Do infinite space models contradict Olber's paradox?

[Huldrich]

Hi, I am new here and I don't know if I am in the right forum. I have a master in physics and am actually reading the book Gravity of James B. Hartle. I could not answer a question about infinite, homogenous and isotropic models of the universe based on the FRW-metric. This model requires that matter is distributed evenly all over the universe. But since it is a flat infinite model, homogeneity implies that the quantity of matter should be infinite, which cannot be because of Olber's paradox. However, if matter is finite the universe cannot be homogenous at all points. There must be some kind of cloud of matter, beyond which matter starts to rarefy to finally disappear completely. So homogeneity contradicts infinity in my opinion.

 

I am also asking myself if there can be a observable difference between the expansion of space and expansion of matter in an infinite universe. In a closed system, it is clear that space expands. But an expanding flat infinite universe doesn't make sense to me: it can't get bigger because it's already infinite. So I am asking myself if it is equivalent to say that only matter expands, not space, in such a model.

 

Do you agree or can you show me where I am wrong?

Edited August 29, 2012 by Huldrich

[D H]

Olbers' paradox results from assuming an infinitely old, infinitely large, and static (non-expanding) universe. A universe that is infinitely large but has a finite age and is expanding does not run afoul of the paradox.

[Spyman]

But an expanding flat infinite universe doesn't make sense to me: it can't get bigger because it's already infinite.

The expansion is scalar. Try to imagine how a flat infinite universe would appear to you, if you and your measuring ruler would be shrinking.

[Huldrich]

Ok, but if the quantity of matter is infinite, how then I have to understand the big bang, which is seen as singularity? Does it make sense that to say that an infinite quantity of matter was concentrated at one point at time 0 ? And when the universe expanded, in any case matter must have been distributed over a limited region of the infinite universe, otherwise it wouldnt be a singularity. I think that homogeneity of matter is only required to be over a limited region, maybe over the visible universe. Unfortunately I cant read this explicitly in Hartle's book. This is why I am not sure about it. Maybe someone can confirm?

[Spyman]

We don't understand the initial part of the Big Bang yet, since we don't have a fully working theory of quantum gravity, as such there is no confirmed singularity at the beginning of the Big Bang and the Big Bang theory itself currently starts from an early hot, dense phase shortly after the Bang.

 

The Big Bang theory is not about an explosion sending out matter from a concentrated point into a surrounding empty void. In the Big Bang theory there is no edge of the Universe with a infinite empty void outside, the Universe is everything and not a container inside something larger.

 

We don't know how big the Universe is or how large it was at the initial moment of the Big Bang, all we know is that the part we can observe was much more dense back then and will become much more diluted in the future. The Universe could very well have been infinite already at the initial Bang.

 

Extrapolation of the expansion of the Universe backwards in time using general relativity yields an infinite density and temperature at a finite time in the past. This singularity signals the breakdown of general relativity. How closely we can extrapolate towards the singularity is debated-certainly no closer than the end of the Planck epoch. This singularity is sometimes called "the Big Bang", but the term can also refer to the early hot, dense phase itself, which can be considered the "birth" of our Universe.

http://en.wikipedia.org/wiki/Big_Bang#Timeline_of_the_Big_Bang

 

However, certain physical phenomena, such as singularities, are "very small" spatially yet are "very large" from a mass or energy perspective; such objects cannot be understood with current theories of quantum mechanics or general relativity, thus motivating the search for a quantum theory of gravity.

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

 

The Big Bang is not an explosion of matter moving outward to fill an empty universe. Instead, space itself expands with time everywhere and increases the physical distance between two comoving points. Because the FLRW metric assumes a uniform distribution of mass and energy, it applies to our Universe only on large scales-local concentrations of matter such as our galaxy are gravitationally bound and as such do not experience the large-scale expansion of space.

http://en.wikipedia.org/wiki/Big_Bang#FLRW_metric

 

The universe is immensely large and possibly infinite in volume. The region visible from Earth (the observable universe) is a sphere with a radius of about 46 billion light years, based on where the expansion of space has taken the most distant objects observed.

