Speed of time immediately after big bang relative to now?

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?

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.

Ipm

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

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?...?

phinds

Why do you think it was any different?

PeterDonis

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.

PeterDonis

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

bcrowell

We have a FAQ about this: http://www.physicsforums.com/showthread.php?t=506990

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.)

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

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?

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.

Ipm

Ok... How about this:
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...???

PeterDonis

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.

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?)

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.

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.