Is Infinity Possible? A Discussion on Hawking's Theories of the Universe

[Born2Perform]

Quoting Stephen Hawking: "...

In "Universe in a Nutshell", if in english sounds like that, Hawking said:

"universe cannot be infinite because...bla bla...if it would be, every view line will approach to a star, and the sky would appear to us brighter than the sun; obviusly this does not agree with our experience."

but in a infinite universe the light of the most far stars would not have the time to reach us, so all will appear as it appears now. or not?

 

[Labguy]

In "Universe in a Nutshell", if in english sounds like that, Hawking said:

"universe cannot be infinite because...bla bla...if it would be, every view line will approach to a star, and the sky would appear to us brighter than the sun; obviusly this does not agree with our experience."

but in a infinite universe the light of the most far stars would not have the time to reach us, so all will appear as it appears now. or not?

Do a search on "Olber's Paradox", on PF or Google.

 

[marcus]

Do a search on "Olber's Paradox", on PF or Google.

hello Labguy,
glad to see you.
I thought you were going to Arizona but it looks like the weapons-ranging business has taken you to Iowa instead. hope the nights are clear and seeing conditions good.

Let's see if we can help this guy Born2. His problem seems to be with Hawking. It sounds like Hawking said something wrong, or else confusing.

that wouldn't be so surprising. books for popular audience can be have mistakes or be unclear in places, no matter who writes them

and Hawking might actually have said something else, he might have meant IF THE UNIVERSE WERE SPATIALLY INFINITE AND ALSO wasnt expanding and WENT INFINITELY FAR BACK IN TIME

I don't like Hawking's popular writing from what I've sampled, so I avoid his books. But maybe someone has seen this Nutshell book and can explain what has confused Born2.
====================

Born2,
basically what Labguy says is right. Do a google on Olber's paradox. whatever you learn is probably right and Hawking must have said something unclearly.
the universe does NOT have to be spatially finite. It CAN be spatially infinite as long as you make other assumptions that would allow the light not to have reached us yet

or other assumptions that make it so that a lot of the light that reaches us is so stretched out (by expansion) that it is redshifted into total harmlessness. stretching out light, to have very long wavelength, deprives it of its energy, so it cannot dazzle or cook you.

there IS light coming from all directions in the sky, but it is harmless: it is called the CMB. if you could see CMB waves, then the night sky would NOT be dark.

 

[SpaceTiger]

basically what Labguy says is right. Do a google on Olber's paradox. whatever you learn is probably right...

For some subjects, I would agree with this, but Olber's paradox is very often mistreated on the web. One of the most common solutions you'll see is "dust obscuration". However, even if we took all of the dust and absorbing gas away, the night sky would still not be uniformly bright. Furthermore, in an infinitely old and infinitely large universe, the dust would eventually reach equilibrium with the background radiation and begin shining with the rest of the night sky.

The best explanation, I think, is the first one you gave -- the universe is not infinitely old, so only so much light could have reached us since the big bang.

 

[marcus]

... very often mistreated on the web. One of the most ...

Yeah, come to think of it that is right. In fact I suspect unselective googling is always something of gamble! It is good to be warned in general (and SpaceTiger says especially about web treatment of Olber's paradox in particular).
Wikipedia is good about a lot of things, but even that is not infallible.

 

[baryon]

I think the reason that the sky appears dark to us at night, rather than lit up like the day time, is because of the Big Bang. Matter is so sparsely distributed in the universe that we just don't see a lot of the light coming from the stars. It is, as was previously stated, stretched out so much and cooled down so much, that it appears only as faint cosmic rays. Possibly tachyons?
CMB is also given as evidence of the Big Bang. With minor fluctuations, the temperature of space everywhere is roughly 4 deg K.

 

[Parlyne]

*Picks up handy-dandy copy of "The Universe in a Nutshell"*

I knew there was a reason I kept this thing on my bookshelf (and not just for the pretty pictures).

Marcus and SpaceTiger have it exactly right. What Hawking was saying here is that the fact that the sky is not uniformly bright tells us that it can't have existed for an infinite period of time. In fact, this is how he introduces his section on the expanding universe.

