The contraction p'u¡, where p' is the four-momentum and u' is the four-velocity, is:
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why is the contraction p^i u_i conserved under a change of reference frame?
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- Show that the defi nition of linear momentum, p' = mv' , has the same form p mv under a Galilean transformationAs seen by one observer, two firecrackers are set off at the same place but separated by 4 seconds in time. As observed by a second observer, moving with respect to the first, the two firecrackers detonate at places separated by 3 light-seconds in space. As observed by this second observer, how much time is there between the two detonations?In the theory of relativity, the mass M of a particle with velocity v is mo M(v) = V1- v²/c²
- Choose the option that makes the following statement cor- rect. Two events at a single location define a time interval. The proper time interval At, is measured by an observer [(a) at rest; (b) moving] relative to the location where the two events Occur.A light source G is moving, with respect to an observer O, at an angle θ=�=154∘∘ between the direction of relative motion and the line of sight from O to G. The redshift of the light emitted by G and measured by O is z=0�=0. Find the speed of G with respect to O in units of c�, the speed of light. Enter your answer to 3 decimal places.There are two twins, A and B. While twin A stays home, twin B travels with a speed (12/13)c to a far planet. Once twin B arrives at the planet, they turn around and travel back home at the same speed. When twin B arrives home, they find that they are 32 years younger than twin A. Quantitatively prove that twin A cannot be younger than than twin B when they get back together.
- An object is moving with ordinary speed 0.5c in S reference frame along a direction making an angle (tan 9 = 2) with respect to the positive x - axis. Find the zeroth component of the proper velocity.Einstein concluded that the speed of light is the same in all inertial frames. Prove that the analysis of the Michelson-Morley experiment (see attached image) is in error.