# The Big Bang. . . just one little question

1. Feb 27, 2010

### Rob060870

Dear members,

i am new to this website and i feel that i am really out of my depth with the many clever people who are on here and i am no scientist!. i am just somone who is interested in science and technology.
i have a question which i havent been able to find the answer anywhere and if you could help i would be most greatfull.

If the universe began in a bigbang which was a singlarity, then how did the matter energy and spacetime escape from it when we know that even light cannot?

thankyou.

2. Feb 27, 2010

### sylas

I think you may be mixing up the notion of "singularity" with "black hole". A black hole is a certain kind of singularity -- or contains a certain kind of singularity.

The word "singularity" simply refers to a condition in which functions diverge, or become undefined. It is a mathematical term. For example, there is a singularity at x=0 in the function y=1/x.

Classical physics is described using certain mathematical equations, and in some conditions those equations break down into a singularity. For example, there is a singularity in the mathematics of relativity at the center of a black hole, or at the origin of the universe.

Put another way, we don't have a consistent mathematical description for what happens under those conditions at which conventional classical relativity diverges into a singularity. Presumably there is some more complete way to describe the conditions under which relativity breaks down in this way... but we don't know what it is, as yet.

The singularity within a black hole is a region within a larger space, where matter density and curvature of space all diverge off to infinite values. Any sufficiently dense object will have such a singularity, in the sense that descriptions break down at that point. There is also an "event horizon" around the singularity, and anything which crosses the event horizon will inevitably be drawn down into the central singularity, with no hope of ever getting back out past the event horizon again. That's not what the universe or the big bang singularity is like.

The big bang involves a singularity... a condition in which relativity breaks down into a great big divide by zero.

The singularity of the big bang is not a "thing" from which matter escapes. All the universe is still "inside" that same expanding spacetime of the big bang. It's just that mathematical descriptions break down at a point in the past when the density of the universe diverges off towards infinite values in the classical theory.

Cheers -- sylas

3. Feb 27, 2010

### marcus

I agree with Sylas' answer to your question. Here's something you could do to learn more (from an online site using non-technical language).

Google "einstein online cosmology".

The top hit is the cosmology section of a public outreach website called "einstein online".
It is the outreach information website of a German research institute. Reasonably solid and professional but they use everyday language, not too much math and jargon.

If you google "einstein online cosmology" you get
http://www.aei.mpg.de/einsteinOnline/en/spotlights/cosmology/index.html [Broken]
and one of the first things they list, to click on is:

It can help relieve confusion to have someone explain the two different senses in which the term "big bang" is used. And what "singularity" means. It is just a breakdown that occurs in the 1915 General Relativity theory (and is used by scientists as a convenient reference point) but does not necessarily describe nature.

There are various possible ways to fix the original 1915 theory so it does not suffer from the singularity glitch. They mention that on the webpage called "A tale of two big bangs."
We are not yet sure what the correct fix is, and what modified theory will replace the 1915 version, and what will replace the "singularity" failure point. But as E-O says: researchers would be quite surprised if it actually turned out that nature failed ..

==quote from E-O's tale of 2 bbs==
Whether or not there really was a big bang singularity is a totally different question. Most cosmologists would be very surprised if it turned out that our universe really did have an infinitely dense, infinitely hot, infinitely curved beginning. Commonly, the fact that a model predicts infinite values for some physical quantity indicates that the model is too simple and fails to include some crucial aspect of the real world. In fact, we already know what the usual cosmological models fail to include: At ultra-high densities, with the whole of the observable universe squeezed into a volume much smaller than that of an atom, we would expect quantum effects to become crucially important. But the cosmological standard models do not include full quantum versions of space, time and geometry - they are not based on a quantum theory of gravity. However, at the present time we do not yet have a reliable theory of quantum gravity. While there are promising candidates for such a theory, none are developed far enough to yield reliable predictions for the very early universe.

Thus, while some cosmologists do not have a problem with assuming that our universe began in a singular state, most are convinced that the big bang singularity is an artefact - to be replaced by a more accurate description once quantum gravity research has made suitable progress. To be replaced with what? Nobody knows for sure. In some models, we can go infinitely far into the past (one example is presented in the spotlight text Avoiding the big bang)...
==endquote==

Last edited by a moderator: May 4, 2017
4. Feb 27, 2010

### Rob060870

Thankyou for explaning that for me i appreciate you taking the time to reply and i am looking forward to reading the link that you have provided.
Robert

Last edited by a moderator: May 4, 2017
5. Feb 28, 2010

### Chalnoth

This is perhaps a little bit overly-simplistic, but I think it captures the general idea rather well:

General Relativity ensures that nothing, not even light, can ever escape a black hole. You don't think that matter or light escapes our universe, do you?