 

[SpaceTiger]

baryon's answer would seem to be relevant as well. After all, there was a time (before recombination) when the night sky would have been uniformly bright. The reasons for this, however, are unrelated to what Olbers was puzzling about. He was more concerned with question of how, given an infinite and eternal universe, the current night sky was not uniformly bright. It doesn't matter how diffusely matter is dispersed in the universe, we still expect a uniformly bright sky in an infinite and eternal universe. Nowadays, although it may still be infinite in size, we know it is not eternal, so there is no longer a paradox.

 

[marcus]

we know it is not eternal,

Personally I don't believe I know this. I think that eternal is a reasonable possibility that cannot, as yet, be excluded on experimental grounds.

You may have meant something different, that I am missing.

 

[SpaceTiger]

Personally I don't believe I know this. I think that eternal is a reasonable possibility that cannot, as yet, be excluded on experimental grounds.

You may have meant something different, that I am missing.

The universe as concerns Olbers' Paradox certainly isn't eternal. Light was not free to travel before recombination and all other particles are limited by the end of inflation. This is the sense in which I meant it.

Obviously, there are models of the early universe that are eternal (e.g. eternal inflation, cyclic universe), but this is well beyond the scope of the thread. Perhaps you'd like to discuss it in another one.

 

[Mike2]

If all space were expanding, then there is more of it to come. And if there is room for more, then it cannot be infinite in size. If it is not infinite in size and has always been expanding, then it must have had a beginning. That beginning may have been with exponentially smaller size with time. It may be infinitely old, but only with ever smaller size. Right?

 

[baryon]

Why doesn't it matter how diffusely matter is dispersed throughout the universe?

 

[marcus]

The universe as concerns Olbers' Paradox certainly isn't eternal. Light was not free to travel before recombination and all other particles are limited by the end of inflation. This is the sense in which I meant it.
...

Good! LIGHT is not eternal and PARTICLES are not eternal. (regardless of whether spacetime is or not.)

All the light coming to us had a beginning a finite time ago and all the particles we are made of and encounter began a finite time ago.

This is a good point to make.

Actually you know one of the useful things about this kind of discussion is just refining the language one uses----finding clearer more precise ways to say things. Sometimes we can have the same mental picture and use different words, so that there is an illusion of disagreement.

You mentioned various models where the universe past is not obviously bounded----the past extends back indefinitely. I would say that Loop Cosmology bounce scenarios are an example. You mentioned some others.

An important point to make about these (possibly "eternal" but in any case) unbounded-past models is that regardless of whether or not the universe is eternal, the light and particles we see only go back so far. This is what i get from your post, and I agree.

 

[Harry Costas]

Hello All

The Universe is endless and ageless. If you exposed your eyes for 1 year the amount of stars that you would see would be blinding.

I think some of you above need to read up on a lot of things.

The nutshell size is determined by the knowledge of information.

As for the Big Bang, what is it that holds you to it.
Look at this simple calculation.

We see 13.2 billion light years deep field in one direction and 13.2 billion in the opposite direction and we see existing galaxies over 10 billion years old.. This gives us 26.4 lbillion light years travel and 10 billion years ,all up 36.4 billion years. We have the Big Bangers tell us that the universe is 13.7 Billion years old. The BB's will use fantasy and have matter traveling at 100 times the speed of light just to make their model correct.

I'm just sick and tied of being sick and tied of a model that has become a standard model and for people to have followed such a fantasy. This will be the greatest laughter of the 20th century.

I can give you a list of hundreds of cosmologists and scientists who think the same.

If someone can give me actual evidence for the BBT without fantasy i would be very happy.

 

[Parlyne]

Hello All

The Universe is endless and ageless. If you exposed your eyes for 1 year the amount of stars that you would see would be blinding.

Blinding, perhaps; but, the sky would still not be truly uniformly bright in all directions. If it were, exposure time would be irrelevant.

I think some of you above need to read up on a lot of things.

