Why Think Universe Is Finite?

Factual Questions
21

tony1234:

The evidence I noted strongly proves that the “ordinary” universe is finite in both space and time. The COMB is especially telling: It’s hard to explain unless you assume that all the mass of the universe was at one time in a small area. There a lot of things that might have happened after the big bang, but it really seems clear the ordinary universe started off a finite amount of time ago with finite space; such a condition would naturally persist today.

Time flies like an arrow. Fruit flies like a banana.

22

And now the rest of the story:

It appears that our universe seems carefully tuned to support life. If many of the physical constants of the universe (which are not dictated by the standard model of QM, but have to be determined from experiment) were even slightly different, the universe would not be able to be old enough, or have sharp enough energy gradients (stars), or be complex or simple enough (exactly three big spacial dimensions and one time dimension).

If the universe were different, we wouldn’t be around to speculate as to its origins. This is the “weak anthropic principle” and is really tautological. We must search more carefully for a more satisfying explanation.

It may well be that there is are good fundamental reasons, that have nothing to do with life, that compel the nature of laws of physics and the physical constants. But if so, we haven’t found them yet.

The universe may well be a product of design. There may indeed be a God who tuned things up so that life had a chance to evolve. However finding evidence to rule out the alternatives in favor of this one seems difficult.

An interesting idea in the standard model is that the physical constants “froze out” when the universe cooled, more or less arbitrarily. In which case, the natural progression is to hypothesize various “many universe” theories, in which case we naturally live in one that’s favorable.

One possibility is hyper-inflation. In various inflationary scenarios, some mechanism causes space to undergo exponential expansion for some period of time (there’s no reason that space itself cannot expand faster than the speed of light). In the hyper-infationary scenarious, this expansion leads to an enormous universe, orders of magnitude larger than the observable universe. In which case, the physical constants may well have cooled out differently in different areas, but inflation and the speed of light kept them from ever communicating with each other.

These explanations also provide a good explanation of the observation that our universe is nearly flat in the General Relativistic sense; If we can only see a small part of the whole, it would seem flat to us regardless of its overall curvature.

Another compelling explantion are the various multi-universe explanations. Whether arising from black holes or from a truly enormous field with random inflationary events, again we find ourselves in one universe among many, our universe is one of those that supports life.

As yet there is no evidence to support any theory, not even Intelligent Design; it’s uncertain whether we can gather such evidence. Until then, all we can do is create plausible speculations.

Time flies like an arrow. Fruit flies like a banana.

23

SingleDad,

Pardon my ignorance of these matters, but could the COMB be explained by the hypothesis that all of the observable matter in the universe (or perhaps many times that much matter) was at one time in a small area? Would it necessarily have to be all the matter? Couldn’t a sufficently dense, but infinitely extended, universe along time ago also account for the COMB?

In general, why is it that our scientific theories ever need to hypothesize about “all” rather than merely “a suffient amount to account for the observable data,” and leave the question of “all” open? I don’t mean to be unduly philosophical or contentious, but that question is what is behind much of my puzzlement.

Thanks,

Tony

Two things fill my mind with ever-increasing wonder and awe: the starry skies above me and the moral law within me. – Kant

24

Not really. The temperature and density of an infinite amount of mass in a finite area would be infinite; no matter how much it expands, the temperature and density would remain infinite. The fact that we observe a finite temperature for the COMB indicates that it is finite.

Because of the “tune up” conundrum I mentioned in my second post. We don’t yet have a good understanding of why the universe should be so amenable to life.

Time flies like an arrow. Fruit flies like a banana.

25

Correction: The fact that we observe a finite temperature for the COMB indicates that it has always been finite.

If we were part of a spacially infinite universe it’s unlikely that we would see any background radiation at all.

Time flies like an arrow. Fruit flies like a banana.

26

Regarding your first statement above, by “it” do you intend to refer to the temperature of the universe or to the universe? If the former, that seems consistent with the idea that universe has always been infinitely extended with infinite mass. For finite temperature, you only need finite density which you may have even if the universe is infinite. If you mean the latter, I do not see the grounds for your inference.

