Space Finite: Flat/Open Universe Possibilities

[εllipse]

If space is flat or open, does that make it infinite? Is a closed universe the only type that would be finite, or would a flat or open universe also somehow be finite?

 

[Garth]

If space is flat or open, does that make it infinite? Is a closed universe the only type that would be finite, or would a flat or open universe also somehow be finite?

Welcome to these Forums ellipse! A good question even if it seems obvious at first.

Generally speaking if space is flat or hyperbolic (like the 'seat' of a saddle shape at every point) then it would be open and infinite and unbounded.
If space is spherical (a 3D analogue of the 2D surface of a sphere ) then it would be closed and finite although still unbounded. Go off in a straight line and hypotheticaly you could return to where you started from. Actually while the universe is expanding you would have to go faster than light to get round and therefore this journey is impossible in standard GR cosmology.

However as I said here (post #26) the evidence of the data of the CMB from WMAP, BALOON and COBE seems to indicate that while the universe appears flat there is some indication that it is also finite in size. As an alternative to my suggestion in that link, this led to the proposal that the universe was like a football (soccerball) with flat hexagonal plates welded together into a 'sphere'. Each plate would be like a space invaders game, go off stage left and you would reappear stage right! I don't think this model has lasted very well.

Garth

 

[Hurkyl]

Generally speaking if space is flat ... then it would be open and infinite and unbounded.

Not true. It's fairly easy to construct closed, finite topologies that are everywhere flat. For example, the usual model of a 3-D torus.

 

[Garth]

Yes, my "generally speaking" was referring to the three Friedmann models.
The Torus is joined by the cylinder and cone as conformally flat models that are finite.
Garth

 

[εllipse]

The followup question

Thanks, so if space is infinite then would the amount of matter in the universe be infinite? I've read that it's believed matter is evenly distributed throughout the universe, which would seem to suggest an infinite amount of it, but I'm just asking for clarification.

 

[Garth]

Yes, indeed, that would be the inference of an infinite universe, infinite volume but finite (and actually very small) density, and consequently infinite mass.

One point, which many find difficult if the universe is open, is imagining the BB from a zero volume singularity expanding instantly into an infinite volume universe. But that's singularities for you!

Garth

 

[yogi]

Thanks, so if space is infinite then would the amount of matter in the universe be infinite? .

In an infinite Universe, all things would be repeated an infinite number of times - imagine an infinite number of Yogi's to forever perplex all the Hurkyls and Garths

 

[Garth]

In an infinite Universe, all things would be repeated an infinite number of times

And everything that is not forbidden is compulsory!

Garth

 

[εllipse]

Thanks, Garth. I recently read on these forums a "size" of the universe. If I remember correctly, it was around 74 billion light years. Is this correct? And if so, is the term "universe" in this sense being used for something else (maybe the observable universe). I only just now remembered reading the size of the universe, so now I'm confused as to how cosmologists believe there's a good possibility that the universe is open (which would imply an infinite universe as you stated) but still quote a size for the universe. Could you help clear this up? And could you point me to a reputable web reference that covers the probability of the universe being infinite vs finite or atleast the current mainstream views? I fear doing a search on google won't be as valid as something someone here could provide. Thanks again!

edit: I just found a similar thread stating the observable universe is estimated to have a 47 billion light year radius, so I guess that answers my question. I'd still like a good website to read about this, though, if anyone could help with that. Thanks.

 

[Chronos]

The observable universe is clearly finite. It is enclosed within what is referred to as the Hubble volume, which limits how much of the universe is visible to any given observer at any given time in the universe. It became logically apparent a long time ago that the universe cannot contain an infinite number of stars and be infinitely old. The night sky would otherwise be as bright as the sun. This is referred to as Olbers paradox. It was not clear which aspect was not infinite until the big bang theory arrived on the scence. So we know the universe is not infinitely old, although it could still be infinitely large.

 

[Garth]

Olber's Paradox is dependent on three necessary properties of the universe that were all thought true in pre-GR days since Newton.

1. The universe is infinitely old.
2. The universe is infinitely large.
3. The universe is static.

If anyone of these three conditions do not hold the paradox is resolved.
The standard model breaks the first and third of these conditions and it may also break the second if the density parameter Omega_total > 1.
In the Steady State Cosmology universe conditions 1 & 2 held and 3 was replaced by the Perfect Cosmological Principle. The paradox was then used to place an upper limit on the brightness of the night sky in order to constrain the theory. SSC was consistent with the observed background upper limit.

Garth

 

[Dr.Brain]

First of all, there have been numerous theories on the structure of our universe.Remember that none of those have been proven , only proposed.

