The speed of light needs to be the same for all observers.
If I’m flying by you at half the speed of light and we both have a flashlight pointed forward, the light I emit and the light you emit should travel at the same speed, and we should both measure that speed to be the speed of light.
If we adhere solely to classical physics, the light I emit should travel at 1.5c and the light you emit would be at 1c, and what I observe should my light traveling at 1c and your light traveling at .5c. This isn’t what happens and isn’t possible, so time dilation is how we account for it. This is special relativity.
General relativity is where gravitational fields cause time dilation. This gives us the idea that space and time are part of the same thing (spacetime). Large objects basically bend space around, and since space and time are the same thing, it also bends time, causing it to slow down. It comes from the same idea that light needs to travel at the speed of light regardless of the observer but involves an accelerating observer, rather than one already moving at a high speed. This is what Interstellar deals with. Since the planet is so close to the black hole, it’s in that large gravitational field, which slows down time.
This is kind of a half assed explanation of general relativity, so if you want a better one, I can provide one. It’s just a lot more subtle and deal with the bending of light.
Imagine you have two identical computers without clocks measuring external time and other external sensors, one is running at 3 GHz and another is running at 1 GHz frequency. And they run the same software. They have no choice but measure time as the number of instructions executed. For simplicity let’s say each instruction takes one clock cycle and define one “day” as 86 trillion instructions.
Obviously if these computers meet after being separated the first computer is going to be three times older in days than the second.
Think of going through time as riding along a wavy road. Near a massive object, like in interstellar, spacetime is stretched so you experience fewer waves compared to unstretched spacetime. You essentially run on lower frequency like a computer.
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