This had better not be an infinite universe, because if it is, then it contains everything. EVERYTHING. Even a universe that is not infinite.
All possibilities would become realities, given infinite time and space:
    A planet full of failed carpet cleaning businesses
    Another planet full of the people who sold the machines to the carpet cleaners who ran the businesses into the ground
    An entire galaxy full of the psychiatrists to the parking meter attendants who ticketed the veteranarians of the sickly dogs of the former owners of the few customers of the failed carpet cleaning businesses
And so on, ad suicidem.

SmokeyBarnable's assertion can be best understood as implicitly using the following analogy:

If an irrational number is not normal1, then every possible sequence of numerals appears in its infinite decimal expansion.

And so if the universe could be considered infinitely not normal, then it would indeed contain an infinite number of different proctologists. However, we have no reason to believe this of the nature of the universe's infinity (if such is the case). It may be that the universe is a tesselation (either in space or time), or even it just contains you or an infinite number of bananas is true.

However, if this is the case then by Kolmogorov Complexity the universe is compressible. In fact, if determinism is true then the description of the universe can be compressed to a description of Cosmic Egg at the Big Bang. I'm not sure what the metaphysical consequence of that is, other than:

Either the universe is not normal and infinite, or it is finite, or you are not a beautiful and unique snowflake.

1: I will leave the discussion of whether this is the case to Gorgonzola and ariels.

Statements about cosmology should be based on science. All ontological arguments aside, it's becoming more and more apparent that the universe is indeed infinite, with an inifnite amount of matter and energy. Scientists are led to this by current theories of physics and astronomical observations.

After I originally posted this, I argued this subject back and forth via /msg with various noders for several weeks. I was forced to go back and make sure that I remembered the cosmology I learned so long ago correctly. It turns out I had, with a big however at the end.

In the early 20th century, Albert Einstein's theory of General Relativity showed that matter curves the space around it. Our idea of space in the Universe as a whole is a 3-manifold embedded in a larger spacetime. This is really a matter for another node1, but we will touch on it later.

Meanwhile, one interpretation of Einstein's theory was that the universe was continually expanding (which Einstein disliked so much that he threw a fudge factor called the "cosmological constant" into the theory to get rid of it). The universe's expansion became widely accepted after Edwin Hubble's observation of red shift in almost every other galaxy in the late 1920's, and confirmed by the observation of cosmic microwave background radiation of Arno Penzias and Robert Wilson in the early 1960's.

So, physicists were led to one of two possibilities:

  • Either matter in the Universe is dense enough to slow down the expansion, make it reverse itself, and contract and eventually cause a Big Crunch (a closed universe);
  • or it is not, in which case the Universe will keep expanding forever (an open universe as well as a flat universe).

The density of matter in the Universe determines not only its fate, but also its size. Strangely enough, it is an inverse relation.

  • A closed universe has a finite volume, like the finite surface area of a balloon. Consequently, it can hold only a finite amount of matter. Not only that, the denser matter is in a closed Universe, the sooner the Big Crunch will come. In other words, the denser the matter is, the less matter there is overall! An analogy may help you understand this better: We can observe a closed universe from the outside, as a black hole in another universe that contains it. Now, Stephen Hawking showed that black holes evaporate due to a strange process of quantum physics now called Hawking radiation. The less matter in a black hole, the smaller it is, and the sooner it will evaporate.
  • An open universe is infinite in extent, and was infinite as soon as the Big Bang happened. Now, matter has to be (more or less) evenly distributed throughout the universe. Otherwise, the Universe contains a finite "speck" of matter with an infinite void around it (if there is more than one, each is an infinite distance from the other, effectively putting each in its own infinite open universe). Spacetime isn't an object in and of itself, it is a structure built from the interactions between its contents. An infinite void with nothing in it simply can't exist. Put another way, the laws of physics2 would have had to be different in the vicinity of the "speck" for it to be created, violating the concept of Universality, one of the basic assumptions underlying the theory of relativity. We must conclude that an open universe contains an inifite amount of matter.

Unexpectedly, it has been recently observed that the expansion of the Universe is speeding up. The cosmological constant has been resurrected as an idea, but we are also forced to discard the possibility of a closed universe. Without some new physics, we will have to accept the idea of a forever-expanding, open, infinite universe.

