# The bigger the mass, the more time slows down. Why is this?

If I were to stand by a pyramid, which weighs about 20 million tons, I would slow down by a trillion million million million of second. Don't know if that's exactly right, but you get the point. Also, if you went into a black hole, time would stop at the event horizon (as measured by a clock of a distant outside observer). Why is this?

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BHs do have limited mass. It's just a dead star. If a star has limited mass, then how could a dead star become so unlimited..? Can't understand why you're considering it as unlimited ;-) –  Waffle's Crazy Peanut Jan 24 '13 at 3:49

The effect you're talking about is called gravitational time dilation. The effect is easily calculated from the metric (typically the Schwarzschild metric) but when you ask "why is this?" I'd guess you're asking if there is a way to understand why this happens without working through all the algebra. The answer is no, not really, but I can attempt to give a rough sketch. However note well that this is not an accurate description of the physics and will mislead you if you push it too far. But to do any better does involve diving into the maths.

Consider the thought experiment shown above. We have a mirror hovering above a black hole at some fixed distance $r$, and from well away from the black hole we shine a light ray onto the mirror and time how long the light ray takes to reach the mirror and return. The distance from us to the mirror is $d$ as measured in our coordinate system. We know light moves at a fixed speed of $c$, so the time for the light to reach the mirror and return is just $t_0 = 2d/c$ i.e. distance divided by velocity.

Well, no. The time I've calculated above only holds in flat space i.e. if the black hole isn't there. When we have a black hole curving space there is a problem because if we solve the equations of motion for the light ray in the presence of the black hole we find it moves further than $d$, and the time we measure for the return journey, $t_{bh}$ is therefore longer than $t_0$.

So the light appears to be moving more slowly when the black hole is present, because it takes longer to reach the mirror and return than we think. But we know the speed of light is fixed at $c$, so the only other explanation is that time has slowed down for the light ray as it neared the black hole, and this is the gravitational time dilation.

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I dimly recall a thought experiment by Einstein where he studied a free fall of two clocks in a gravitational field only with the assistance of SR and Newtonian gravity. It should be in section V of this article but unfortunately my German is on "ordering a currywurst" level and I cant find an english version. He shows even the $(1+\phi/c^2)$ time dilation factor so it is possible to see dilation even with the usual SR thought experiment. –  Void Sep 10 '14 at 21:53

I understood that time is just a perceived measurement of say an oscillation of a photon. A strong gravitation field stretches the spacetime so much that the photon has "longer" distance to travel. Because it travels longer/stretched distance, we perceive it as slower. (the distance between a tick and the tock is stretched)

So to an outside observer, time seems to have slowed down. To the photon, the "time" is traveling at normal pace, but everything on the outside of the gravitational hole is happening a lot faster.

Same thing with the pyramid. When you stand close to it, your time is "flowing" at what you see as its normal rate. But everyone else's time, away from the pyramid is traveling faster compared to yours.

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What John is saying is mainly true, but the part where the conclusion is that time slows down is technically not the case. The conclusion in general relativity is that space itself is warped so it is not necessarily that time has slowed, but that spacetime is longer and so takes longer for light to travel what we perceive as a short distance.

In terms of why you slow down, imagine a right angled triangle and the hypotenuse is c, the speed of light. Now regard yourself as having a "speed" through time, which is the adjacent side of the triangle. When you have no "speed" in space, the opposite side of the triangle, the adjacent is equal to the hypotenuse, i.e you move through time at the speed of light. When you start to have "speed" in space, to keep the hypotenuse the same length, your speed through time must shorten.

The easiest way of explaining this application to gravity, is that you know that for any gravitational object you have an escape velocity. So imagine that to stay still you have this velocity "deficit" that you are spending "speed" to fill. Hence, time slows for you.

Finally, it is wrong to say that black holes have infinite mass. They do not. If they had infinite mass then everything within it's observable universe would hurtle towards it with infinite acceleration. The black hole has a finite, measurable mass, the one at the centre of our galaxy weighs about 10^30 suns. (I say weights, obviously that's a misnomer, I just mean has the mass of) Black holes simple warp space to the point that at their "event horizon" the escape velocity is equal to the speed of light, and so nothing can ever escape them. It also means your entire hypotenuse of that triangle falls along the "speed" axis and so you cannot move in time.

If you shrunk the earth down to black hole density, it would have a radius of the event horizon of 3mm. :)

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