Finite Universe

[SuperFastJellyfish]

In the exact words of Steven Hawking:

"In an infinite and everlasting universe, every line of sight would end on the surface of a star. This would mean that the night sky would have been as bright as the surface of the Sun. The only way of avoiding this problem would be if, for some reason, the stars did not shine before a certain time."

Just because Stephan Hawking said it, doesn't make it true. If there were infinite stars in an infinite universe then there were infinite planets, infinite asteroids, and infinite specks of dust as well. All of these infinitely eclipse the light that has been infinitely traveling. This is simple logic. I'm no scientist, but this makes sense to me.

[Deutherius]

I'm afraid you are not in a position to realistically argue this point. Sorry but he is a lucasian professor of mathematics!

I don't mean to be rude but you cannot reasonably argue with what someone like S.H says as his views are based on years of complex mathematics and study. Yours is based on, what?

The argument's logic should stand on its own, not on the reputation of the person proposing it.

Both of these comments are rude and wrong, whether you meant them to be or not.

[andrewas]

Just because Stephan Hawking said it, doesn't make it true. If there were infinite stars in an infinite universe then there were infinite planets, infinite asteroids, and infinite specks of dust as well. All of these infinitely eclipse the light that has been infinitely traveling. This is simple logic. I'm no scientist, but this makes sense to me.

In an infinite universe, all sightlines end on a star or on other matter. Photons from the stars heat the other matter. They re-radiate the heat, but that radiation hits either a star or another lump of cold matter, nothing can radiate into empty space. So, all the matter in the universe heats up till it glows like a star. All sightlines end on a star or something as hot as a star.

[ZetaX]

In an infinite universe, all sightlines end on a star or on other matter. Photons from the stars heat the other matter. They re-radiate the heat, but that radiation hits either a star or another lump of cold matter, nothing can radiate into empty space. So, all the matter in the universe heats up till it glows like a star. All sightlines end on a star or something as hot as a star.

As I said: if you go that way, you won't end at star's brightness. The universe would heat up to infinity and everything will be infinitely hot and bright (whatever that actually means).

Thus this assumption is moot. You could still have infinite time in the past, but at there were not always that many stars.

[Greenfire32]

I think the universe is finite to us in the same way the Earth is finite to ants.

Technically, yes. But for all intents and purposes...it's infinite.

[Bill Phil]

In the exact words of Steven Hawking:

"In an infinite and everlasting universe, every line of sight would end on the surface of a star. This would mean that the night sky would have been as bright as the surface of the Sun. The only way of avoiding this problem would be if, for some reason, the stars did not shine before a certain time."

This would be true, except for the fact that when a star is behind another star and a little to the side (relative to the observer) the second star would appear much less bright. If the second star is far enough away, it's practically invisible. Over thousands of lightyears, the dimmer stars start to be less and less visible. Now, when we add onto that the fact that relative brightness is less when the distance increases, the effect is compounded. We people on Earth can't see all of the Milky Way stars, or even the ones a few thousand light years away.

[ZetaX]

Now, when we add onto that the fact that relative brightness is less when the distance increases, the effect is compounded.

Be careful: the inverse square law does not diminish the brightness in the infinite stars argument.

The best way to imagine why is to go the other direction: a star looks 1/4-th the size at twice the distance; we also get 1/4-th the light by the law; thus in total we get the same (!) amount of light per area it covers in our field of vision.

[Bill Phil]

Be careful: the inverse square law does not diminish the brightness in the infinite stars argument.

The best way to imagine why is to go the other direction: a star looks 1/4-th the size at twice the distance; we also get 1/4-th the light by the law; thus in total we get the same (!) amount of light per area it covers in our field of vision.

I don't think size scales the same way as the amount of light....

[ZetaX]

I don't think size scales the same way as the amount of light....

Visible size scales with 1/d²; with a minor correction if you get close; for distances where the distance d is over a hundred times larger than the object in question this is insignificant (and in our case we are not talking about a factor of 100 but 10^8 or more).

[Bill Phil]

Visible size scales with 1/d²; with a minor correction if you get close; for distances where the distance d is over a hundred times larger than the object in question this is insignificant (and in our case we are not talking about a factor of 100 but 10^8 or more).

Source?

[ZetaX]

Source?

Umm... try yourself with a sheet of paper or any ball-shaped object¿

It's basic geometry: a ball of radius r at distance d has a visible angle of arcsin(2r/d). For small x we have, e.g. by Taylor expansion or some simpler considerations, sin(x)~x [all angles in radians] and similiarly arcsin(x)~x. Thus the visible angle is ~2r/d if d is much bigger than r, i.e. proportional to 1/d.

