What is the calculational definition of the 'big bang'?

[pellman]

You sometimes see statements regarding so-many-minutes after the big bang. Or 10^-23 seconds after the big bang. But this exactly is the event this is measuring from? How is it defined? I presume it has some definition from within the framework of general relativity.

 

[Chronos]

It's a scale factor thing. When you run the math backwards you find that temperature increases, and temperature tells us what processes were ongoing. It is rather simple to calculate the time after the big bang [i.e., since t=0] this way.

 

[pellman]

But how is t=0 defined? That's really what I'm asking (I think).

 

[Naty1]

t = 0 is the moment of the actual big bang...not the models we actually use which start moments later. Nobody knows exactly what the big bang itself was...

graphical timeline here:

http://en.wikipedia.org/wiki/Graphical_timeline_of_the_Big_Bang

another timeline here:

http://en.wikipedia.org/wiki/Graphical_timeline_from_Big_Bang_to_Heat_Death

 

[Drakkith]

But how is t=0 defined? That's really what I'm asking (I think).

I think t=0 is simply the point where our math cannot describe the universe adequately due to failures in our understanding of physics at such extreme energy levels.

 

[Chronos]

t=0 is the instant when the big bang occurred - which is also the point at which all of our theories are rendered completely useless.

 

[pellman]

t=0 is the instant when the big bang occurred - which is also the point at which all of our theories are rendered completely useless.

ok, so we've established that the big bang is t=0 and t=0 is the big bang. But what does it mean? What is special about t=0? can that condition be stated in terms of observable quantities? Temperature, density, etc.

As long we're considering time scales on the order of years, it doesn't much matter. But if we talk about the state of the universe 1 second "after the big bang", we must have some physical definition of what that means. Why not call that time t=0? What's 1 second more or less?

 

[Drakkith]

ok, so we've established that the big bang is t=0 and t=0 is the big bang. But what does it mean? What is special about t=0? can that condition be stated in terms of observable quantities? Temperature, density, etc.

No. The math breaks down and no longer makes accurate predictions at t=0.

 

[pellman]

No. The math breaks down and no longer makes accurate predictions at t=0.

This is circular. You have to know what you mean by t=0 before you can something about it like "the math breaks down."

I'm looking at a line in my old copy of Joseph Silk's The Big Bang, chapter titled The First Millisecond, in which he says at about 10^-23 seconds the size of the observable universe "is the dimension of an atomic nucleus, or about one ten-thousand-billionth of a centimeter."

That statement must be calculated from something. Maybe it is the time when a(t) in the Friedmann–Lemaître–Robertson–Walker metric is equal to zero? Something like that? You guys are making me do all the work. :)

 

[marcus]

ok, so we've established that the big bang is t=0 and t=0 is the big bang. But what does it mean? What is special about t=0? can that condition be stated in terms of observable quantities? Temperature, density, etc.

As long we're considering time scales on the order of years, it doesn't much matter. But if we talk about the state of the universe 1 second "after the big bang", we must have some physical definition of what that means. Why not call that time t=0? What's 1 second more or less?

well there are issues of mathematical convenience but apart from that it does seem to be a conventional time-marker and you could do what you are suggesting and establish a new
"t = 0" in such a way that the classical model (without quantum corrections) fails exactly at "t = -1".
So then the classical model would give definite numbers back to but not including "t = -1"

The fact that it is an arbitrary time-marker was discussed in a public outreach essay at the "Einstein Online" website of the AEI (a national research institution in Germany). the essay was called "A Tale of Two Big Bangs".
http://www.einstein-online.info/spotlights/big_bangs

Nowadays at the major conferences on general relativity and cosmology many of the papers are about non-singular cosmic models intended to replace the classical one that has the breakdown at t=0. These newer models go farther back in time.
They still use the same timescale (no reason not to), they simply do not break down at t=0, so there is a finite predicted density at the moment of rebound (or whatever the model says is going on at the start of expansion).

It isn't true that all our theories are rendered completely useless at t=0 since there is a strong trend in research to work out TESTABLE models that go farther back in time and do not fail at t=0. This is as useful as any other progress in cosmology---understanding more about the universe we see around us, constructing mathematical models, and checking the against observation.

 

[martinbn]

I thought that in the corresponding model (FLRW) the isotropic observers' world lines have finite length in the past i.e. finite proper time. So t=0 is that much time in the past as the length of your world line. Of course that is not part of the manifold.

May be this analogy would help. Thing of the upper half of the usual plane i.e. points with coordinate y>0. Then although points with y=0 (or less) are not part of this set it still makes sense to say that a particular point has y=14 billion for example or y=10^{-42} and so on.

 

[Chalnoth]

You sometimes see statements regarding so-many-minutes after the big bang. Or 10^-23 seconds after the big bang. But this exactly is the event this is measuring from? How is it defined? I presume it has some definition from within the framework of general relativity.

The time t=0 is basically a matter of convenience. This time is determined by simply assuming that General Relativity is absolutely correct (no quantum gravity), the universe is composed of matter, radiation, and dark energy, and nothing else, and extrapolating back in time to the point where there is a singularity. This time is t=0.

Now, this physical picture is incorrect. We know that this simple process of extrapolating back in time cannot possibly be correct if you go far enough back, either because some other form of energy was significant for the very early universe (e.g. inflation), or because quantum gravity was important early-on, or a combination of the two. The problem is, without knowing the precise behavior of the very early universe, we can't set a "t=0" that corresponds to an actual event. So instead we just set it to a convenient time based on an incorrect model.

Fortunately, this isn't likely to be very misleading. If we imagine that the model that describes the very early universe as being inflation, for example, then a reasonable "t=0" would be the event known as reheating, when inflation ended and the classical big bang model became valid. We don't know exactly when this event occurred, but it isn't going be different from the classical "t=0" time by more than a few times $10^{-30}$ or so. That is small enough of a difference that it doesn't really matter much for most any later events we might deign to think about.

Other early universe models tend to have similar events that differ little enough from the classical t=0 that we don't need to worry about those differences either.

So in the end, a good way to understand t=0 is to imagine it as the time that the classical big bang theory became an accurate description of the universe, give or take a few times $10^{-30}$ seconds.

 

[pellman]

Thanks, guys.