In The Finite Multiverse I computer-painted a picture to illustrate my point that not every conceivable universe can, in fact, exist. My picture was the clock tower of Big Ben draped with a vast Nazi swastika flag. Now the BBC have a trailer for a miniseries they’re going to run this month – and guess what? – it’s the Houses next door that the flags adorn, not Big Ben. So I was close, huh?
If you believe Anthony Aguirre and Max Tegmark, parallel universes with every possible history do exist. That’s because they believe that the multiverse is infinite (but that’s not what I want to talk about here – for that discussion, see either The Finite Multiverse or, elsewhere in my blog, No Man in the High Castle). Perhaps the most remarkable claim of Aguirre and Tegmark is that these doppelgängers and quasi-doppelgängers not only exist, but they are to be found in our own universe, although so far away as to be physically inaccessible to us.
When I first came across their claim, intriguing as it was, I felt uneasy about it. Then it dawned on me why. Each of the different “worlds” (universes) in Hugh Everett’s Many Worlds Interpretation is in a specific quantum state. In fact, each universe is in what is called an eigenstate, and one of the characteristics of an eigenstate is that a quantum system cannot be in two different eigenstates – it can be in only one.
Aguirre and Tegmark were obviously assuming that the quantum state of our universe does not extend beyond our Hubble volume. (The spherical edge of the Hubble volume is where objects are receding so fast from us, because of the general-relativistic expansion of space, that their speeds reach that of light.)
However, it struck me that, if you were sitting near the edge of my Hubble volume, you, of course, would be at the centre of your own Hubble volume, and I would be near the edge of yours. Your Hubble volume would be in a single quantum state, mine would be in a single quantum state – and we’d be sharing the space between us. So we must both be in the same quantum state – the quantum state of my own Hubble volume must extend well beyond its edge to the far edge of yours.
What’s more, you can continue that process forever, so that every part of our universe must be part of the same quantum state. Since that state has to be an eigenstate, Tegmark’s Hubble volumes, with their different eigenstates, cannot reside within our own universe. So what I am saying is that our universe, and all of its parallel universes, cannot share the same space but must be mathematically separated (into what are called separate Hilbert spaces).
I have posted a new paper on arXiv explaining this in more detail.