Regarding your second quote, I do not understand the basis of your inference. Granted, if the universe were spacially infinite and had finite matter, there would be no average temperature. But if it had infinite matter and were infinitely extended, it could have a finite temperature. Temperature is mostly a matter of density.

All of this assumes the possibility that the universe “started” infinitely extended with infinite matter, but always a finite density (a finite time ago), not that it started as a point. But what empirical evidence to we have for the latter supposition? Why does the COMB not merely imply facts about former density, not about (infinite extension + infinite matter) v. (finite extension + finite matter)?

Any light you could cast on this would be appreciated.

Tony

Two things fill my mind with ever-increasing wonder and awe: the starry skies above me and the moral law within me. – Kant

27

tony1234: I’m not sure I can explain it better; I’m not a professional scientist or mathematician. I suggest you look at some books on both transfinite mathematics and cosmology. I suggest Infinity and the Mind by Rudy Rucker, as well as The Whole Shebang, which I cited earlier.

Time flies like an arrow. Fruit flies like a banana.
[Note: This message has been edited by manhattan]

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Infinity and the Mind

29

Sheesh, you step away from the board for a measly 27 hours, and your post gets buried! Yeah, tony, I guess I did kind of gloss over the issue of why recollapsing Universe = finite Universe. The idea is, that matter curves space. If there’s enough matter (or strictly, density), then we have a space that’s positively curved. It so happens that this density is the same as required to halt the cosmological expansion. Now, on a large enough scale (or so it’s believed), the density of the Universe is pretty much uniform. This means that the curvature is also uniform. The only shape that has a positive and uniform curvature is a sphere, or higher-dimensional equivalent therof (sorry, not sure how to prove that easily), so if space has this sort of curvature, then it has to eventually curve back around on itself and close spatially. It IS possible to have an infinite space where the the curvature is everywhere positive, such as the surface of a paraboloid, but it (the curvature) wouldn’t have the same value everywhere. We’d then have to think of some good excuse why we happen to be right at the point where everything looks isotropic about us.

SingleDad–
The CMB only requires that there was at one time a large amount of mass in a small area, not that that mass was all of the mass in the Universe. You can take a finite amount of perfectly ordinary gas in the lab and compress it, and it’ll get hot and emit radiation. It won’t be quite as hot as the Universe was at that time, because the density probably won’t be as high, but it’s the same effect-- the gas glows regardless of whether there’s other gas in the Universe or not. This is perfectly consistent with infinite-Universe models, in which what would later become a big but finite chunk of the Universe, say, a galaxy’s worth or so, was squeezed into a relatively small finite area. At no time do these theories call for the infinite mass of the whole Universe to be squeezed into a finite volume, except perhaps at the initial singularity, at which all bets are off anyway.

“There are only two things that are infinite: The Universe, and human stupidity-- and I’m not sure about the Universe”
–A. Einstein

30

One problem you can run into when dealing with an infinite number of stars, is multiplying probabilities. For example, multiply infinity by the odds that any one star system will have developed a civilization will have developed the technology to fly to earth in our lifetimes, times the probability that any civilization would try to do it, times the probability that there will be a chartreuse alien monkey race a few cubicles from Boris B, and that’s a lot of chartreuse monkeys. The point is not that this disproves there are an infinite number of stars; it just proves that you can’t really multiply stuff by infinity.

I was wondering about the whole gravity thing. Now, I probably haven’t digested this whole thread properly, and I certainly haven’t read enough of the important physics stuff, so explain something to me. If there were an infinite number of stars, there’d be infinite gravity, right? An infinite force pulling us in each direction…? No, it would all cancel itself out, providing that we were at the center of mass. Now, the thing that is wiggling my brain mercilessly is, where the heck is the center of a cloud of infinite mass? Is every point in it the center?

I don’t have as much of a philosophical problem with infinite space being filled with finite mass. There’s a kazillion stars, maybe, but not an infinite number, so their gravitational effects are safely finite (i.e. much less than that of the earth and the moon). Likewize, the known universe might be tugging slightly on the solar system, but the Milky Way is tugging much harder. So, basically, it is much easier to ignore the non-local parts of the universe if it is finite.

