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1、Motivation for Special Relativity1Coincidences in classical physics led Einstein to propose SR.Classical mechanics: motion of things (in space, as function of time)Space: 3dimensional and Euclidean => Cartesian coords can be established and distance between 2 point
2、s (x, y, z) and 1112221/2(x, y, z) is d = [ (x x) + (y y) + (z z) ]222121212Absolute space defines a standard of rest. Time exists independently of space and is 1dimensional. Space and time are homogeneous and space is isotropic.An event is a particular point in s
3、pace at a particular time: (x, y, z, t)Motion of a particle consists of a series of events. 2Newton's Laws of Motion:1. Free particles (those on which no forces act) move with constant velocity (i.e., with constant speed along a straight line). 2. f = m a3. f =
4、 f1221stNewton's 1 Law applies in the ref frame of absolute space and also in any frame that moves at constant velocity wrt abolute space; such frames are called inertial reference frames. Technical note: For each ref frame, there are an infinite number of ref coord
5、systems. All are equally valid because ofhomogeneity and isotropy.'32 inertial ref frames S and S in “standard configuration”:S' moves with speed v alongxaxis rel to S.t = t' = 0 when origins coincideSuppose an event has coords (x, y, z, t) rel to S and (x', y', z', t
6、') rel to S'Standard Galilean transformation:x' = x – vt y' = y z' = z t' = t Nonstandard config: x' = x – vt t' = t4Suppose a particle moves with velocity u rel to S and u' rel to S' :u' = u –v Acceleration:a' = du'/dt' =
7、 d(u – v)/dt = du/dt = a(invariance of accel under transformations between IFs)Mass and force are assumed to be invariant => invariance of Newton's 3 Laws (“Galilean relativity”)=> no mechanical experiment can indicate which inertial frame is at rest wrt absolut
8、e space!Most classical physicists: This is an interesting coincidence. Einstein: This suggests that absolute space
