Exploring the Possibilities of an Infinite Universe

[misanthropist]

So it's possible the universe could in fact be infinite and expanding? A singularity has an finite volume but infinite density, correct? Then isn't it possible for an infinite expanding universe to have an end? I recall reading the Theory of Everything by Hawking where he talked about how if you were able to travel at the speed of light and make it to the end of the universe you'd end up on the opposite side. Would this also work for an infinite expanding universe? Also, is it possible for there to be more than one singularity?

 

[jamie]

the is more than one singularity if fact there are many,black holes the big bang etc.
Hawking descibes in "the universe in a nutshell" the no boudary condition were as the universe has no boundary because it is warped to the point were it is sperical like the suface of a ball. This implies that if you traveled to the end of the universe you would arrive back at the begining.
bear in mind that this is only a theory and not fact but it would remove the possiblity of an infinite universe
regards jamie

 

[Nenad]

If you solve einsteins equations of general relativity, you see that the universe started from a singularity and will in fact end at some time in a singularity. And for the more than one singularity thing, jamie is right, black holes and primortial black holes are singularities also.

 

[nautica]

If you solve einsteins equations of general relativity, you see that the universe started from a singularity and will in fact end at some time in a singularity. And for the more than one singularity thing, jamie is right, black holes and primortial black holes are singularities also.

Yes, but this does not take into account Quantum theory and the uncertainty principle.

Nautica

 

[meteor]

There are people that claim that the initial singularity can have an infinite volume, but I'd like a reference for that. Looking at my book "An introduction to modern cosmology", by A. Liddle, he says in page 112:
"At the time of the Big Bang, all the material in the Universe is crushed into a point of infinite density, and physical laws as we know them break down. For that reason. the Big Bang is also known as the initial singularity."

He speaks about a point. But, of course, he may be wrong

 

[marcus]

Lineweaver "Inflation and the Cosmic Microwave Background"
you know the link
I will find a page for you
figure 1 should do it, actually

Like you say, Liddle could be wrong
or he could be right!

infinite extent (or else some positive finite volume) would happen in the case the universe is spatially flat
(the Ω = 1 case)

and also the &Omega; < 1 case, but people mostly talk about the flat case.

Beginning from a point would only happen in the positive curvature &Omega; > 1 case.

You must have seen the error bounds, the figure for Omega derived from current data is something like

&Omega; = 1.02 +/- 0.03

this means it could be flat (and have come from an infinite expanse of classical singularity)

or it could be >1, the positive curvature case (and have come from a classical point singularity)

and the current data does not help!

-------------
It is in any case just a manner of speaking because there is no singularity in nature only in mathematical models. But the current data does not distinguish between the universe having started expanding from a spatially infinite flat thing, or from a small pointlike thing.

the error bound on Omega includes both possibilities.

I guess I should find you a page reference for this fact:

&Omega; = 1.02 +/- 0.03

It is in every publication of the main WMAP results. but I can also find it in familiar reader-friendly places like Michael Turner or Lineweaver.
Back soon

 

[marcus]

Yeah, here are lots of links.
this is the firstpost of the Astronomy Reference library sticky thread:

------quote----
Charles Bennet et al.
http://arxiv.org/astro-ph/0302207
see table 3 on page 33---"Best" Cosmological Parameters
from the article
"First Year WMAP Observations, Preliminary Maps and Basic Results"

Charles Lineweaver
http://arxiv.org/astro-ph/0305179
"Inflation and the Cosmic Microwave Background"

Michael Turner
"Making Sense of the New Cosmology"
http://arxiv.org/astro-ph/0202008

Wendy Freedman and Michael Turner
"Measuring and Understanding the Universe"
http://arxiv.org/astro-ph/astro-ph/0308418

The finiteness or infiniteness of space turns on how accurately they can measure a number called Omega. This is the first thing listed at the top of Bennett's Table 3.
The current WMAP data say that Omega = 1.02 +/- 0.2 which is tantalizingly close to one. If Omega is exactly one, then space is flat and infinite. But if Omega is even slightly greater than one, then space may LOOK flat but on a very large scale it may curve around on itself and be finite. Based on observations as of right now we cannot be sure either way.
-------end quote----

apparently you just have to look in Bennett Table 3.
https://www.physicsforums.com/showthread.php?p=136400#post136400
Just tell me if more detail or confirmation is needed.

