Guillermo Navas
- 9
- 3
- TL;DR
- Error in explaining gravitational time dilation using the equivalence principle and the Doppler effect.
In Box 2.4 of the book "Black Holes & Time Warps" by Kip S. Thorne, he explains gravitational time dilation using the equivalence principle. For this he uses an experiment thought analogous to the one used by Einstein in 1911 to postulate the existence of a gravitational Doppler shift, but slightly modifying the initial conditions.
Thorne's thought experiment is as follows: consider two identical clocks that are dropped in free fall into a gravitational field from different heights. Light pulses are sent from the highest clock to the lowest clock. The clock on the ceiling emits its first pulse of light when it begins its fall, while the lower clock begins its free fall when it receives the first pulse of light. The detailed explanation can be seen in the image on the Box 2.4 pages, Thorne says: “Because the ceiling clock was dropped before the floor clock, its downward speed is always greater than that of the floor clock (diagram b); that is, it moves toward the floor clock. This implies that the floor clock will see the ceiling clock’s light pulses Doppler-shifted (Box 2.3); that is, it will see them arrive more closely spaced in time than the time between its own ticks”.
Can you see which the error is?
Thorne's thought experiment is as follows: consider two identical clocks that are dropped in free fall into a gravitational field from different heights. Light pulses are sent from the highest clock to the lowest clock. The clock on the ceiling emits its first pulse of light when it begins its fall, while the lower clock begins its free fall when it receives the first pulse of light. The detailed explanation can be seen in the image on the Box 2.4 pages, Thorne says: “Because the ceiling clock was dropped before the floor clock, its downward speed is always greater than that of the floor clock (diagram b); that is, it moves toward the floor clock. This implies that the floor clock will see the ceiling clock’s light pulses Doppler-shifted (Box 2.3); that is, it will see them arrive more closely spaced in time than the time between its own ticks”.
Can you see which the error is?
