Nothing puzzles me more than time and space; and yet nothing troubles me less, as I never think about them.
Charles Lamb

Have you ever been in these attractions at the amusement park or pier where you are allowed to be in free fall? That doesn't last for long, but for a moment, a from a fraction of a second to a couple of them depending on the attraction, you can feel this wonderful feeling: there is no gravity.

We don't know if Einstein ever had the opportunity to experience this feeling, of which you can sometimes get a hint in a lift or on a speed bump, but he relates this feeling to the happiest thought of his life: "Because for an observer in free-fall from the roof of a house there is during the fall—at least in his immediate vicinity—no gravitational field."

So keep this feeling well in mind, and imagine yourself now in empty space, floating around (no gravity, like at this one point when the pirate's boat reverse direction). Imagine that it is also dark but that you have a flashlight, which gives a pulse of light whenever you push it. So here you are, at rest, floating around, emitting pulses of light, at regular intervals.

Now you realize there is another point, from where flashes of light are emitted. There is somebody else, out there, flashing light.

Falling house: no preferred reference frame.

That there seems to be no preferred reference frame is actually a principle as old as 'modern' physics itself, modern in the sense of its emergence from the combined use of the experimental method (Galileo) and mathematical treatment (Newton).

Newton's equations are, indeed, Galilean invariant.

But another set of equation, Maxwell's equations, turn out not to be Galilean invariant. In fact we do not even have to go into the details of Maxwell equations themselves, but consider instead one of their consequences (that led to the postulate that light was electromagnetic): the wave equation.


Woldemar Voigt

if we apply a Galilean transformation to these coordinates, the wave equation is not satisfied with respect to the transformed coordinates.

Voigt considered the question of whether there is any linear transformation that leaves the wave equation unchanged.


There's no coordinate system, 


Galileo:

However, one might call it a conspiracy theory.

Maxwell's equations

time in meters

distance in seconds

==

reference frames



invariance of spacetime intervals (Lorentz intervals)

Lorentz-Minkowski geometry


events



if events happen where we are, time separation reads directly as interval: proper time.



charting spacetime (page 37)



while special? (linear or inertial frames)

A short bibliography of relativistic texts

  1. David Hogg's Special relativity (see online version here). To the point, short (53 pages) exposition.