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.
• Let us assume the classical ideas of space and time are correct, so that there could only be one frame, the “ether frame,” in which light traveled at the same speed c in all directions. It seemed unlikely that the earth would be exactly at rest in this frame and one might reasonably have guessed that the earth’s speed v relative to the ether frame would be at least of the order of our orbital speed around the sun (v ≈ 3 × 104 m/s). (a) What would be the observed speed (on earth) of a light wave traveling parallel to v? (Give your answer in terms of c and v, and then substitute numerical values.) (b) What if it were traveling antiparallel to v? (c) What if it were traveling perpendicular to v (as measured on earth)? The accepted value of c is 2.9979 × 108m/s (to five significant figures).
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