class28 - 1 Special Relativity Recall the Galilean...

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1 Special Relativity Recall the Galilean transformation of Newtonian physics: this relates the the coordinates x, y, z, t in one inertial reference frame S to the coordinates x , y , z , t in a di ff erent inertial reference frame S , moving with velocity with respect to the first u (along the x axis, by convention). With synchronized clocks (at t = 0), running at the same rate: x = x - ut, y = y, z = z, t = t (1) We proved that this implied F = m a = m a = F (2) Newton’s laws of physics are valid in all inertial reference frames. In the 19th century, physicists were not able to grant the same freedom to electromagnetic theory, which did not seem to obey the same principle of Newtonian relativity. Classical EM theory, described by Maxwell’s equations, have the consequence that the speed of light (EM waves) is independent of the motion of the source. Consider the Galilean transformation for the speed of light in two frames moving with constant velocity to each other. Suppose that there is a light source emitting light waves at the origin 0 of S . If the position of a point P of some given wave surface on the x-axis is x , then in the frame S the velocity of the point P is ˙ x = c . The corresponding velocity of P in the frame S is ˙ x = c - u . Thus, in the moving frame, the speed of light is no longer
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