If you tried to poop in -128.6°F cold......just kidding
Think of it like your a jar filled with marbles, where each marble represents a type of atom. If you keep randomly pouring marbles into other jars, eventually the arrangement of marbles (atoms) will match a specific configuration, like yours. Even though it might take an unimaginable amount of time, because space is infinite, the odds are that somewhere, a jar with a configuration exactly like yours will exist.
This idea suggests that, in an infinite universe, the same combinations of atoms could repeat, creating exact replicas of you and everything else. With infinite space and time, your configuration could eventually occur again, over and over, because there are only so many ways atoms can be arranged. So, in a sense, you could already exist elsewhere in the universe or could come back in the future, just as a natural consequence of infinite possibilities.
could this make the concept of parallel universes obsolete or at least less significant?
we don't know for certain that the universe is infinite. While the idea of an infinite universe is supported by theoretical models and some observational data, like the flatness of space-time and the large-scale structure of the universe, we don’t have direct proof.
So we would have infinite universes, each one being infinite itself. Infinite infinite universes. Infinite * infinite = infinite. So not obsolete, but less significant, I'd say. Like, if you have infinite finite-universes, you'd also have infinite replicas of yourself in some of them. Or, just as in Futurama, the universe is not infinite, and they go to the limit of ours to see the other side, which is another universe. Fry asks "then, there are infinite parallel universes?" to which the professor answers "no. Only two." Then on Fansworth's Parabox it's shown there are way more than 2.
This reminds me of the article "we live forever in pi", where if pi is a normal number (no proof yet) it would mean it contains every combination of numbers. Thus, everything which can be described by numbers, e.g. subatomic particle energy levels, values for their wave funcion for position/speed, quantum superposition, entanglement, etc., eventually there's a chain of numbers that describes not only you as you are now, but also another chain which describes your next state, and even another chain with the current state of all the universe. It even includes a chain in simple ASCII which describes how to find and decode those chains to replicate an apple, a person, or a supermassive black hole colliding with a galaxy. Of course, in any language.
It is strongly believed that pi is a normal number, that is, each digit has the same probability of appearing, regardless of the base used to express pi. However, just like the infinite universe, there's no actual proof, just many arrows pointing in the same direction.
Trivia/spoiler: in Carl Sagan's novel Contact, the main character discovers wether pi is normal or not.
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That's actually very relevant. The universe isn't like pi; it's mostly empty and what isn't empty is mostly hydrogen and helium. To guarantee that every finite combination of atoms exists, and that there are infinite copies of every finite combination of atoms, you need that "normal" distribution that pi seems to have and the universe doesn't.
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Actually the universe seems as "normal" as pi. I don't remember who said what and why, so I'll tell what I remember. There's a theory that predicts that the universe is more or less the same regardless of which direction you look. OFC at small scale, our solar system looks empty, with some rocks around a flame. 4 light years until our next neighbour. But at big scales, the universe IS more or less the same. You can say "it seems to be a high density spot here" but in the big scale, it's more or less the same all the time. It's like foam. Some bubbles would be larger than others, there could be a cluster of small ones here and there, but overall foam is foam.
I specifically choose the foam analogy because on a certain scale, our universe seems structured like foam. Big bubbles of near-vacuum and the matter gathers on the surfaces that each bubble shares with the touching bubbles. I don't remember where I read that, but it was a very interesting article.
So, I can't say that mathematically speaking the universe is normal, just like pi might be, but indeed it seems to have the properties to be.
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I don't know that the self-similarity you're talking about is as strong as pi being "normal". In pi, as far as we know, every digit appears evenly distribute, no matter what base we use. The distribution of atoms in the universe is not like this. Maybe the normalness only appears on the large scale, so solar systems and galaxies are normally distributed in some sense, but that doesn't equate to normalness at the atomic scale.
Fun conversation.
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That's what I said. Pi being normal is not the same as the universe being "more or less" the same no matter where we look at, on a large scale. But pi on a short scale isn't normal either. Let's say, for example, that the equivalent of atomic scale in an infinite universe, compared to pi, is ten digits. Take any ten consecutive digits from pi. It would be quite rare that the resulting number is normal. If we'd take, let's say 100, we would find groups that appear normal, and groups that deviate from what we'd consider a normal number. The decimal digits of pi appear normal only in large scale. But, as I said, I don't know how it is comparable. However, having infinite universes, or one infinite universe, would be roughly equivalent. As you said, the universe seems to be mainly empty. We could also say that the digits of pi (if normal) are mainly random, with only some chains forming something with meaning. It would contain all written books, and also all books that haven't been written. In plain ASCII. But, go and search for them.
It all is nice and fun as a mental experiment, but realistically, it serves no purpose. For now...
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