The nutshell size is determined by the knowledge of information.

As for the Big Bang, what is it that holds you to it.

The observational evidence, I should think. Let's start with the fact that almost every single galaxy in the universe is moving away from us. Add in the cosmic microwave background radiation. And, consider that the relative abundances of light elements (those existing before the first stars) fit perfectly with the parameters which properly describe the other two effects.

Look at this simple calculation.

We see 13.2 billion light years deep field in one direction and 13.2 billion in the opposite direction and we see existing galaxies over 10 billion years old.. This gives us 26.4 lbillion light years travel and 10 billion years ,all up 36.4 billion years. We have the Big Bangers tell us that the universe is 13.7 Billion years old. The BB's will use fantasy and have matter traveling at 100 times the speed of light just to make their model correct.

What is it you think would have to have traveled 26.4 light years? Certainly no light that we see has. And, light from the most distant objects we see in one direction has certainly not reached the most distant object we see in the opposite direction.

To be very clear, in Big Bang cosmology there are no violations of known physics. In fact, the class of cosmological models comes directly out of the general theory of relativity.

Specifically, these models do not allow objects to travel through space faster than the speed of light. However, the recession rate of an object due to the expansion of the space between us and it is not constrained in any such way, nor should it be, since the rate of expansion is the same everywhere.

I'm just sick and tied of being sick and tied of a model that has become a standard model and for people to have followed such a fantasy. This will be the greatest laughter of the 20th century.

I can give you a list of hundreds of cosmologists and scientists who think the same.

Ah, but then we would have to respond with a list of hundreds of scientists named Steve who think that the current model is well supported.

If someone can give me actual evidence for the BBT without fantasy i would be very happy.

This board has quite a bit of it; and there are quite a few resources on the web which do as well.

 

[Chronos]

Olber's paradox is one of the profound examples of scientific thinking. It asserts the universe cannot both be infinitely old and infinitely populated by luminous objects [stars]. The logical consequences are obvious - the entire sky would be lit up like the surface of a pretty average star [like our own sun]. And as others have pointed out, intervening dust grains would be glowing like stars after being struck by an infinite number of background photons.

 

[baryon]

If all space were expanding, then there is more of it to come.

Fallacious logic, sir. There does not have to be "more of it to come." It can be like an inner tube that is being inflated with nothing in the middle.

 

[Mike2]

Fallacious logic, sir. There does not have to be "more of it to come." It can be like an inner tube that is being inflated with nothing in the middle.

I equate expansion to "more of it to come". If it is expanding everywhere, no matter what it is, then it is not infinite yet. Name me one thing that is expanding and inifinite... besides the universe.

 

[baryon]

Mike2, what do you mean "not infinite yet"?

 

[SpaceTiger]

The simple flat or open FRW models are spatially infinite and they are expanding. Keep in mind, however, that these are just toy models that rely on universal validity of the cosmological principle. The models well describe the observable universe but have not been shown to be valid for the universe at large. It's possible that we will never know how to describe the universe at large, since our observations are all limited (by, for example, the CMB) in the cosmological scales they can probe.

 

[Mike2]

Mike2, what do you mean "not infinite yet"?

Just that there seems to be a contradiction of terms to say that a measure is increasing and infinite at that same time. dx/dt means more x with time. If you can add a bit more to something, then it was not infinite in measure before you added the more. And if you can add a differential amount to it, then it is not infinite after you add just the differential amount.

 

[marcus]

hello baryon
I see you are a comparative newcomer and like explaining stuff and responding to people's questions. hope you have a good time here.

I want to show you an example. Tell me if you think it would work with the kind of people you often find yourself explaining things to. It requires a decent high school math background, so it may not work with everybody.

Think of the REAL LINE: the numbers from -oo to +oo,
usually denoted R but we may not need even that much notation

I am going to put a time-dependent DISTANCE FUNCTION on the real line so as to show it EXPANDING in the sense that astronomers mean when they talk about a spatially infinite universe expanding.
what they mean is there is a time-dependent metric on it where distances between points steadily increase.

