Time dilation (split from The speed of time)

[md65536]

On 8/24/2022 at 7:37 AM, swansont said:

We know time depends [...] on your gravitational potential 

Gravitational potential is only meaningful in some simpler metrics like Schwarzschild.

Assuming our universe is flat on the largest scales, do we say it's flat because it has uniform mass distribution, and is that independent of the total mass? Then, assuming it's flat and that the big bang happened, theoretically it was always flat? Or is it flat specifically because it has very little average density, and wasn't always flat?

 

On 8/24/2022 at 8:42 AM, joigus said:

What is the standard clock against which time is seen to change?

If what I wrote above makes sense, you'd be trying to compare a clock in flat spacetime, to a clock in flat spacetime after inflation. Could it make sense to do it with a Doppler analysis? If you compared clocks at different places, the Doppler shift would mostly be due to inflation, but would there also be a gravitational shift over time even for a single inertial clock?

If gravitational time dilation requires curvature, and the curvature of the universe didn't change in general, then I would guess there's no measurable change in the rate of time for an inertial clock (in the general case) now relative to the same clock earlier, and no theoretical change either.

Edited August 25, 2022 by md65536

[swansont]

1 hour ago, md65536 said:

Gravitational potential is only meaningful in some simpler metrics like Schwarzschild.

!

Moderator Note

Given the question in the other thread, I think this is well beyond that scope, and the questions are not directed at the OP, so I split this discussion off

 

[joigus]

5 hours ago, md65536 said:

Gravitational potential is only meaningful in some simpler metrics like Schwarzschild.

Assuming our universe is flat on the largest scales, do we say it's flat because it has uniform mass distribution, and is that independent of the total mass? Then, assuming it's flat and that the big bang happened, theoretically it was always flat? Or is it flat specifically because it has very little average density, and wasn't always flat?

Ok. I will try to think about this more carefully tomorrow. Or more likely, over the weekend.

But flatness of the universe, as commonly expressed in cosmology books, seminars, etc., refers to spatial flatness. Not to Doppler effect. Doppler effect has to do with ratios d(tau)/dt; that is, proper time over coordinate time. It's, for lack of a better word, some kind of "time curvature". Flatness of the universe refers to flatness of the spatial sections of it.

Because the question stemmed from a post on "velocity of time", and you mention Doppler effect, I think there might be the rub. Does that make sense to you?

 

[md65536]

2 hours ago, joigus said:

But flatness of the universe, as commonly expressed in cosmology books, seminars, etc., refers to spatial flatness. Not to Doppler effect. Doppler effect has to do with ratios d(tau)/dt; that is, proper time over coordinate time. It's, for lack of a better word, some kind of "time curvature". Flatness of the universe refers to flatness of the spatial sections of it.

Oops, I was thinking of gravitational redshift and often mistakenly call it gravitational Doppler shift. I was assuming that if there was a difference in the rate of time due to inflation, it would be due to a change in spacetime curvature. Can there be spatial flatness, but curved time, with a constant speed of light? Or would a changing rate of time require a changing speed of light? 

 

2 hours ago, joigus said:

Because the question stemmed from a post on "velocity of time", and you mention Doppler effect, I think there might be the rub. Does that make sense to you?

I think it does. I assumed "speed of time" meant rate, and interpreted it to mean "How would the rate of a clock now compare to the rate of the same clock shortly after the big bang (assuming the most general case possible)?" The more I think about it the less sure I am that it even makes sense to ask.

For example it makes sense to say, "I've aged one year less than my twin because of those two years (Earth time) I spent traveling when I aged at half the rate that I'm aging now," but this only makes sense with that second clock to compare to. In another frame, I'm aging at a half rate now, relative to some time I was traveling. Trying to "define things in a vacuum" as you mentioned, I was always aging 1 yr/yr and never aged slower. But then again!, I can just treat myself now and in the past as 2 different clocks and I can compare them, basically label my past self my "twin", and it's fine to say my past self in a different reference frame aged slower relative to me now, and for my past self to say "my future self will age slower relative to me now!"

But back to the case of inflation, I was thinking maybe it's possible to measure your own past clock relative to your current clock. For example if you could define a light clock where the only thing that changes over time is gravitational time dilation (is that even possible to do?), then there might be a red or blue shift occurring in the light clock over time. But how? For example you could make the clock inertial, and say it has 2 mirrors and you keep the mirrors relatively stationary throughout time. But if space is expanding during that time, keeping them stationary for one observer (you) means moving the mirrors according to another observer, so are you really making gravitational time dilation the only thing that affects the redshift? Anyway I got stuck without figuring that out. Without a way to measure it, I can't make sense of what it means to compare the rate of a clock in the past with itself now.