As if my brains weren’t wiggling enough, I though of something else. Maybe the universe is infinite, but maybe only a finite amount of it is a finite distance away. I.e., maybe the bulk, say, 100%, of the infinite stars are a long distance, say, infinity meters away. But again, I’m sticking infinity into algebraic equations, which gets you a whack from a ruler in THIS classroom, young man.

31

Let me reply to some of the remarks of Chronos and Boris B:

First, Chronos, what do you say to my earlier point that because the curvature of the universe (whether its positve or negative) is not known, it follows that whether the universe is infinite in the sense of currently containing an infinite number of stars in infinite space is not known. But much of the writing in cosmology seems implicitly or explicitly to refer to a finite universe. Why is this. Do you agree that it may well be that the universe is infinitely populated.

Second, regarding your positive curvature argument. As a layman, I don’t what to dismiss it at all, but I am also somewhat suspicious of overly theoretical arguments. So let me try to be concrete. The curvature of space-time is basically a function of the density of matter and energy in the region. Thus, you are telling me it is impossible for there to be a universe in which the averge distance between any two stars is below a certain limit, and that universe is infinite. There seems to me nothing impossible about this. I can certainly imagine it. Is this hypothesis inconsistent with some empirical data then? If so, what data? It does not seem inconsistent with the evidence that light can be “curved” by a gravitational source. That fact, I take it, is the basic empirical foundation for the idea that space-time is curved. So the notion of curvature itself won’t get you there.

Now maybe this is the point (and this ties into Borris B’s remarks). The idea may be that if this was infinite mass in the universe, and the mass was sufficiently close, gravitation at every point would be infinite and we would be crushed. This argument, however, seems to me to be just the grativational analogy to the argument that is the universe were infinite we woyuld be blinded by an inifinite number of stars. As I have argued in previous posts, the argument is fallacious because not all the light would have reached us yet. The same objection applies for the gravity argument.

Finally, regarding Borris B’s point about the implications of an infinite universe, he’s right. If the universe were infinite in my sense, it would be certain that there were an infinite number of suns like ours with an infinite number of planets like ours and an infinite number of people typing like me. Disconcerting, eh? But just because it’s disconcerting doesn’t mean it not true. Some people no doubt think the idea of a finite universe, with all the aribrary limitations that implies (“why only this number of stars?”) is disconcerting.

tony1234

Two things fill my mind with ever-increasing wonder and awe: the starry skies above me and the moral law within me. – Kant

32

tony–
Ok, first of all, there is at this time absolutely no observational evidence one way or the other, that the Universe is inifinite or finite. That being the case, theorists are free to toy around with either possibility. Many of the theories they’ve come up with seem to require a finite total amount of mass, and in many other theories, a finite Universe is regarded as more “elegant” or “aesthetic”. Of course, if it were discoved observationally that the Universe is, in fact, infinite, then those theories would have to be either discarded or adapted.
Another possibility, is that some of the papers you’ve noticed discussing an apparently finite Universe, were just talking about the observable Universe, which is, indeed, finite. This is rather common, since in science, we’re usually not concerned with things that we cannot possibly observe.
As to the curvature/finite part: If I understand you correctly, you’re positing a Universe in which no two stars are greater than a certain finite distance apart, and yet, that Universe is in some sense infinite? Do you mean infinite volume, or containing an infinite number of stars, or both? I confess to being unable to visualize this… which might, of course, just mean that it exists, but that my visualization skills arn’t quite up to the task. You say you can imagine such a possiblility; is there any way you might give me a clearer picture of what you have in mind?
Also, on to more familiar territory, the resolution to the infinite Universe = infinite gravity is, indeed, the finite age of the Universe, just as for the infinite light puzzle (and yes, gravitational fields only propagte at the speed of light). As an aside, this puzzle is commonly referred to as Olber’s Paradox.

