# Finding yourself in the multiverse

Simon Williams, who is studying MSci physics with particle physics at Royal Holloway, University of London, asks whether you've ever wondered what the world would be like if there was another you? Identical to you in every way, this other you would live on a blue-green planet called Earth, which itself resides in a solar-system of eight planets orbiting a star called the Sun ...

## Doppelgänger

Actually, this person has had exactly the same life experiences as you, but perhaps at this exact moment in time, they make a decision that you choose not to. The idea of a doppelgänger is a bizarre one, and one that seems completely impossible, but in fact if you accept today’s most popular cosmological model then you have to accept that there is an exact copy of you somewhere out there in space. Paraphrasing the cosmologist Max Tegmark: sometimes we just have to live with the implausible.

This cosmological model states that a short time period after the big bang the universe went through a stage of inflation: exponential expansion where space expanded faster than the speed of light. The idea of inflation solves many of our problems including the isotropy of the universe, and why the cosmic microwave background (CMB) radiation is evenly distributed throughout the universe. However, this theory does throw up some peculiar ideas, one of which is the existence of the multiverse.

## The multiverse

About 10^{-30} seconds after the big bang, an unimaginably small period of time, the universe was a bubbling soup of quantum fluctuations. These fluctuations were randomly spread across the universe due to the nature of the big bang, and so at this time all possible arrangements had a non-zero probability. Quite literally, anything could have come out of this soup. Think of the most peculiar idea of a universe, and that would be possible!

However, inflation begins and the universe starts to cool. As the temperature drops, matter clumps together, we get stars and ta-dah: we have the universe that we experience. But if we look back to how inflation started, one could assume that it was triggered by a quantum fluctuation. So it is possible that any of the quantum fluctuations at the beginning of the universe could trigger inflation. Although this may be a huge assumption, one interpretation of quantum mechanics suggests that if something is possible, it happens. So what happens if each of the quantum fluctuations triggers its own inflation, but at slightly different times? We would have universes bubbling up from this quantum soup. Every possible universe would then exist as a bubble in this weird space we call the multiverse.

In the simplest model of inflation, this space is infinite, with bubble universes coexisting alongside each other like the bubbles in a bath.

## Infinite space

How can the space be infinite? Let’s imagine a finite universe; if I travel to the end of the universe, what is there? Is there a sign that says “No entry, this is the end of the universe. Nothing exists beyond this point”? But what is on the back of this sign? I would still be tempted to look beyond the sign, but in this finite universe I would see nothing.

Nothing is a more troubling concept than infinity. To combat this Einstein postulated that the universe could be finite, but with no end. If the universe was convex in shape, for example a doughnut shaped universe, one could travel along the surface of the doughnut forever and never get to the edge of the doughnut, thus space could be finite but with no end. As lovely as this idea is, it turns out that in the most recent measurements the geometry of the universe is actually flat. So one would be pushed to assume the space was infinite; the multiverse is not doomed yet!

Okay, so space has no end but does ‘stuff’? One could assume that matter peters out towards the end of our universe. Then these other bubble universes next to ours would have no matter within them, they would be pretty boring places. Once again, experimental evidence from measurements of the CMB radiation comes to the rescue. In fact, matter seems to be constant throughout our universe, and so it would be logical to assume that matter is just as infinite as space! So all the evidence seems to be suggesting that these other universes can exist, but why can’t we see them? The human mind can accept the existence of something it can’t see, for example watching a ship sail over the horizon; we know it exists but we can no longer see it. The idea extends to why we cannot see the rest of the multiverse, but this time instead of the curvature of the Earth being the restriction, it is the speed of light. The universe is approximately 13.8 billion years old, and so light can only have travelled 10^{26} metres in that amount of time, and consequently the furtherest thing we can see in the universe is 10^{26} metres away. The simplest form of the cosmological model suggests that your nearest cosmological twin is within 10^28 (10 to the power 10^{28}) metres from here. This is a huge number in comparison to the width of the universe we live in and the distance to the farthest thing we can see. This result pretty much assures that we will never see our cosmological twins, but perhaps in millions of years to come, our ancestors will see their twins and maybe even visit them!

## The problem of infinity

There is still the problem of infinity. What happens if it turns out that space is not infinite, but has some finite size? Still good news for the multiverse. In fact if one has a universe that is approximately 10^100 (a googolplex) metres in diameter then the probability of a doppelgänger starts to become very large. In a universe of this size it is almost certain that there is an identical copy of you somewhere out there in the multiverse. This size is called a Hubble volume and is calculated from assuming the universe before inflation was no hotter than 10^{8} degrees Kelvin. This volume contains every possible universe that could have arisen from such an early universe, and so if one could travel beyond this distance then you would start to see the universes repeating.

Thus, if you travelled far enough, you would meet your identical self in an identical universe, assuming they decided to stay at home that day and not go out looking for you.