The Universe: Finite or Infinite?

[Chronos]

Why is that surprising? You are solving for an indefinite integral.

 

[Dmitry67]

Aha... what is the difference between "not defined/defined" and "not exist/exist"?

Not exists:
number of smth = 0

Not defined:
number of smth = FATAL ERROR.

 

[DevilsAvocado]

Not exists:
number of smth = 0

Not defined:
number of smth = FATAL ERROR.

Okay, thanks Dmitry6.

I was "hooked" on the "parallel" to:

ln(1E-100) = -230,258509338289
ln(0) = FATAL ERROR

(My "intuition" tell me that if you claim to create smth, then you probably also need a "creator", and that's not "likeable". On that I agree with +110%!)

Let's talk about:
1) "So the initial inflation may be a solution. But it is difficult to provide more details now."

2) "Very likely, in string theory, or LQG the very nature of time is different few plank times after t=0."


Q1) If the universe is infinite; I derive from 1 that you accept the thought that spacetime/matter/laws was "spread" infinitely at t=0+1plank? I.e., it was NOT infinitely already "there", for some kind of "spontaneous symmetry breaking", right?

Q2) GR says that gravity slows down time. Could the extreme density at t=0 have made "room" for an "infinite inflation spreading" of CMB/laws?

Q3) If (the yet speculative) LQG is correct, then Q1 must also be correct, right? Since we are talking about the Big Bounce, right?

Q4) If Q1 is wrong: How can one singularity (Big Bang/Big Bounce) be infinite?

Q5) Is your opinion that an infinite universe needs to have the same CMB/Laws of physics?

 

[Dmitry67]

Q1. No, if universe in infinite now, it was ALWAYS infinite.
Q2. Time is slowed down for the objects inside gravity wells relatively to other observers outside. In the Universe, all observers were in the same conditions, and there were no 'outside' observers, so the answer is NO
Q3. Why? Big Bounce is compatible with both Finite and Infinite universes.
Q4. Singularity is not a point (while it is a point in some cases). Singluarity means 'some physical variable becomes infinite'. In infinite universe singularity (inifinite density) was just everywhere.
Q5. It is difficult to imagine how physical laws can be different in different areas or in different times. In both cases it would require some 'border line' with some laws on the left and another on the right.

 

[DevilsAvocado]

A fish cannot comprehend the existence of water. He is too deeply immersed in it. - Sir Oliver Lodge

Thanks Chronos! For the solution!
I must explain; I am a layman finding my way thru the "deep water"...
The background for this is (https://www.physicsforums.com/showpost.php?p=2466119&postcount=116":

... if k is zero or negative, the universe may have infinite volume, depending on its overall topology. It may seem counter-intuitive that an infinite and yet infinitely dense universe could be created in a single instant at the Big Bang when R=0, but exactly that is predicted mathematically when k does not equal 1.

And Dmitry67 hated the word "created".
And the explanation for my clumsy way thru the "water" is maybe here https://www.physicsforums.com/showpost.php?p=2470490&postcount=123".

So, what's your opinion – is the universe Finite or or Infinite? (with all respect to the "deep water" )

 

[DevilsAvocado]

Q1. No
Q2. NO
Q3. Why?
Q4. In infinite universe singularity (inifinite density) was just everywhere.
Q5. it would require some 'border line' with some laws on the left and another on the right.

Thanks!

The good news:
Q5 is a BIG relief for me. I was struggling with the (nervous ) 'borderline' question here https://www.physicsforums.com/showpost.php?p=2462473&postcount=113".
At least some indication that 'layman thinking' works to some extent...

Q2: Thanks. Missed relativity in GR completely.

The bad news:
I think the answer for Q1, Q3 and Q4 is way over my present understanding...?

