Problem
Galileo vs Einstein. Galileo’s principle of relativity states that the laws of mechanics are the same in all inertial frames. Einstein’s extends this statement. What does the extension consist of?
Solution
Galileo’s principle. No mechanical experiment performed inside a laboratory in uniform rectilinear motion can determine whether the laboratory is at rest or moving: the laws of mechanics have the same form in all inertial frames. This is the idea of Galileo’s ship (below deck, everything happens as if the ship were at rest).
The first extension: all the laws of physics. Einstein extends the principle from “the laws of mechanics” to all the laws of physics, including electromagnetism. No experiment of any kind (mechanical, optical, electromagnetic) can detect absolute inertial motion. This does away with the idea of an “ether” defining a privileged frame.
The second extension: the second postulate. Since Maxwell’s equations predict that light travels at speed , and these equations must hold in every inertial frame, it follows that
regardless of the motion of the source. This second postulate is incompatible with Galilean velocity composition.
The consequence. To reconcile the two postulates, one must abandon Galilean transformations (with absolute time) and adopt the Lorentz transformations, from which time dilation, length contraction and the relativity of simultaneity arise.
Links
Topics: Relatività ristretta Concepts: Trasformazioni di Lorentz Skills: Cambio di sistema di riferimento