“There are only two things that are infinite: The Universe, and human stupidity-- and I’m not sure about the Universe”
–A. Einstein

33

Chronos,

Thanks for your informative reply. Some thoughts.

First, it seems to me that science is generally concerned with things that cannot be observed. That is why we have theories: to make claims about unobserved phenomena. I’m asking what I take to be the most basic question possible; is the universe fiite or infinite. I assume you don’t think the question is in princple unanswerable. But perhaps it is. After all, the speed of lihght is finite, some we will never be able to directly answer the question because we can’t have direct evidenec about things beyond our event horizon, if I have used that term properly.

Second, regarding the argument that “if the universe has a positive curvature (and is isomorphic) it must be finite.” Here is the the scenario I am imagining that would be a counter example: The universe would have one sun-like star in every cubic ___ number of parsecs. (Fill in the blank with any number needed to get “a positive curvature.”) The gravitational field of the stars causes light to “curve”, i.e., locally distory space-time, consistent with observational evidence. Furthermore, there are an infinite number of stars occupying an infinite number of cubic parcecs. Why isn’t this possible? Do not tell me that what I have presented is contradictory because if space-time were curved there could be “cubic” parcecs. That is the assumption I am questioning. Why does a high degree of local distortion (positive curvature) imply large-scale finiteness? (Perhaps you answered this earlier with your remarks about “a sphere must be finite.” Not having a lot of math, I might have to accept the fact that that is the only model possible.)

*** My computer informs me that there has been another post to this topic. I’m going to send this off and look at it now.

Tony

you seem to admit that there is no evidence whether the universe is finite or infinite (and as always, by infinite, I mean not “will expand forever,” but “is currently occupied by an inifinite number of stars, any two of which are a finite distance apart.”)

Two things fill my mind with ever-increasing wonder and awe: the starry skies above me and the moral law within me. – Kant

34

ok, I think I’ve got what you’re saying here. I guess you could say that it’s a distinction between local curviture, and globally averaged curvature. Global curvature is what’s relavent to the shape of the whole Universe-- if the average curvature is positive and uniform, then it’ll look like a sphere. What you’re suggesting is having a bunch of local curvatures. If, around each of these umpteen stars, there are regions of positive curvature, and regions of negative curvature, then it’s possible to have an average curvature of zero. An example would be those foam egg-crate things with all the fingers… There’s a lot of local curvature on the surface, but there’s as much positive as negative, so the average is flat. On the other hand, if you have more positive curvature than negative, the average curvature is going to be positive (I wish I could draw a diagram here). I hope this helps; if not, I sort of suspect that we’re just talking past each other, and aren’t going to make much progress… :confused:

“There are only two things that are infinite: The Universe, and human stupidity-- and I’m not sure about the Universe”
–A. Einstein

35

No, I don’t think we’re talking past each other. The egg crate example was exactly the sort of thing I had in mind. But, given my limited mathematical background, I doubt that you will be able to explain to me why a lot of local curvature necessitates a finite universe, rather than an infinite universe with a lot of local curvature. But that’s ok. I’m satisfied knowing that existing evidence does not strongly disconfirm the hypothesis that the universe is currently infinitely extended with an infinite number of stars (suffienctly far away from each other so that the average curvature in not positive).

Tony

Two things fill my mind with ever-increasing wonder and awe: the starry skies above me and the moral law within me. – Kant

36

ok so i didnt read all the posts. i got through about 7 or 8 of them and it seemed like no one was getting anywhere so i got bored and quit reading. Just wanna throw my 2 cents in here though. Check out “The Holographic Universe” by Michael Talbot. Life, reality, and the universe will make a hell of alot more sense to you after you read that book. Also, wasnt the big bang theory officially debunked a few years ago?

37

No.

jrf

38

Im reading a book called “The Physics of Immortality” which mathmatically proves the existance of God, Heaven, and immortality, (and the fact that the univers is infinate). It’s not light reading, but very interesting. I’m only a bit into it, but if I learn anything interesting, I’ll let you know.

JonF: but it should have been (just my personal opinion)