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The clock hypothesis is the assumption that the rate at which a clock is affected by time dilation does not depend on its acceleration but only on its instantaneous velocity. This is equivalent to stating that a clock moving along a path measures the proper time, defined by:
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In Fig 4-2, the observer whose reference frame is given by the black axes is assumed to move from the origin O towards A. The moving clock has the reference frame given by the blue axes and moves from O to B. For the black observer, all events happening simultaneously with the event at A are located on a straight line parallel to its space axis.
Gravitational time dilation has been experimentally measured using atomic clocks on airplanes, such as the Hafele–Keating experiment. The clocks aboard the airplanes were slightly faster than clocks on the ground. The effect is significant enough that the Global Positioning System's artificial satellites need to have their clocks corrected. [13]
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"Two clocks are depicted as moving in Minkowski space. Clock B is moving in a localized momentum wave packet with average momentum p B, while clock A is moving in a superposition of localized momentum wave packets with average momentum p A and p0 A. Clock A experiences a quantum contribution to the time dilation it observes relative to clock B ...