Two clocks, at rest with respect to each other, are 1 mile apart in their proper

Question

Two clocks, at rest with respect to each other, are 1 mile apart in their proper frame. Someone (person A) in the same frame of reference synchronizes them. Another person (person B) moves past the first person and his two clocks at 100 miles per hour, in a direction parallel to the line connecting the two clocks. Take the speed of light to be 671,000,000 miles/hour. Does person A say the two clocks are synchronized? Does person B say the two clocks are synchronized? According to person B, does the front clock or the rear clock read the later time? According to person B, what is the time difference between two clocks? In other words, by how much are the two clocks out of synchronization? Based on your answer to, is it acceptable for our everyday purposes to synchronize two clocks by bringing them to the same location, setting them to read the same time, and then moving one or both to different locations? Explain.

Explanation / Answer

100 mph is nothing compared to the speed of light The formula t = to/{sqrt[1 - (v/c)^2]} gives us t = to/{SQRT[1 - 2.2 E-14]} ~ to/SQRT[1] = to/1 = to Person A says they are synchronized. Person B, when he is in the one mile between the clocks is moving along with the light from the back clock and moving towards the light from the front clock. When he is between the clocks, the light from the clock behind him will take a little extra time to catch him so it will be from an earlier time, and the clock behind him will appear slow compared to the clock in front of him. So the clock ahead of him will read a later, more recent, time. The two clocks will be off by double this time or (1- {SQRT[1 - 2*2.2 E-14]})s There is no way to measure this tiny time. Yes, it is fine to move clocks at speeds humans are able to move clocks without relativistic effects messing things up.

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