http://en.wikipedia.org/wiki/Universe#Size.2C_age.2C_contents.2C_structure.2C_and_laws

 

No evidence exists to suggest that the boundary of the observable universe constitutes a boundary on the universe as a whole, nor do any of the mainstream cosmological models propose that the universe has any physical boundary in the first place, though some models propose it could be finite but unbounded, like a higher-dimensional analogue of the 2D surface of a sphere which is finite in area but has no edge.

http://en.wikipedia.org/wiki/Observable_universe#The_universe_versus_the_observable_universe

[Huldrich]

I appreciate your effort Spyman, thanks. However, you don't tell me something new. I already wrote in my first question that I know that a flat infinite universe is supposed to be homogenous as for its distribution of mass. So evidently there can be no boundary. But in this case an infinite universe must contain an infinite amount of matter. This is what I don't understand. It may not contradict with Olber's paradox since it uses another model as stated by DH. I just can't figure out an infinite universe filled everywhere with matter. It's nonsense. In my opinion, expansion of space implies that the universe is closed, like a 3-sphere for instance. The amount of matter in such models is finite. Models that lead to infinite matter can be ruled out in my view although I can't exactly say why.

Edited August 30, 2012 by Huldrich

[Spyman]

Well to be honest, I don't think I am able to grasp an infinite universe either, homogenously filled or not.

 

But if you want to advance the thread and discuss this further, then you need to focus on what is troubling you with "an infinite universe filled everywhere with matter", why "expansion of space implies that the universe is closed" and how "models that lead to infinite matter can be ruled out".

 

Can you ask more specific questions or present detailed logic which the discussion can continue around? Because right now, all I can interpret is that you don't understand how an infinite universe can contain an infinite amount of matter, which seems pretty evident to me.

 

Is it the *must* that troubles you, from the cosmological principle?

 

In modern physical cosmology, the cosmological principle is the working assumption that observers on Earth do not occupy an unusual or privileged location within the universe as a whole, judged as observers of the physical phenomena produced by uniform and universal laws of physics. As astronomer William Keel explains:

 

The cosmological principle is usually stated formally as 'Viewed on a sufficiently large scale, the properties of the Universe are the same for all observers.' This amounts to the strongly philosophical statement that the part of the Universe which we can see is a fair sample, and that the same physical laws apply throughout. In essence, this in a sense says that the Universe is knowable and is playing fair with scientists.

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

[Iggy]

I am also asking myself if there can be a observable difference between the expansion of space and expansion of matter in an infinite universe. In a closed system, it is clear that space expands. But an expanding flat infinite universe doesn't make sense to me: it can't get bigger because it's already infinite. So I am asking myself if it is equivalent to say that only matter expands, not space, in such a model.

I think saying that matter expands through space is equivalent to saying that space expands. Here is a popular FAQ that answers:

 

Are galaxies really moving away from us or is space just expanding?

 

This depends on how you measure things, or your choice of coordinates. In one view, the spatial positions of galaxies are changing, and this causes the redshift. In another view, the galaxies are at fixed coordinates, but the distance between fixed points increases with time, and this causes the redshift. General relativity explains how to transform from one view to the other, and the observable effects like the redshift are the same in both views.

Part 3

of the tutorial shows space-time diagrams for the Universe drawn in both ways.

 

link

 

But, I don't understand your assumption that only part of a spatially infinite universe can have matter.

 

Ok, but if the quantity of matter is infinite, how then I have to understand the big bang, which is seen as singularity? Does it make sense that to say that an infinite quantity of matter was concentrated at one point at time 0 ? And when the universe expanded, in any case matter must have been distributed over a limited region of the infinite universe, otherwise it wouldnt be a singularity. I think that homogeneity of matter is only required to be over a limited region, maybe over the visible universe. Unfortunately I cant read this explicitly in Hartle's book. This is why I am not sure about it. Maybe someone can confirm?

