Quote:
Originally Posted by speach
The part of the universe that has expanded can and does have a dimension, but it's expanding so this dimension is continually changing. Lets take the analogy, that cosmologists are so fond of, a balloon. As the balloon expands it does so into nothing, but nothing is already part of the whole to allow it to be expanded into. So the conclusion must be that the emptiness it's expanding into is part of the universe.
 to the confusing world of mind experiments 
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This is wrong on many counts.
Firstly it is incorrect to assert that only part of the Universe has expanded.
The entire Universe both observable and unobservable expands.
A distant galaxy that passes over the particle horizon from the observable to unobservable Universe doesn't stop receding.
Secondly you do not understand the meaning of dimension in the context of space. Dimension isn't some measured quantity but represents the degrees of freedom an object can move in space.
Since we live in what is essentially 3 dimensional Euclidean space, you are confined to 3 degrees of freedom in the "up-down", "front-back" and "sideways" directions.
Expansion changes the scale factor of space not its dimension.
Thirdly analogies are limited in their descriptions of Cosmology.
The flaw in your example is that you seem to assume this is a 3 dimensional Universe. The surface of the balloon is the Universe in this case and the observers are two dimensional whose degree of freedom is confined to the surface. The observers do not perceive movement in the third dimension namely the radial expansion of the balloon.
Hence it is meaningless to refer to the expansion of the balloon into this "nothingness".
Fourthly the idea that "nothing is already part of the whole to allow it to be expanded into" as a condition for the entire Universe being infinite is not only illogical but fails mathematically. As has already been alluded to there is nothing preventing the entire Universe being bounded and finite.
While cosmologists have measured the local curvature of the observable Universe to be zero and therefore flat, the global curvature of the entire Universe could very well be a torus!!
A torus shaped Universe is topologically flat, bounded and finite.