Big Bang

[Solanalos]

I want to understand it better. I would appreciate corrections to the following (my understanding of it) if need be.

1. The Big Bang occurred everywhere in the universe and everything that now exists (matter, energy, spacetime) comes from it.

2. The Big Bang began at a point of singularity and expanded from there.

3. The universe in it's early stages was small.

How can the universe be infinite if it was at one time finite?

If my above understanding of the early universe and the Big Bang is correct, that is the question that sticks out at me. Here's what I need to know: Does spacetime come from the Big Bang or not? Is the Big Bang an explosion in spacetime or is spacetime within the Big Bang?

The only way I can see the possibility of an infinite universe is if spacetime preexisted the Big Bang and was already infinte. I can't understand how something can "make the jump" from finite to infinite?! :confused:

I'm probably missing something fundamental, but that's why I made this post. Thanks in advance for filling me in. :)

[Kalkin]

Yes, you are missing something fundamental. According to modern cosmology, the universe is not infinite. (I think.);)

[Solanalos]

Originally posted by Kalkin
Yes, you are missing something fundamental. According to modern cosmology, the universe is not infinite. (I think.);)

I'm under the impression that the jury is still out on this.

[wade-w]

I'm certainly no cosmologist, but mathematically, a space can be infinite, but still be bounded.

[Lobstrosity]

Originally posted by Kalkin
Yes, you are missing something fundamental. According to modern cosmology, the universe is not infinite. (I think.);)
I believe it is considered infinite by modern cosmology in that there's no boundary out there that we'll one day reach if we go far enough. The universe is assumed homogeneic and isotropic, which, as far as I know, would proclude the existence of boundaries. The only way it could be finite in extent is if the universe were closed (geometrically speaking). In such a universe you would (in theory) eventually come back to where you started if you travel far enough in a "straight" line. The only caveat is that such a universe would collapse in on itself more quickly that it would be possible to complete a round trip, so in practice you'd never be able to pull it off. At any rate, WMAP seems to strongly indicate that the universe is flat, which according to modern cosmology means an infinite Euclidian 3-space. (The third possibility is an open universe, which would be a 3-dimensional hyperboloid embedded in an abstract 4-dimensional Lorentzian space. An open universe would also be infinite in extent, in theory.)

[Kat_Somm_Faen]

Naw,

the Universe ( at least the observable to the surface of last scattering ) is quite finite. It is just reeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeee eeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeely big ( well its bigger than that I just did not feel like putting in all the billions of e using up all the space on the boards :D ).

Yeah it should be in the teens of billions light years across. I believe 14-16 billion light years range. Someone please feel free to correct me if I am wrong. Its a closed system, flat geometry and apparently bound to be forever expanding.

[Solanalos]

Originally posted by wade-w
I'm certainly no cosmologist, but mathematically, a space can be infinite, but still be bounded.

Are you talking a closed infinity like ending up where you started if you went far enough? I guess I can kind of see that. Even then, though, it would seem an added, unnecessary condition of spacetime. Then again, I'm no cosmologistm, either (or mathematician for that matter) - just your run-of-the-mill armchair scientist. I know common sense has little place in the realms of quantum mechanics and cosmology.

[Kat_Somm_Faen]

I believe wade is thinking of infinite sums ( or parts ) still making a finite quantity... Kinda like one of the Zeno's paradox explanations.

Am I right, wade?

[Solanalos]

Originally posted by Lobstrosity
I believe it is considered infinite by modern cosmology in that there's no boundary out there that we'll one day reach if we go far enough. The universe is assumed homogeneic and isotropic, which, as far as I know, would proclude the existence of boundaries. The only way it could be finite in extent is if the universe were closed (geometrically speaking). In such a universe you would (in theory) eventually come back to where you started if you travel far enough in a "straight" line. The only caveat is that such a universe would collapse in on itself more quickly that it would be possible to complete a round trip, so in practice you'd never be able to pull it off. At any rate, WMAP seems to strongly indicate that the universe is flat, which according to modern cosmology means an infinite Euclidian 3-space. (The third possibility is an open universe, which would be a 3-dimensional hyperboloid embedded in an abstract 4-dimensional Lorentzian space. An open universe would also be infinite in extent, in theory.)

