# Why does Cooper stay the same age when he is far away from Earth?

I had an argument at school with one of my friends about this. I said that Cooper stays the same age because he is ages away from Earth, but my friend said that I'm wrong because he is in an Earth-like environment therefore he ages the same as he would on Earth - is this true?

• I just have to post a link to Why didn't the Normandy crew experience time dilation? (Mass Effect). Turns out there isn't much time dilation when you limit yourself to being survivably close to a black hold. Jul 21, 2015 at 14:07
• @NathanCooper: Gargantua was extremely large compared to Sagittarius A*. It was also spinning quite fast, which creates additional time dilation from the velocity. Jul 21, 2015 at 14:10
• Because the film is told from his point of view? Jul 22, 2015 at 0:12
• He doesn't "stay the same age", he just ages at a normal rate from his (and our - we are in his reference frame) perspective. Jul 22, 2015 at 9:30

You both seem to be misunderstanding the science behind Interstellar. The reason that Cooper stays the same age while his children continue to grow old is due to the theory of relativity, specifically time dilation and more specifically gravitational time dilation.

A brief overview of the idea is that in places where gravity is higher, time passes slower. As such, we can see in real life that clocks in orbit around the Earth will end up out of sync with clocks on Earth by very small amounts.

But when the difference in gravity is stronger, the effect is too. So when Cooper and his crew travel to a planet orbiting a supermassive black hole called Gargantua, the difference in gravity between Earth, the ship in outer space and the planet they travel to means that from their perspective very little time has passed, but the astronaut on the ship (and the people still on Earth) see about 23 years pass.

In short, the difference in how Cooper ages in Interstellar has (almost) nothing to do with his distance from Earth or the Earth like conditions he is living in - rather, we see the effects of gravitational time dilation in extreme circumstances.

• @Thomas: “fleshed” out. Jul 21, 2015 at 9:42
• @Thomas Just 29 seconds. Although in Cooper time, that could be months. Jul 21, 2015 at 9:42
• ah ok so the reason why he stays the same age is because gravity is stronger therefore time is slower and cooper doesn't see any changes where as the astronaut on the ship sees as you said about 23 years pass. thank you for clarifying it for me. Jul 21, 2015 at 10:08
• A Fletched-Out answer would be one with 23% more Chevy Chase Jul 21, 2015 at 13:37
• Technically speaking, the astronauts in the ISS are aging less than they would on earth, since they're higher up than us--albeit extremely minutely (cf. this Physics.SE post). OP is correct to some extent, however, the proximity to Gargantua (i.e. the Waterworld & Slingshot manuever) are what really makes Cooper & Brandt stay so young. Jul 21, 2015 at 13:51

You are slightly correct, but also wrong at the same time.

## Why you're slightly right

As shown in this Physics.SE post, astronauts further away from the gravitational field of Earth (in the cited example, it is on-board the ISS) will actually experience time dilation, albeit extremely minutely: the time difference is roughly a 10-9 second change. Note that this means that it will take a hundred years for you to notice a 1 second difference between someone on-board ISS and someone on Earth.

## Why you're wrong

That said, the reason Cooper appears to stay around 35 years old throughout the film is because1 of Gargantua, the super-massive black hole (SMBH), and the associated gravitational time dilation of this SMBH, as mentioned by Dr R Drizzle.

Gravitational time dilation is a phenomena encountered in general relativity

whereby time runs slower when in a higher gravitational potential. Put simply, the closer you are to a large body like the Earth the slower time runs, thus time runs slower for someone on the surface of the earth compared to someone in orbit around the earth."

The strength gravitational potential inversely depends on the radial distance from the object, so by being in close proximity to the SMBH, the experienced time between Cooper & someone on Earth is necessarily different. The two big instances of this effect in the film are:

• The trip to the water world took about 3 hours in Coopers time, but for Romiliy on-board the orbiting ship, 23 years passed2.
• The sling-shot maneuver seemed to take a few minutes, but another 51 years was elapsed on Earth (cf. the 2:30 mark of the linked YouTube video and Dr Brand's subsequent comment, You don't sound so bad for someone pushing 120.).

Note that this was a big part of the point of the movie: Kip Thorne (scientific consultant & executive producer of the movie) wanted the populace to see black holes and relativity in a scientifically accurate way3. The effects of Cooper & Brand's trips are scientifically correct and even the footage of the SMBH came from a simulation of Einstein's field equations (that also produced two research publications).

There were also a fair number of questions asked on the Physics StackExchange site about the movie Interstellar. This simple site query should provide you with a starting point for some of the physics behind the film. Most relevant would be:

1 Obviously ignoring the whole "it was filmed in ~1 year & Matthew McConaughey can't possibly have aged 120 years in that short time" reason
2 I am supposing Earth-based time, but I don't think this point is ever discussed in the film.
3 Cooper's fall into the SMBH notwithstanding here, the tidal forces would have torn his body apart.

• +1 for clearly knowing significantly more than I do about the real life science in Interstellar. Jul 21, 2015 at 15:10
• @DrRDizzle: Being (a) in a physics graduate program and (b) in the Physics.SE chatroom when the movie was released to theaters led to frequent discussions about it. Jul 21, 2015 at 15:28
• After reading your answer and your sources I feel knowledge improoved but there is one thing that sounds contradicting to me: Why time on the ISS is slower then on earth? Since we are closer to the heavy object earth in this case shouldn't it be vise versa? Or is it because they are closer to the sun? but then it should also be rellevant on which side of earth they are, shouldn't it? Jul 22, 2015 at 14:07
• @Zaibis: The gravitational potential energy depends only on the mass of the body & radial distances, so "the side of earth" doesn't matter, just the distance. In the case of ISS, it is actually the velocity that causes it to be slower than on Earth. For geosynchronous orbits (equal velocities at different heights), the ISS astronauts would be aging faster than their ground-based friends (the case for GPS satellites). But since they're moving much faster (~8 km/s vs ~0.5 km/s), the velocity is affecting the time-dilation as well. Jul 22, 2015 at 14:35

Either I don't understand your arguments correctly or you both are wrong: It has nothing to do with the earth like environment or the distance to earth. The gravity of the black hole slows time if you are in its influence radius. This is why he only ages a bit while his children grow up and even get older than himself. They try to explain how it works in the movie, but to fully understand I would recommend to read some literature concerning Einsteins Relativity Theory on which the aging is based in the movie.

• Mathematically speaking, you're always in the "influence radius" of a black hole. It's just a matter of degree. Jul 21, 2015 at 16:01
• @Ajedi32 And even more importantly, it's not about some absolute gravitational potential value or whatever - difference is the key. If we're both just as close to two identical black holes, time is going to pass at the same speed for us. Jul 22, 2015 at 7:23