Infinite universe and big bang singularity

[kuartus4]

Hello. Cosmologists leave open the possibility that the universe as a whole may be infinitely big. My question is, does that mean that the entire infinite universe was compressed into the initial singularity? And how can a universe go from a singularity to being infinitely big in a finite time?

 

[Number Nine]

"Singularity" doesn't mean "point in space", it refers to a mathematical phenomenon that signals that our models no longer work (or, at least, probably don't describe physical reality). A singularity is a quirk of the equations, not an actual, physical "thing".

 

[phinds]

Hello. Cosmologists leave open the possibility that the universe as a whole may be infinitely big. My question is, does that mean that the entire infinite universe was compressed into the initial singularity? And how can a universe go from a singularity to being infinitely big in a finite time?

To add to what Number Nine said, the universe is known to have been MUCH smaller at one Plank Time after the singularity than it is now, but it MIGHT have been infinite then (which of course implies infinite now). If it was not infinite then, it is not infinite now.

Our observable universe (currently some 90+ billion light years in diameter) at that time is stated in various reports as sizes ranging from a golf ball down to much smaller. Reports that put it as a point are patently ridiculous.

 

[marcus]

"Singularity" doesn't mean "point in space", it refers to a mathematical phenomenon that signals that our models no longer work (or, at least, probably don't describe physical reality). A singularity is a quirk of the equations, not an actual, physical "thing".

Well said. Thanks, it's an important message to get across to new members. People get fooled by the word "singularity" because it sounds like it refers to a "single point". But instead it refers to a failure of some man-made mathematics. History shows that in the past physicists have gotten rid of singularities in various other theories by improving the equations so they don't blow up. Now they are working on curing the singularity that occurs in the conventional model of the cosmos, right at the start of expansion.

An equation does not necessarily fail at a single isolated point. It can fail everywhere along a wide frontier--at infinitely many points. In which case the singularity is said to occur throughout the whole region where the model breaks down.

As Phinds rightly indicated, it is logically possible that our universe began expanding with an infinite volume. It would necessarily have begun infinite if it is spatially infinite today. We do not yet know whether to consider space finite or infinite. The region we are now looking at is evidently not the whole thing.

 

[jcsd]

Describing singularities in general in GR is a problem let alone trying to describe them physically (not that I think singualrities are physical). That said some singualrities do, for example, resemble points in space.

An infinite universe is always infinite until the point of the singularity; however at the singularity all distances between objects, no matter how far apart they are later in time, goes to zero.

 

[marcus]

...at the singularity all distances between objects...

At the classical model's singularity, distances between objects are not defined. What "objects"?
The model blows, it no longer applies to nature and it is meaningless to talk about distances between objects being this that or the other thing. That's my take on it. If you want to imagine differently, fine.

There are now rival models, waiting to be tested, which go back further in time to before the start of expansion, where the classic 1915 model blows up. I'd guess you know about them and currently which are getting the most research attention.
In the new models it is NOT true that all distances are zero at the start of expansion.
However with the new models at least you might be able to talk meaningfully about that kind of stuff. What the highest density is, that is reached at the moment the bounce happens, and so on...

The idea of objects and distances between them is somewhat nebulous under the circumstances, but the energy density (how much crowded into a unit volume) is finite and well-defined and can sort of take the place of the "distance between objects" idea.

 

[jcsd]

At the classical model's singularity, distances between objects are not defined.
The model blows, and it is meaningless to talk about distances between objects being this that or the other thing.

There are now rival models, waiting to be tested, which go back further in time to before the start of expansion, where the classic 1915 model blows up.
In the new models it is NOT true that all distances are zero at the start of expansion.
However with the new models at least you might be able to talk meaningfully about that kind of stuff. What the highest density is, that is reached at the moment the bounce happens, and so on...

I said "go to zero" (well I actually made a gammatical error due to editing and said "goes", but that's neither here nor there).

edit: just to make this clear I am saying that as t->0 where 0 is the big bang singualrity d->0 (where is d is the distance between any two objects).

