Thanks Zenbeam. That makes sense.
Which leaves open the question on the shape of the universe. Is it believed to be a sphere in the sense that a straight line becomes a loop?
If the universe is indeed infinite is it bigger than a singularity inside a black hole? It seems like size and distance lose their meanings when dealing with infinities.
Its density is decreasing.
The answer to this question is not completely known. If it is spherical in that sense (the technical term would be “positively curved”), then the radius of curvature is significantly greater than any distance we can observe, such that it is very close to flat. Alternately, the Universe could be exactly flat or even negatively curved and still “wrap around”, if it has a nontrivial topology (the simplest example would be something like many video game worlds, where if you go off the top edge of the map you end up coming back in on the bottom edge, and likewise for left and right). Again, if this is the case, then the relevant scale must be very large, as we have not been able to observe any evidence of it.
This is exactly right. We often talk about the expansion of the universe, but using that term is what confuses people. When we think of something expanding, we think of a thing of a definite size getting bigger.
But that’s not what we observe. We don’t know what the size of the universe is. It could be a large finite size, or it could be infinitely big. What we do observe is that everything within the universe is getting farther apart. We can compare it to an expansion, since if we were to observe a fluid expanding, we could see something similar. But it’s only an analogy. We can’t see the universe from the outside, and by definition it’s impossible to be “outside” the universe anyway.
The expansion of the universe is shorthand for the density of the universe decreasing. This is why we can say the “expansion” has no center, or that it doesn’t matter whether the universe is finite or infinite. It’s also why I get a little annoyed when the beginning of the universe is described as the entire universe compressed into something the size of an atom, or a grapefruit, or whatever. At the time of the Big Bang the universe could have been enormously big or even infinitely big. What was different then is that the entire universe was extremely dense. It would certainly feel smaller, but you’d still have no way of knowing what the actual size of it was. The important factor is not size, but density.
Unfortunately there isn’t really a nice analogy to compare it to, so we’re stuck with inflating balloons.
OK… Moving on (for me) that the universe contains infinite matter and is infinite in size, there’s still a problem. How big was the universe at time zero? A singularity, correct? So on a quantum scale, how big was it at 10E-100 seconds? Any measurable size? If so, then it’s STILL a measurable size.
Rate of Expansion * 16 billion years * Some measurable size = Some NEW measurable size! Big yeah, but not infinite.
The only way for it to be infinite now is if the rate of expansion is infinite. And that’s clearly not the case or all particles in existence would be quite lonely.
Good question again.
In big bang cosmology there’s something called the scale factor represented as the function a(t) (where t is time). The exact details of what the function is and how it is arrived at isn’t important (for this discussion anyway), but it is defined thusly:
If two galaxies are distance d(t[sub]0[/sub]) apart at time t[sub]0[/sub], at time t they will be distance d(t) = a(t)*d(t[sub]0[/sub]) apart.
If we say at the big bang t = 0 then the singualrity occurs because a(0) = 0 (n.b. this is not because with have choosen to arbitarily label the big bang as time ‘0’). Therefore the distance d(0) between any two galaxies becomes zero. So in other words the universe does become pointlike (though I’ll sound a notion of caution in that it’s better to view the singularity as a boundary, rather than representing the physical state of the universe).
However at any point after t = 0, then a(t) > 0. This means that an infinite universe will contiune to be infinite right up to the point that t=0, at which point the whole model breaks down anyway.
In some ways it shouldn’t be suprising that a singularity makes something that should be infinite (i.e. the volume of the universe) go to zero as that’s just the kind of thing they do and it’s what makes them problematic.
*well to get all technical we actually mean isotropic observers, but we’ll assume galaxies approximate them fairly well
Thanks for all the answers!
In fact, I think it is a problem that it can be described in mathematical terms. But it’s more of a philosophical issue, I guess.