Does Gravity Also Affect Clocks?
We have just seen that the equivalence principle predicts that light bends in a gravitational field. What are the consequences of the equivalence principle for time?
- Consider a clock at the top of the rocket which sends light pulses to a clock at the bottom of the rocket at a definite frequency f0.
- If the rocket is accelerating in the direction of the top clock, the bottom clock will receive the pulses at a frequency f > f0.
- Why? Since the clock at the bottom will be moving at a different speed when it receives the pulses, it will see the light. Doppler shift!
- In the time it takes the pulses to travel to the bottom clock, the rocket has increased its velocity by an amount: v = at = aL/c ? = v/c = aL/c2
?tbot = ?ttop - (v?ttop)/c ? ?tbot = ?ttop (1-?) ???? f = f0 / (1 - ?)