6. Feb 28, 2010

### Rob060870

Dear Chalnoth, thats very interesting. So are we then inside something like a black hole? Maybe in reverse instead of sucking everything in expanding out?. I was imagining the whole universe as small as an atom with infinite mass with so much gravity it wouldn't be able to expand in the first place. Thanks.

7. Feb 28, 2010

### Dmitry67

No.
Black hole is finite-sized object in some less cureved spacetime.
It was an oversimplification.

But you're right, IF universe was static, then it would collapse because of it's gravity. Einstein had realized that, trying to 'save' the idea of static universe adding the repulsive force.

So GR tells us that Universe can not be static, and this is why it is expanding. What is interesting is that the expansion rate is very close to critical, so it is just enough for the Universe not to collapse in the very beginning.

8. Feb 28, 2010

### Chalnoth

Well, in a way. As I said, that was a bit overly-simplistic. But basically, if you could see our region of the universe from the outside, then it would necessarily look like a black hole.

One subtlety here is that this is inconsistent with basic GR: if it looks like a black hole from the outside, then, in basic GR, everything inside is inexorably drawn to the singularity at the center.

Another is that if you work it through, imagining a new region of space-time popping out of the vacuum, that region will look, from the outside, like a black hole, but the catch is that it almost immediately evaporates. This means that if a new region of space-time is generated, then it very quickly becomes completely disconnected from its parent universe: it may last for a long time, but it just isn't accessible.

Well, that's what is called a white hole, and it's just the time reverse of the black hole. But a white hole requires global entropy to decrease, so it's not really possible.

9. Feb 28, 2010

### Rob060870

thanks,
also im interested to hear that the expansion rate in our universe is very close to critical so that its just enough not to collapse does that mean that if our universe wasnt expanding at an ever increasing rate then we could have already started the big crunch?(i know it also depends on how much total matter is in the universe) also would that mean time flows in reverse?

Last edited: Feb 28, 2010
10. Mar 1, 2010

### marcus

I'll leave most of those questions for somebody else. They are good questions. But supposing there was no dark energy and no acceleration, that wouldn't necessarily mean big crunch. I have to go, back later.

EDIT: I got back to this, Rob. But now I see Sylas has done a complete job on it! Nothing left for me to add!

Last edited: Mar 1, 2010
11. Mar 1, 2010

### sylas

I think "time flows in reverse" isn't really a useful notion at this point, so I'll just propose "No" as my answer for the last question and consider the notions of expansion, reversing expansion to a crunch, and being "critical".

As for expansion rate being "critical"; this isn't actually much of an issue these days, with the discovery of dark energy. Our expansion rate isn't actually "critical", I think.

This is older terminology which was popular when the big question was whether there was enough matter to reverse the expansion and bring about a big crunch, or whether the expansion would continue for ever. That was how the question was discussed in the early 1990s and earlier. Back then, the expansion of the universe was considered to be moderated by the effects of matter, and of curvature. There was no Λ, no cosmological constant.

For any given matter density, there was a critical expansion rate which would mean that the universe would expand forever. This was also the zero curvature case. Less density for the critical expansion rate, or more rapid expansion for the critical density, would give an "open" universe which expanded forever, and more density would give a "closed" universe.

In older accounts of the Big Bang, you often find three simple alternatives considered. They are:

(1) Closed universe (with no Λ)

Assuming no Λ, this case could be identified four ways.
• The universe is closed. That is, curvature is positive, and space is finite (though very big). The available volume of the universe is finite but without any edge, just like the available area of the Earth's surface is finite but without any edge. It curves back on itself.
• Density is super-critical. That is, there is more matter in the universe than is required to bring expansion to a stop.
• Expansion is sub-critical. That is, the expansion rate is too slow to allow the expansion to continue indefinitely.
• The universe will collapse into a Big Crunch. Eventually, expansion will slow, stop and reverse. This is not a reversal of time. It just means things start to compress together rather than expand apart, with a singularity in the future when everything is compressed with arbitrary density.

Assuming no Λ, any one of the four qualities implies the other three.

(2) Open universe (with no Λ)

Assuming no Λ, this case could be identified four ways.
• The universe is open. That is, curvature is infinite, and space is infinite.
• Density is sub-critical. That is, there is not enough matter in the universe to bring expansion to a stop.
• Expansion is super-critical. That is, the expansion rate is too fast to ever be brought to a halt.
• The universe will expand forever.