Now a spherical cone of angle x occupies (1-cos(x))/2 of your vision (see http://en.wikipedia.org/wiki/Spherical_segment). For small x we have 1-cos(x) ~ x²/2 by similiar arguments than for sin(x). Thus we get that our ball occupies ~(2r/d)²/4 = (r/d)² of our vision. In other words, it scales with 1/d².

[Jovus]

If the stars in the universe can be modeled as an infinite plane, then ZetaX is correct.

Unfortunately (or actually very fortunately!) they can't. We have a fairly good measurement of the mass of the universe. Whether or not space is infinite, the amount of matter certainly isn't.

[ZetaX]

If the stars in the universe can be modeled as an infinite plane, then ZetaX is correct.

You are probably attributing a claim to me that wasn't mine.

We have a fairly good measurement of the mass of the universe.

Where from¿ AFAIK we only have one for the _visible_ universe.

[LABHOUSE]

Those are the words of Steven Hawking. I will take his view over most. Also, dust obstruction and star death is moot as light has had an infinite amount of time to travel, there too would be an infinite number of stars. This is the intrinsic problem with infinity. it is fraught with paradoxes.

It is thought that infinity is merely a product of our poor mathematics.

To say there was anything before the big bang is meaningless. It isn't within the realms of science.

Nothing in our universe, and the bing bang never happened... there are other ways of become something.

[Guest]

@Majorjim Try not to be so dogmatic when discussing such a clunky subject based purely on speculations.

That is the very mature of science.

The thepry we have about the creation of the world are nearly as imprecise and symbolic as ancient greece mythos

[xXIndestructibleEVAXx]

I think the universe is infinite in the sense that a circle is infinite. The universe is likely curved in 4d, so if you went forward far enough, you would eventually reach where you started.

Also, LABHOUSE, I don't think that you can really reject the big bang on a scientific standpoint. It's difficult to think of any other way the universe could of began within the realms of science.

[Kohai_Khaos]

I love how the people in this thread talking about the starlight paradox here are arguing that the universe must be finite in space because it cannot be both infinite in space and backwards in time, while the people honestly asking if the universe could possibly be infinite are questioning purely about whether or not the universe can be infinite in space, without any question in regards to time, and in fact some of them have mentioned accepting that the universe had a beginning a finite amount of time in the past.

The starlight paradox is only a paradox if space is infinite, the amount of matter in the universe is infinite, and one of the following is true: 1, that light travels at an infinite speed, going from source to destination with 0 time elapsing. This one is patently and demonstrably false, so it's not a concern. Or 2, that the universe extends infinitely backwards in time; this is a minority belief in modern times, and goes directly against even the layman's idea of the big bang theory.

Oh, and by the way, even if the universe were infinite in size and extended infinitely back into time and light moved instantaneously from source to destination, that alone would not make the starlight paradox matter. Because you also need an infinite amount of matter to make up your infinite number of stars. It is not impossible for the universe to not be homogenous overall, nor does the lack of matter's presence make space stop being space. The assumption that the universe is homogenous in composition on large scales is just that: an assumption.

If anyone here can bother to explain how the universe cannot be infinite in space while having a finite amount of time in its past, feel free to do so. But the starlight paradox has zero relevance to the given situation. I would love to hear this explanation, but I've never heard anyone actually give one.

Yes, the observable universe is finite. This is because time extends back finitely, therefore limiting the distance we can see into space (or everything past that is redshifted out of our view, of course, or there's just no matter out past that point). But that's not the question being asked, now is it?

EDIT: And yes, I understand that the universe might be curved, rather than flat, and that would allow for a finite universe with no boundaries, but that's also not the question. Since we don't know whether or not it's curved, flat, or some other shape, or if there are any boundaries at the "edge", we can't exactly go "No, it's not possible to be infinite." just because it is possible for it to be finite.

Edited March 28, 2015 by Kohai_Khaos

[Vanamonde]

Has Oblers' Paradox been mentioned yet? Of special interest is the explanations section.

[Kohai_Khaos]

Oblers' Paradox is basically the argument that all the people arguing against the possibility of an infinite universe are referring back to; I referred to it as the "starlight paradox" in my post above, and pointed out how it's irrelevant to the discussion of a universe with infinite space.

[Bill Phil]

Umm... try yourself with a sheet of paper or any ball-shaped object¿

It's basic geometry: a ball of radius r at distance d has a visible angle of arcsin(2r/d). For small x we have, e.g. by Taylor expansion or some simpler considerations, sin(x)~x [all angles in radians] and similiarly arcsin(x)~x. Thus the visible angle is ~2r/d if d is much bigger than r, i.e. proportional to 1/d.