I must be missing something. If everything was once in the finite conditions of the early universe, how is it a flat infinity now?

Edit: Why isn't it just an ever expanding finity?

[EGGO]

I guess we can look at a seed growing into a giant redwood as a parallel?

Well maybe not...the seed DOES need some sort of nurturing.

[Gothic_J]

I was told something freaky recently - the universe is finite, but is shaped like an egg, so you wont notice. the surface of the egg is zillions of galaxies, and inside is empty space, where the galaxies used to be.

[Lobstrosity]

Originally posted by Kat_Somm_Faen
Yeah it should be in the teens of billions light years across. I believe 14-16 billion light years range. Someone please feel free to correct me if I am wrong. Its a closed system, flat geometry and apparently bound to be forever expanding.
If inflation is correct, you're wrong. It's looking more and more like inflation is correct.

[Lobstrosity]

Originally posted by Solanalos
I must be missing something. If everything was once in the finite conditions of the early universe, how is it a flat infinity now?

Edit: Why isn't it just an ever expanding finity?
Unless I'm mistake as to the prevailing view of modern cosmology, everything wasn't once in finite conditions. The metric for our universe, if flat, would be given by the familiar:

dl² = a²(dr² + r²dθ² + r²sin²θ dφ²)

This arises from the Friedmann model, which assumes a priori that the universe is homogeneous and isotropic--assumptions that do have some empirical backing. Now note that this metric describes a universe of infinite volume (so long as a is not zero) since r ranges from zero to infinity. Theta ranges from zero to pi and phi ranges from zero to two pi. a is a scale factor that determines the overall scale of the spatial metric. This scale factor is not a function of r, θ, or φ, which means that it does not violate homogeneity or isotropy. It can be, however, a function of time. The Hubble constant is defined as [(da/dt) / a].

Basically, what you have is a universe that is always infinite in size but whose characteristic length scale is changing with time.

Or maybe I'm talking out of my ass. Let's wait for someone with more working knowledge of cosmology to come along and set us straight (as this is a question I've always wondered about--people always describe the origins of the universe as a single finite point, so then how does something finite expand into something infinite?). All I know is that the current cosmological models are founded on the principle of homogeneity and a finite universe certainly isn't homogeneous. I also know that the model that is currently used for cosmology (the Friedmann model) deals with a universe of infinite extent (so long as it's flat or open), though perhaps this model is not completely accurate.

[Tetlepanquetzatzin]

I see Lobstrosity has already made some good points. Here are my points, which to some extent is a repetition of Lobstrosity's post.
Originally posted by Solanalos
1. The Big Bang occurred everywhere in the universe and everything that now exists (matter, energy, spacetime) comes from it.
Correct. The Big Bang model is based on Weyl's postulate, stating that if we follow the geodesics of all particles backwards in time they will eventually converge to the same point.
2. The Big Bang began at a point of singularity and expanded from there.
The Big Bang is a singularity in the sense that general relativity no longer remains a valid approximation very close to the Big Bang.

3. The universe in it's early stages was small.

How can the universe be infinite if it was at one time finite?
The universe has either been finite during all its history or infinite during all its history. This is consistent with Weyl's postulate, because the cosmological metric (given in co-moving coordinates) is of the form

ds^2 = (c dt)^2 - a(t)^2 dr^2

Here, dt is a small difference in time coordinates and dr is a small difference in spatial coordinates (this is somewhat simplified). Even if no coordinates change, the distance will change in time because of the scale factor a(t) (this is how the expansion of the universe is represented in the math). The scale factor goes to zero when get close to the Big Bang, so no matter how large difference in spatial coordinates is the spatial contribution to the distance will go to zero close to the Big Bang (compare with Weyl's postulate!). The scale factor will make all particle trajectories converge as we approach the Big Bang even if the universe is infinite.
If my above understanding of the early universe and the Big Bang is correct, that is the question that sticks out at me. Here's what I need to know: Does spacetime come from the Big Bang or not? Is the Big Bang an explosion in spacetime or is spacetime within the Big Bang?
Space-time does not come from anything (except, possibly, a black hole in another space-time a la Smolin), since "come from" is a concept that only makes sense within a space-time. The Big Bang is not an explosion.
The only way I can see the possibility of an infinite universe is if spacetime preexisted the Big Bang and was already infinte. I can't understand how something can "make the jump" from finite to infinite?! :confused:
It is easy to become a little confused by this subject. That is good, because confusion is often the state that preceedes insight. Once you study the metrics used in our cosmological models you will realize that there is no finite-to-infinite transition, and your confusion will be converted into insight. When we say that the universe was small in the past we mean nothing more nor less than that the scale factor was small.

