Cooper could take a watch into the shallows, raise his wrist after sixty minutes and find that precisely an hour had passed.
Whose Clock Measures The Hour On Miller’s Planet?
Cooper could take a watch into the shallows, raise his wrist after sixty minutes and find that precisely an hour had passed. His pulse, his thoughts and the motion of his companions would agree. The shock comes when he compares his experience with that of someone who stayed farther from Gargantua. Both clocks can work perfectly and still record radically different elapsed times.
The figure given in Interstellar is roughly seven years far from the black hole for an hour on Miller's planet. In round numbers that is a ratio of about 61,000 to one. A single minute on the surface therefore costs the distant observer about six weeks. Take five minutes to recover equipment and somebody waiting elsewhere has had time to live through roughly seven months.
Why Two Good Clocks Can Disagree
Relativity assigns an elapsed time to the route a clock takes through spacetime. Different paths between departure and reunion can accumulate different amounts. Gravity and motion both matter in this story. A planet deep in a black hole's gravitational environment is also moving rapidly on its orbit. You cannot reconstruct its clock rate simply by looking at how close the water seems to the black disc in the sky.
Gargantua is a rapidly rotating black hole. Rotation changes which orbits are possible close to it. The scientific model behind the film requires an extraordinarily rapidly spinning black hole and an extraordinarily close orbit to deliver so large a ratio. Ordinary planets orbiting ordinary stars do not give away decades every time someone stops for lunch.
It is tempting to imagine that a visitor would feel time becoming syrupy as the spacecraft comes down. Yet thinking and checking a watch are themselves local physical processes. If the visitor's watch and body follow essentially the same journey, there is no separate fast-running clock inside their head against which they would notice the effect.
Why Is The Landing Such A Bad Bargain?
The crew are investigating evidence from a previous explorer. On Earth, a signal that has been arriving for years might suggest someone had years to evaluate a planet. Under these conditions, very little time may have passed for the person sending it. A long sequence of hopeful observations at the receiving end need not represent a long and thorough exploration at the source.
The same arithmetic turns a delay on the water into a disaster aboard the mission. A decision that feels hasty to the people making it can consume an enormous interval for the colleague awaiting their return. By the time the travellers reunite with Romilly he has experienced more than twenty-three years. The reunion makes an abstract ratio legible in the age of a familiar face.
There is a quieter consequence in the messages from Earth. Cooper can play them in succession, but the events they describe did not happen in succession to the family living through them. Children grew up during the ordinary intervals between birthdays. From their perspective their father failed to come home, day after day. The cleverness of Miller's planet is that one calculation answers two questions. It explains why Cooper looks much the same and why the people he loves no longer do.
