Time dilation from galactic gravitational mass

[Ibix]

The fact that "dark matter" is proportional to the visible mass is why I had an inkling that it seems highly likely that it's just a side-effect of matter we're not accounting for

I don't think it is. There are dark matter-free galaxies and cases where the halo is mis-aligned with the visible matter.

I am curious, though, why time dilation couldn't be one of these pieces (I agree, it may not be the only one)

Above, Peter points out that at most, it's 3/2, "same order of magnitude"

It's way too small. @PeterDonis was saying the real value of time dilation must be the same order of magnitude as his "everything is spherical" approximation, not that it was similar to the magnitude of dark matter effects. You can plug a galaxy mass and radius into his formula and see this easily enough.

So it seems that time dilation could actually push the predicted value a lot closer, and would also explain the proportionality to visible matter

No. You're misreading Peter's comment.

 

[PeterDonis]

Peter points out that at most, it's 3/2, "same order of magnitude"

You need to read more carefully. What I actually said is that the gravitational time dilation at the center of a spherically symmetric massive body of constant density is 3/2 of the gravitational time dilation at the surface of that body. And we already know, from calculations that others had already posted in this thread, that the gravitational time dilation at the surface of such a body is many orders of magnitude too small to account for galaxy rotation curves. Therefore the gravitational time dilation at the center is also many orders of magnitude too small to account for galaxy rotation curves.

 

[Vanadium 50]

There are dark matter-free galaxies

Well, maybe. Two have been identified, right next to each other, and the "DM Free" inference depends on the distance, and the distance a) is questionable, or at least arguable (as determined by people actually arguing about it in the literature), and b) correlated between the two examples.

Further, the history of how these galaxies managed to be stripped of their DM is far from cleart: the story is not that they never had any, the story is that they used to have some but now it's gone. However, this interaction has not disrupted the stellar population. You need to have this happen via multiple "glancing blows" in interactions with other galaxies.

I don't think this is a settled issue, and am pretty sure everybody would like to see more examples discovered.

 

[strangerep]

It's perhaps worth noting that people do seriously consider the possibility that other GR effects are responsible for "dark matter" galaxy rotation curves. Time dilation won't cut it, but there's an awful lot of rotating mass in a galaxy and we know that rotating masses can (in some circumstances) "frame drag" and cause free fall paths to co-rotate. It's not inconceivable that this kind of effect could cause galaxies to spin faster than Newton would suggest. There was a relatively recent solid proposal along these lines by a man called Deur.

I wouldn't call it "solid". Not at all. See the Deur thread over in BTSM.

The jury is still very much out on that one (the maths is not simple, even by GR professionals' standards), [...]

Well, I reckon it's not worth anything. Try getting Tully-Fisher out of Deur's method...


Moreover, these flat rotation curve effects happen in regimes of very low velocity, and very weak fields (hence low acceleration) -- which is why Newtonian gravity is used in much of standard galactic dynamics theory. But the observed RC phenomena could more accurately be called "sub-Newtonian" -- meaning slower+weaker than we're normally familiar with in terrestrial and solar gravitation. Imho, going from Newtonian up to SR+GR is headed in the wrong direction.

 

[strangerep]

I am curious, though, why time dilation couldn't be one of these pieces

In the low-acceleration regime, the observations point to a scale-invariant equation of motion governed by an acceleration scale constant (i.e., different from the usual EoM in Newtonian gravity, which follows the non-uniform scaling implied by Kepler's 3rd law), together with the well-known Tully-Fisher law. (Newbies tend to ignore, or be unaware of, the importance of the latter phenomenon.)

See this MOND paper which explains why these two pieces of phenomena severely restrict the ways that one might fruitfully modify the Newtonian (or even GR) equations of motion.

 

[strangerep]

Wouldn't the change in gravitational potential be significantly different for a 3D sphere (where the mass is evenly distributed in 3-space and as we move in 3 dimensions, the calculation is ^3) vs a flat surface (where the mass isn't evenly distributed in 3-space and so it's ^2)?