Q1: I 'my world', if you take the "Cosmology point of view/God’s eyes view/Bird’s view" of the universe at t=2, and then look again at t=200, you must see some difference in size, since we can prove that the universe is expanding at least 2c?? As you explained in https://www.physicsforums.com/showpost.php?p=2457103&postcount=72"; "Now expand this line to 200%: every point on then new line will be 2*X. All distances now doubled.". To me, if distances are doubled, it means that the overall (Bird's) size must also be greater? I can't get this into my head...

Q3: Same as Q1. (Big) Bounce to me, means something is getting bigger/smaller/bigger (in cosmology).

Q4: I can imagine an extremely large singularity, but not infinite. In 'my world' you need to concentrate/contract matter to make a singularity, hence moving it from other parts towards a more common center. Only solution to this (for me) is to 'create' more matter, so that the density increases globally/infinitely. But that's not feasible... I think?

 

[Dmitry67]

I think the thing which puzzles you is the behavior of infinite sets.
You try to apply the concepts of 'total mass' or 'total volume' to infinite sets, while it is well known that such measures are not applicable.

There are 3 ways to compare sets:
1. measures, like length or volume. You can use it when sets are finite, or areas are finite, and when sets are 'smooth' enough
2. number of dimensions (when some spatial metrics is defined on the sets). Space can be infinite;
3. cardinality. cardinality is applicable to any sets, nothing is required. If Axiom of Choice is accepted, then any sets can be compared using cardinality.

You always think about #1, while it is not applicable for infinite set.
When all sizes in the universe are doubled, and you believe then now it is 'twice is size', ask yourself, on what level are you talking: 1,2, or 3. If 1, then you can't use it for infinite sets.

To challenge your intuition, what set is 'bigger': a line or a 3D volume? Common sense tells us, that there are 'much more' points in 3D space then there are on the line. Yet, both sets have the same cardinality: you can map all points of a line to 3D space and all points of 3D space to a line so no point will be left and there will be 1-to-1 relationship. So you can't trust common sense.

 

[Dmitry67]

I can imagine an extremely large singularity, but not infinite.

Why not?
Say, density P=1/t everywhere in 3D space.
So P(X,Y,Z)=1/t
Here is an example of singularity infinite in size at t=0

 

[Chris Davison]

Hi everyone, I return after a couple of years,

Does the Universe have a limited life span or permanent existence? Is it limited or infinite in size? Is Earth the only inhabited planet? Has there ever been a period when no life of any sort existed anywhere in the Universe?

We can have a useful idea of the size of a lake or a forest, even of a state or country; however, looking away from Earth into space stretches the imagination to the extreme. Aware of my limitations I submit the following:

A choice needs to be made between finite and infinite size and between finite and infinite life-span.Without an understandable explanation as to what lies beyond the limits; my choice is for infinite in both cases.The finite-size view seems to be assuming a state of “absence of everything” at the edge of an Island-Universe. The finite-life view requires this same “absence of everything” before and after a limited life-span and it must also require a super-power capable of both universal creation and destruction. This power is not required if the assumption is made that the Universe had no origin and will always exist.Of course, infinite size and lifespan are not understandable concepts in the same way as the size of a lake or wood. This leads to the basis of my argument—in English, finite means limited, and to say that the Universe is limited is to say that once the limit is reached all trace of everything disappears including dimension; Now this is more difficult to accept than to assume infinite lifespan and size—It is reasonable to ask those who claim limited size and lifespan to explain how space and material came into existence from nothing, how it will disappear again, and to explain the situation beyond the edge of a finite-sized Universe; otherwise, are we not forced into the conclusion that the size and lifespan of the Universe are unlimited?

Barely detectable distant galaxies are very near objects indeed in a limitless Universe: they are as closer than the next grain of sand on an infinitely large beach. Although our tiny microcosm ( the detectable universe) will follow universal laws there has not been proof,observational or otherwise, of big-bang expansion.Infinite size contradicts the big-bang theory because the "proof" of the "Big Bang" is in part observational and the flawed calculations "proving" the "Big Bang" are based on the assumption that the Universe is finite in size and lifespan.also of course the Law of Conservation of Mass completely contradicts the "Big Bang" theory.In a Universe of infinite size, if there was a “bang” it was a local mini-bang, big only by our microscopic standards and not connected with”the origin”of a Universe that had no origin.

