|MadSci Network: Physics|
Time measurement, in special relativity, is done from an inertial reference frame; and, the speed of light is the same in every inertial reference frame. One of the difficulties with the scenario you have suggested, is the measured times would be dependent upon the inertial reference frame used. An additional difficulty, for the measurement of time in the spacecraft making the two runs across the galaxy, is the accelerations and deccelerations needed in the course of the trip. Making the assumption that time measurements are made from the non- accelerating inertial reference frame of an observer at the launch point, it would not take longer to travel one direction across the galaxy as opposed to another. There are also no differences in energy required, that are dependent upon the direction of travel; as long as one doesn't have to consider mass anomalies traveling in preferred directions independent of the direction of travel of the galaxy and a host of other difficulties that I am not qualified to even list. There is an interesting discussion on pages 96 to 97 of Walter Scheider's 'Maxwell's Conundrum: A serious but not ponderous book about Relativity', Cavendish Press, Ann Arbor, Michigan, 2000, isbn 0-9676944-0- X. The discussion is about a racer who distrusts the judges and decided to carry his own stopwatch. The next few pages afterwards are about muon's and the differences in time measurements in the reference frame of muon versus that for a laboratory on the Earth's surface. Both examples offer insights to the nature of time measurements in special relativity and may be helpful in unravelling the mysteries of the scenario you have proposed. Thanks for your question. In addition to the reference noted, there are many postings in the MadSci archives on inertial reference frames. On the web, using search terms such as +special_relativity will reveal many excellent references on all aspects of relativity. sid
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