The universe's size : always infinite?

1. Jun 15, 2011

pedersean

I came across a startling position on more than one occasion while reading "The Fabric of the Cosmos: Space, Time, and the Texture of Reality" by Brian Greene. The position is that our immeasurable universe is infinite. He continues by writing that any mathematical modification to the size of the universe will always result infinite. Perhaps my understanding of infinity is misleading, but I've always held the position of infinity being obtainably intangible and impossible. Instead I prefer to hold that infinity is instead a special numerical placeholder of the extraordinarily large, and with subtracting from infinity a given tolerance becomes greater. Adding to infinity decreases that tolerance by bringing the actual number closer to its equivalent of the all powerful forever number. Am I nuts to argue that an expanding universe can not persist its size?

2. Jun 16, 2011

It basically which side of the fence you are on

If you think that the universe was created by the big bang, then it is physically impossible to fit infinite mass inside a ball the size of a pea (yes I know, laws of physics has been broken before). Then I would say that the universe is expading an it does have it's limits if you consider the theory that energy cannot be created or destroyed.

If you are one of those people who say that the universe has been here since the dawn of time and will always be here, then no... the universe isn't expanding (somehow :P)

as for the question is it infinite, I believe that rather than the universe being never ending, I think its in a big loop (like how people thought that earth was flat, but it's in a sphere, if you go in one direction for long enough you will eventually arrive in the exact same place that you have started from. ;)

Live Long and Prosper \ m /

3. Jun 16, 2011

sicarius

Infinity is a funny thing. For example, lets say you have an infinite amount of water. That means for every 1 oxygen atom you have 2 hydrogen atoms. While you obviosly have 2x as many hydrogen atoms, you at the same time have equal amounts, since there are infinite amounts of both hydrogen and oxygen. (1*∞)/3 = (2*∞)/3

If you take 1/2 of an infinite volume you still end up with an infinite volume. ∞/2 = ∞. Only if you divide an infinite volume infinitely do you get a finite number: (2*∞)/∞ = 2

So, if the universe is infinite it would have to be expanding infinitely fast, as there is an infinite amount of space to contribute to the expansion. But when you take an infinitely small portion of the universe (like what we can measure) that expansion rate can be finite. So if the universe were to gain 10% size over a given time, it could do so and still be infinite as 1.1*∞ = ∞.

All this seems counter intuitive and hard to accept, but the math is the math. Without accepting infinity as a real possibility than things like a singularity become impossible. An infinite universe also nicely explains expansion. While the universe was a finite size each point had an infinite amount of energy contributing to its expansion. Only once it reached an infinite size would there be a finite amount of energy at each point and be able to start to cool down.

Hope this helps.

4. Jun 16, 2011

BruceW

The current theory of the universe says that the universe is of finite size.
But there are models of the universe that say it could be infinite.
At the moment, they think its finite.

5. Jun 16, 2011

DragonPetter

Wouldn't an infinite universe imply infinite energy? For example, two objects infinitely away from each other would have infinite potential energy. What if 2 objects fall at each other from opposite "sides" of an infinite universe, would they accelerate more and more as they got closer to each other? Would they be infinitesimally approaching the speed of light as they accelerate closer to each other, or would it just take infinite time for this to ever happen anyway?

6. Jun 16, 2011

Haroldingo

Well for all intents and purposes the universe is infinite, in the fact that if we travel from one end to the other we find ourselves back at the place from which we started.

7. Jun 16, 2011

WannabeNewton

WMAP has found, to some degree of experimental error, that the universe is flat. This means that when one looks at the Friedmann model for a flat universe it is infinite in extent not finite. However, we can only view a finite portion (observable universe) of it because there are regions of the universe that are expanding faster than the speed of signals from those areas.

8. Jun 16, 2011

sicarius

Yes an infinite universe implies infinite energy. If the universe was empty execpt for those two obejects then yes they theoretically would fall towards at speeds approaching the speed of light, and yes they would never actually reach eachother. It is also possible that gravitons from one object would never reach the other and the falling would never even begin. We don't know enough about gravity to say for sure.

9. Jun 16, 2011

Nano-Passion

Wow, that was interesting.

But can there be an infinite velocity? I mean, Einstein proved that the speed of light can not be breached. Unless you are telling me that space needs not follow that rule.

If so it would be pose very interesting questions to space and its affects.

10. Jun 16, 2011

WannabeNewton

Precisely, space does not follow that rule.

11. Jun 16, 2011

Nano-Passion

Space is indeed interesting and mysterious. It really challenges your imagination and reasoning to the extreme. 0__o

Too many people take the word "space" for granted. We all grew up in it. Space to most people is just the room in their kitchen. Most people think of space as nothing. But in physics space actually has a life and physics of its own. Wow, I only got to appreciate it when I started to deeply ponder..

I wonder how much we truly understand about it?

12. Jun 17, 2011

sicarius

Thank you.

The speed of light is a measure of movement through space, and that speed cannot be breached. Expanding space is not "moving through space" and does not hit the same limitations.

13. Jun 17, 2011

Nano-Passion

Yes I've heard that before -- though I wonder about the mathematics behind these sort of things and I'm dumbfounded how we can use math to describe phenomena such as that. Unless there is no rigorous math to it and it is philosophical reasoning to the idea of expanding space.

