Blog Entries: 9
Recognitions:
Gold Member

Speed of time immediately after big bang relative to now?

 Quote by Warp Making claims about the topology ("no center") is contradictory with the claim that we don't know said topology.
We don't know the topology precisely, but we know enough about it to say that there is no center. All of the possible topologies share the property that space, on average, is homogeneous and isotropic; all spatial points are the same. A "center" would violate that property by picking out one particular spatial point as different from the others.
 Anyways, I would still like to know what exactly would happen if the universe were not expanding so fast, and you were to just traverse away from Earth indefinitely. ("The universe does not expand like that" only sounds like evading the question rather than answering it. If a different expansion rate would affect the topology, then what would that topology be, and what would happen in that situation?)

Blog Entries: 9
Recognitions:
Gold Member
 Quote by Warp Anyways, I would still like to know what exactly would happen if the universe were not expanding so fast, and you were to just traverse away from Earth indefinitely.
There are basically two possibilities:

(1) If the universe is closed (this is the "finite but unbounded" topology that phinds referred to), then if you flew off in some direction, and kept on flying without ever changing direction, eventually you would return to your starting point. In other words, the spatial topology of the universe in this case is the topology of a 3-sphere, similar to the way the Earth's surface has the topology of a 2-sphere, so if you start off in some direction on the Earth and never change direction (meaning you follow a great circle), you will eventually return to your starting point.

(2) If the universe is open, then it is spatially infinite, so the spatial topology is that of Euclidean 3-space (though the spatial *geometry* may not be Euclidean). In this case, if you flew off in some directly and kept on flying without ever changing direction, you would just go on and on forever.

Our current best-fit model has the universe being open, but there is enough uncertainty in the data that it's still possible for it to be closed.
 Recognitions: Gold Member I would add to what Peter said that 1) expansion and topology are not necessarily linked in any way 2) even in the finite but unbounded topology, you MIGHT not be able to ever get back to where you started, not because you are not pointed in that direction, but becuase you can't travel faster than c but the expansion can so the point where you started could be moving away from you faster than you can travel.
 What does the phrase "speed of time" even mean????

 Quote by PeterDonis (1) If the universe is closed (this is the "finite but unbounded" topology that phinds referred to), then if you flew off in some direction, and kept on flying without ever changing direction, eventually you would return to your starting point. In other words, the spatial topology of the universe in this case is the topology of a 3-sphere, similar to the way the Earth's surface has the topology of a 2-sphere, so if you start off in some direction on the Earth and never change direction (meaning you follow a great circle), you will eventually return to your starting point.
Wouldn't that mean that there's a point in the universe that's the farthest away from Earth that's possible (and any direction you could choose from there would make you go towards Earth)? Could this maximum distance be considered the size of the universe?

 Our current best-fit model has the universe being open, but there is enough uncertainty in the data that it's still possible for it to be closed.
But I thought the universe is finite. How can it have been a singularity that expanded if it's not finite?

Blog Entries: 9
Recognitions:
Gold Member
 Quote by Warp Wouldn't that mean that there's a point in the universe that's the farthest away from Earth that's possible (and any direction you could choose from there would make you go towards Earth)? Could this maximum distance be considered the size of the universe?
Yes, in the case of a closed universe there is a "size", just as there is a size of the Earth's surface (its circumference). The size changes with time as the universe expands.

 Quote by Warp But I thought the universe is finite. How can it have been a singularity that expanded if it's not finite?
You're assuming that the singularity is "finite", or that it is a "point". It's not. By which I mean, the topology of the singularity is not the topology of a point. However, that probably doesn't make things much clearer. I'm not sure I can explain this quickly, and I don't have time to explain it long-windedly right now. Instead, I recommend taking a look at Ned Wright's cosmology tutorial:

http://www.astro.ucla.edu/~wright/cosmo_01.htm

Section 3 is probably the most relevant to this discussion, but I would recommend starting at the beginning and working through all of it. It's a good overview of our current model of the universe and the Big Bang, and it also talks about the actual observations on which the model is based, which a lot of treatments don't really get into.

 Quote by PeterDonis You're assuming that the singularity is "finite", or that it is a "point". It's not. By which I mean, the topology of the singularity is not the topology of a point.
A singularity can be infinite? Would that make it an infinite line or surface? (Hmm, could it be an infinite 4-dimensional surface?)

Do I understand correctly, however, that a singularity has zero volume? (Or can there be a singularity with non-zero volume?)

Blog Entries: 9
Recognitions:
Gold Member
 Quote by Warp A singularity can be infinite? Would that make it an infinite line or surface? (Hmm, could it be an infinite 4-dimensional surface?)
It's not quite that a singularity can be infinite; it's that the *topology* of the singularity, which you have to define via some kind of limiting process (see further comments below), may be something infinite like a line or a surface instead of a point.

 Quote by Warp Do I understand correctly, however, that a singularity has zero volume? (Or can there be a singularity with non-zero volume?)
The Big Bang singularity does have zero volume, in the sense that if I take the limit of the volume of the universe at time t, as t -> 0 (where t = 0 is the Big Bang), the volume goes to zero.

However, that in itself isn't enough to tell me the topology of the singularity, because there are other limits I can take as t -> 0 that tell a different story. That gets into the stuff I don't really have the time to go into detail about.

Recognitions:
Gold Member
 Quote by Warp A singularity can be infinite? Would that make it an infinite line or surface? (Hmm, could it be an infinite 4-dimensional surface?) Do I understand correctly, however, that a singularity has zero volume? (Or can there be a singularity with non-zero volume?)
Singlarity in the cosmological sense does not mean "point" it means "the place where our models/math break down and we don't know WHAT is happening". I often see it said here on this forum that the "singularity" of the big bang could well have been infinite in extent.

 Quote by phinds 1) expansion and topology are not necessarily linked in any way
Or maybe they are. The assumption that universal topology affects expansion rate seems to me to be a pretty reasonable one. But, as you suggest, no way to know.

 Quote by phinds Singlarity in the cosmological sense does not mean "point" it means "the place where our models/math break down and we don't know WHAT is happening".
This the the way I've always thought about it. Not that anyone should pretend to 'know' what's happening anyway, but "singularity" refers to the point beyond which there is no meaningful (not necessarily scientific, but meaningful in the sense of being based on current accepted mathematical physics) mathematical extrapolation.
 Back to the rate of time - and ignoring speed of travel for a bit now... 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? And conversely, immediTely after the Big Bang when the universe was much much much smaller, would time by definition generally have been much slower? And at the moment of the big bang itself time generically went from non-existent to remarkably slow (in the initial stage of expansion presumably there was a vast amount of concentrated mass) to gradually faster and faster...?

Blog Entries: 9
Recognitions:
Gold Member
 Quote by Ipm 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.

 Quote by Warp 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.)
 Quote by PeterDonis 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?)?

Blog Entries: 9
Recognitions:
Gold Member
 Quote by Ipm 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".

 Quote by Ipm 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.

 Quote by Ipm 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".