 

[Didd]

"So it's possible the universe could in fact be infinite and expanding?"
According to the recent discovery of astronomers, yes! It is a special kind of force which is playing a role in the expansion of the universe.

 

[meteor]

Hi there
I've been peering both articles, Lineweaver's (i had it printed), and Bennett (very interesting indeed)
I can't find any reference in Lineweaver's article that suggests an infinite volume singularity. In Lineweaver's figure 1 there are only the trajectories of the different horizons, but i don't see why all that is showed in the figures can't emerge from a point.
Bennett's table 3 only gives a value of cosmological parameters,but I can't figure how it implies an infinite volume singularity
I need a reference. This thing of an infinite volume singularity has always annoyed me

 

[marcus]

... In Lineweaver's figure 1 there are only the trajectories of the different horizons, but i don't see why all that is showed in the figures can't emerge from a point.
Bennett's table 3 only gives a value of cosmological parameters,but I can't figure how it implies an infinite volume singularity
I need a reference...

I can well appreciate the frustration with these ideas.

I believe that to satisfy you I must convince you of two things:

A. If it is infinite now then it must always have been infinite.

B. One of the possibilities for a "spatially flat" universe, at the present time, is for it to be spatially infinite.

-------------------------
For A. I cannot think just now how I may persuade you it is true, so I will postpone that. It has always seemed intuitively obvious that something now infinite could not have come by any conceivable process of expansion from something that was finite in the past. But I cannot think how to make an argument to prove this, right now. So let us think about B.

-----------------------------
In discussing B we are just considering the universe at present. Is it spatially infinite or not? We cannot tell for sure. We only know that it seems spatially flat and that one of the likely possibilities for flat is infinite.

You have looked at Bennet WMAP data and that should suffice.

We get told that Omega =1 or else very close like Omega = 1.01

(people seem rarely to think about the Omega = 0.99 case these days, it is always assumed to be 1 or just on the positive side of 1)

the Omega = 1 case is called "spatially flat" and that implies that the universe either has some nontrivial topology like toroidal----which BTW is a bit awkward to imagine coming out of a point!-----or else that it is spatially infinite.

the Omega = 1.01 case is called "positive curvature" and it definitely implies finite! Probably that is the most intuitive and satisfying to picture.

So far i am not sure that I have provided any help at all. but will post this anyway, and perhaps can return to it later, or if you reply then I can see what needs the most explanation.

Meteor, the GR17 conference at Dublin has started.

BTW Rovelli posted at his website the Panel Discussion questions that people raised at the May LoopFoam conference in Marseille.
It occurs to me that Barcelona is not too far from Marseille and you may have thought of going there.
the Panel discussion (which was at the end of the conference) raised many probing issues, some people
like Hendryk Pfeiffer and Etera Livine asked many questions of the panel
but perhap you have seen the list already

 

[meteor]

the Omega = 1 case is called "spatially flat" and that implies that the universe either has some nontrivial topology like toroidal----which BTW is a bit awkward to imagine coming out of a point!-----or else that it is spatially infinite

That's the problem marcus! I don't see why a flat universe implies an infinite universe. I assume that the universe is flat (euclidean, two parallel lines never meet, etc...). I really think that is not a coincidence that the value of omega is so close to 1. It really has to be 1!. But why flatness implies infiniteness? Why can't the universe suddenly stops at a certain distance?
I agree that a universe that started in a point singularity, and being flat now, cannot be infinite. But all the articles and books that I've read declare:
a)the universe started in a point singularity
or
b)the universe started in a singularity
no one says "the universe started in an infinite volume singularity".