The Universe cannot expand or contract: these terms do not apply to infinite size, something of infinite age cannot be evolving with time. Matter: in one form or another always occupies infinite space and is not an“island” otherwise the “beyond the island” question remains. Only the components of space are subject to curvature not space itself; otherwise an understandable explanation of “curved nothing”is required.

The Universe does not have an “edge” or an “age”and any component or change would take an impossible infinite time to “cross” the Universe. (Of course, the expression”to cross”does not apply to infinite distance) Unlimited space, time and material have always and will always produce life at various levels; However, conditions required to produce life will occur infrequently by our standards and contact is unlikely. The nearest of a endless number of examples could well be located too far away for any form of communication.


I like and recommend Dr Rhawn Joseph's YouTube video on this subject:





Chris Davison

 

[Dmitry67]

Sorry, is it poetry or physics?

 

[DevilsAvocado]

Why not?
Say, density P=1/t everywhere in 3D space.
So P(X,Y,Z)=1/t
Here is an example of singularity infinite in size at t=0

This is spacey!

I have to think some more before 'computing' infinite sets... And jump on to the much easier part – infinite singularity!

Okay, maybe it’s because I think in 'pictures' and you think (the right way) in mathematics, that this doesn’t work for me. I’m going to try to get as close to your math as possible.

The density of a material is defined as its mass per unit volume:

\rho = \frac{m}{V}\,

I take it the same rule goes for the (infinite) universe? Ok, then if we then take the '2D Balloon Surface' as an analogy for universe, and use the Earth as the balloon (and forget about mass 'inside', and place all mass on the surface of Earth instead, and hope that it will work? ).

Now the surface of Earth will weigh 5.9736 × 10e24 kg at a radius of 6371 km (still hope that it will 'hold'!? ). For this to turn into a singularity, we use the Schwarzschild solution:

r_{s} = \frac{2GM}{c^{2}}

I skip the math , and pick the right answer from the web, and we get that the radius has to shrink from 6371 km to 9 mm (peanut-size), for the Earth mass to turn into a singularity!

Maybe this is not applicable on a 3D space? But I hope you see what I aiming at? The shrinking of volume to get higher density, to finally reach the Schwarzschild 'border'... and then I remember that you just mentioned that volume is not applicable to infinity, man this is weird...

But, now another question pops up! In an infinite universe, with infinite matter – how can you avoid the thing from turning into a singularity immediately at t=0+1plank... Schwarzschild would go bananas??

 

[DevilsAvocado]

Sorry, is it poetry or physics?

Ehhh well... right now my brain is somewhere in-between infinite poetry and finite physics... I think?

 

[DevilsAvocado]

Hi everyone, I return after a couple of years,

[Disclaimer: I’m only a layman]

Hi Chris, lots of questions and I’m going to give it a try:

"Does the Universe have a limited life span or permanent existence?"
We can’t tell yet, and the word existence is hard to put on the universe. What we do know is that the age of universe is 13.73 ± 0.12 billion years, since Big Bang. This is measured physically by the expansion using type Ia supernovae, temperature fluctuations in the CMB, and the correlation function of galaxies.

"Is it limited or infinite in size?"
Ask Dmitry67. (could be either)

"Is Earth the only inhabited planet?"
No one has called yet... But, my personal feeling is NO. The nearest galaxy Andromeda contains one trillion (10¹²) stars, and our own Milky Way contains 400 billion stars. There are probably more than 100 billion (10¹¹) galaxies in the observable universe (46.5 billion light-years). And we have found exoplanets (a lot!). So, it looks like a terrible waste of material if Earth was the only planet with excellent forums like this one!

