I'll start off by saying that I actually really like the first part of your theory. The probability of absolutely nothing happening in an infinite
amount of time is indeed 'zero' - but not really, since we can't just assume that something is impossible. If it was truly 'zero', then it was
always impossible, and thus could
never have happened in the first place. But I'm going to try your theory using 'approaches zero' instead
of 'zero'. By that logic, the probability of 'anything' else happening (individually) must also be 'zero' - for practical purposes we'll call
it 1/infinity (assuming that the amount of outcomes in the universe is infinite, or so large that it is reasonable to call it 'infinite' - I will
use infinity and 'a very large number' interchangeably). This actually makes a pretty good case, mathematically at least, for the infinite universes
theory.
By definition, something is that absence of nothing, or the logical opposite to nothing. It also, by definition, defines a 'set' which includes
anything that could happen. Ill buy it, but this would make the probability of event 'something' approach 1 (since the sum of 1/infinity,
infinity times, is equal to 1). Here's where the theory breaks down: you propose that this should be impossible, since 1 is a positive number, and 0
cannot give way to 1.
But wait - I thought we were talking about states? Your original thesis implied that the state of the universe is a Bernoulli random variable (value
of 0 or 1), considering you used the word 'chances' - probability? With this kind of random variable, you don't 'get' something from nothing, the
event simply 'is' (1) or 'isn't' (0). So let's set up your original experiment:
Assume
There are infinite 'anything's that could happen in the universe, each with an equal probability approaching zero.
Pa = 1/infinity
Let
'nothing' = (0)
'something' = Set S{'anything' =/= 'nothing'} = (1)
Pn ~ 0
Ps ~ 1
infinite time units = infinite probability experiments with event set S'{0, 1}
You perform this experiment an infinite number of ties and what do you get? Obviously, it converges to event (1). Interestingly, given the previous
assumptions, these probabilities imply that 'nothing' basically could
never have happened. Even
more interestingly, it suggests that
assuming the probability of our
particular universal state and 'nothing' are equal, that the probability of our universe existing is equally
as likely as the 'nothing' scenario
. There's a neat little paradox. Finally, since the probability of each of these events is so infinitesimally
small, and only their total combined probability is significant,
each universal state cannot exist without an infinite number of alternate
universal states. Sounds strange, but given the properties of infinity, it actually makes sense (any number that is not infinity is infinity times
smaller).
To be honest, I don't know how well probability holds up in this situation, but if this is correct then I think I can draw a bit of a different
conclusion: it is necessary for every state (that is not nothing) of the universe to exist at once, or else none of them can exist.
I hope this helps, but then again maybe I misinterpreted what you were trying to say.