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Answer - Open Yale Courses

Physics200 Problem Set 7 SolutionQuickoverview:Althoughrelativity can be a little bewildering, this problem set uses just a few ideasover and over again, namely1. Coordinates (x, t) in one frame are related to coordinates (x , t ) in anotherframe by the Lorentz transformation Similarly, space and time intervals ( x, t) in one frame are related to inter-vals ( x , t ) in another frame by the same Lorentz transformation formu-las. Note that time dilation and length contraction are just special cases: itis time-dilation if x= 0 and length contraction if t= The spacetime interval ( s)2= (c t)2 ( x)2between two events is thesame in every Energy and momentum are always conserved, and we can make efficient useof this fact by writing them together in an energy-momentum vectorP=(E/c,p) with the propertyP2=m2c2. In particular, if the mass is zero thenP2= and sun are light-minutes apart. Ignore their relative motion for this problem andassume they live in a single inertial frame, the Earth-Sun frame.

3. The spacetime interval (¢s)2 = (c¢t)2 ¡ (¢x)2 between two events is the same in every frame. 4. Energy and momentum are always conserved, and we can make e–cient use of this fact by writing them together in an energy-momentum vector P = (E=c;p) with the property P2 = m2c2. In particular, if the mass is zero then P2 = 0. 1.

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