In fact, if I type in google "infinite volume singularity", the only things that appear are a pair of articles about AdS/CFT correspondence, and a article about QCD, nothing to do with Big Bang Cosmology

 

[setAI]

I don't see why a flat universe implies an infinite universe.

if the universe is truly flat then we exist in an infinite space- this is a subtle tautology-

the universe cannot simply cease- it must either curve back into itself or extend forever because Nothing does not posess the quality of existence so Nothing cannot provide a mechanism such that it forms a physically existent spherical boundry around the universe- only Something can provide a physical boundary- and if the boundary is something- then it is by definition a part of the universe

continuing- I believe- or rather I feel that it is unavoidable and not merely a belief- that ultimatly the whole cosmos- All existence MUST be infinite/eternal regardless of the flatness of our observed universe- even if our universe where finite- it is axiomatic that infinite other universes must exist- as literally Nothing could prevent other universes from existing- if our universe is a finite space from a singularity- then there is no rational way to deny that such singularities exist/have existed "elsewhere" throughout "eternity"-

the common sense vew that is emerging is that we live in an infinite [or transfinite] universe and that there also are an infinity of infinite universes-perhaps in infinite dimensions as well

some feel that this infinity/eternity cannot be assumed- but I'm quite sure that it is all tautology- Spinoza seemed to figure this all out long ago-

AXIOM OF INFINITY: we can define a system X as finite because it is limited by NOT-X [all things other than X]- this works for all systems because no system includes everything- but if X is All Existence- if X DOES include everything- then Not-X is NON-Existence which is necessarily self-negating and cannot limit X- thus if X is Existence- then it is infinite QED [a succinct encapsulation of Spinoza’s Ethics]


___________________________

/:set\AI transmedia laboratories

http://setai-transmedia.com

 

[meteor]

if the universe is truly flat then we exist in an infinite space- this is a subtle tautology

I don't see the reason in your tautology. Imagine it: the door of your house is flat, but not infinite

the universe cannot simply cease- it must either curve back into itself or extend forever because Nothing does not posess the quality of existence so Nothing cannot provide a mechanism such that it forms a physically existent spherical boundry around the universe- only Something can provide a physical boundary- and if the boundary is something- then it is by definition a part of the universe

Nothing does not have to provide any mechanism, is only space expanding into nothing, (or perhaps there's something after all?. i mean, a superuniverse encompassing our universe and others. Think about it, it has always occurred along the history, first our solar system, then it was thought that the only thing that existed was the galaxy, then,...)

I will end with this quote of wikipedia(i have not edited it)



http://en.wikipedia.org/wiki/Big_bang
Using current physical theories to extrapolate the Hubble expansion of the universe backwards leads to a gravitational singularity, at which all distances become zero and temperatures and pressures become infinite. What this means is unclear, and most physicists believe that this is because of our limited understanding of the laws of physics with regard to this type of situation, and in particular, the lack of a theory of quantum gravity

At which all distances become zero: that is, a point

 

[marcus]

I really think that is not a coincidence that the value of omega is so close to 1. It really has to be 1!

I sympathize very much about this. It is so close that it seems as if it really should be exactly 1.

But there may be some other explanation, something in somebody's inflation scenario, something speculative that might later be verified.
Maybe future cosmologists will find some reason why, even though it is not exactly 1, it is force to be very close.

IIRC the apparent flatness was one of the motivations for Guth to invent inflation scenarios. It would be an explanation, he hoped, for why it is so close to spatially flat.

it is all too frustrating. We humans do not know enough yet. though I half-believe and want it to be flat, I must not let myself believe this, because it is not known

But why flatness implies infiniteness? Why can't the universe suddenly stops at a certain distance?

the unspoken assumption is that it is a differentiable manifold---the kind of model for space given us by Riemann around 1840-1850.
It is in that context that we say "curvature = zero" and "flat". the idea of manifold gives these terms meaning and it is the basic model in cosmology.

a 3D flat manifold must be infinite, or it must be analogous to a donut, in some sense.

