Problems are listed in approximate order of difficulty. A single dot (•) indicates straightforward problems involving just one main concept and sometimes requiring no more than substitution of numbers in the appropriate formula. Two dots (••) identify problems that are slightly more challenging and usually involve more than one concept. Three dots (•••) indicate problems that are distinctly more challenging, either because they are intrinsically difficult or involve lengthy calculations. Needless to say, these distinctions are hard to draw and are only approximate.
•• A traveler in a rocket of length 2d sets up a coordinate system S′ with origin O′ anchored at the exact middle of the rocket and the x′ axis along the rocket’s length. At t′ = 0 she ignites a flashbulb at O′. (a) Write down the coordinates x′F, t′F and x′B, t′B for the arrival of the light at the front and back of the rocket. (b) Now consider the same experiment as observed in a frame S relative to which the rocket is traveling at speed v (with S and S′ arranged in the standard configuration). Use the Lorentz transformation to find the coordinates xF, tF and xB, tB of the arrival of the two signals. Explain clearly why the two limes are not equal in frame S, although they were in S′. (This illustrates how two events that are simultaneous in S′ are not necessarily simultaneous in S.)
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