What`s the difference between Lorentz- and Galileian-transformation?
The Galileian transform is merely the idea, prior to SR that velocities are added linerally. In other words for the train at v, a beam of light sent across the train, proceeds at c+v from the caboose and at c-v if sent from the engine.
one possible difference is that in galileo relativity light propagates with infinite velocity whereas in Einstein's relativity it propagates with finite invariant velocity.
The Galilean transformation tells you how the coordinates of an event (t,x,y,z) transform when you go from one inertial frame to another in the non-relativistic case. Or rather, in the considered space-time before relativity.
Taking into account the fact that the speed of light is the same in all inertial frames the transformation laws are changed and these are called the Lorentz transformations.
Prior to relativity the Galilean transformation was certainly well known, but barely used. Nobody bothered to give it a name. It's actually pretty a trivial transformation and doesn't deserve such a fine name.
I think this should read "in galilean relativity the fastest signal propagates with infinite velocity whereas in Einstein's relativity it propagates with finite invariant velocity". If I recall correctly, the speed of light was known to be finite around the time of Galileo or soon thereafter.
if i recall correctly Galileo measured the two way speed of light measuring the involved time interval using the beats of his heart obtaining for it a zero value and as a consequence light was cconmsidered to propagate with infinite speed. i do not think that the precision of time intervals measurement took place soon after Galileo.
http://en.wikipedia.org/wiki/Speed_of_light agrees with your characterization of Galileo's experiment. However, Romer (1676) [compare with Galileo (1564-1642)] was apparently the first to observe the finiteness of the speed of light.
In any case, I think it's safe to say that the speed of light (whether finite or infinite) played any key role in the first formulations of Galilean relativity or the Galilean transformations. Only in historical retrospect is there a relationship... in the sense that the speed of light is the maximum signal speed, and that the Galilean transformations are a limiting case of the Lorentz Transformations via this maximum signal speed.
galileo and lorentz
In a recent paper
Ralph Bayerlein, Two myths about special relativity," Am.J.Phys. 74(2) 2006 looks for an answer to the question "Does the Lorentz transformation reduce to the Galilean transformation when the ratio v/c is small"? The answer is no as the author shoes.
...meaning that no matter how small v is (with a finite c), relativistic effects can be detected, e.g., with a precise enough clock.
But when v/c is zero, a condition that Baierlein explicitly avoids, (realizable, e.g., by allowing c->infinity while keeping v fixed), the Galilean transformation is a limit of the Lorentz transformation.
Thank you for all the answers!
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