r/mathematics • u/RemarkableMarzipan23 • 1d ago

Parallel Universe Odds

Suppose there are infinitely many parallel universes, and a wormhole opens up that allows people to travel between them. My friend jumps into the wormhole and is transported to a randomly selected universe. A minute later, I jump into the same wormhole. My destination is also completely random and independent of his.

Here's my question: What is the mathematical probability that I end up in the exact same universe as my friend?

My initial intuition is that the probability would be 1 divided by infinity, which would be zero. But here's what confuses me: If the probability is zero, does that mean it's mathematically impossible for us to end up in the same universe? Or could it still happen despite having a probability of zero?

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u/jack101yello 1d ago

The probability is 0, and having a probability of 0 does not always mean impossible.

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u/RemarkableMarzipan23 1d ago

Thanks, but doesn't your answer assume the universes form an uncountably infinite set, like the real numbers between 0 and 1?

I'm imagining countably infinitely many universes: Universe A, Universe B, Universe C, and so on, with each universe having exactly the same chance of being selected.

From what I understand, you can't actually have a uniform probability distribution over a countably infinite set. So wouldn't that mean the probability is undefined rather than zero?

In other words, isn't there a difference between saying my chances are zero and saying that the way I've described the random selection isn't mathematically possible in the first place?

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u/daavor 1d ago

You cannot define a probability distribution on a countable set with the probability of each given point being equal

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u/Gold_Ad8890 1d ago

it depends a great deal on what "a random infinite universe" means. if you mean a uniform distribution on infinitely many universes, the probability is 0, and in fact a uniform probability distribution over an infinite set of outcomes is kind of nonsensical for exactly that reason. the sum of probabilities of all outcomes must be 1, but in such a distribution it would be 0 since the probability of each outcome is 0. another factor here is that universes are discrete.

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u/BigPenis_MathGenius Misleading username 5h ago

"uniform probability distribution over an infinite set of outcomes is kind of nonsensical for exactly that reason"

Just to be pedantic: over a countably* infinite set.