Homogeneity means that any large area of space you look at will have the same density. General relativity, which breaks down at the singularity like Spyman said, also does not actually describe the topology of the universe. From a 1999 Scientific American:

 

A broader issue, however, is that relativity is a purely local theory. It predicts the curvature of each small volume of space--its geometry--based on the matter and energy it contains. Neither relativity nor standard cosmological observations say anything about how those volumes fit together to give the universe its overall shape--its topology. The three plausible cosmic geometries are consistent with many different topologies. For example, relativity would describe both a torus (a doughnutlike shape) and a plane with the same equations, even though the torus is finite and the plane is infinite. Determining the topology requires some physical understanding beyond relativity.

 

link

Edited August 30, 2012 by Iggy

[Huldrich]

Can you ask more specific questions or present detailed logic which the discussion can continue around? Because right now, all I can interpret is that you don't understand how an infinite universe can contain an infinite amount of matter, which seems pretty evident to me.

 

It is not the mathematical side I don't understand: assuming that space is evenly filled with galaxies, one can suppose that they are like particles in an infinite volume and approximately constitute a cosmological fluid. So you get a matter density, which you can integrate over the volume to obtain the amount of matter contained in it. Since the volume is infinite, the matter is too. That is perfectly clear to me. The problem is that I feel uneasy with a universe of infinite matter, not because there is no center. I just think that it is not physical and it should be possible to show some contradiction. I first thought that it should lead to Olber's paradox. But it doesn't because there the universe is static while here it is expanding. As can be read in Hartle's book Gravity, light rays can only reach us from a certain distance in a expanding infinite universe, so even if the sky contained an infinite number of stars their light that reaches us would be finite and the sky would not be bright but dark.

 

My point of view is rather philosophical. I very like a spherical closed universe because it is similar to Earth's surface on which we live. Its volume is also expanding but finite as well as the matter in it. Such a universe is much more familiar to me than an infinite one with infinite matter. Physically spoken, matter cannot be infinite in my opinion even though mathematically it can. It's just a subjecive feeling. But I am sure that someone will once find an argument against infinite universes or experimental data will show it.

 

As can be read on Wikipedia: The Shape of the Universe "The latest research shows that even the most powerful future experiments (like SKA, Planck..) will not be able to distinguish between flat, open and closed universe if the true value of cosmological curvature parameter is smaller than 10⁻⁴. If the true value of the cosmological curvature parameter is larger than 10⁻³ we will be able to distinguish between these three models even now." If the universe is infinite flat, the cosmological curvature parameter is exactly 1. It seems to me that it is very unlikely that a continuous physical parameter can exactly be a natural number. And with the dark matter that is more and more discovered, the cosmological curvature parameter, which in fact is made up of densities, is more likely to be > 1 than < 1. In this case the universe is spherical. I think this eventualty would have pleased most Greek and medieval philosophers...

[JohnStu]

Didn't stars not form until after the Big Bang? Thus stars 13.5 billion aprox plus light years away don't have their brightness

[Spyman]

Didn't stars not form until after the Big Bang? Thus stars 13.5 billion aprox plus light years away don't have their brightness

No, while we can't see light older than the Big Bang there is nothing preventing stars to exist much further away and current expansion of space lets us observe stars in a sphere with a radius of about 46 billion light years.

 

The age of the universe is estimated to be 13.7 billion years. While it is commonly understood that nothing can accelerate to velocities equal to or greater than that of light, it is a common misconception that the radius of the observable universe must therefore amount to only 13.7 billion light-years. This reasoning makes sense only if the universe is the flat, static Minkowski spacetime of special relativity, but in the real universe, spacetime is curved in a way that corresponds to the expansion of space, as evidenced by Hubble's law. Distances obtained as the speed of light multiplied by a cosmological time interval have no direct physical significance.

http://en.wikipedia.org/wiki/Observable_universe#Misconceptions

 

The universe is immensely large and possibly infinite in volume. The region visible from Earth (the observable universe) is a sphere with a radius of about 46 billion light years, based on where the expansion of space has taken the most distant objects observed.

http://en.wikipedia.org/wiki/Universe#Size.2C_age.2C_contents.2C_structure.2C_and_laws