I understand that it is expected that there might be a Universal Speed Limit and that this seems with extremely high probability to coincide with the speed of em transmission in a vacuum.
Btw does the existence of this universal speed limit necessitate the invariance of the speed of light (and massless objects)?
All massless objects must travel at 'c'. This is not necessarily true for light. The "phrase" speed of light to mean the velocity 'c' is more of an historical artifact due to what einstein was trying to explain and the general lack of thinking in geometric terms. Einstein was trying to reconcile maxwell's equations with classical mechanics and so he made use of the fact that in maxwell's equations, the speed of light is a constant, independent of frame. Hence the idea that the speed of light has something to do with relativity seems to be pervasive, even though it need not be.
Around 1914, Proca demonstrated a perfectly relativistic theory of electromagnetim in which light propagated just like any other massive particle, the consequence being that light was no longer massless. But, it was perfectly consistent with relativity. The upshot of this is that relativity is the geometry of thr universe and whether or not light is massless and propagets at 'c' or if it has a mass and propagates like anything else with mass, is more properly reserved for theories of electromagnetism. If the photon has a rest mass, it is known from experiment to be less than around ##10^{-17} eV##
Finally, the choices that have potential to describe the universe have been Galilean relativity and special relativity (neglecting gravity). From those two possibilities, you can deduce the phyical laws of mechanics. A priori, thee is no reason to choose one over the other, so the reason for choosing the geometry of the universe to be special (or general relativity) over Galilean relativity is a matter that only experiment can distinguish and so it is experiment that tells us that of the two choices we have, (einstein) relativity is the correct choice.
It's also possible to write galilean relativity using time as a coordinate, but it becomes somewhat less transparent on how you end up with classical mechanics, so, I will skip over that.
