5.3 Who ordered that?
With apologies to Isaac Rabi
So, have we completed our journey? On the way, we have tested theories such as the Bell Inequality and put together clues from quantum measurements such as Alain Aspect’s experiments and we have arrived at an exquisitely beautiful structure – our multiverse – in which our particular universe is but one of an unimaginably large, but nevertheless finite, number of other universes, grouped in such a way that we can at last account for our observations. We have understood that this grouping of universes means that there is a level of reality above our own within which such groupings can be arranged. So, what did I mean when I referred above to a profound consequence of the structure of our multiverse? Well, I suppose you could call it the Ultimate Mystery, and I’m choosing my words deliberately.
We start by considering the kind of mathematical structures that can exist apart from our own universe and multiverse. A sphere is an example. The Game of Life is another – it can be a stand-alone Game, or a nested hierarchy like the structure we used to show that each level of a structure has its own reality. And, of course, our universe as part of our multiverse, and universes like ours, are also mathematical structures that can exist.
What about a universe that is identical to our own, up to the moment within our own past light cone where we conduct a sequence of 10,000 60º experiments – but where every outcome of each of the 10,000 measurements is spin-down? Is that logically possible? Yes, of course it is and, indeed, one or more such universes must exist within our own multiverse: such a universe was referred to as a “maverick universe” by deWitt in his article promoting Everett’s Many Worlds Interpretation. Of course, if you happened to be in one such maverick universe, and measured spin-down 10,000 times, you’d certainly be querying the settings of your experimental apparatus. However, if you repeated the sequence of 10,000 experiments, this time you’d almost certainly find the expected 7,500 results with spin-up, give or take 100 or so. How can we be so sure of that? Simply because in the overwhelming majority of universes in our multiverse, the percentage of spin-up outcomes is very close to 75% for such a sequence of experiments, and so the chance that you would be in one where the percentage is 0% is incredibly low.
Each histogram represents an identical multiverse to ours up to the point where we conduct sequences of 10,000 60º experiments. However, where we find 75% of outcomes are spin-up (shown in red), all the other multiverses are structured as mavericks, where the outcome of every one of the 10,000 experiments is spin-down (shown as the black line at the origin – 0%). If there is an indefinitely large number of such maverick multiverses, then the chance that we would be in one where around 75% of our results are spin-up is zero.
Now, here’s the twist. There is nothing to rule out the existence of another multiverse – another mathematical structure – where most, or even all, of the universes are identical mavericks, where sequences of 10,000 experiments, or even a billion experiments, all have the same result: spin-down! Since such a multiverse is a possible structure, then it exists. To make matters worse, the number of such universes in that multiverse can be far greater than the total number of universes in our own – billions, trillions, quadrillions of times greater! So it is far more likely that we are in one of the universes in such a maverick multiverse than in the well-behaved multiverse where the universes are arranged according to the Born rule for the sequence of 10,000 experiments. We wouldn’t know we were in such a maverick universe until we conducted the 10,000 experiments: the past light cones of all of the universes can be identical. The existence of so many maverick multiverses essentially rules out the likelihood of us getting sensible results for our sequences of experiments!
But of course we find that the results of our quantum experiments are well-behaved and rational. Did we make a mistake in our argument? Well, at the end of the day, the difficulty arises because of the existence of parallel universes. If ours were the only universe, then we wouldn’t be talking about the likelihood of being in a universe with the right number of quantum outcomes, and we wouldn’t be fretting about why our universe seems so well-behaved when it should be far more likely that we are in a maverick universe.
However, as we have seen, outcomes of quantum interactions are absolutely unpredictable within our universe, and yet, given enough interactions, patterns emerge. The unpredictability cannot be generated by a random number process for the reasons we have discussed, and the only remaining explanation for the patterns that overlie the unpredictability is a Born-rule arrangement of parallel universes with different outcomes, so that you don’t know which universe you’re in – one in which an outcome is spin-up, for example, or one in which the outcome is spin-down. It seems that we are stuck with parallel universes.
Were we wrong, then, to assume that all logically possible universes and multiverses exist? We appealed to the idea that our multiverse is purely a mathematical structure, which opened the door to every other possible mathematical structure (including multiverses), which in turn led to a natural explanation for our multiverse as just one of an immense number of other multiverses with slightly different, and less life-friendly, fundamental constants (MUEG). But it is this very plethora of other multiverses that has landed us in trouble through effective “contamination” of the quantum outcomes that we expect to find in our own multiverse. No, the case for MUEG is strong, but, despite the arguments to the contrary, it is nevertheless becoming increasingly difficult to avoid the conclusion that our multiverse is a unique mathematical structure.
Does that mean we have failed in our quest? Not a bit of it! We set out to follow the whispers that there seems to be a higher reality than our own, and our conclusion (that there does seem to be such a higher reality, based as it is on the observed underlying unpredictability of our universe, combined with the overarching patterns in quantum outcomes that we can measure and predict) appears to be robust. As we have seen, other interpretations of quantum mechanics, including, in particular, the de Broglie-Bohm account, fall short, and the Copenhagen Interpretation (perhaps wisely!) doesn’t even attempt to explain observed quantum outcomes. The Many Worlds Interpretation does try to make sense of it all, but it still accommodates splitting universes, and indeed it predicts an infinity of such split worlds.
What has happened is that, when we thought we were within sight of the summit of our journey, and we stood and looked back over the route we had come, we saw in the distance a higher peak – the mystery of why our multiverse seems to be unique. That sounds familiar – it wouldn’t be the first time that someone has commented on the remarkable uniqueness of our universe! But no, ours is a road untravelled until now. The uniqueness that we have identified is what remains after the conventional route to the Multiple Universes Explanation for Goldilocks has been explored. It seems that MUEG isn’t valid, and that our quantum multiverse stands alone.
Notice that, in concluding that our quantum multiverse is unique, we didn’t have to agonise over just what are the ingredients that make up a Goldilocks Universe. We didn’t have to make the case that there is something special about carbon-based life and wonder what it was that made the universe just right for it. Nor did we have to make the case that there is something special about any base for life – silicon, maybe – or even the case for the very existence of atoms themselves. No, our conclusion of uniqueness comes from the simple observation that the outcomes of quantum experiments form a pattern – the Born rule, as it happens – because no pattern could arise amidst the chaos of other “spoiler” mathematical structures. We see the quantum patterns, and so we can conclude that we are unique. It has nothing to do with the fact that our multiverse happens to contain universes that support life.
While we have made the case very thoroughly that our universe is a substructure within the purely mathematical structure of our multiverse, in the end, mathematics seems to have come up short, because it hasn’t supplied a plethora of other multiverses. It seems that we need something more to supplement the story of our reality. It’s as though there is a kind of filter for mathematics – a meta-mathematical censor, if you like – that doesn’t allow the existence of other multiverses that are similar but not identical to ours. I’m reminded of Brian Greene’s description of a first encounter between human beings and aliens where they let us into the ultimate secret of reality: “Ah, math. We tried that. It only takes you so far. Here’s the real thing…” Greene doesn’t tell us what the real thing is, though.
It may well be that we are literally incapable of understanding at a visceral level the complete explanation of why our quantum multiverse is unique, and why its universes are arranged according to quantum rules. The central conclusion of this website, that there is probably a higher mathematical structure than our own universe – a higher reality than our own – is astounding; the new revelation, though, that our uniqueness defies mathematical logic, is beyond mind-blowing.