[beachmaster]

Perhaps the only way to view the quandary is that the universe is finite with infinite potential (open universe)?

[eh]

It's not just infinite because it will exist without end, but because it is spatially infinite. It has always been infinite, even at the instant of the big bang. In such a case the empty space between galaxies expands over time, but the overall size remains infinite. In the early universe, everything becomes very dense. Only a finite universe is very small at this time, though exactly how small is an open question.

[Jesse]

If the universe is closed, then 3-D space would be curved and finite in a way similar to the surface of a 4-D hypersphere (just like the surface of a 3-D sphere is a curved and finite 2-D surface). But if the universe is flat or open, space is infinite. Whether our universe is closed, flat, or open depends on the density of mass/energy in space (see this (http://www.astro.ucla.edu/~wright/cosmo_03.htm) page for more)--I believe cosmological observations suggest it is flat or very close to it, but it might be possible that it's close to flat but not exactly so, in which case perhaps it could be closed with a very large but finite size.

If the universe is closed, then as you go back in time it's like the 4-D hypersphere shrinks, so the total volume of space decreases. If the universe is flat or open, then space was infinite at every finite time after the big bang. But space still can "expand" in a flat, infinite universe--think of a giant chess board where all the squares are expanding in size simultaneously (like what you'd see if you zoomed in on a picture of a chess board), but the pieces stay the same size and remain at the center of their respective squares. Likewise, as you go back in time the squares shrink while the pieces stay the same size and get crowded closer together. At the moment of the big bang, the area of each square would go to zero, as would the distance between any pair of squares.

[Friar Bellows]

Originally posted by Jesse
But if the universe is flat or open, space is infinite.

Unless, of course, the topology of the universe is multiply connected. Then it could be finite despite having a constant spatial curvature of zero (i.e. spatially flat) everywhere.

[Solanalos]

Thank you all for your insights. They have helped me tremendously. The scale factor aspect rearranged my concept. I do see it a lot more clearly than before, but not enough to allow me to fully visualize it. I'm having a hard time imagining a scale factor of zero in an infinite universe. I am, however, sneaking peeks when I ponder for a while. Goddamned freaky universe! :D

[spacer1]

Originally posted by Tetlepanquetzatzin:
Once you study the metrics used in our cosmological models you will realize that there is no finite-to-infinite transition, and your confusion will be converted into insight. When we say that the universe was small in the past we mean nothing more nor less than that the scale factor was small.
Do you mean that there are only ever or larger or smaller scales of measurement? If so, it seems to suggest an infinite universe, since it assumes no limits. Or, might you be saying that infinity and zero are only idealized limits which can never be achieved in reality?
Originally posted by Jesse:
At the moment of the big bang, the area of each square would go to zero, as would the distance between any pair of squares.
Might it be better to say that the area of each square and the distance between squares approaches zero? Infinitely small doesn't equal zero, surely. It must be an infinitely small quantity of the thing we are measuring, which must, therefore, have existence. Wouldn't zero size (in all dimensions) denote non-existence?

[Jesse]

Originally posted by spacer1
Might it be better to say that the area of each square and the distance between squares approaches zero? Infinitely small doesn't equal zero, surely. It must be an infinitely small quantity of the thing we are measuring, which must, therefore, have existence. Wouldn't zero size (in all dimensions) denote non-existence?

