(September 20, 2012 at 9:28 pm)Darkstar Wrote: How can something that is infinitely large get bigger? Wouldn't the infinite number of spaces, no matter how small each one was, take up an infinite amount of space and leave no room for expansion? Infinite is not just 'big beyond comprehension', it is everything, that is why we cannot assign a value to infinity-10^99999999; it would still be too large.
Infinite is not a concept that has a tangible equivalent in daily life, so it is hard to think clearly about it without making the mistake of trying to shoehorn a model derived from everyday experience into a situation requiring a mathematically sound model.
So to think clearly about infinity you have to use math to help you. In math, infinity has the property of being arbitrarily divisible, and yet each part would remain just as infinite as the whole.
So 1/2 of infinity, or one trillionth of infinity, or one googleplexeth of a infinity, each party would be different from the whole, but yet no less infinite than the whole. Similarly, duplicate inifinity a googleplex time and the collection of all product from the replication would be different from before, but no more infinite.
This is conceptually how an infinite universe can expand. Put a ruler in space along any direction, and the ruler can go on literally forever. The universe is infinite in that direction. But look at each inch on the ruler. Each inch division on that ruler can grow, until it is now 2 inches long. The ruler still goes on forever. The universe is still infinite. But every portion of it is now twice as large.
(September 20, 2012 at 9:28 pm)Darkstar Wrote: If they could still expand, that would suggest that the 'space' the universe is expanding into was bigger than infinity, which is impossible
Again, you are tripping yourself up by forcing a mental image from daily life in which everything exists in a small part of space, into an inappropriate analogy for all of space itself. Space does not expand into anything. Space s everything. Space just expands by becoming bigger, without displacing anything. All that ever is is getting bigger. It is not getting bigger by taking up space belong to something else before. It is creating more space where no existed before. Space can be infinite, can can always have been infinite, yet try to visualize every unit of space as spawning more space. This is how infinite space can expand.
(September 20, 2012 at 9:28 pm)Darkstar Wrote: If you said that an infinite amount of potential space was contained in the singularity, but not infinite mass, and that space was simply becoming less dense with matter as it expanded, being infinite all the way, I'd be willing to believe that much.
The singularity vision of the beginning of the universe only applies to the visible portion of space. It is only looks like a singularity because our physics breaks down somewhere before things got really small. The origin of the visible portion of our universe probably had some dimension, in the neightborhood of a planck length, or about 10^-35 meters. It may not have quite been infinitely small.
Along the same vein, the universe that is currently beyond our visible horizon, not all of it may have fitted into the same notional singularity.
Go back to the divide infinity by googleplex concept. What our physics imperfectly descibes as the singularity that spawned everything we can see now may have been part of a larger, perhaps infinitely larger, construct that began an expansion at the time we call the Big Bang.
