Season 17, Episode 41: Explaining Time Dilation on Miller’s Planet from Interstellar

Hey StarTalkians! Episode 41 of season 17 was a Cosmic Queries edition, and the very first question Neil and Paul tackled touched on time dilation and Miller’s Planet from Interstellar:

Cosmic Queries – Pure Spacetime

(from 2:50)

Neil’s explanation was good, but the curse of cosmic queries is going over tricky concepts in a lightning-fast format. So here’s a deeper look at the physics, and the original question: looking from Miller’s Planet, what would you actually see?

Light Clocks and Relativistic Time Dilation

Imagine two mirrors separated by some distance a, with a light pulse bouncing back and forth between them. When the light hits each mirror, it increases the value on a counter. For every a the light travels, the number goes up. This is called a “light clock”.

Now imagine the same clock moving a distance, b, to the right with each tick. Watching from the outside, the light would move a upwards (or downwards), and b to the right for each tick – a diagonal line. Pythagoras’ Theorem tells us that the path the light seems to take, c, follows a^2 + b^2 = c^2. This means that c > a, i.e. the path in the second case is longer.

If you were travelling with the light clock, it would still look like it had only moved a, but from the outside, the distance is c. Since relativity tells us that light travels the same speed in each frame of reference, there is only one solution: time itself runs slower when you’re moving.

Gravitational Time Dilation and Miller’s Planet

Gravity works by warping spacetime. It’s hard to escape the Earth because it literally bends the space around us. Think about what this means for a light-clock. Far from gravitational sources, the pulse basically moves in a straight line. But on warped spacetime, its path becomes bent and therefore longer.

Just like with the moving light-clock, this means that close to a gravitational source, time runs slower. So on Miller’s Planet, with a black hole nearby, time runs very slow.

This is a very real effect, confirmed with atomic clocks on planes and in even simpler experiments.

What Would You See?

Looking from Miller’s Planet at the observers in lower gravity, you would see their time move fast, as Neil answers. It would be like watching in fast forward – their light clock would tick multiple times for each tick from yours.