You could say the area of each square approaches zero as time approaches zero, the moment of the Big Bang itself. But general relativity is a continuous theory, so there's no problem talking about points (with zero size) in spacetime, just like we can talk about real numbers as points on the number line. Singularities are points where a finite amount of mass/energy becomes compressed into a point of zero volume, resulting in infinite density--this would be true of the point that's the Big Bang along with the point that's the center of a black hole. But quantum gravity may show that this prediction of general relativity is wrong, and that singularities won't actually turn out to have real physical existence in our final theory of gravity.

[Kat_Somm_Faen]

Jesse,

I was under the impression that "closed" reffered to the system as in the physical definition of a system i.e. nothing is coming into the system through the system boundary?

[Jesse]

Originally posted by Kat_Somm_Faen
Jesse,

I was under the impression that "closed" reffered to the system as in the physical definition of a system i.e. nothing is coming into the system through the system boundary?

That's the meaning of "closed" in thermodynamics, but it means something different in the context of cosmology: there, "closed" refers to overall positive spatial curvature, as opposed to zero curvature (flat) or negative curvature (open). See this (http://superstringtheory.com/cosmo/cosmo21.html) page for some more details.

[schu]

If the universe is expanding, what is it expanding into?

If the galaxies we see are 14 billion light years away are we not seeing them as they were and where they were 14 billion years ago? Can we know where they are now and what they look like?

[wiploc]

Originally posted by Solanalos
I want to understand it better. I would appreciate corrections to the following (my understanding of it) if need be.

First, let me establish my credentials, so you'll know how seriously to take me:

1. I've read some Asimov.
2. Some of my friends know something about physics.

In other words: no credentials. As Bokonon said, "All the sweet truths I am about to tell you are lies."



1. The Big Bang occurred everywhere in the universe and everything that now exists (matter, energy, spacetime) comes from it.

It seems to me that you are mixing metaphors here, or mixing paradigms. If you think of the Bang as happening everywhere, then you don't want to think of things as coming from it. If you think of stuff as coming from the Bang, then you want to think of the Bang as tiny and in a specific place and time. Both ways of thinking about it are legitimate.





2. The Big Bang began at a point of singularity and expanded from there.

I don't think anybody believes this anymore. It is an old relativist model. Quantum mechanics rules the small stuff, and the Bang started small. If we "play the film backward," and watch the universe shrink towards the singularity, we see that it doesn't actually get there. Either it is unbounded in some sense (curving off into imaginary time; or like a circle not quite touching a point; or does a Zeno's Paradox because time is a ray with a circle on one end rather than a dot; or whatever) or it just stops. If it stops, it stops when it is small enough for everything to everything jump to the singularity in a single quantum leap.

So, playing the film forward again, the universe starts (if it starts at all) just "after" the singularity. The first frame of the film shows a finite universe. There is no frame showing a singularity.



3. The universe in it's early stages was small.

How can the universe be infinite if it was at one time finite?

In what sense are you thinking it's infinite?




Does spacetime come from the Big Bang or not? Is the Big Bang an explosion in spacetime or is spacetime within the Big Bang?

All of those formulations seem somehow misleading. I'm tempted to say that spacetime _is_ the big bang.

How about, the Big Bang is an explosion _of_ spacetime?

Picture a very small (point sized) firecracker. Now remove the rest of the universe so that nothing but the firecracker exists. Set off the firecracker; see the universe expand. Is there time? Yes, because there is change. Is there space? Yes, because there is matter. But, did the spacetime "come from" the firecracker? No, because, uh, you know, it's like spacetime is a description of matter in motion, or an aspect of it, or a parameter of it. Spacetime doesn't come from matter in motion in the same sense that acceleration doesn't "come from" a sports car.

The Big Bang isn't an explosion _in_ spacetime because there is no spacetime without the explosion. The explosion fills every bit of space and time, and the spacetime exists only because of the explosion. It is tempting to say that the explosion _is_ spacetime.

Spacetime isn't "within" the Big Bang any more than the Big Bang is within spacetime. Neither can exist without the other.

Your question is something like asking whether circles are caused by radii or radii are caused by circles. Spacetime and matter-in-motion are more closely related than Siamese twins.

I hope this helps. And I hope someone corrects it if it's wrong. :)

crc