14. Jun 17, 2011

sicarius

I may be wrong here, but I think that it is more like they have not found any math that disallows this, not so much as they have mathematically proved it.

15. Jun 17, 2011

BruceW

There is a rigorous mathematical explanation for the universe being able to expand faster than the speed of light. It is called general relativity.
The universe is highly curved at large scale, which is why two faraway objects can be moving away from each other faster than the speed of light.

16. Jun 17, 2011

WannabeNewton

The universe is flat, according to observations, at the large scale and two objects don't really move faster than each at the speed of light but rather the space between them expands faster than the speed of light.

17. Jun 17, 2011

ZapperZ

Staff Emeritus
Closed, pending moderation.

Zz.

18. Jun 18, 2011

bcrowell

Staff Emeritus
Hi, pedersean,

Welcome to PF!

It would have been better to post this in Cosmology rather than in General Physics. Typically people who are most knowledgeable about a particular field will only pay attention to posts in the relevant forum. Because the discussion had drifted off track, the thread was temporarily locked. I've moved it to Cosmology and opened it back up again.

This is not really right, and since Brian Greene is a competent physicist, I think probably what's happened is that you misinterpreted or oversimplified something he wrote. We have an entry on this topic in the cosmology FAQ: https://www.physicsforums.com/showthread.php?t=506986 We actually don't know whether the universe is spatially finite or spatially infinite.

This sounds like another case where the message got garbled somewhere along the line. This would depend on what was meant by "mathematical modification."

The Math FAQ has a good entry on infinity:
https://www.physicsforums.com/showthread.php?t=507003 [Broken] The truth or falsehood of your statement would depend on what you meant by "obtainably intangible and impossible."

This kind of statement really can't be decided, because it uses undefined terms like "all powerful forever number." The real number system doesn't include infinite numbers. The math FAQ entry gives some examples of number systems that do include infinite numbers.

Not nuts, just incorrect :-) I'm not clear here on why you use the word "persist." Are you discussing the possibility that it would start out infinite and then become finite at some later time? (This would seem to go along with what you said above about "mathematical modification.") According to general relativity, if the universe is finite at one time, then it's finite at all earlier and later times; if it's infinite at one time, then it's infinite at all earlier and later times. This can be proved mathematically based on the Einstein field equations plus some other very reasonable physical assumptions that we have good reason to believe hold in our universe: http://arxiv.org/abs/gr-qc/9406053 The term for this is "topology change."

This actually doesn't quite work in cosmology. There is no principle of conservation of energy in cosmology. We have a FAQ entry about this: https://www.physicsforums.com/showthread.php?t=506985

Mass and energy are equivalent in relativity, so we actually can't define the total mass of the universe (regardless of whether it's spatially finite or spatially infinite). However, we can discuss things like how many hydrogen atoms there are. "The size of a pea" would only apply to cosmologies that are spatially finite (and therefore spatially finite at all times). In these cosmologies, there is only a finite number of hydrogen atoms (or any other particle) in the universe.

The thing to be careful about here is that unless you specify a particular number system (with certain axioms), these statements about arithmetic operations involving infinity are neither true not false. You also have to be careful about your implicit assumption that there is only one infinite number, which is not true in all number systems that include infinite numbers. The math FAQ entry does a good job of explaining this.

This is sort of right, except that you haven't really defined what you meant by "infinitely fast." Maybe you mean the velocity of one galaxy relative to another galaxy that is at a cosmological distance from it? In this case, there is actually no uniquely defined way to talk about the velocity in GR. However, one reasonable way to talk about it is to let $v=\Delta L/\Delta t$, where L and t are the quantities defined in this cosmology FAQ entry: https://www.physicsforums.com/showthread.php?t=506990 In that case, v is finite for any two galaxies, but in an infinite universe there is no upper bound on v (and v can be greater than c).

This is incorrect, because, as discussed above, GR says changes of topology aren't possible.

Nope. The cosmology FAQ entry discusses this.

No, the wrap-around thing would apply to a spatially finite universe (one with finite volume), but as explained in the FAQ, we don't know if it's spatially finite or spatially infinite.

This is not quite right. As explained in the FAQ entry, the universe is within error bars of being flat. Therefore it could have either positive curvature (with finite spatial volume) or negative curvature (with infinite spatial volume).

Sorry, but this is basically all wrong.

It's not an question of space versus physical objects, it's a question of local versus global. Relativity only prohibits objects from zooming right past each other at >c. For cosmologically distant objects, velocity isn't even uniquely well defined (see above).

It is rigorous math. It's how general relativity works.

This is a common way of explaining it nonmathematically. Mathematically, "speed" is just not defined in this context, and expansion of space, although a possible verbal description, is not the only way of verbally describing the mathematics of an expanding universe.

-Ben

Last edited by a moderator: May 5, 2017
19. Jun 18, 2011

Bob3141592

No, not if the universe is a mixture of positive and negative energy, unevenly distributed on small scales. Then you could have an infinite universe with zero or really any finite amount of energy.

20. Jun 18, 2011

bcrowell

Staff Emeritus