Lets assume , if universe was flat ...flat like what?... a sheet of rubber with dents due to large celestial bodies?...or something like liquid in which everything floats?... or more like imaginary flat spacetime fabric ...? ...we just cannot exactly decipher what we mean by 'flat'..

And if it was open ,?... like a straight plane that extends everywhere randomly?...or more like a hyperbola that never ends...?

On one side we are proposing so many possibilities...who knows a Universe is a speck of dust on somebody's else shoulder?...Maybe The universe rotates around something else?... Maybe what appears to us so big and vast...is something which is part of something massive?

 

[turbo]

Olber's Paradox is dependent on three necessary properties of the universe that were all thought true in pre-GR days since Newton.

1. The universe is infinitely old.
2. The universe is infinitely large.
3. The universe is static.

If anyone of these three conditions do not hold the paradox is resolved.
The standard model breaks the first and third of these conditions and it may also break the second if the density parameter Omega_total > 1.

There is a 4th necessary property upon which Olber's Paradox depends.

4. Light propagates through space for infinite distances with no loss of energy.

It can easily be demonstrated that if EM waves interects with the aether of the quantum vacuum (and gradually loses energy in the process), that light from a distant enough source will be redshifted into undetectability. If this effect is real, Olber's Paradox cannot produce a bright night sky even in a static universe that is both temporally and spacially infinite.

 

[Hurkyl]

You still get infinite energy, it's just redshifted to the lower end of the spectrum.

 

[turbo]

You still get infinite energy, it's just redshifted to the lower end of the spectrum.

Absolutely right. The energy level can be extreme, but when is is redshifted to the point that we can no longer even measure its frequency relative to the ground state, it has essentially joined the ground state of the vacuum. We have no reference to a perfectly empty vacuum from our universe, so we cannot measure the difference between the ground state of our universe and a "perfect" vacuum.

It's analogous to rectifying AC (flattening its oscillation relative to ground) into DC in an old tube audio circuit. The B+ voltage (rail) can be be hundreds of volts above ground, but without access to ground, we cannot measure its magnitude.

 

[Hurkyl]

The doppler effect worries me greatly, though. Suppose in one frame we have this infinite, "undetectable" bath of radiation. If something moves at high velocity with respect to this frame, it would blueshift the radiation. By moving closer and closer to the speed of light, we can blueshift an arbitrarily large magnitude of radiation into, say, the visible range. (and it would all be going in one direction)

 

[turbo]

The doppler effect worries me greatly, though. Suppose in one frame we have this infinite, "undetectable" bath of radiation. If something moves at high velocity with respect to this frame, it would blueshift the radiation. By moving closer and closer to the speed of light, we can blueshift an arbitrarily large magnitude of radiation into, say, the visible range. (and it would all be going in one direction)

If we move relative to this ground state (lets call it the CMB just for grins) we might expect to see some anisotropies in the observed temperatures.

 

[Chronos]

I object to your fourth condition on Olbers paradox, turbo. Energy is simply lost in that scenario, which rewrites the laws of thermodynamics. If it is absorbed by some sort of background state, the background temperature should increase over time, not decrease - which is what is observed.

 

[hellfire]

Olber's Paradox is dependent on three necessary properties of the universe that were all thought true in pre-GR days since Newton.

1. The universe is infinitely old.
2. The universe is infinitely large.
3. The universe is static.

If anyone of these three conditions do not hold the paradox is resolved.

There is a fourth condition. The distribution of light sources is homogeneous and isotropic, or at least, with a fractal dimension greater than two. Otherwise (fractal dimension less than two), the paradox is resolved in a static, spatially infinite and enternal universe.

 

[Garth]

There is a fourth condition. The distribution of light sources is homogeneous and isotropic, or at least, with a fractal dimension greater than two. Otherwise (fractal dimension less than two), the paradox is resolved in a static, spatially infinite and enternal universe.

Homogeneity and isotropy are assumed; however, as the darkness of the whole night sky is taken to be isotropic (more or less) could it be otherwise?

Garth

 

[turbo]

I object to your fourth condition on Olbers paradox, turbo. Energy is simply lost in that scenario, which rewrites the laws of thermodynamics. If it is absorbed by some sort of background state, the background temperature should increase over time, not decrease - which is what is observed.

The energy is not lost, but transferred to the aether (the virtual particle field of the quantum vacuum).

Eddington calculated in 1926 that the contribution of all the radiating sources in the universe would cause the temperature of the vacuum in empty space to be about 3 degrees K (he later refined it to 2.8 K). About 40 years later, this was found to be correct. Somehow, Wilson and Penzias' discovery has come to be acclaimed as the most resounding success of Gamow's Big Bang model, which predicted a background temperature of 50 degrees K.