 

[DrStupid]

at the singularity all distances between objects, no matter how far apart they are later in time, goes to zero.

This is valid for finite distances but in an infinite universe there are also infinite distances.

 

[Number Nine]

This is valid for finite distances but in an infinite universe there are also infinite distances.

Eh...that's a touchy issue. Even on the plane (which is infinite), any two defined points have a finite distance between them. It's entirely possible that two points could never reach each other (say, due to FTL expansion), but the distance between any two points is finite.

 

[jcsd]

This is valid for finite distances but in an infinite universe there are also infinite distances.

No there are no infinite distances, even in an infinite Universe- in standard big bang theory anyway

 

[DrStupid]

No there are no infinite distances, even in an infinite Universe- in standard big bang theory anyway

Assuming we have n+1 points in a row with equal distances dr. Than the distance between point 0 and point n is r=n·dr and the limes of r for n->oo (this is possible in an universe with infinite size) is infinite.

 

[DeepSpace9]

Does the observable universe make up 80% of the universe? Or 20%? I have heard different numbers..

 

[Calimero]

Nobody can't tell you that, there are some lower bound estimates which tells that hole thing must have some considerably larger volume then OU (hate to dig for exact number right now), but then again it can be infinite, which means that it is infinitely larger then OU.

 

[jcsd]

Assuming we have n+1 points in a row with equal distances dr. Than the distance between point 0 and point n is r=n·dr and the limes of r for n->oo (this is possible in an universe with infinite size) is infinite.

But assuming n \in \mathbb{N} then n is never equal to ∞ and hence r is never equal to ∞ as well. Of course that doesn't conclusively show that there are non-existence of infinite proper distances in standard big bang cosmology, however it is the case.

 

[DrStupid]

But assuming n \in \mathbb{N} then n is never equal to ∞ and hence r is never equal to ∞ as well.

Of course not. ∞ is not a number. But if the limes of r is ∞ than you get r'=0·∞ when the scale factor goes to zero. This term is not necessarily zero. It could even be infinite.

 

[kuartus4]

When I was reading roger penrose book the road to reality, he seemed to say that general relativity should be regarded higher that quantum mechanics and that general relativity should not have to compromise to fit with quantum physics but the other way around. I could be mistaken. Most of the book went over my head. But if Penrose is right about relativity being correct, then doesn't that mean that per the hawking penrose singularity theorems a primordial singularity before the hot big bang is inevitable?

 

[Number Nine]

Of course not. ∞ is not a number. But if the limes of r is ∞ than you get r'=0·∞ when the scale factor goes to zero. This term is not necessarily zero. It could even be infinite.

The problem is that you're now talking about something completely different. The distance between any two given points is finite; the fact that the distance tends towards infinity as you move the points further apart only means that distance is unbounded, which is something different entirely.

 

[DrStupid]

The problem is that you're now talking about something completely different. The distance between any two given points is finite;

I am still talking about infinite distances. Distances between given points are something completely different. The latter are finite and shrink to zero in the big bang singularity. The former do not need to be zero in the singularity which therefore do not need to be a point.

 

[Naty1]

kuartus:

[Penrose] ... seemed to say that general relativity should be regarded higher that quantum mechanics and that general relativity should not have to compromise to fit with quantum physics but the other way around. I could be mistaken. Most of the book went over my head. But if Penrose is right about relativity being correct, then doesn't that mean that per the hawking penrose singularity theorems a primordial singularity before the hot big bang is inevitable?

no, he did not say the GR is predomininant...In fact on page 713 he points out that for a black hole singularity

...It seems unavoidable that the realm of quantum gravity...[will require]...these expectations of the classical theory ...to be modified in accordance with this...

and no the the second part as well:

...Hawking's singularity theorem is for the whole universe, and works backwards-in-time: in Hawking's original formulation, it guaranteed that the Big Bang has infinite density. Hawking later revised his position in A Brief History of Time (1988) where he stated "There was in fact no singularity at the beginning of the universe" (p50). This revision followed from quantum mechanics, in which general relativity must break down at times less than the Planck time. Hence general relativity cannot be used to show a singularity.

