Face

All my points before, and following are assuming one dimension, infinite dimensions, by default would result in infinite possibilities. But the thing to remember is that something capable of infinite possibilities does not necessarily include everything conceivable.

I was stalking about the what the OP outlined at first. A universe with infinite space and time, not necessarily what we have in our universe. If we take the proposed universe, then all it would take is one (non-decaying) particle to produce an infinite number of possibilities given infinite time and infinite space. Even thoughthere is only one particle, one dimension and all it's doing is changing it's location (if a location can even be assumed in infinite space with one particle...lets just say two so we can have infinite relative positions).

In order for this particle to produce infinite possibilities it cannot be constrained be time, or space (or you can replace time with speed effectively the same thing), at least two of these variables must be infinite for it to theoretically achieve the infinite possibilities.

In our universe, space can be seen to be expanding at an increasing rate, that doesn't mean it is infinite at THIS point in time if you could theoretically freeze time. So for this point in time there are not an infinite positions the particle could take, therefore all other particles are also limited, and an infinite number of possibilities are not possible.

But the entire theory assumes on the concept that particles/energy occupy discreet points and are not infinitely variable. Otherwise there are infinite possibilities of the position of the particle within 1mm, infinite space isn't needed in given that assumption.

But that is only bulletproof if we are still completely separating space and time. Because theoretically (and in actuality) our time is just another dimension of space. One never exists without the other, since they are one of the same (space-time).