# Speed of time immediately after big bang relative to now?

1. Nov 29, 2012

### Ipm

Can someone answer this for me please: is it possible to work out how much time has elapsed for a theoretical (and for argument's sake, mass-less) observer at the centre of the big bang whose speed of time then subsequently remained constant (rather than massively speeding up with the rest of the universe)? *Or to put it another way, if there were a (again mass-less!) stopwatch that carried on ticking at the same speed as it's first second during the big bang, how much time would have elapsed on it until our now?

2. Nov 29, 2012

### phinds

I can't answer your question about time, but you are polluting it with the false premise that there was a center to the big bang. There was not.

3. Nov 29, 2012

### Ipm

Ok, how can I ask the same question without the false premise? A stopwatch somewhere within the newly existing universe?

4. Nov 29, 2012

### Ipm

Or perhaps a more simple question to get the ball rolling - how slow was time in it's first second compared to time on earth now? A million times slower? A billion?...?

5. Nov 29, 2012

### phinds

Why do you think it was any different?

6. Nov 29, 2012

### Staff: Mentor

Why do you think that the "speed of time" has "massively speeded up" since the Big Bang? "Speed of time" is not a standard concept in relativity or cosmology, so you'll have to explain what you mean by it, and why you think it has changed.

7. Nov 29, 2012

### Staff: Mentor

A second is a second. It's a unit of time. How can it "change"?

8. Nov 29, 2012

### bcrowell

Staff Emeritus
9. Nov 30, 2012

### 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.)

10. Nov 30, 2012

### FalseVaccum89

I think I know what the OP's getting at: Per GR, high local spacetime curvature has the same effect on duration as accelerating closer and closer to the speed of light does in SR.

Though, I'm unsure whether this translates to a situation involving high *global* spacetime curvature.

/my two cents

11. Nov 30, 2012

### Ipm

Thanks, Warp - it is precisely that difference that I'd be interested in - so perhaps I can make the question more precise to make this easier(!)
- if A were an observer on the edge of the expansion in the first second after the big bang, presumably going ridiculously fast (faster than the speed of light?), would A's second be much slower than a second that we experience on the earth's surface now? And if so, do we know precisely how much slower?

12. Nov 30, 2012

### phinds

There is no edge. There is no center. Say this to your self over and over. There is no edge. There is no center.

And as for speed, you have to specifiy relative to what? . Speed is not a meaningful concept unless you say what it is that you are measuring the speed relative to.

13. Nov 30, 2012

### Ipm

2 observers in the first second after the Big Bang, both moving away from each other at enormous speed. Each perceives themselves to be stationary, but thinks of the other as moving away very very fast. What is the relative measurement of a second for each of them, but from the point of view of only one of them?
Ie: I'm stationary, my own second naturally equals one second. My pal, increasingly a long way away and going very fast, his second looks to me as though it equals...???

14. Nov 30, 2012

### Staff: Mentor

This statement isn't as general as you appear to think it is. It only applies in special cases, where there is some common reference for comparing "rates of time flow". For example, if you are sitting at rest on the surface of a neutron star, say, and I am floating in space far away from the neutron star and at rest relative to it and you, then we can meaningfully compare our "rates of time flow" and see that yours is slower than mine.

If you have a colleague who is in orbit around the neutron star, it's more complicated, but we can still do the comparison. The key is that, because your colleague is in orbit, i.e., his motion is periodic, we can use some periodic event that happens once per orbit (such as when he passes directly overhead relative to you) as a reference to compare rates of time flow between him and you (and therefore between him and me).

All that breaks down in a more general case, however; you and your colleague and I can't meaningfully compare our rates of time flow to that of an observer that's near a quasar a billion light years away and moving away from us due to the expansion of the universe, because we are not at rest relative to each other, and there is no periodic phenomenon we can use as a common reference.

15. Nov 30, 2012

### Warp

This is actually something that has always evaded my comprehension, possibly because my limited brain is unable to visualize 4-dimensional space. What exactly is the geometry of the universe?

Let's assume that the universe were not expanding so fast, and that you could reach any point in the universe if you so wished. What happens if you just move away from Earth indefinitely?

(Or is the geometry of the universe, perhaps, actually tied to the expansion rate?)

16. Nov 30, 2012

### phinds

The topology of the universe is not known.

Givem that the rate of expansion is now far in excess of c even for just the observable universe, you can't even reach "any" point in the observable universe much less the entire universe, WHATEVER its topology. Assuming otherwise doesn't help solve the problem of figuring out what IS the topology of the actual universe.

EDIT: there ARE proposed topologies that would allow you too see the back of your head IF light were infinite in speed ... this is the class of "finite but unbounded" topologys.

17. Nov 30, 2012

### Warp

Then how can one say "there's no center" if the exact topology is unknown?

Making claims about the topology ("no center") is contradictory with the claim that we don't know said topology.

18. Nov 30, 2012

### Staff: Mentor

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.

19. Nov 30, 2012

### 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. ("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?)

20. Nov 30, 2012

### Staff: Mentor

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.