Are there Infinite Versions of You?

If the universe goes on forever, does that mean there are infinite versions of you? The cosmological equations that so beautifully describe our universe make an uncomfortable prediction: interpreting them within the most straightforward way, they tell us that the universe is also infinite. Or not; it could end up that the universe contains enough matter and energy to shut in on itself and be finite, or perhaps the only interpretation of the cosmological equations is simply too simple. But in keeping with our greatest theoretical understanding, an infinite universe seems a minimum of possible - and a few would say likely. If so this raises a good more crazy possibility. An infinite universe may literally contain every possible thing allowable by the laws of physics - each in infinite multitude, which includes infinite versions of you. Today I’m visiting try and convince this version of you that everyone those other versions are real. 

To start out with we want though we'd like some monkeys. In fact, we'd like infinite monkeys. You’ll have heard the old thought experiment - if an infinite number of monkeys tap randomly on an infinite number of typewriters, eventually one in all them will accidentally type out the entire works of Shakespeare. This proposition is that the infinite monkey theorem. The reasoning is easy enough: assume each monkey is tapping in any respect keys randomly. There’s an opportunity that a given monkey will tap the primary character of the primary play: a capital “A”. Let’s say there’s around a 1 in 100 find a typical typewriter assuming capital "A" is as likely as small "a." Then the second character - an area - 1 in 100 again so on. “A tempestuous noise of thunder and lightning heard...” the prospect of that's 1/100^50 or 10^-100 - and that’s 100 billion times less likely than winning a raffle attract which there are as many raffle tickets as there are particles within the universe. Probably that monkey will spoil on the very next character ... but given enough monkeys one will eventually get through the Tempest, go on to the 2 Gentlemen of Verona, Merry Wives, etc., with 99 out of 100 monkeys giving up at each subsequent character. And 99 out of each hundred monkeys that make it to the last character of the last play will devastate there. But one amongst those monkeys will correctly complete Cymbeline and every one of Shakespeare’s First Folio with a probability of 1/100^3.75 million. That’s right, I counted all the characters altogether Shakespeare's plays. This can be an unthinkably small probability. But it’s not zero probability, and therefore the Infinite Monkey Theorem tells us that any non-zero probability event will certainly happen given a sufficiently sizable amount of trials.

Perhaps you'll be able to start to determine how this is applicable to there being infinite yous in an infinite universe. in a very perfectly deterministic universe, the starting conditions in any given region - like positions, velocities, etc. of all particles - perfectly determines the long run history of any point thereupon region. That is, until the disrupting influence of external regions has time to achieve that time. The properties of every region are effectively random - set within the beginning of the universe by quantum processes. If they’re set good then the longer term history of that region are similar to our part of the universe, resulting in the formation of the galaxy, the Earth, Shakespeare, and you. The probability of getting every particle good is unthinkably smaller than the already unthinkably small probability of a monkey typing out Shakespeare. But it’s not a zero probability, so with infinite regions of the universe - infinite trials, the infinite monkey theorem tells us it has to be compelled to happen somewhere. In fact, it has to be compelled to happen infinite times and with infinite variations. So infinite yours and infinite versions of you. That is, IF our assumptions are right. to make a decision if this is often really the correct conclusion there are some things we want to induce straight. First up, in such an infinite universe we wouldn’t find everything - only everything that would happen from the range of initial conditions developing under the laws of physics. Infinite monkeys with standard English typewriters will eventually reproduce all of Shakespeare and each Harry Potter, but lacking an inverted punctuation could never do the first Spanish version of Borge’s Library of Babel. Similarly, there’s no version of you out there where you've got Captain Marvel superpowers. Though i assume there may well be one where you’re Batman. Or NOT Batman, if, you know, you’re already Batman during this one. OK, so refining our question: in an infinite universe, does every POSSIBLE thing happen infinite times? Well still, not necessarily. If there are infinite possible starting configurations for anybody region of the universe, then there will be infinite regions with none doubling up. But if there are finite starting points then a minimum of a number of those starting configurations must be repeated infinite times. Technically we could imagine that our part of the universe is exclusive and it’s just other regions that are duplicated, but we've got no good reason to assign that kind of specialness to our region. So if there really are finite possible starting conditions then this region is maybe repeated.

So what does it mean for 2 regions of the universe to possess the identical starting conditions? It means every particle, or chunk of quantum field,  or whatever elementary pixel of reality - has matching properties between the two regions. How closely matching would they need to be? Close enough that the subsequent 13 and a half billion years of bouncing around leads to indistinguishable results - and to you existing now. In such a chaotic system, even tiny differences in the starting conditions will lead to massive divergences in that future history. But in principle there is an allowable level of ridiculously tiny deviation in the starting conditions between two regions that would still lead near-identical 13.5 billion year histories. We can’t tune the starting conditions to an infinite degree and still get different results - and that’s the key point. It seems there must be finite possible starting configurations. That means at least some regions must be repeated infinitely. Therefore you’re Batman. I should also note that it’s not just the particles that define starting conditions; there are also the laws of physics themselves. The constants of nature or the energy of the vacuum may well be different between regions. But in most cases we expect these values to repeat themselves infinite times in an infinite universe - eventually leading to an exact-enough repetition of both the laws of physics and the arrangement of particles. Repetitions of the initial conditions are inevitable as long as the properties defining those conditions can take on a finite range of values. If one or more properties of the universe can take on values over an infinite range then no repetitions would be necessary. For things like the mass or charge or other properties of individual particles, an infinite range means going to very, very high values for these properties - and that tends to be prohibited by a combination of conservation laws and the formation of black holes. 

It is technically possible for the energy of the vacuum itself to have any value, even enormously large. But universes with large vacuum energies will exponentially expand, until that vacuum energy decays to lower values in smaller regions within. In fact that’s essentially the eternal inflation picture - one of the most popular ways to produce infinite universes. I simplified this argument a bit, but elaborating doesn’t change the conclusion. For example, you could argue that fundamental quantum randomness will cause even identical starting configurations to produce different results. But that still doesn’t give us an infinite number of distinguishable histories because the number of possible configurations of particles at every instant is still finite. In fact, quantum randomness could allow different starting conditions to evolve into a universe that looks like this one. There’s actually a much simpler proof that there’s a finite number of different possible configurations of any region of the universe. Jacob Bekenstein and Steven Hawking showed that the maximum amount of entropy in any region of space is proportional to the number of tiny Planck areas covering its surface. We can interpret that Bekenstein bound as the maximum number bits of hidden information. And 2 to the power of which is the number of different possible configurations for that volume. For our 46-billion light year observable universe there are definitely no more than 2^10^123 possible unique configurations. As long as the greater universe has more than that many observable universe-sized regions, one of them should be identical to this one. And actually, the Bekenstein bound is the hard upper limit - for non-black holes the number of possible configurations is much, much lower. 

So unless there’s something weird hiding in the laws of physics that we don’t understand, an infinite universe probably does duplicates its parts infinite times. We covered most of the important assumptions in this crazy hypothesis - except the main one. That the universe is actually infinite at all. Now this may never be testable - we can measure the observable part of the universe to greater and greater precision and see if it has an open or closed geometry... but even then we still have to hope that it’s reasonable to extrapolate our cosmological equations forever. On the other hand, if we somehow verify the eternal inflation picture then it’s very hard to avoid an infinite universe, or at least one that’s infinite-enough to duplicate itself. On the other-other hand, many good physicists are very uncomfortable allowing infinities into any models describing the physical universe - and their intuition shouldn’t be entirely discounted. In a nutshell, answer is YES but it's probability of happening is very, very less.

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