The following thoughts were prompted by trying to figure out what the question, “Is the Universe infinite?” is really asking. “How could it be?” I ask. If we know the age of the Universe is finite, and we know that the fastest anything with energy/information can travel is the speed of light, isn't the “size” of the Universe merely the age multiplied by the speed of light? But how is the Universe defined? Some say that space is infinite and that the matter is expanding into it. But, if my limited understanding serves me, wasn't there no space before the Big Bang and the existence of matter? Also, there has been much work done on particular periods of inflation. Is this not the Universe starting from a smaller size and getting larger? If so, at what point did the Universe go from being finite to infinite? Is the theory that precisely at the Big Bang, space was made infinite, and then inflation caused it to be more infinite? I'm not even sure the word “infinite” has much meaning in this case. If there is a boundary of any kind which cannot be exceeded, how can one call this infinite? Because it always has the possibility to keep expanding? Perhaps they are saying, “The Universe will be infinite in size after an infinite amount of time.” Well, so be it. This is more a statement of the future of the Universe than its current state; a statement that the Universe will forever expand.
Maybe I'm simplifying, but it seems to me that the entity which includes all the mass and energy created in the Big Bang should be called the Universe; and if current time and maximum speed are finite, so its size must also. What am I missing?
So what of this boundary that marks the edge of the Universe? If you've read about General Relativity at all, it's likely you've seen the expansion of the Universe analogized to the following. There is a balloon with an array of equally spaced dots drawn on its surface. Now, blow up the balloon further. If you look at any single dot, all of its neighboring dots are moving further away. If you do the same analysis to one of the aforementioned neighboring dots, all of its neighboring dots are also moving further away from it. It's a beautiful demonstration of how all things can be moving further apart from one another simultaneously.
But our space is in three dimensions, whereas the surface of the balloon is in two. Ask yourself: what is the “boundary” in the case of the balloon? Is it the surface of the balloon? In the analogy, if each dot symbolized something like a galaxy, then the entire surface of the balloon would be the whole universe. So is the question, “Is the Universe infinite?” actually asking how much the balloon can be blown up? Assuming a balloon that doesn't break, maybe the concept is that we are blowing up this balloon in our living room and once it gets big enough to hit the walls and ceiling, that's it: the Universe is finite. In that case, however, the “Universe” not only consists of the surface of the balloon (which represents all the galaxies and space), but also the room in which it's being blown up. This is a higher dimension than that which the surface of the balloon exists.
In the case of our 3-D space expansion, that would mean the “room” exists in four dimensions. When we ask if the Universe is infinite, are we really asking about the size of the room in four dimensions? If so, there's no wonder why I was confused!
I would venture to make an educated assumption that our fourth dimension in this case is time. Just as saying that the size of the room being infinite suggests the balloon can become infinite as well, is it not equivalent to say that the Universe being infinite is equivalent to time being infinite? Once again, this seems like a statement about the potential of the future, not about a current property of the Universe.
Just to confuse matters more, let's think about what it means to be on the surface of this 3-D balloon. Aside from small fluctuations, everything is moving further away from us. Check. It's common knowledge that as we look into space, we are in a very real sense looking back in time, due to the fact that it takes time for light to travel from the object to our eyes. So everywhere we look, it happened in the past. The location of the “present” is right here. But of course, “right here” is different depending on if it's you, me, or some being in a different galaxy. We're all simultaneously in the present and past, depending on who you ask. I guess it becomes a question of “whose present?” and “whose past”? I always imagined the edge of the Universe to be some source of light, hauling ass at 300 billion meters per second “outward”, as if I was in the middle of the balloon watching it's surface expand outward. But this is not accurate. It seems we are all simultaneously on the “edge” of the Universe, which is defined by the present time and we are being propelled “outward” into the future.
In sum, I still don't think I understand the question: “Is the Universe infinite?” It seems to me, with my limited knowledge and probably faulty logic, that it is equivalent to asking if time is infinite. But that seems to depend on the fate of the Universe and isn't a property of it in the same sense as “total energy” or “total mass”. Whether the Universe collapses into the “Big Crunch” or expands forever is an interesting question, but if that is what's meant by asking if the Universe is infinite or not, please clarify!