5.3 Time dilation  (Page 6/8)

In 1971, American physicists Joseph Hafele and Richard Keating verified time dilation at low relative velocities by flying extremely accurate atomic clocks around the world on commercial aircraft. They measured elapsed time to an accuracy of a few nanoseconds and compared it with the time measured by clocks left behind. Hafele and Keating’s results were within experimental uncertainties of the predictions of relativity. Both special and general relativity had to be taken into account, because gravity and accelerations were involved as well as relative motion.

Summary

• Two events are defined to be simultaneous if an observer measures them as occurring at the same time. They are not necessarily simultaneous to all observers—simultaneity is not absolute.
• Time dilation is the lengthening of the time interval between two events when seen in a moving inertial frame rather than the rest frame of the events (in which the events occur at the same location).
• Observers moving at a relative velocity v do not measure the same elapsed time between two events. Proper time $\text{Δ}\tau$ is the time measured in the reference frame where the start and end of the time interval occur at the same location. The time interval $\text{Δ}t$ measured by an observer who sees the frame of events moving at speed v is related to the proper time interval $\text{Δ}\tau$ of the events by the equation:
  
  $\text{Δ}t=\frac{\text{Δ}\tau }{\sqrt{1-\frac{v^2}{c^2}}}=\gamma \text{Δ}\tau ,$
  
  where
  
  $\gamma =\frac{1}{\sqrt{1-\frac{v^2}{c^2}}}.$
• The premise of the twin paradox is faulty because the traveling twin is accelerating. The journey is not symmetrical for the two twins.
• Time dilation is usually negligible at low relative velocities, but it does occur, and it has been verified by experiment.
• The proper time is the shortest measure of any time interval. Any observer who is moving relative to the system being observed measures a time interval longer than the proper time.

Conceptual questions

Problems