Using another clock to compare to is fine, the "standard clock" you asked for, but like you say: how? For example in flat spacetime in SR you can define a reference clock free from the effects of time dilation simply by making it inertial. But how would you bring a reference clock through an era of inflation without having it affected by it?

Edited August 26, 2022 by md65536

[swansont]

10 hours ago, md65536 said:

But back to the case of inflation, I was thinking maybe it's possible to measure your own past clock relative to your current clock. For example if you could define a light clock where the only thing that changes over time is gravitational time dilation (is that even possible to do?), then there might be a red or blue shift occurring in the light clock over time. But how? For example you could make the clock inertial, and say it has 2 mirrors and you keep the mirrors relatively stationary throughout time. But if space is expanding during that time, keeping them stationary for one observer (you) means moving the mirrors according to another observer, so are you really making gravitational time dilation the only thing that affects the redshift? Anyway I got stuck without figuring that out. Without a way to measure it, I can't make sense of what it means to compare the rate of a clock in the past with itself now.

Using another clock to compare to is fine, the "standard clock" you asked for, but like you say: how? For example in flat spacetime in SR you can define a reference clock free from the effects of time dilation simply by making it inertial. But how would you bring a reference clock through an era of inflation without having it affected by it?

You seem to be switching between expansion and inflation as if they are the same thing, and they aren't.

They have measured time dilation owing to expansion by comparing the light curves of type Ia supernovas, and of quasars.

[md65536]

8 hours ago, swansont said:

You seem to be switching between expansion and inflation as if they are the same thing, and they aren't.

They have measured time dilation owing to expansion by comparing the light curves of type Ia supernovas, and of quasars.

Then I'll stick to expansion, unless inflation gives different answers to the main questions.

You're talking about time dilation between distant clocks, right? But that doesn't say anything about how a clock compares to itself in the past.

 

Also, the original topic isn't just whether expansion of space on its own would cause a clock to change its rate. I can't see any reason to think it would, because locally nothing's changed. Rather, could the changes in our universe's past caused by expansion, change the rate of a clock? Or more generally, would a clock in a uniform (flat?) space with very high density of matter, tick differently than a clock in a uniform space with low mass density? And if there's no way to connect the two to compare them, without some curved space in between, could they describe the same clock before and after expansion, and be compared? 

[swansont]

4 hours ago, md65536 said:

You're talking about time dilation between distant clocks, right? But that doesn't say anything about how a clock compares to itself in the past.

A clock will read a later time, of course. What does that have to do with expansion?

[md65536]

http://curious.astro.cornell.edu/about-us/102-the-universe/cosmology-and-the-big-bang/the-big-bang/586-did-time-go-slower-just-after-the-big-bang-advanced

has the closest to an answer that I've found so far. From there:

Quote

"clocks run slower in a deep gravitational field than they do in a shallower gravitational field". So it's true that if you compare a clock in the present epoch to a hypothetical clock in the early universe, just after the Big Bang, you'll find that time ran "slower" in the early universe because the mass density was so high. But does such a statement have any physical meaning?

Not much. At the time when it was so dense that time went appreciably "slower", the whole Universe had that high density. So some hypothetical observer wouldn't notice anything strange, as they'd have no way of comparing their clocks to someone in a low density universe.

It seems everyone agrees there's not a lot of physical meaning to comparing such clocks.

I don't understand "clocks were slower because mass density was so high" enough to believe it. A "shallow gravitational field" doesn't make sense to me, I think he means higher relative gravitational potential, but like in the first post I'm not sure that gravitational potential even makes sense here.

It seems that to compare the "gravitational depth" here, it would be more correct to compare "the metric tensor of the universe in local coordinates of a clock in the past, to the metric tensor in local coordinates of a clock in the present." Is that the right way to say it? It still makes no sense to me, because if you could compare those, why can't you just compare the clocks?

But basically it sounds like evolving from a high density uniform universe to a lower density uniform universe due to expansion of space, can be considered to be moving to a higher gravitational potential --- and when I write it like that it sounds just plain wrong because there's nowhere to fall to, where the gravitational potential is relatively lower. However it seems like it would be measured as if it was the same, for example light from an older clock would redshift as it traverses through expanding space, losing energy as if it were climbing out of a gravitational well. So, I'm still confused.

 

Edit: Or is it, the metric in local coordinates of a modern clock, could tell you the gravitational (only) time dilation factor between the two clocks? Or is it pointless to talk about metrics without a better understanding first?

Edited September 13, 2022 by md65536