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

This again shows an emphasis in favor of quantum theory over relativity.

 

[jcsd]

I am still talking about infinite distances. Distances between given points are something completely different. The latter are finite and shrink to zero in the big bang singularity. The former do not need to be zero in the singularity which therefore do not need to be a point.

There no such thing as 'infinite distances', at least not in this scenario.

What you are trying to say is that whilst all distances tend to zero, the length of say an infinitely-long curve in space will not tend to zero will remain infinite as t->0.

This is somewhat moot as the singularity is not a point on the manifold.

 

[phinds]

I am still talking about infinite distances. Distances between given points are something completely different. The latter are finite and shrink to zero in the big bang singularity. The former do not need to be zero in the singularity which therefore do not need to be a point.

No, that would imply that the singularity was a point. I'm not aware of any reputable physicists who think that the singularity was a point in SPACE, as you imply, it was a point in TIME and no one KNOWS what it was in space, except that it wasn't a point because that would make no sense.

 

[jcsd]

No, that would imply that the singularity was a point. I'm not aware of any reputable physicists who think that the singularity was a point in SPACE, as you imply, it was a point in TIME and no one KNOWS what it was in space, except that it wasn't a point because that would make no sense.

If you read what I said earlier, he is correct all proper distances tend to zero at the singualritiy. The big bang singualrity is a bit like a "place" and a bit like a "time", as by artifically inserting an event to represent the big bang singularity you can make a "manifold with boundary" (at least for idealized solutions).

However the big bang singualrity is not naturally an event in spacetime and there's no general way of adding boundaries to manifolds to represent singularities.

 

[Naty1]

However the big bang singualrity is not naturally an event in spacetime ...

I just happened to see Roger Penrose description of the big bang singularity in THE ROAD TO REALITY pg 722...He uses the balloon [surface] two dimensional analogy...

 

[jcsd]

I just happened to see Roger Penrose description of the big bang singularity in THE ROAD TO REALITY pg 722...He uses the balloon [surface] two dimensional analogy...

I think that's spefically to do with the Euclidian path intergral approach to quantum gravity.

 

[phinds]

If you read what I said earlier, he is correct all proper distances tend to zero at the singualritiy. The big bang singualrity is a bit like a "place" and a bit like a "time", as by artifically inserting an event to represent the big bang singularity you can make a "manifold with boundary" (at least for idealized solutions).

However the big bang singualrity is not naturally an event in spacetime and there's no general way of adding boundaries to manifolds to represent singularities.

I agree w/ "tend to zero", which I take to mean "approach zero without reaching it". He said "go to zero" which I take to mean REACH zero, which I disagree with. Do you believe that the singularity was a dimensionless point in space? If it was not, then the distance only tends to zero, it does not GO to zero, and my statement stands.

 

[jcsd]

I agree w/ "tend to zero", which I take to mean "approach zero without reaching it". He said "go to zero" which I take to mean REACH zero, which I disagree with. Do you believe that the singularity was a dimensionless point in space? If it was not, then the distance only tends to zero, it does not GO to zero, and my statement stands.

I think we often say "goes to" as a synonym for "tends to", I certainly used it in that sense earlier in the thread.

The singularity as a dimensionless point that constitutes the whole of space is certainly one way of looking at, with the reservations I expressed above though.

 

[DrStupid]

I think we often say "goes to" as a synonym for "tends to"

I am not sure about the correct English wording. How about "The limit of r as t approaches zero is zero for a finite r. But it do not need to be zero if r is infinite."? In German I say "r geht gegen Null". I literally translated it as "r goes to zero". Maybe this was wrong.

Just to make clear, what I mean with infinite distances:
Separate the distance r between two objects into finite segments of equal length an number them beginning with 1. Now assign segment 1 to segment 2, segment 2 to segment 4 and so on. If you can assign each segment i to another segment 2·i than r is infinite.