SpecialRelativity

Special Relativity (A. P. French)

  • Very good introduction. Lots of historical context.
  • The most important result of general character to which the special theory has led is concerned with the conception of mass. Before the advent of relativity, physics recognized two conservation laws of fundamental importance, the law of the conservation of energy and the low of the conservation of mass; these two fundamental laws appeared to be quite independent of each other. By means of the theory of relativity they have been united into one law.
  • The story of 19th C physics was, in large part, the story of the triumph of the wave theory of light.
  • A wave speed of more than a hundred thousand miles per secondwas many orders of magnitude greater than the speed of any other mechanical disturbance, and demanded a medium which, although so tenuous that the planets could travel through it year after year with no detectable loss of speed, must nevertheless develop very strong restoring forces when displaced from equilibrium – since the speed of propagation of a wave depends on this resorative property of the medium.
  • The view that most physicists took was that the ether existed and motion through it was real, but compensating effects were at work.
  • x and t should be linear function of x' and t'. Linearity is a fundamental property of the transformation equations. If they did not have this form, a motion recorded as motion at constant velocity along a straight line in one frame (S) would not be rectilinear motion in S'. This would therefore conflict with Galileos law of inertia and with our basic dynamical condition that all inertial frames are equivalent.
  • A seeming paradox: A burst of light begins speading out (in vacuum) from the oringi of frame S at t=0. At any later time t the light will have reached all the points on a sphere of radius R, centered on the origin of S such that r=ct. Then if this same phenomenon is observed with respect to a frams S' moving with respect to S with any velocity v, the description of the expanding burst of light is again a shpere, in this case centered on the origin of S' – even though, by definition the origins of S and S; coinicide only at the instant t=t'=0. This result is bound up with teh relativity of simultaneity. Points wihch as measured in S are reached at ther same time t, are reached at different times as measured in S' in such a fashions that the light is properly described as lying on a spherical shell expanding at c in both frames.
  • In Minkowski diagrams, the time axis for any frame is parallel to the tangent drawn at the point where the calibration hyperbola cuts the correponding x-axis.
  • The question does the Lorentz contraction really take place? has no single, enequivocal answer from a relativitstic point of view. The whole emphasis is on defining what actual observations we must make if we want to measure the length of some object that may be in motion realtive to us. And the prescription is simply that we measure the positions of its end at the same instant as judged by us. What else could we possibly do? Thus the contraction when we observe it is not a property of matter but something inherent in the measuring process.
  • We are not prevented from having purely geometric velocities greater than c. The supercelocity is not associated with the motion of any material object of with the transport of energy or informatino from one point to anther over (eg the moons surface).
  • Some of the most important observations in atomic physics involve measurements on the radiatino from moving atoms or nuclei. The apparent frequency (or quantum energy) of emitted radiation depends on the relative motion of the source and observer.
  • The main lesson to be learned from the above calculations (related to relativistic acceleration is a quantity of limited and questionable value in special relativity. Not only is it not an invariant, but the expressions for it are in general cumbersome, and moreover its different components transform in different ways. Certainly the proud position that it holds in Newtonian dynamics has no counterpart here.

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