28.2 Exercise 1

In 1971, American physicists Joseph Hafele and Richard Keating verified time dilation at low relative velocities by flying extremely accurate atomic clocks around the Earth 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, since gravity and accelerations were involved as well as relative motion.

1. What is $\gamma$ if $v = 0 .\text{650} c$?

2. A particle travels at $1 . \text{90} \times \text{10}^{8} \text{m}/\text{s}$ and lives $2 . \text{10} \times \text{10}^{- 8} s$ when at rest relative to an observer. How long does the particle live as viewed in the laboratory?