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quasar987
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Summary:
 thought experiment proving momentum is not conserved
Main Question or Discussion Point
On p.170 of French's book on special relativity there is this thougth experiment attributed to Lewis and Tolman (1909). It is about two individuals throwing identical balls of mass M at each other with identical speed. The balls bounce against each other and are caught again.
See attached picture. More precisely, individual B is on the enbankment and individual A is on the railway carriage. The relative motion is along the x axis and the balls are thrown along the y axis. The Lorentz transformations imply that, according to A's frame, A's ball is thrown at velocity [itex]u=(0,u_y)[/itex] but B's ball is thrown at velocity [itex](v,u_y/\gamma)[/itex]. The point of this thought experiment is that if the balls bounce back with the same (absolute) velocity that they were thrown, then Newtonian momentum is not conserved along the y axis:
$$Mu_y  Mu_y/\gamma \neq Mu_y + Mu_y/\gamma$$
My question is simply this: why do we assume without a doubt that the balls bounce back with the same speed that they were thrown? If B's ball bounces back with speed [itex](v,u_y)[/itex] and A's ball bounces back with velocity [itex](0,u_y/\gamma)[/itex] then Newtonian momentum is conserved.
See attached picture. More precisely, individual B is on the enbankment and individual A is on the railway carriage. The relative motion is along the x axis and the balls are thrown along the y axis. The Lorentz transformations imply that, according to A's frame, A's ball is thrown at velocity [itex]u=(0,u_y)[/itex] but B's ball is thrown at velocity [itex](v,u_y/\gamma)[/itex]. The point of this thought experiment is that if the balls bounce back with the same (absolute) velocity that they were thrown, then Newtonian momentum is not conserved along the y axis:
$$Mu_y  Mu_y/\gamma \neq Mu_y + Mu_y/\gamma$$
My question is simply this: why do we assume without a doubt that the balls bounce back with the same speed that they were thrown? If B's ball bounces back with speed [itex](v,u_y)[/itex] and A's ball bounces back with velocity [itex](0,u_y/\gamma)[/itex] then Newtonian momentum is conserved.
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