Using the term nothing gets a bit confusing because it has a slightly differnt context in different situations and its meaning can get a bit ambiguous. For instance "nothing can exist." What am I saying there? To keep things clear, I'll use "nothingness" to describe the entity (or lack of) that is thought of in a similar way as empty space. I'll use "nothing" to describe a collection of objects/attributes/etc., such as in "nothing is wrong with me."
HeXp£Øi± said:
Nothingness is nothing. Space is something.
Saying nothing can't exist is a bit of a paradox wouldn't you agree?
Yes, by definition it is a paradox. There can be a state of "nothingness" but by definition nothing exists there. To keep it simple, I'll just say that nothingness can exist, and that state is different than "empty space," which is something. Nothingness is what was before space was created during the big bang, and is what lies outside spacetime (as if outside has any real meaning here, but there isn't any other appropriate word to use).
Alright let's try this oli, for arguements sake we'll imagine that the universe is 20billion years old. Let's pretend we're another 20billion light years outside the known universe observing it yet we're independent of all matter.
We need to clarify this from the beginning. The size of the universe isn't limited to the size light has traveled since it began. Inflation for one (and Magueijo's alternative) provide one reason why. We also aren't sure if there are spaces which have had no information exchange (or ever will, for that matter). But I'll continue with the example to see where it leads.
Now let's imagine that all matter begins to reverse itself until it is back in it's infinitely small space or until there is nothing, whichever you prefer.
What is going to cause matter to reverse itself? Gravitation? If that's the case, then you must remember that gravitation also affects "empty" space. If matter "reversed" itself, then so would the expansion of space.
Now, are we not still surrounded by an infinite amount of space(nothing)? Space will still exist.
No. If gravitation caused a collapse of space and matter, then we would be carried along with space into the big crunch.
What you are describing is geometrically known as a hypersphere. It is the four dimensional equivalent to a sphere. It represents a volume that is finite, but unbounded, meaning you can travel forever and a day in one direction and never reach the "edge" or "end" of space, and yet there is still only a finite volume contained in space. How is that possible? Think of the Earth's surface for an analogy (this gets back to a curved object in a space of one greater dimension, in this case a two dimensional curved surface in a three dimensional space). The area of the surface of the Earth is finite, yet unbounded. You can travel due west for as long as you please and never reach the edge of the Earth. However, if the Earth began collapsing, and you were confined to its surface, there is nowhere you could run, nowhere you could hide, to avoid being carried along with the surface into the resulting crunch.
How does this translate to the geometry of space-time? Well, if the universe
does eventually collapse (as in your example) then we already know that it has the topology of a hypersphere. This is commonly referred to as a closed universe. If our universe is closed, then you could shine a laser in one direction and one day it would return to you from the exact opposite direction, having never been obstructed. All geodesics form closed loops. You could not sit in your spaceship "outside" space and watch matter collapse. During the collapse, you would find that the volume of space in which you could explore continually became smaller. It would take less and less time for the laser light to return to the source having made a complete loop. You would be carried along
with space, and everything in it, into the big crunch.
Evidence today suggests that the universe is open and will not collapse. In that case space may be finite or infinite, but would still be unbounded in either case. Though this topology is a bit more difficult to describe, it doesn't remove the fact that space is "something" and was created during the big bang.
Before the big bang there was no space in which your space craft could have existed. There was only nothingness.