Manifolds have been "classified" by mathematicians. there are only limited possibilities. If it does not loop around and join itself

The donut I am thinking of is a flat piece of paper with the right edge "identified" with the left edge. and the top edge with the bottom. all the metric geometry stuff you do on the paper is familiar flat euclidean---except when the pencil runs off the right ede it reappears on the left etc.

that is what i mean by a donut and there is a flat compact 3D space analogous to that.

let us call it a "toroidal" flat 3D space

the mathematicians prove to their complete satisfaction that if a 3D manifold is flat it must be toroidal or infinite.
------------------------

whoah! you also want to consider manifolds with BOUNDARY. I was not thinking of manifolds that have some kind of edge. that makes it more complicated. I cannot picture the universe having an edge.

maybe someone else has considered that case. normally I don't think one does but maybe someone can talk about it. I am limited to discussing universes that don't have any boundary.

so positive curvature, for me, means like a sphere (and it can come from a point initially I guess)
and zero curvature, in my simple view, means toroidal or more likely infinite euclidean 3D space (I can't see either one coming from a point)

I agree that a universe that started in a point singularity, and being flat now, cannot be infinite. But all the articles and books that I've read declare:



a)the universe started in a point singularity
or
b)the universe started in a singularity
no one says "the universe started in an infinite volume singularity".

this could be raised as a criticism of those articles and books

they talk about the universe starting at a singularity but they take for granted that the reader understands that a singularity does not have to be a point but can have extent, so they neglect to say it.

this carelessness or negligence on the authors part is a big nuisance
and causes a lot of misunderstanding

If only they would make it a custom to always remind people that a singularity can be infinite extending in various dimensions. It can be a 3D singularity, or a 1 D singularity (a long line where the equations blow up at every point on that line). Singularities that one meets in Gen Rel can be various sizes and shapes--so why can't the cosmology-writers regularly point this out to us?

maybe you would be satisfied if ONE authoritative source mentioned the possibility, I think perhaps the Ned Wright Cosmology FAQ does. Let me go look. I will be right back.

 

[setAI]

I don't see the reason in your tautology. Imagine it: the door of your house is flat, but not infinite

the door is bounded by air and the door frame and the spacetime/causality which allows these forms to exist as they do- which is something

Nothing does not have to provide any mechanism, is only space expanding into nothing,

Nothing has no qualities such as a "place" for which something can exist or expand into- Nothing cannot be an empty space becasue an empty space is something- Nothing by definition can have no dimension/ no extent/ no causality/ no aspect which can in any way affect or be affected by something- Nothing doesn't even have the quality of existence-

the point is- if the universe we observe exists as a finite volume and does not curve back into itself- it MUST be bounded by SOMETHING- whether that is an empty space or some other space- a SPACE is something very specific- it is not nothing no matter how "empty" it is- emptiness is something- ultimately and unavoidably Nothing by definition does not exist- it's a human created illusion/paradox


___________________________

/:set\AI transmedia laboratories

http://setai-transmedia.com

 

[meteor]

I think that all we agree that if the universe started in a point cannot be infinite now
Ok, give me a reference that say that the universe started in a not pointlike singularity and I will believe you.
yes, marcus, manifolds with boundary. They seem attractive to me

 

[marcus]

Sure, here for example

http://www.astro.ucla.edu/~wright/cosmology_faq.html#HOLE

"Is the Big Bang a Black Hole?


The Big Bang is really nothing like a black hole. The Big Bang is a singularity extending through all space at a single instant, while a black hole is a singularity extending through all time at a single point. For more, see the sci.physics FAQ."

----------------------
a black hole singularity is like an infinitely long line----a point extended in time

a big bang singularity can be pictured as an infinitely extending 3D space where something occurred at one instant in time
-----------------------

maybe we should look at the sci.physics FAQ that they refer to

before doing that let's look at other ned wright FAQ
http://www.astro.ucla.edu/~wright/infpoint.html

"How can the Universe be infinite if it was all concentrated into a point at the Big Bang?

The Universe was not concentrated into a point at the time of the Big Bang..."
----------------------
http://www.astro.ucla.edu/~wright/cosmology_faq.html#RB

"Is the Universe really infinite or just really big?