Assuming no Λ, any one of the four qualities implies the other three.

(3) Flat universe (with no Λ)

Assuming no Λ, this case could be identified four ways.
• The universe is flat. That is, space is infinite, with no curvature. Space looks a bit like an infinite cartesian grid R3.
• Density is critical. That is, there is just enough matter in the universe to slow expansion down to as slow as you like, without ever quite coming to a stop.
• Expansion is critical. That is, the expansion rate is just fast enough to avoid ever being halted.
• The universe will expand forever, but more and more slowly over time, without limit.

Assuming no Λ, any one of the four qualities implies the other three.

(4) Dark energy (Λ)

In the 1990s, a fourth alternative came back into consideration... the cosmological constant, or dark energy, or a kind of pressure that counteracts the tendency of gravity to pull things back together, and rather tends to drive them apart, accelerating the rate of expansion.

This suddenly makes all the older descriptions confusing, because it is no longer the case that being open/closed/flat is the same as being sub-critical/critical/super-critical.

You can represent the universe with three qualities, any two of which gives the other. There's the amount of matter. There's the amount of dark energy. And there's the amount of curvature. Strictly speaking I am telling you lies here, because you can get more variations than this, but this simple case is widely used, as the ΛCDM model of the universe.

For any given rate of expansion, there is a certain critical density, which corresponds precisely to the critical matter density of the older "flat" universe case without Λ. So for the given rate of expansion H0, there are three numbers considered, which have to add up to 1, and which are all dimensionless ratios: fractions of a critical density.
• Ωm. The amount of matter, as a fraction of critical density. We think this is very close to 0.27 in the current universe, and most of this is dark matter.
• ΩΛ. The amount of dark energy, as a fraction of critical. (Critical being the amount to give a flat universe without any matter.) We think this is very close to 0.73 in the current universe.
• Ωk. The contribution of curvature. By definition, it has to be 1 - Ωm - Ωk. It is 0 for a flat universe, negative for a closed (finite) universe with positive curvature; and positive for an open (infinite) universe with negative curvature. The sign of curvature is the opposite of the sign of Ωk. We think this is very close to 0 in the current universe.

Hence these days, you are much more likely to hear cosmologists wondering why the universe is flat, rather than why the expansion rate is critical. Without going into all the details, dark energy means that the expansion rather isn't critical. It is, apparently, accelerating, and will continue to accelerate indefinitely. Flatness is usually explained by appealing to an inflationary epoch in the very early universe... another topic in its own right.

You may enjoy the following diagram

from cosmology lectures by James Schombert at Uni of Oregon. Horizontal blue lines give constant Ωk, the red lines give constant Ωm and the green lines give constant ΩΛ. Our universe is currently located on the diagram at about ΛCDM. The two other cases are SCDM, for case (3) above, the flat universe with critical matter density and no Λ; and OCDM, for case (2) above, the open universe with no Λ.

Homework. Locate case (1) on the diagram.

12. Mar 2, 2010

### Rob060870

thankyou for that!, SYLAS.
im sure that you must have writers cramp after that!

now i have given it my best shot and i hope im right! if not im sure you will (mock) er i mean tell me lol!.

now you have given me a bit of a headache thinking about this. just to reiterate that i am NO mathematician, however i think that a case (1) universe ( a Closed universe with no Λ)

Ωk must be less than zero
Ωm must be 1.3 or more
ΩΛ with no Λ

so i think the answer to your question, locate case (1) on the diagram is
Assuming no Λ, in the blue area of the diagram to the left of the ΩΛ green line. however i think is it possible to be in the bottom left of the yellow line in the green area? as it says (expands), i assume as long as its not as high as zero of the blue line it should still eventually collapse into a big crunch?

all the best Rob060870

Last edited: Mar 2, 2010
13. Mar 2, 2010

### sylas

Well done. You got it. Although in fact all you need is Ωm > 1, ΩΛ = 0, in which case you also have Ωk < 0. This is very close to the solid red line, and on the green line corresponding to ΩΛ = 0. If you zoomed in on that, it would be seen to be in the shaded blue region to the left of the solid red line. The red line is very close to, but not quite directly at, the green line, although that isn't visible at this resolution of the diagram until you get about Ωm > 1.3 or so.

The Ωm > 1 means matter density is super critical.
The Ωk < 0 means the universe is closed (in space), very large but finite size.
The blue region means there is a big crunch looming, though it would be many billions of years into the future.