There are two flies in our ointment that may lead to "new physics":

  • The theory of the Big Bang has actually been replaced with one of cosmic inflation, which has led some to the notion that the Universe we observe arose from a quantum fluctuation in some other primoridal outer universe that got out of hand. So, we may not understand the structure of our Universe completely. I'd like to believe that the topology of spacetime is conserved, and our Universe is connected somehow to the one that spawned it. This would definitely lead to a localized area with "different laws". We are then left with the conundrum of what the "outer universe" is like, and whether there is an infinite regress or not.
  • More recent astronomical observations have postulated that the fine-structure constant had a slightly different value billions of years ago, soon after the Big Bang. This variance of the laws of physics through time does not mean they vary through space at a particular point in time, but it opens the door to possibility.

There is an important valid objection to the picture I've painted above, which has to be addressed: A universe that expands forever doesn't necessarily have to be infinite in extent to start with (if it wasn't to start with, it never will be). If we delve into the subject matter of Which 3-manifold do we live in? and Which 4-manifold do we live in?, 3-D slices of the Universe for particular points in time could possibly be compact (= finite for our purposes) even if the slices extend forever. It is possible that we are embedded in some sort of 4-dimensional hypercone or hypertrumpet.

All of that said, the standard model of cosmology still portrays an open universe as spatially infinite at any given point in time. According to General Relativity, the curvature of space (determined by the matter embedded in it) controls its shape. A closed universe has negative curvature; an open universe has zero or negative curvature.

While our hypertrumpet and hypercone have negative curvature in timelike directions, they both have positive curvature in spacelike directions. An infinite volume is still the only 3-manifold with zero curvature (and an infinite hyperbolic paraboloid is still the only manifold with negative curvature) explained by General Relativity alone.


It turns out that compact hyperbolic manifolds (such as the Weeks Space) exist. A 3-torus would work in a flat universe. But then, we would have to live in a universe with a really funky topology (I should have read Which 4-manifold do we live in? first). However, results from the Wilkinson Microwave Anisotropy Probe seem to indicate that the universe is flat.

Another objection: An infinite amount of matter will result in an infinite gravitational pull. There are a couple of possible ways out of this, all hinging on the observed fact that the Universe is expanding:

  • If gravity behaves in a quantum manner similar to the electromagnetic force, with gravitons that behave like photons, then some analogy of redshift applies to gravity. In a way, the "infinite gravity" problem is similar to Olbers' paradox, which of course is resolved by redshift.
  • If, as a few physicists think, gravity is transmitted instantaneously, it still has to overcome the initial "force" of the Big Bang, not to mention whatever is making the expansion speed up. Since an infinite universe is an open or flat Universe, we already know it's flinging itself apart too fast for gravity to overcome.

1Please read Which 3-manifold do we live in? and Which 4-manifold do we live in?
2By the "laws of physics", cosmologists usually mean the values of certain "magical" fundamental constants, rather than its underlying mathematical basis.

It is easy to prove that the universe is not infinite in size. If the universe, as is almost universally accepted, started at a finite size (actually a point, followed by the Big Bang and/or Cosmic Inflation), and has always expanded at a finite rate (there is no evidence to show otherwise), then it would take an infinite amount of time to reach infinity in size. Since a finite amount of time has passed since the beginning of the universe, then the universe must be finite in size.
The only way the universe could be infinite is if it started off infinitely large, or it ever had an infinite growth rate.

If the universe is infinitely large, it could still be growing. If, from any point in the universe, the rest of the universe seems to be moving uniformly away from the observer, then the universe is obviously growing--even if it is infinite in volume!

In fact, we know from redshift that the rest of the universe is moving away from us: stars, nebulae, galaxies, entire clusters of galaxies--all are moving away from us. The farther away they are from us right now, the greater their speed away from us. (See: Hubble constant.)

A commonly used analogy to help explain this is to picture some two-dimensional beings living on the surface of a balloon. The beings, unaware of the curvature of the balloon in three-dimensional space, look in all directions and see an infinite expanse of two-dimensional space. If one of them decides to embark on a journey to "the end of the balloon" by walking in a straight line, he will eventually circle around and end up exactly where he started, without ever having reached a boundary or deviated from his straight-line path. The two-dimensional being is completely within his rights in assuming that his balloon universe is infinite.

Now imagine a careless Everything user comes along and starts blowing more air into the balloon. Pandemonium! Squiggly flat people who were standing right next to each other having a conversation just moments ago are suddenly across the room from each other. On the next breath of air, the balloon grows even bigger and suddenly these people aren't even in the same city! Chaos ensues, the squiggly flat peoples' government breaks down; martial law is declared, and eventually the squiggly flat peoples' society reverts to despotism.

Now the squiggly people are dead or dying, hopelessly spread out across the vast area of their expanded, infinite universe. I hope you're satisfied!

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