"Has there ever been a period when no life of any sort existed anywhere in the Universe?"
Yes, definitely. From Big Bang until about 400 million years there were no stars = no life.

"...there has not been proof,observational or otherwise, of big-bang expansion"
Wrong. Actually in 1998 the http://en.wikipedia.org/wiki/Supernova_Cosmology_Project" published evidence that the expansion of the Universe is accelerating!

"Only the components of space are subject to curvature not space itself; otherwise an understandable explanation of “curved nothing” is required."
Wrong. The gravity from a massive object (such as a galaxy cluster or black hole) is warped space-time, bending everything in it – including the paths followed by light rays from a bright background source, creating Gravitational Lensing.

 

[Chronos]

Thanks Chronos! For the solution!
I must explain; I am a layman finding my way thru the "deep water"...
The background for this is (https://www.physicsforums.com/showpost.php?p=2466119&postcount=116":


And Dmitry67 hated the word "created".
And the explanation for my clumsy way thru the "water" is maybe here https://www.physicsforums.com/showpost.php?p=2470490&postcount=123".

So, what's your opinion – is the universe Finite or or Infinite? (with all respect to the "deep water" )

Thanks for the easy out, my view is the universe is observationally finite. I avoid speculating beyond that because it cannot be falsified.

 

[Dmitry67]

But, now another question pops up! In an infinite universe, with infinite matter – how can you avoid the thing from turning into a singularity immediately at t=0+1plank... Schwarzschild would go bananas??

Look at the formula for Schwarzschild raduis. Do you see something strange? r is propotional to M. Intuitively one could expect r^3 (as volume).

So yes, you must compress Earth to 6mm to make it a black hole. Now make Earth (using the same material) 10 times bigger (radius of equator). It is now 1000 times heavier, as we assume the same density, and volume increases as r^3. So Schwarzschild raduis will be 6meters. It contains 1000'000'000 more space, then before to accommodate 1000 time more mass, so the density of that object, to be converted into a balckk hole, is 1000'000 times less now!

As you see, for a constant initial density, Schwarzschild radius grows as r^3 of the object radius. So, it 8always* catches with an actual raduis! It means, that you can make a black hole of any material without compressing to - from ground, earth, air, and even interstellar gas, you just need to make a big enough volume of that material.

Einstein was the first who had realized that. For the infinite Unvierse it means that it collapses into black hole now matter how low an average density is. That is why he introduced the lambda, trying to save the Universe.

However, it is applicable to the static universe only, if Universe if expanding, then its density depends on an average density and rate of expansion. So, regrding 'why it does not form singularity immediately' - because it MUST be expanding!

 

[Dmitry67]

The density of a material is defined as its mass per unit volume:

\rho = \frac{m}{V}\,

I take it the same rule goes for the (infinite) universe?

Yes, you just use it 'locally', for small volumes here and there, you don't need (and you cant) to calculate the nominator and denominator for the WHOLE universe.

 

[DevilsAvocado]

It means, that you can make a black hole of any material without compressing to - from ground, earth, air, and even interstellar gas, you just need to make a big enough volume of that material.

Einstein was the first who had realized that. For the infinite Unvierse it means that it collapses into black hole now matter how low an average density is. That is why he introduced the lambda, trying to save the Universe.

However, it is applicable to the static universe only, if Universe if expanding, then its density depends on an average density and rate of expansion. So, regrding 'why it does not form singularity immediately' - because it MUST be expanding!

Thanks a lot. I feel shivers down my spine... maybe there is small possibility for me to really understand this... I’m going to take my calculator and actually solve the equations... this is maybe not as hard as I imagine from start... fantastic...

I’ll be back. Thanks again.

 

[DevilsAvocado]

Thanks for the easy out, my view is the universe is observationally finite. I avoid speculating beyond that because it cannot be falsified.

