Dear Tuomo,
You have stated that Galileo's relativity was incorporated into Einstein theory after revising the concepts of time and space. I have to disagree with you. Einstein NEGATED Galileo's principle and incorporated a fake imitation of it. What Einstein incorporated was the very antithesis of Galileo's principle. This is why Einstein could not fulfill his own dream of extending thermodynamics into whole of physics:
See: http://fqxi.org/community/forum/topic/1549
You wrote: "In the 1500s, Galileo Galilei noticed that any observer in uniform motion may regard his state as the state of rest. The Galilean relativity was inherited in Newton's laws of motion and further, after a redefinition of the concepts of time and distance, into Einsteinian relativity".
Did Galileo just postulate this principle or did he painstakingly explain it? We must note that he did the latter.
In his book "Dialogue Between The Two Chief World Systems" in the chapter on Second Day (157 pages in all) he takes example after example and showed that the reason why the effects of motion of a place (i.e. observer's location) in uniform motion cannot seen by the observer is because the observer and the observed objects (in motion relative to the observer) shared a COMMON MOTION with that place.
Galileo started off his discussion on the principle of relativity in the following way: "Then let the beginning of our reflections be the consideration that whatever motions comes to be attributed to the earth must necessarily remain IMPERCEPTIBLE to us and as if non-existent, so long as we look only at terrestrial objects; for as inhabitants of the earth, WE CONSEQUENTLY PARTICIPATE IN THE SAME MOTION" (p. 114).
"The cause of all these correspondences of effects is the fact that the ship's motion is common to all the things contained in it" (p. 187).
In Galileo's relativity, (as opposed Poincare's version), it the relative motion between the objects, that remain unaffected by motion of the place (Local reference frame), and not the discrete motion per se of a given object.
Newton brings this out clearly in his statement of the principle of relativity: Newton wrote the principle of relativity (in Principia, Corollary V) as follows: "The motions of bodies included in a GIVEN SPACE are the same AMONG THEMSELVES, whether that space is at rest or moves uniformly forwards in a right line without any circular motion" (p. 20).
"Motion of bodies ....among themselves" means motions RELATIVE to one another, and not the motion of each body relative to the given space. (According the Galileo's principle Relative motions between bodies remain invariant, but not discrete motions of individual bodies).
Poincare started to twist Galileo's tail from 1900 to insist that a) there is no common motion with the local frame b) Motion of each body remained unaffected by the motion of the local frame. (This is the basis of equivalence of all reference frames). In 1904 St. Louis Speech he announced his Principle of Relativity. (According to Poincare's principle, discrete motion of each body remains invariant. "Motion of A BODY is independent of the motion of the system")
Einstein dropped Galileo-Newton principle of relativity and grabbed hold of Poincare's principle. The rest is history of confusion for 100 years.
BTW, Tuomo, you may remember me from the London PIRT(2008) Conference.
Best regards,
Viraj
