This is Miller's planet it's the closest planet to the fictional black hole Gargantua, so what's so special about this scene? Well, just in the span of this 5-second clip from this planet, a lot has happened as Earth might be wondering why, well just after they touch down on the planet, what he means by, if they spend one hour on that planet, time will pass seven years back on Earth, so how is that possible?
The time dilation! While bringing the context of what happens in Interstellar, the influence of a strong gravitational field, time slows down, so if you're just hanging out in a near massive object, you will experience the effect of time going slower, but gravity isn't the only thing that can warp time according to another one of Einstein's theories, special relativity, time slows down for an object when it moves, combining these two concepts, we could consider this scenario, suppose that we walked up a flight of stairs, our body is slowly moved away from Earth, meaning that we will experience time going faster, but at the same time, since we are not stationary while going up, we should experience time going slower, so being farther from the pull of gravity, causes our clock to tick faster, but moving counteracts this effect, of course, this is all oversimplified time dilation.
Gravitational Redshift! Let's consider two comparable cases, we have person A, floating nearby a massive object with a lot of gravity, and person B just casually floating in an empty void of space, person A shines a green laser beam towards person B, because light is a form of vibration, the laser beam has a color that corresponds to 600 trillion vibrations each second, now, light is also a form of energy, and as that beam of light comes out of that gravity of the massive object loses a lot of energy, this loss means that there is a decrease in frequency, so by the time that beam of light reached person B, its frequency will have decreased by some factor, that means, instead of the green light at 600 trillion vibrations a second person B gets only -let's say 10 billion vibrations per second which is a microwave radio beam, this phenomenon is called gravitational redshift, but not so fast Individual wiggles don't just go anywhere and disappear, since person A creates 600 trillion wiggles every second, while person B only gets10 a billion every second, the only way this can happen is if one second on one astronaut's clock is not the same as one second on the other astronaut, in other words, it only takes one second for person A to create those 600 trillion wiggles, but it will take 60,000 seconds or nearly a day for person B to receive them, so this is what happens, our clocks run at widely different rates, and by clocks, I don't mean just mechanical or electronic devices but also biological clocks like your heart, lungs, your brains, person A takes a breath takes another breath and measures a few seconds between the two, for him, everything feels normal, clocks tick the way they are supposed to, on the other hand person B, watching person A through a telescope sees everything in slow motion, several days passed between the two breaths, so now revisiting this scene from Interstellar, you should get a better understanding as to why Cooper says that he will be the same age as his daughter by the time he comes back from the mission.
Time Dilation in Interstellar! Time dilation according to several measures to Einstein's special relativity, the greater the acceleration of an object the slower that it will move through time, gravity's pull is modest on Earth, where time is slowed by only a few micro seconds per day, on the surface of a neutron star, where time is slowed by a few hours per day, gravity's pull is enormous, and at the surface of a black hole, time is slowed to a halt, where the gravity is so humongous that nothing can escape, not even light, the concept of the slowing of time plays a major role in interstellar, in the movie, Miller's planet is depicted to be present in the warped space, very close to a black hole Gargantua, because of this, the pull of gravity on Miller's planet is enormous, so if we apply Einstein's relativity here, we would know that Miller's planet would experience time at a very slow rate, but here on Earth, the gravity is at a modest rate, and the gravitational force of the sun is also a billion times weaker than Gargantua, so people on Earth experience time faster than that of the three astronauts on Miller's planet, and of course, all of this information is brought to you from the book "The Science of Interstellar" written by the scientific consultant of the film, in real life, this process is happening everywhere in space, one interesting example is our International Space Station, at the ISS, time runs slower than compared to time here on Earth, technically speaking, it is a different time reference than we are, so by calculating the difference through Einstein's equations could correct the time at the ISS.
Technicalities in Interstellar! Because we use a lot of references to the movie Interstellar here we might as well just take one case study of how filmmakers do this time dilation feel in the movie, in the opening scene when Cooper and his team stepped on Miller's Planet intense music with clock-ticking elements starts, the tempo changes throughout the song, where time dilation takes effect because of the proximity to a singularity, for every 60 seconds of the track, there are 48 ticks of the secondhand sound, so each stick is 1.25 seconds, according to the movie, one hour on Miller's planet equals about seven years on Earth, let's do the math on this, there are 3,600 seconds in an hour and there are 24 hours in a day, so to get 7 years, we need to multiply: (seconds in a day) * (days in a year) * 7Roughly we'll get about 221 million seconds in seven years, this gives us a conversion factor of about 61,400 seconds which passes on earth for every second spent on Miller's planet, multiply this by the interval between each tick, and you'll get 77,000 Earth seconds or about 21 hours, so each tick you hear is almost a whole day passing on Earth, and this is side by side with what happens on Miller's planet versus earth in real-time.
The Problems! After grasping all of this piece of information, of course, we want to ask if this extreme time dilation is possible on such a planet? Could we even walk on the surface of it? At one point, we are told that the gravity on this planet is 130% of the Earth's gravity, we see the actors panting, a little under duress because of the extra gravity, but is this enough for this kind of time dilation? Well, not even close if you've visited the surface of our Sun which is not a supermassive body but still much more massive than Earth, you would gain about 66 seconds per year to get to an extreme dilation where one hour corresponds to seven years, you would need such a strong gravitational field essentially the event horizon of a black hole, there is simply no planet that can have this kind of gravity and if you try to land on the surface, it'll be so strong that it would crush you the weight of the astronauts would be several million tons, and that's even without doing the math, but anyhow, if they wanted to get all the science right, we wouldn't be able to enjoy the movie, after all, it's science fiction, and to make a great film, a superb filmmaker often pushes things to the extreme, but in our case today, it's sufficient to turn the concept of time dilation into a beautiful film" We'll find a way, professor, we always have".
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