Time dilation near black hole event horizon


How are fundamental laws of physics set up in such a way that you get the same effect (correct me if I’m wrong) if you move with speed near C as well as if you stay near the event horizon?
To me, these two “activities” are different but yet time dilation (and space contraction) happens in both.

In: 0

First you have to understand that the phrase spacetime exists because space and time are just different manifestations of the same thing. So, if you stretch space, such as near a black hole, you also stretch time. The definition of the event horizon is the point at which acceleration due to gravity is equal to the speed of light. So, when you are near the event horizon that is functionally equivalent to travelling near the speed of light and this causes time dilation.

This is special relativity vs general relativity.

Special relativity was thought of because it was proven that all observers should be able to determine the same value for the speed of light. Imagine a train going by with a laser that shoots up, hits a mirror, and goes back down. The person on the train should be able to tell how long it takes for the laser to make that trip based on the distance it goes d, and speed light moves at, c. Well the person on the ground sees the light travel in a diagonal line, because the train is moving horizontally, but the light still travels at c, even though it travels a longer distance, d’. The explanation we have for this is special relativity, time must move slower for the person who it moving. This has been proven experimentally, and we know that light must always travel the same speed for 2 reasons, 1. Before it was the speed of light, it was calculated as the speed of causality, the fastest something can react to something else, that’s why it’s c and 2. The Michelson-Morely experiment proved light doesn’t travel through a medium.

[Special relativity](https://youtu.be/ajhFNcUTJI0)

Now this raises an interesting point, the twin paradox. If you have 2 twins and one goes on a spaceship very fast away from Earth and then turns around and returns, who is older? From the perspective of Earth, the space twin went faster and should have aged slower, but from.the perspective of the space ship, the earth moved very fast, and therefore the Earth twin should’ve aged slower. This is where general relativity comes in to show that the space twin aged slower. (There were also other factors like precession of Mercury’s orbit that couldn’t be explained by classical physics)

[Twin paradox](https://youtu.be/Bg9MVRQYmBQ)

General relativity is much harder to explain, but ill do my best. Moving fast isn’t the only thing that makes time move slower, accelerating does too (including accelerating due to gravity in the case of a black hole). Imagine, you’re in a windowless box here on Earth or in one in space accelerating up at 9.81m/s^2 and you don’t know which one. What experiment could you do inside the box to tell which one you’re in? Under special relativity, if you shine a light out horizontally, the light should curve toward the floor and on Earth, following a longer path than it would if it went in a straight line, but an outside observer would see a straight line, and again, the person accelerating must be experiencing time slower. (This is why the earth twin is older, when the space twin is turning around, both twins agree that space twin is accelerating, and is experiencing time.slower during that acceleration)

[Twin paradox resolved](https://youtu.be/0iJZ_QGMLD0)

And then, back to the experiment in the box on Earth, why is the box’s acceleration so special that it can curve light? Why can the Earth’s gravity replicate every effect we know of except light? Well it can bend light but an outside observer would need to see the same straight line, just like the accelerating box’s experiment. This is where bending spacetime exists. To an observer outside of Earth’s gravity, the light travels in a straight line across the bent spacetime, and to an observer in Earth’s gravity, the light follows a curved path and both travel at c, but different distances in different amounts of time. And thus, gravity affects the speed at which time passes.

[General relativity](https://youtu.be/eNhJY-R3Gwg)

Who know? That’s what Einstein postulated to be true, and thus far had held up under every possible test.

The key reason for this postulate is the fact that gravity cause the *same* acceleration to *every* objects. That led Einstein to suggest that maybe gravity is an illusion: these “falling” objects are actually moving “straight” but we look at it from the wrong perspective. If we accelerate from a different object, from our perspective it’s the object itself that is accelerating. Once you accept that postulate, then acceleration is the same as being under the effect of gravity.