After a lot of thought, and reading a few websites, with a vague understanding of gravity I learnt 7 years ago, here is what I came up with:
The force a body experiences while at rest in earth is g times its mass where g = acceleration due to gravity or the pulling force exerted by earth on all objects.
It is this force that causes the cell to wear off eventually which is what we call ageing.
There are other factors that cause ageing but gravity is the prime reason why we age.
Now, what if we exert a force opposite to the gravitational force? In that case, the 2 forces cancel out each other and the stress experienced by the cell is that much lesser.
Thus it ages slower under low stress conditions.
Even clocks run slow in these conditions. This is why Cooper never looked aged.
This holds good even if you are running at a speed of 11.2 km/s which is when you don't need to spend any more of your energy to escape the force of gravity.
Ideally, you wont age. Any speeds lesser than that introduces ageing relative to the rate of ageing while at rest.
Einstein's special relativity tells us that bodies moving at phenomenal speeds (any speed is subject to relativity but the higher speeds give us a chance to detect time dilation as the results are measurable through today's technology) tend to slow down time for them relative to another body moving at very slow speed.
We know that we always measure speed of light same (3 x 10^8 m/s) irrespective of the speed of the observer, this phenomenon led Einstein to discover that time is a relative entity and runs slower of objects moving at greater speeds in a relative reference frame.
This time dilation factor (along with Lorentz contraction) helps to establish the fact that speed of light is a constant in vacuum.
After a few years Einstein made yet another discovery (arguably the best in his life), he found that gravity and and the force of acceleration are same (general relativity).
This equivalence tells us that there is no physical means to tell if you are in a room and experiencing the force of gravity or you are in a rocket speeding at 9.8 m/s^2 in space (unless you look out to figure what's happening).
Now this implies that gravity and acceleration are the same thing and hence gravity should also affect time in the same way as speed does for moving objects, and this is now experimentally verified that in regions of higher gravity (the top of a colossal building, just an example) has time running slower when compared to a region of relatively lesser gravity (basement of the same colossal building).
To add to it there is a complex mechanism of curved space time that increases the length between two points (a,b) within the effective vicinity of a massive object that has a direct relation to the phenomenon due to which the time dilation is experienced.
Time dilation in Interstellar occurs in accordance with the Theory of General Relativity that Einstein came up with.
In this, he showed that space and time were not separate and instead were interlinked as space-time.
This space-time is distorted as a result of mass, which manifests itself as a higher gravitational field.
An additional effect shown by Einstein's equations were that the stronger the gravitational potential (the closer the clock is to the source of gravitation), the more slowly time passes.
The black hole "Gargantua" exhibited an extremely strong gravitational field, and the first planet (the one with the water in it) was close enough to the "gravity well" of the black hole that time dilation was strong enough for 1 hour on the planet to correspond to 7 years on earth.
His ageing rate or metabolism was in no way affected.
It is just that time is relative, and in his frame of reference less time passed.
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