Originally posted by Mike2
Isn't String Theory itself a description of how manifolds emerge from other manifolds and then join
Is that because the splitting and joining of world-sheets is itself all only one manifold with holes in it, and not creating separate manifolds?
I'm refering to logical conjunction of two propostions held to be true. Consider the following statements of propositional calculus:
(The symbol "[tex] \to [/tex]" stands for material implication, and "[tex]\cdot[/tex]" symbolized conjunction.)
(p \cdot s) \to (p \to s)
and by symmetry:
(p \cdot s) \to (s \to p)
Together they prove:
(s \to p) \cdot (p \to s) = (p=s)
It seems obvious that particle creations imply expansion since we could not distinquish one particle from another unless they are separated in space which must expand in order for that distinction to exist.
And the expansion of any manifold from nothing implies at least the existence of one particle, the particle described by that initial manifold that expands.
So perhaps it's not such a great leap to conjecture that it is a general truth that the expansion of one manifold is equal to the creation of submanifolds.