We have observations that say that the radius of curvature of the Universe is bigger than 70 billion light years. But the observations allow for either a positive or negative curvature, and this range includes the flat Universe with infinite radius of curvature. So we know empirically that the Universe is bigger than several times the observable Universe. Since we can only look at small piece of an object that has a large radius of curvature, it looks flat. The simplest mathematical model for computing the observed properties of the Universe is then flat Euclidean space. This model is infinite, but what we know about the Universe is that it is really big."

that is, the simplest model of the universe is flat infinite, and we have no data that disproves this, but we do not know for sure. it could possibly be non-infinite, but just very big.
---------------------

I can't get to the sci.physics.FAQ page that he gives the link to, right now.
maybe later.
but I am curious if this is informative enough
ned wright is one writer who at least takes the trouble to say explicitly
what so many others seem to neglect to mention!

 

[meteor]

Thanks. Ned Wright clarifies all.
But anyways is HIS opinion against the opinions of other important people that say that the Big Bang started in a point singularity

 

[setAI]

I think that all we agree that if the universe started in a point cannot be infinite now
Ok, give me a reference that say that the universe started in a not pointlike singularity and I will believe you.
yes, marcus, manifolds with boundary. They seem attractive to me

infinte universe conjectures do not say that the universe expanded from merely a single point that was isolated in a void- the idea is that the universe was already an infinite space of infinite heat/density/etc and that the universe we observe expanded from a single point WITHIN that infinite space[ie a very small region- I personally feel that it is impossible for a universe to emerge from a true singularity becasue a zero-size point cannot expand- or rather it can expand infinitely but becasue it is zero-size even if it expands for eternity will always be zero size ] - so that the universe is still infinite but expanding [an infinite space can infinitely expand without paradox]-

here are some animated models of this: http://www.anzwers.org/free/universe/bigbang.html

___________________________

/:set\AI transmedia laboratories

http://setai-transmedia.com

 

[marcus]

Thanks. Ned Wright clarifies all.
But anyways is HIS opinion against the opinions of other important people that say that the Big Bang started in a point singularity

meteor I don't know of any important cosmologist, writing in this century, who says the Big Bang started at a point.

there may be string theorists who say this, they say many things.
there may also be Inflation Scenario people and Multiverse people
who deal with highly speculative stuff that has no experimental checks on it. Fantasy basically. Andrei Linde, for example, might take it into his head that the universe started with a point---a little pimple in some other universe maybe.

But suppose we filter out all these highly speculative Scenario writers and just look at working cosmologists.
these are the people for whom cosmology is observational
they have a model----Friedmann equations---and it has parameters and they send up satellite observatories and carefully measure CMB and count galaxies and examine supernova statistics and gravitational lensing statistics and Xray stats and all that and they try to refine the measurment of the parameters of the model.

Wendy Freedman
Sean Carroll
Ned Wright
Michael Turner
Charles Lineweaver
Tamara Davis

If a professional society wants a survey talk or review paper on the current state of cosmology they ask one of these. And there are some other names I just can't think of now---but basically there is an idea of mainstream working cosmologist

None of these people, so far as I know, claim that the universe came from a point!

But you may know different! It would be interesting for me if you would come up with someone who is a working cosmologist actively trying to fit the model to the data (not just dreaming about Multiverses or whatnot) who says it came from a point.

My sense is that these people think a finite universe coming from a pointlike thing is definitely possible. And they probably think that eventually they will eventually be able to say yes or no. We pay them to decide questions like that. these are precisely the people paid to get the data and decide issues like that. But for now they can't say, and the simplest thing to assume is flat infinite. so that is a kind of working assumption to use until and if one gets evidence of finiteness with some definite radius of curvature.

But if you provide an online source that contradicts this it would be especially nice for me and potentially educational. Particularly if recent, since 2000 say. If I can see it as serious mainstream and the guy
says somehow he knows the U is finite and came from a point that would
broaden my perspective and would represent a welcome change.

BTW everybody agrees that the observable came from a point AFAIK, just to be sure that is not what we are discussing. I don't think there is anyone arguing about that.

that is what you see in lineweaver Figure 1, the horizons all come out of one point----but the big bang singularity is all along the X axis and in one of his figures you see the X-axis stretch away indefinitely to the right and left-----that is the initial singularity extending out beyond the middle of the figure where the observable stuff and the horizons are

so the observable comes from a single point in the infinite-volume bigbang singularity.

and the hideously boring and frustrating fact is that this is just a working assumption! it is only the best picture we have to work with so far. nobody really knows for sure