That’s probably a healthy approach to the problem. On the other hand, we have really 'bad fishes' in 'the water', who doesn’t even care there’s an http://en.wikipedia.org/wiki/Multiverse" ...

 

[DevilsAvocado]

Yes, you just use it 'locally', for small volumes here and there, you don't need (and you cant) to calculate the nominator and denominator for the WHOLE universe.

Okay thanks. That, my brain is slowly accepting.

 

[naeemakhtar]

re:universe:Finite or infinite.
i have gone through the all dicussion on the finiteness or infiniteness of the universe.When we talke about finiteness or infiniteness then we percieve a goematrical figure describing (length,area or volume) terms of the numbers.Whole dicussion revolves arroud some definte geomatrical figures(which maths has discoverd) to comprehend the structure of the universe,do we excuse to accept the probablity of existence of some undiscovered geomatrical figures or shapes which could have potential to explain the struture of the universe at BB(big bang) and transition in it explicitly.or Mathematics
is insufficient to cater the qustion.

 

[naeemakhtar]

re:universe:Finite or infinite.
i have gone through the all dicussion on the finiteness or infiniteness of the universe.When we talke about finiteness or infiniteness then we percieve a goematrical figure describing (length,area or volume) terms of the numbers.Whole dicussion revolves arroud some definte geomatrical figures(which maths has discoverd) to comprehend the structure of the universe,do we excuse to accept the probablity of existence of some undiscovered geomatrical figures or shapes which could have potential to explain the struture of the universe at BB(big bang) and transition in it explicitly.or Mathematics
is insufficient to cater the qustion.

 

[QuantumDream]

What a great topic and an amazing level of thought has been put into the discussion.

I tend to think the Universe does have it's limits and may have a degree of boundary outside the scope of matter verses spatial volume.

Spacial volume may be infinite, in that the room for a growing and expanding Universe may not bump into a large wall of matter to hinder it's expansion.

Matter however within this Universe does appear to be limited and finite based on the vast amount of spatial volume by which it is scattered. Matter appears finite within an infinite volume of space.

I find it hard to imagine a limit to the volume of space, but easy to imagine a limit to the length of our Universe within that infinite volume. Gravity is taking care of keeping what matter that does exist within this spatial volume some what contained.

Based on gravity, the matter in the Universe will have some type of boundary at the edge of its furthest length of expansion. What lies beyond? Empty space? The edge of another Universe? We can only imagine.

 

[DevilsAvocado]

naeemakhtar,
thanks for your thoughts.

Personally, I’m not that concerned about the 'shape' of the universe, it’s more like the 'scope' that is infinitely on my mind.
(as you can see )

 

[DevilsAvocado]

QuantumDream,

Nice and poetic thoughts, but I’m afraid I must put some 'brutal' science logic on the conclusion...

On the most basic level we could say that the universe consist of only two components: spacetime & matter (= energy), and spacetime is defined as the 'stuff' between the matter/energy.

Conclusion: No Matter = No Space

The universe is expanding, not into 'something', rather nothing...

This is the explanation from the experts.

(Even if my brain gets swollen by this into-nothing-logic )

 

[DevilsAvocado]

Einstein was the first who had realized that. For the infinite Unvierse it means that it collapses into black hole now matter how low an average density is.

Dmitry67, I’ve talked to Santa...

And he promised me a brand new Power Calculator for Christmas...

http://upload.wikimedia.org/wikipedia/en/thumb/6/6f/Powercalc.PNG/500px-Powercalc.PNG

With the new calculator, I will find time in the coming holidays to investigate infinite sets and the Schwarzschild solution, and come back with new (tiring ) questions in the beginning of the infinite year of 2010!

 

[cragar]

can this question ever really be answered?

 

[marcus]

...But, now another question pops up! In an infinite universe, with infinite matter – how can you avoid the thing from turning into a singularity immediately at t=0+1plank... Schwarzschild would go bananas??

Look at the formula for Schwarzschild raduis. Do you see something strange? r is propotional to M. Intuitively one could expect r^3 (as volume).