You can get a feel for the difference by just looking at the Newtonian case -- where the non-relativistic gravitation (Poisson) equations are solved for various mass distributions. This is explained in considerable detail at Bovy's Galactic Dynamics Online Book, especially ch8 et. seq.

 

[Ibix]

I wouldn't call it "solid". Not at all. See the Deur thread over in BTSM.

In the context of this thread I was merely meaning that it was a fleshed-out mathematical proposal from a serious physicist, as opposed to the "hey wouldn't it be cool if..." idea in this thread which can be dismissed with an order of magnitude calculation. I suspect I'm not qualified to have an opinion on Deur's idea's plausibility.

 

[strangerep]

In the context of this thread I was merely meaning that it was a fleshed-out mathematical proposal from a serious physicist, [...]

I don't think it's "fleshed out".

But I hope other people here with good proficiency in GR will take a closer look at it, and offer their well-considered opinions on this point.

 

[Vanadium 50]

The fact that "dark matter" is proportional to the visible mass is

This is not a fact. The mass-to-light ratio for galaxies varies by quite a bit: more than a factor of about 5.

 

[malawi_glenn]

This is not a fact. The mass-to-light ratio for galaxies varies by quite a bit: more than a factor of about 5.

Another missuse of "proportionality" :(

 

[Vanadium 50]

Well, you can always divide any two quantities A by B and say "look, they are proportional!" Just not sure where that gets you.

 

[Musant]

So the claim is that even with a difference in mass density on the order of 10^8 between the region of the core of the galaxy and the solar neighborhood for example, the difference in time dilation and length expansion is negligible. Hard to believe.

 

[PeterDonis]

Hard to believe.

You don't have to "believe". You can do the math and see. Or you could just read the earlier posts in this thread where the math is already done.

 

[PeroK]

So the claim is that even with a difference in mass density on the order of 10^8 between the region of the core of the galaxy and the solar neighborhood for example, the difference in time dilation and length expansion is negligible. Hard to believe.

Perhaps you've watched Interstellar too many times.

 

[Musant]

You don't have to "believe". You can do the math and see. Or you could just read the earlier posts in this thread where the math is already done.

The time dilation factor I had seen previously, and the one I usually consider is simply SQRT(1-2GM/(rc^2)).

Question for you: In a time dilated reference frame where the time units of c are dilated, shouldn't one also expand units length such that c remains constant? If so, wouldn't the radius term in the expression for time dilation factor be a function rather than a constant?

 

[PeterDonis]

The time dilation factor I had seen previously, and the one I usually consider is simply SQRT(1-2GM/(rc^2)).

This is for a single spherically symmetric gravitating body. As was already pointed out earlier in the thread (which, btw, is almost two years old), a galaxy does not even come close to meeting that description.

In a time dilated reference frame where the time units of c are dilated

What does this even mean?

 

[Musant]

This is for a single spherically symmetric gravitating body. As was already pointed out earlier in the thread (which, btw, is almost two years old), a galaxy does not even come close to meeting that description.


What does this even mean?

I apologize if that wasn't clear. The units of c are, for example, in meters per second. Time dilation affects the length of a second. We assume that light always travels the same number of meters per second in a vacuum. So if the second is longer, then light would travel a greater number of meters in that longer interval. It follows that when time is dilated, length should also 'dilate' in order that the constant c remain constant. But, I'm happy to be shown the error in that logic. Thank you for your courteous replies.

 

[PeterDonis]

Time dilation affects the length of a second.

No, it doesn't. Time dilation amounts to a comparison of arc lengths along different timelike worldlines. Those arc lengths are measured in the same seconds along both worldlines.

I'm happy to be shown the error in that logic.

Your starting premise is wrong. See above.

 

[Musant]

No, it doesn't. Time dilation amounts to a comparison of arc lengths along different timelike worldlines. Those arc lengths are measured in the same seconds along both worldlines.


Your starting premise is wrong. See above.

But you might find that the two things 'amount' to the same.

 

[PeterDonis]

But you might find that the two things 'amount' to the same.

No, you won't.

At this point I am closing the thread since we are already off topic, and it's two years old anyway. @Musant, I would strongly encourage learning more about how relativity actually works.