Can gravitational time dilation explain the galaxy rotation curve?

[sha1000]

Hello everyone,

By considering the effects of the gravitational time dilation the speed of the inner stars must be higher for the local observer than for the external one. So why the gravitational time dilation can not potentially explain the galaxy rotation curve? I already read that the answer is "No", but I would like to know the fondamental reason for that.

 

[Orodruin]

Uhmmm, why would you think it could explain galaxy rotation curves? The effects of gravitational time dilation are way waaaaay too small to do anything like that. Physics is not about making words fit together, it is a quantitative science.

 

[Bandersnatch]

By considering the effects of the gravitational time dilation the speed of the inner stars must be higher for the local observer than for the external one.

Have you tried calculating what the ballpark figures are? Go to Wikipedia's page on gravitational time dilation, take the equation provided therein (for our purposes it doesn't matter much if you pick the one for a stationary observer or in orbit), and plug in some numbers for a few fanciful scenarios. We treat the Milky Way as a ball - because once again, it's just for ballpark figures. The Schwarzschild radius of the entire MW mass is approx. 0.25 ly.
E.g. shrink the MW 100 times to accentuate the effect and see what dilation is there for two observers, one at the edge of such mass and one infinitely far away. Compare with observed vs expected (for no DM) rotational velocities within the Galaxy.
Note that pretty much every simplification and omission made causes this number to be an overestimate.

 

[sha1000]

Uhmmm, why would you think it could explain galaxy rotation curves? The effects of gravitational time dilation are way waaaaay too small to do anything like that. Physics is not about making words fit together, it is a quantitative science.

Could you explain why you are so sure that the gravitational time dilation is "way too small"? This is actually what I want to know.

 

[sha1000]

Have you tried calculating what the ballpark figures are? Go to Wikipedia's page on gravitational time dilation, take the equation provided therein (for our purposes it doesn't matter much if you pick the one for a stationary observer or in orbit), and plug in some numbers for a few fanciful scenarios. We treat the Milky Way as a ball - because once again, it's just for ballpark figures. The Schwarzschild radius of the entire MW mass is approx. 0.25 ly.
E.g. shrink the MW 100 times to accentuate the effect and see what dilation is there for two observers, one at the edge of such mass and one infinitely far away. Compare with observed vs expected (for no DM) rotational velocities within the Galaxy.
Note that pretty much every simplification and omission made causes this number to be an overestimate.

Thank you for your reply.

What mass of the MW should I use in this model? The observed mass or the one which includes the dark matter? Or maybe I can treat the mass as the unknown variable?

 

[Orodruin]

Could you explain why you are so sure that the gravitational time dilation is "way too small"? This is actually what I want to know.

Because I know the mathematics that describe gravitational time dilation, which is how physics is done.

 

[Ibix]

What mass of the MW should I use in this model? The observed mass or the one which includes the dark matter?

Either. It won't make a significant difference to the conclusion that time dilation is many orders of magnitude too small to have anything to do with this.

 

[Bandersnatch]

@sha1000 as Ibix said. Just run the numbers you like and see what comes out. Then maybe change some values and do it again. The point of the exercise is to gain an intuition for how the numbers interact. It's a bit like with the gamma factor in special relativity. Once you get the feel for how the equation works with different values, you then immediately know if a value of this or that order of magnitude will or won't output something noticeable.

 

[Benplace]

Because I know the mathematics that describe gravitational time dilation, which is how physics is done.

Sorry, but this is why more people don't come to this forum. You could have answered him in a way he could understand, but instead you chose to belittle him. A lot of people are simply curious and responses like this make them go elsewhere for discussion.

 

[Orodruin]

Sorry, but this is why more people don't come to this forum.

This is nothing but conjecture.

You could have answered him in a way he could understand, but instead you chose to belittle him.

I did not, I gave him a factual answer: If you do the math, the effect is way too small. I could have quoted numbers but it would not have done much except telling you exactly how much too small way too small is. I could have given him the math, but without background knowledge it would not have told the OP much.

 

[Vanadium 50]

Serious time dilation in this thread...the complaint is about a four year old message. "How dare you write something I didn't like four years ago! The horror! The horror!"

 

[Ibix]

You could have answered him in a way he could understand,

If you're going to make a complaint like that, you really ought to lay out how you think Orodruin should have answered the question in a lot more detail than "you could have said something different". I'm not actually sure how he could answer "why are you so sure" without saying "because the maths says so". The only thing I can immediately see that I would have done differently would be to reference Bandersnatch's ballpark calculation method in #3 as a "you can try it for yourself and see".