Speed of time immediately after big bang relative to now?

[PeterDonis]

as we're using the term spacetime - does this imply that the rate of time is also related to (affected by) the 'size' of the space it is in? Ie: does time move slower in a more expansive bit of the universe compared to a more concentrated bit of space? And therefore as the universe is expanding would that mean that the experience of time somewhere in distant space (ie not in eg the solar system) is gradually changing?

As I said in an earlier post, in an expanding universe, there is no common point of reference that can be used to compare "how fast time is moving" in distant locations. So the questions you are asking don't really have a well-defined answer.

 

[Ipm]

Time passes at different speeds depending on the geometry of spacetime. Time on the surface of the Earth has a different speed than time on orbit, and a different speed than between stars.
You can measure the difference and say that "1 second here is 0.9 seconds there". So it can be different.
(IIRC the deeper you are in a gravity well, the slower your time passes in relation to the rest of the universe.)

As I said in an earlier post, in an expanding universe, there is no common point of reference that can be used to compare "how fast time is moving" in distant locations. So the questions you are asking don't really have a well-defined answer.

Ok, but I'm thinking it must be theoretically possible to get a reasonably well-defined answer (albeit not easily, of course):
If we can measure the relative time dilation between the different spacetime geometries of the Earth's surface and any given star, then presumably if we know (or can estimate) the mass of the Earth and the mass of the star (and therefore estimate the different distortions or contractions of spacetime geometry in those two gravitational fields) then surely it is possible to work out the relationship between gravitational impact on spacetime geometry and the resulting impact on time dilation?
[I'd be very grateful if anyone could point me to any actual figures/data on this!].

And if that is possible, then is it not conceivable that someone could attempt to estimate the
time dilation related to the expansion of spacetime itself, at different stages of the universe's size/density? Although this time dilation can't be experienced, nor can it be directly measured (it all being in the past), surely there must be a way of working out mathematically what the probable difference is in average rates of time between an isotropic universe of one size (small) and the same isotropic universe at some time later (vast)?
This seems a logical question to me, if time is directly related to the space in which you are measuring it (surely that is what general relativity is all about?)?

 

[PeterDonis]

If we can measure the relative time dilation between the different spacetime geometries of the Earth's surface and any given star

You can do this if the Earth and the star are at rest relative to each other; if they are in relative motion, doing this will only be an approximation, and how good an approximation will depend on the relative velocity. As long as you're OK with the approximation, yes, you can compare time dilations and therefore masses this way. For example, I believe the gravitational redshift of light coming from the Sun has been measured, giving an estimate of its mass. (The light from the Sun does blueshift slightly as it "falls" into Earth's gravity well, but that effect is too small to affect the calculation of the Sun's mass--which is another way of saying that the Earth's mass is very small compared to the Sun's.)

But all of this depends on having some common point of reference; for example, the measurement of the Sun's mass by the above method implicitly relies on a hypothetical "point of reference" that is very far away from the Sun and the Earth and all other gravitating bodies, and at rest relative to the Sun and the Earth, to serve as a point of "zero time dilation".

And if that is possible, then is it not conceivable that someone could attempt to estimate the time dilation related to the expansion of spacetime itself, at different stages of the universe's size/density?

Here there is no common point of reference that we can use, so the method described above does not work.

This seems a logical question to me, if time is directly related to the space in which you are measuring it (surely that is what general relativity is all about?)?

Not quite. GR is about spacetime, yes, but that's not the same as saying that "time is directly related to the space in which you are measuring it". Spacetime just means that you can't separate space from time, because of the relativity of simultaneity: if I am moving relative to you, then events which happen at the same time for you do not happen at the same time for me. So what to you looks like pure "separation in space", to me looks like a combination of "separation in space" and "separation in time".