I want to be very specific and concrete, so I will define a particular distance function. Let's say t=0 represents the present, and negative t is the past.

d_t(x,y) = e^t |x-y|

so the DISTANCE AT TIME t, between points x and y, is defined to be the absolute value |x-y| multiplied by exp(t). Here exp(t) is being used just because it is a handy positive increasing function of time.

the point of this example is that you sometimes encounter people (present company excepted!) who confuse EXPANDING (in the astronomers sense of distances between points growing with time) with a possibly vague notion of "increasing in size".

but the size of an expanding thing need not always be well-defined

To take this example, intuitively REAL LINE DOES NOT HAVE A well-defined linear SIZE. It has no linear diameter. The size or diameter of it is not well-defined because the real line is infinite. So there is no well-defined way to say that in this example the "size is increasing". The size is NOT increasing because the thing is infinite and HAS no finite size.
But the REAL LINE CAN EXPAND in the sense astronomers mean when they say space expands, as this example is intended to illustrate.

If you try this on anyone, let me know if it works! for some it will naturally be a dud because they won't go for anything at all mathematical. Some are just purely verbal thinkers and for them "expanding" will always mean "size increasing" and you can't do anything. It is useless to argue. but if you find anyone the example works with. Or if you find some OTHER WAY to explain the idea of space expanding without having any well-defined size. If any strategy for explaining this succeeds for you, please let me know!

 

[Mike2]

hello baryon
I want to be very specific and concrete, so I will define a particular distance function. Let's say t=0 represents the present, and negative t is the past.

d_t(x,y) = e^t |x-y|

so the DISTANCE AT TIME t, between points x and y, is defined to be the absolute value |x-y| multiplied by exp(t). Here exp(t) is being used just because it is a handy positive increasing function of time.

the point of this example is that you sometimes encounter people (present company excepted!) who confuse EXPANDING (in the astronomers sense of distances between points growing with time) with a possibly vague notion of "increasing in size".

but the size of an expanding thing need not always be well-defined

To take this example, intuitively REAL LINE DOES NOT HAVE A well-defined linear SIZE. It has no linear diameter. The size or diameter of it is not well-defined because the real line is infinite. So there is no well-defined way to say that in this example the "size is increasing". The size is NOT increasing because the thing is infinite and HAS no finite size.
But the REAL LINE CAN EXPAND in the sense astronomers mean when they say space expands, as this example is intended to illustrate

Thank you. Present company understands. This is a counter example to my off-hand intuition about the matter.

OK. But now we suppose that the universe was curved to begin with so that travel in one direction eventually leads you back to where you started. In that case there is a measure of how far you can travel before circumnagivating the universe. And in that case there is a size to the universe. Expansion in that case proves the universe is finite, right? Is anyone here suggesting the universe at the very early stages did not have very curved spacetime so that space curved to the point of circumnavigating itself?

 

[Parlyne]

Thank you. Present company understands. This is a counter example to my off-hand intuition about the matter.

OK. But now we suppose that the universe was curved to begin with so that travel in one direction eventually leads you back to where you started. In that case there is a measure of how far you can travel before circumnagivating the universe. And in that case there is a size to the universe. Expansion in that case proves the universe is finite, right? Is anyone here suggesting the universe at the very early stages did not have very curved spacetime so that space curved to the point of circumnavigating itself?

If the universe happened to be curved in such a way (what is referred to as a closed topology), then it would remain that way. In other words, if it starts out finite, it stays finite, regardless of what the expansion does.

However, the models that best fit with observations do not have closed topology.

 

[marcus]

However, the models that best fit with observations do not have closed topology.

I believe you are mistaken there, Parlyne.
You might be interested in reading Spergel et al's analysis of WMAP3 data that came out this year.

If you say what you claim, you OVERINTERPRET the data. That is, you cannot say (based on recent observational data) that the fit with a flat non-closed universe is BETTER than the fit with a a nearly flat positive-curved universe with closed topology.

The near-flat postive curved closed spatial topology case is JUST AS GOOD A FIT as the flat case.

