Exploring Time Dilation and the Galaxy: Effects of Gravity and Angular Velocity

[PhDnotForMe]

I'm just wondering about time dilation in regards to both special and general relativity within our galaxy. Does time move slower or faster relative to us within the inner parts of the galaxy? I know at the horizon of the black hole time is effectively not moving. This implies that locations closer to the black hole will move slower in time. But we also see stars moving on the outer edge of the galaxy moving around the center of the galaxy with an equal angular velocity as the stars on the inner parts of the galaxy. Could this be explained by time dilation? Current theory uses dark matter to explain why the angular velocity of stars revolving around the center of the galaxy are moving faster than expected, but could it just be that they experience less gravity and thus feel less effect of time dilation causing us to see them moving faster since we are moving slower in time?

 

[Ibix]

Does time move slower or faster relative to us within the inner parts of the galaxy?

In the sense you mean, slower. The effect is tiny, though.

I know at the horizon of the black hole time is effectively not moving.

This is common in popsci descriptions of black holes, but isn't accurate. Schwarzschild coordinate time is singular at the horizon, but that doesn't mean "time stops".

But we also see stars moving on the outer edge of the galaxy moving around the center of the galaxy with an equal angular velocity as the stars on the inner parts of the galaxy. Could this be explained by time dilation?

No. Time dilation is not significant for something as diffuse as a galaxy.

they experience less gravity and thus feel less effect of time dilation

You have this wrong. Gravitational time dilation is dependent on gravitational potential (actually, it's more complex than that in this situation because the galaxy isn't a non-rotating spherically symmetric mass), which is larger near the centre of a galaxy than the rim.

 

[kimbyd]

Basically, you have to be incredibly close to an extremely dense object (such as a black hole or a neutron star) for gravitational time dilation to be noticeable without incredibly sensitive time measurements.

 

[PeroK]

Basically, you have to be incredibly close to an extremely dense object (such as a black hole or a neutron star) for gravitational time dilation to be noticeable without incredibly sensitive time measurements.

It's a good job you weren't the science advisor on Interstellar!

 

[kimbyd]

It's a good job you weren't the science advisor on Interstellar!

Honestly, the science advisor for Interstellar is way, way more knowledgeable about this stuff than I am. Kip Thorne is one of the world's leading experts on General Relativity, and is one of the co-authors on one of the best-regarded GR textbooks (Gravitation by Misner, Thorne, and Wheeler).

The movie makers certainly took some significant liberties with that movie, but what's interesting to me about it was that I definitely recognized the real scientific concepts they were drawing from throughout. Honestly, there were a lot of inaccuracies, but I kind of loved how parts of the movie alluded to real scientific concepts that few people would be exposed to (such as the laws of physics not working in the extra-dimensional space, and the freedom of motion through "time" inside the black hole). Each one was really inaccurate in the movie, but there was also a kernel of real science there.