So yes, you must compress Earth to 6mm to make it a black hole. Now make Earth (using the same material) 10 times bigger (radius of equator). It is now 1000 times heavier, as we assume the same density, and volume increases as r^3. So Schwarzschild raduis will be 6meters. It contains 1000'000'000 more space, then before to accommodate 1000 time more mass, so the density of that object, to be converted into a balckk hole, is 1000'000 times less now!

As you see, for a constant initial density, Schwarzschild radius grows as r^3 of the object radius. So, it 8always* catches with an actual raduis! It means, that you can make a black hole of any material without compressing to - from ground, earth, air, and even interstellar gas, you just need to make a big enough volume of that material.

Einstein was the first who had realized that. For the infinite Unvierse it means that it collapses into black hole now matter how low an average density is. That is why he introduced the lambda, trying to save the Universe.

However, it is applicable to the static universe only, if Universe if expanding, then its density depends on an average density and rate of expansion. So, regrding 'why it does not form singularity immediately' - because it MUST be expanding!

Outstanding response to a frequently asked question. Expansion is the key to why the universe didn't immediately form a black hole when it was at high density, and also the key to why we don't live in a black hole with radius approximately the Hubble radius---things people often ask about. I want to keep track of this post, put it somewhere I can find it. Or maybe I will just adopt the explanation and use it myself.

 

[DevilsAvocado]

Outstanding response to a frequently asked question.

Yes, I agree. As I said earlier, this answer sends shivers down my spine. The thing that really excites me, is the fact that the "Schwarzschild radius grows as r^3 of the object radius", and this made me realize that this is (probably) inside my 'light-cone of mathematical understanding'. And it made me happy. I always thought that this kind of high-level science required (at least) differential calculus and/or integral calculus... and a lot of 'odd' symbols...

It’s been a hectic period before Christmas, but now I finally have the time too really evaluate this answer and do the math. I know it’s not that complicate (mathematically), I just need my brain to accept the 'deal' as well!

2010 is going to be a very interesting year!

 

[DevilsAvocado]

can this question ever really be answered?

Well, I don’t know if I’m the right (lay)man to give you the answer... but I’ll give it a try.

Science and technology have made tremendous progress the last century. If someone would have said in 1900 that in a hundred years – we are going to put a man on the Moon, and then send a remote-control-car to Mars, and then photograph the whole Universe when it was only 400 000 years old, from a satellite, and put the picture on the 'electronic net', so that everyone can sit at home and study the picture any time they like, etc, etc – that person would probably have been sent to a mental hospital...

No one today can say what the next hundred years will look like in science and technology (if we survive the threats against mankind). All we can do is guess that it will be astonishing.

Today: We can say that the shape of the observable universe (local geometry) limit the possibilities for the universe as a whole (global geometry). If the shape of the local geometry is spherical, then the global geometry must be finite.

Problem: Think of a football ground on earth. It seems pretty flat, right? But we do know that the surface of the Earth is round, a sphere! If the local geometry is only a 'football ground' compared to the global geometry, it can be hard to realize it’s actually spherical...

Status: In 2003 (confirmed 2008), scientist studying the data from the WMAP satellite, led to the suggestion that the shape of the Universe is a Poincaré sphere. And what is a Poincaré sphere, one might ask? Well, it’s a homology sphere, also known as Poincaré dodecahedral space. And a dodecahedron looks like this;

Alternatively, "the Poincaré homology sphere can be constructed as the quotient space SO(3)/I where I is the icosahedral group" (according to Wikipedia). And a disdyakis triacontahedron, or hexakis icosahedron, looks like this;

Or, we can make it simple (I like that! ) and say – a common example of a spherical truncated icosahedron, that has full icosahedral symmetry, is a soccer ball!

Now we are back on the flat football ground again!

 

[cragar]

thanks for the response , you put a lot of work into it .