Your statement implies that it is not--that closed U is somehow not as good and non-closed is "best". therefore your statement is false.

You can, however, say that the nonclosed flat universe is CONSISTENT with recent data. Also by the same token it should be noted that the nearly flat spatially closed case is consistent.

If you have any evidence to the contrary please give us a link! I would be very interested to see it---assuming it is recent, authoritative, mainstream stuff.

My main source here is Spergel et al. Excellent summary of the cosmological implications of the 3rd year WMAP data, in combination with several other large data-sets.

I will get the link in case you would like to have a look

 

[marcus]

However, the models that best fit with observations do not have closed topology.

My main source here is David Spergel et al. Excellent summary of the cosmological implications of the 3rd year WMAP data, in combination with several other large data-sets.

I will get the link in case you would like to have a look

http://arxiv.org/abs/astro-ph/0603449
Wilkinson Microwave Anisotropy Probe (WMAP) Three Year Results: Implications for Cosmology
D. N. Spergel, R. Bean, O. Dore', M. R. Nolta, C. L. Bennett, G. Hinshaw, N. Jarosik, E. Komatsu, L. Page, H. V. Peiris, L. Verde, C. Barnes, M. Halpern, R. S. Hill, A. Kogut, M. Limon, S. S. Meyer, N. Odegard, G. S. Tucker, J. L. Weiland, E. Wollack, E. L. Wright

89 pages, 28 figures, submitted to ApJthis was part of the official release of WMAP3 data earlier this year. Note that NED WRIGHT is one of the co-authors. You may be familiar with his website---one of the principle investigators for WMAP.
It is a great paper.

Oh check out page 55 figure 17 That is my favorite. If dark energy equation of state is allowed to vary as well as curvature, one gets a 68 percent confidence interval for Omega which is [1.008, 1.037]
that is the interval does not include the flat (Omega exactly one) case----it ONLY covers the spatially closed slighly positive curved case. I wouldn't go so far as to say it FAVORS the closed case, but it certainly is AS consistent with that case as it is with flat.

This particular figure 17 is based on a combination of WMAP3 with SDSS (sloan digital sky survey) and Supernovae data sets and 2dFGRS data (2 degree field Galaxy Redshift Survey http://www.aao.gov.au/2df/press/modmag.html ).

We have a couple of PF threads discussing it and similar papers. Don't recall if you participated in those threads. It's been a while, perhaps you did and I forgot.
Thanks in advance for any comment.

 

[Parlyne]

I was under the impression that the best value for Omega was slightly under, but within uncertainty of, 1. But, it's quite possible that's out of date.

 

[David Burke]

Infinite is something I have tried very hard to come to grips with as a real, existing phenomenon. To this day I still am undesided. Hawking model uses QM and GR to explain singularities yet we know the two don't agree in many respects, especially in areas of extreme gravitational effects. Granted Hawking and associates are on the top of their intellectual game but being an enthusiastic follower of quantum theory I know you have to take it with a grain of salt (so to speak). I mean infinity is evident in simple but apparently very accurate models of real world effects like the division of an even integer by an odd number where 1/9=0.1 remainder (infinite re-occuring decimal) but 1/9 x 9 = 1. So infinite division seems to be fine and well defined mathematically but QM uses the Heisenberg uncertainty principle to blur this simple idea where any measurement will be obscured at energies equal to or greater than the Plank constant (h). The reason I've used this particular comparison is due to Hawking also incorporating string theory which involves energies (particle/wave) that can be much smaller than the plank constant (about a billion times smaller than a quark). I mean it would be really fortuitous if our understanding of things of this kind of tiny size happened to be perfectly correct especially considering the incredible quirks of quantum behaviour even though the theory is perfectly sound (as far as I can tell). Infinite vs finite is just so big of a question that I think it would be silly of anyone to get to narrow minded about either argument.

PS I am still having difficulty understanding the philosophy of an infinite density point allowing time to stop. I understand the imaginary time concept but I don't think it's a very philosophically responcible way that Hawking has applied it. Anyone interested in discussing the whole time in a black hole concept?