GPS and the Twins Paradox
|Title||GPS and the Twins Paradox|
|Author(s)||Tom Van Flandern|
Satellite clocks in the Global Positioning System have their rates increased by the gamma factor [l/sqrt(1 - v2/c2)] so they tick at rates comparable to ground clocks despite their high relative velocity. It is instructive to place a clock adjusted in a similar way on board the spacecraft in the classic twin's paradox. When that is done, the "GPS clock" on board the spacecraft always reads the same as any local clock synchronized in the Earth frame that it encounters along its journey. And it always reads a factor of gamma more time elapsed than a "natural" clock carried on board. So upon its return to Earth, or indeed at any moment along the journey, the GPS clock (representing the age of the stay-at-home twin) must always read a factor of gamma larger than the natural clock (representing the age of the traveling twin), as expected. This holds true whether or not the spacecraft accelerates or turns around, which events clearly have nothing to do with resolving the paradox. But this thought experiment points up that there are two different logical inferences available about the time at distant locations in other frames: the one given by the Lorentz time transformation, and the one given by the "GPS clock". The former, a consequence of Einstein's special relativity (ESR), has discontinuous jumps if the spacecraft accelerates or turns around. The latter, a consequence of Lorentz's special relativity (LSR), has a preferred frame and a universal time. The discontinuities in distant time in ESR, while mathematically possible, argue against that interpretation on the grounds of physical plausibility.