This model would also mean that the age of the universe was only about 9 billion years old, for our rate of expansion. That falsifies this as a model of our universe, because there are stars that are older than 9 billion years, assuming we are dating stars correctly.

I do get verbose sometimes, but they are often my favourite posts. Glad it was of some use!

Cheers -- sylas

14. Mar 2, 2010

### Bernie G

One year after the claimed Big Bang the universe was smaller than the Schwarzchild radius, but it did not collapse. How is that explained?

15. Mar 2, 2010

### marcus

Why should it collapse, Bernie? Do you imagine that if some mass M is concentrated within a radius of 2GM/c2 that it must necessarily, in every case, collapse? You may not have read the fine print.

It assumes a geometry that is not expanding.

16. Mar 2, 2010

### sylas

The short answer is that the simple account of black holes falls apart when applied to stuff that is expanding.

A slightly longer answer will need to clarify a couple of points.

(1) We don't know how big the universe is, or even whether it is finite or not.

For the experts (in which category I do not belong) there's a reasonable basis for considering answers to this; but the first point for us to appreciate here is that there's a difference between "universe" and "observable universe". When you see descriptions of the "size of the universe" at certain times after the Big Bang, they are usually descriptions of the observable universe. You can think of the universe as volume of "stuff", all of which is expanding away from everything else, so that the density of stuff at any location is falling with time. The "observable universe" is simply a region within the universe which is close enough to our location that we can "see" it... or rather than any influence moving at light speed has had time to reach us.

In an expanding universe, it may take a very long time for light to reach us. The technical details of this get a bit messy.

(2) The universe isn't a thing in space. It's everything and the space as well.

A black hole is a region of space from which nothing can escape. Well, nothing can escape the universe...

This is not really the right way to define a black hole, but it's a point that might be worth bearing in mind.

(3) Expanding matter is different from matter at fixed density

The Schwarzchild radius is proportional to mass... and for a given density, the mass within a certain radius is proportional to the cube of the radius.

Thinking about it, this means that if you have a large expanse of matter at a certain density, there is a certain radius so that any spherical volume of that radius contains enough mass to be a black hole. A vast expanse of matter will thus be bound to collapse...

... except that this analysis breaks down if all that matter is dispersing (expanding) so that the density is falling with time. You can't actually conclude that there's a black hole in that case.

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For a more detailed technical answer, given with more confidence and accuracy than I could manage, I recommend: Is the Big Bang a black hole?, by Philip Gibbs. This is part of the USENET Physics FAQ.

PS. Crossed posts with marcus, who as usual gets straight to the heart of the answer.

Last edited: Mar 2, 2010
17. Mar 3, 2010

### Dmitry67

Wonderful diagram!
It is a pity that it does not show the Big Rip area.

18. Mar 3, 2010

### sylas

There is no "Big Rip" with these models. The "Big Rip" is a speculative consequence of an unusual form of super acceleration where the "cosmological constant" is not constant (like dark energy) but is actually increasing in strength.

The Big Rip has often been described as an unusual prediction or model. It has never been a prediction; only a fun game looking at what would happen if the "equation of state" had ω < -1. Dark energy is a "cosmological constant" with ω = -1. There are strong theoretical reasons for thinking ω < -1 is impossible. But in any case, you can't represent it at all in terms of the parameters of that diagram.

Cheers -- sylas

19. Mar 3, 2010

### Rob060870

thanks again for that i am relieved that i was on the right track!.

i have read that The Schwarzschild radius is the radius of the event horizon surrounding a non-rotating black hole.

question- would a rapidly rotating black hole affect the Schwarzschild radius?
also if there was no time before the big bang then how could events be set in motion to lead to it in the first place?
and regarding the big rip, i thought that spacetime was infinitely stretchy?

thanks Rob060870

Last edited: Mar 3, 2010
20. Mar 3, 2010

### Dmitry67

1 There are many interesting things happening in rotating BH
Here is a list of things to google/wiki:
ergosphere
blue sheet
inner horizon inside the rotating black hole
ring singularity
superextreme black hole

2 Big Bang theory does not cover the Big Bang itself. So there is no answer.
But, very likely, when TOE will be discovered, it would appear that the very concept of time does not make sense around t->0. In any case, you should not be surprised by it. Our world is nothing more than a mathematical solution to some equations. Look at function ln(x). It is not defined at ln(0). Does it ‘suffer’ because of it? Does ln(x) have any problems at small x because it is not defined at x=0? No.