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Unformatted text preview: arrow of time. Violations of the second law lead to perpetual motion machines, and other absurd results. In fact, the second law enjoys a very strong status, stronger than that of any physical theory. If we allow for superluminal propagation, the second law is violated. Relativistic dynamics: momentum In Newtonian mechanics momentum is defines as p := m v . If momentum is conserved in frame S , it is also conserved in S , when the transformation between S and S is galilean. That is, if transformations are galilean, then if p i = p f , then also p i = p f , and all is well. The problem is that we have already concluded that galilean transformations violate the Principle of Relativity. To satisfy the Principle of Relativity, the transformation between two frames need to be the Lorentz transformations, not the Galileo transformations. The problem is, that momentum, as defined above, does not satisfy a conservation law under Lorentz transformations as an exact law, only as an approximate law at small velocities. Consider two frames, S and S , in relative motion with speed v in the x direction. An observer in S throws a ball of mass m (ball A ) straight up relative to her with speed u , and an observer in S throws her identical ball of mass m (ball B ) straight down relative to her with speed- u , and the two balls collide elastically. Let us now analyze the question of whether momentum is conserved in frames S and S . Consider first frame S . If galilean relativity is correct, an observer in S observes ball A to move at speed u before the collision in the y direction and speed 0 in the x direction, and ball B to move in speed- u in the y direction and speed v in the x direction. Because of the symmetry of the two balls and the elasticity of the collision, the y components of the velocities are reversed, and nothing happens to the x components. Therefore, the total momentum both before and after the collision is...
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- Spring '09