Now a spherical cone of angle x occupies (1-cos(x))/2 of your vision (see http://en.wikipedia.org/wiki/Spherical_segment). For small x we have 1-cos(x) ~ x²/2 by similiar arguments than for sin(x). Thus we get that our ball occupies ~(2r/d)²/4 = (r/d)² of our vision. In other words, it scales with 1/d².

That still doesn't change the fact that the light from closer stars starts to block out farther stars, preventing them from "blocking up" the sky.

And even if the ratio of light to surface area is the same, it's still less light.

[ZetaX]

That still doesn't change the fact that the light from closer stars starts to block out farther stars, preventing them from "blocking up" the sky.

"Blocking up the sky" makes no sense: the argument says that every point in the sky would have about the brightness of the sun. The blocking-up doesn't change that one bit.

And even if the ratio of light to surface area is the same, it's still less light.

Less light than what¿ Please re-read the statements, I don't think you understood the brightness argument correctly.

[Bill Phil]

"Blocking up the sky" makes no sense: the argument says that every point in the sky would have about the brightness of the sun. The blocking-up doesn't change that one bit.

Less light than what¿ Please re-read the statements, I don't think you understood the brightness argument correctly.

Blocking the sky with the brightness of the sun at every point. That wouldn't happen because the stars that are closer to the observer would dim the stars farther away. The stars that are nearby in the 2d representation of the stars from the observer. For example, if you have a flashlight in the dark, and a flashlight farther away in the same general direction, the second one will be less bright due to the first light. Plus, the magnitude of each star gets less as they get farther out.

We don't see all the stars in the Milky Way. We see a sphere of stars in the milky way, a maximum radius caused by this effect. So, even if the universe were infinite, the brightness wouldn't be equal to the sun at every point.

Not to mention the fact that there are limited stars in a galaxy. So, they're all divided up. Then the galaxies are astronomically far away from each other, so they're not going to fill up the sky.

It's less light than it would be if it were closer.

[BlueCosmology]

Blocking the sky with the brightness of the sun at every point. That wouldn't happen because the stars that are closer to the observer would dim the stars farther away. The stars that are nearby in the 2d representation of the stars from the observer. For example, if you have a flashlight in the dark, and a flashlight farther away in the same general direction, the second one will be less bright due to the first light.

Sorry, I think I must be misinterpreting you.

Are you saying that you think if you have a flashlight pointed at you from a distance, that flashlight becomes dimmer if one gets turned on closer to you?

[Jovus]

If the stars in the universe can be modeled as an infinite plane, then ZetaX is correct.

You are probably attributing a claim to me that wasn't mine.

Nah. I'm not saying this is what you said. All I'm saying is that this is the only way that the inverse square law of flux gives a non-decreasing flux with distance. If the object behaves like a point source from sufficient distance, then the luminosity falls of like 1/r^2; if it behaves like a line, then it falls off like 1/r, and if it behaves like a plane, then it doesn't fall off, because as you pointed out, the cone subtends more of the source as you pull back. That's all I'm saying.

Unfortunately (or actually very fortunately!) they can't. We have a fairly good measurement of the mass of the universe. Whether or not space is infinite, the amount of matter certainly isn't.

Where from? AFAIK we only have one for the visible universe.

Not to my understanding, though it has been a few years since I seriously studied such. (My specialty is ULXs, not the CMR.) In very broad outline, you use the characteristics of the cosmic microwave radiation along with observable gravitational interactions to come up with a whole-universe estimate. I could be wrong. Here, have a link to a simplistic explanation.

[Brotoro]

The surface brightness of an object does not decrease with distance (although its overall brightness does because it gets smaller in angular size with distance). But if you have a non-expanding universe that is infinite in both spatial and temporal extent, then your line of sight in any direction would eventually intersect the surface of a star. So the sky would have the same surface brightness as the surface of stars. The fact that we do not see this is Olber's Paradox.

Note: Having dust clouds to block the light from far away stars (the reason we can't see all the stars in our Milky Way Galaxy) does not solve this because over the infinite age of the universe, the dust would heat up to the temperature of the stars and end up glowing with the same surface brightness.

The reasons we don't see the sky having the brightness of stellar surfaces is because:

A) the universe is not infinitely old (even though it might be infinite in spatial extent),

the universe is expanding, which red-shifts the emissions from stars out of the visible spectrum.

Edited March 28, 2015 by Brotoro