 

[hellfire]

Homogeneity and isotropy are assumed; however, as the darkness of the whole night sky is taken to be isotropic (more or less) could it be otherwise?

In an universe with a distribution of light sources with fractal dimension less than two (isotropic or not) you do have a dark sky, and so I guess you can have "isotropic darkness". I am not sure I properly understood your question…

 

[Garth]

O.K. homogeneity and isotropy are a fourth condition for the paradox!

Garth

 

[Chronos]

The energy is not lost, but transferred to the aether (the virtual particle field of the quantum vacuum).

Eddington calculated in 1926 that the contribution of all the radiating sources in the universe would cause the temperature of the vacuum in empty space to be about 3 degrees K (he later refined it to 2.8 K). About 40 years later, this was found to be correct. Somehow, Wilson and Penzias' discovery has come to be acclaimed as the most resounding success of Gamow's Big Bang model, which predicted a background temperature of 50 degrees K.

Dodging the question is not an answer. If the 'aether' absorbs the missing energy, should it not be heating up instead of cooling down - as observational evidence indicates? The Eddington story is irrelevant. His reasoning in arriving at the 'correct' answer was ... flawed. He was just as fallible as anyone else, as Chandrasekhar learned. Anectdotal evidence is amusing, but not substantive.

 

[turbo]

Dodging the question is not an answer. If the 'aether' absorbs the missing energy, should it not be heating up instead of cooling down - as observational evidence indicates? The Eddington story is irrelevant. His reasoning in arriving at the 'correct' answer was ... flawed. He was just as fallible as anyone else, as Chandrasekhar learned. Anectdotal evidence is amusing, but not substantive.

Dodging the question? Let's look at the situation. If you radiate an object and increase its energy, it will re-radiate that energy (like a piece of metal sitting in sunlight will absorb UV and optical and IR and radiate heat away in IR). The object will come to an equilibrium temperature and will NOT continue to get hotter and hotter until it is as hot as the Sun. That is a pretty silly concept. The aether is reradiating impinging EM at a very low temperature, and it is in equilibrium.

The Eddington "story" (as you put it) is not only relevant, it is quite telling. If you can show how his reasoning was "flawed" please do. I'll be quite interested.

 

[Garth]

. The aether is reradiating impinging EM at a very low temperature, and it is in equilibrium.

Can you demonstrate this effect in a laboratory?

Garth

 

[turbo]

Can you demonstrate this effect in a laboratory?

Garth

Well, first you might want to read this overview of the history of calculations of the temperature of "empty" space. These fellows (with the exception of Gamow) mostly modeled a static universe that was in dynamical equilibrium and "empty" space or aether in thermal equilibrium. See especially section 13 re: the work of Finlay-Freundlich and Max Born.

http://www.dfi.uem.br/~macedane/history_of_2.7k.html

 

[Chronos]

...The Eddington "story" (as you put it) is not only relevant, it is quite telling. If you can show how his reasoning was "flawed" please do. I'll be quite interested.

http://www.astro.ucla.edu/~wright/Eddington-T0.html

 

[Garth]

Can you demonstrate this effect in a laboratory?

Garth

Okay, I have found this: Laboratory-Scale Test of de Broglie’s Tired-Photon Model
Has anyone tried it?
Garth

 

[turbo]

http://www.astro.ucla.edu/~wright/Eddington-T0.html

Thank you. Eddington nailed the magnitude (summing the energy contributions of all radiative sources in the Universe), as did a number of other people before and after him. The fact that he did not successfully predict the frequency distribution (due to absorption and re-radiation at lower and lower frequencies) does not diminish the acheivement of accurately predicting the magnitude of the signal. Heck, Gamow was boldly predicting 50 degrees absolute in the 1950s. I think it's safe to say that he had heard of Guillaume, Eddington, Nernst, Herzberg, Finlay-Freundlich and Max Born, and chose to disagree with them. He was wrong, yet claimed the Wilson-Penzias observation as confirmation of his BB ideas.

This made good press, but is intellectually dishonest. First, his prediction was off my more than an order of magnitude, when others had been reasonably accurate over the previous 50-60 years. Secondly, even if his prediction had been accurate, one concordant observation does not confirm the accuracy of a model. It only serves to show that the observation does not falsify the model. In this instance, the observation definitely disproved Gamow's BB model that required a CMB temp of 50 deg. absolute.

 

[Chronos]

...The fact that he did not successfully predict the frequency distribution (due to absorption and re-radiation at lower and lower frequencies) does not diminish the acheivement of accurately predicting the magnitude of the signal.

Producing the 'right' answer for the wrong reasons is more often called astrology than science.