Is there more than one of you out there, somewhere?
In a fascinating piece over at Medium, astrophysicist Ethan Siegal waxes mathematical, cosmological, and philosophical on multiverse theory, and its implications for all the iterations of you that may or may not exist:
...would it be possible that there's a Universe out there where everything happened exactly as it did in this one, except you did one tiny thing different, and hence had your life turn out incredibly different as a result?
It's an incredible notion: that there's a Universe out there for every outcome that's conceivable. There's one where everything with a non-zero probability of having happened is actually the reality in that Universe.
But there are an awful lot of ifs that are mandatory to get there. For one, the inflationary state must have happened for not just a long amount of time — not just for the 13.8 billion years that our Universe has been around — but for an infinite amount of time.
Why is that, you ask? Surely, if the Universe has been expanding exponentially — not just for a tiny fraction of a second but for 13.8 billion years, or around 4 × 10^17 seconds — we're talking about a tremendous volume of space! After all, even though there are regions of space where inflation ends, most of the volume of the Universe is dominated by regions where it hasn't ended.
So realistically, we're talking about at least 10^10^50 Universes that started off with initial conditions that might be very similar to our own. That's 10^100000000000000000000000000000000000000000000000000 Universes, which might be one of the biggest numbers you've ever imagined. And yet, there are numbers that are bigger that describe how many possible outcomes there are for particle interactions.
There are 10^90 particles in each Universe, and we need for all of them to have the exact same history of interactions for 13.8 billion years to give us a Universe identical to our own, so that when we choose one path over another, both Universes still wind up existing. For a Universe with 10^90 quantum particles in it, that's asking an awful lot — for fewer than 10^10^50 possibilities to exist for how those particles will interact with one another over 13.8 billion years. The number you see above, for instance, is just 1000! (or (10^3)!), or 1000 factorial, which describes the number of possible permutations there are for 1000 different particles to be ordered at any instant in time. Consider, mind you, how much bigger this number is — (10^3)! — than (10^1000) is.
(10^3)!, for those of you wondering, is more like 10^2477.
But there are not 1000 particles in the Universe, but 10^90 of them. Every time two particles interact, there's not just one possible outcome, but an entire quantum spectrum of outcomes. As sad as the case is, there are way more than (10^90)! possible outcomes for the particles in the Universe, and that number is many googolplexes times larger than a paltry number like 10^10^50.
In other words, the number of possible outcomes from particles in any Universe interacting with one another tends towards infinity faster than the number of possible Universes increases due to inflation.
Even setting aside issues that there may be an infinite number of possible values for fundamental constants, particles and interactions, and even setting aside interpretation issues such as whether the many-worlds-interpretation actually describes our physical reality, the fact of the matter is that the number of possible outcomes rises so quickly — so much fasterthan merely exponentially — that unless inflation has been occurring for a truly infinite amount of time, there are no parallel Universes identical to this one.