Science of Discworld III

occurred.
    String theory not only tells us that we’re here because we’re here – it explains why a suitable ‘here’ must exist.
    The reason why all of those 500plex or so universes can legitimately be considered ‘real’ in string theory stems from two features of that theory. The first is a systematic way to describe all the possible loopy branes that might occur. The second invokes a bit of quantum to explain why, in the long run, they will occur. Briefly: the phase space of loopy branes can be represented as an ‘energy landscape’, which we’ll name the branescape . Each position in the landscape corresponds to one possible choice of loopy brane; the height at that point corresponds to the associated vacuum energy.
    Peaks of the branescape represent loopy branes with high vacuum energy, valleys represent loopy branes with low vacuum energy. Stable loopy branes lie in the valleys. Universes whose hiddendimensions look like those particular loopy branes are themselves stable … so these are the ones that can exist, physically, for more than a split second.
    In hilly districts of the branescape, the landscape is rugged, meaning that it has a lot of peaks and valleys. They get closer together than elsewhere, but they are still generally isolated from each other. The branescape is very rugged indeed, and it has a huge number of valleys. But all of the valleys’ vacuum energies have to fit inside the range from -1 units to +1 units. With so many numbers to pack in, they get squashed very close together.
    In order for a universe to support life as we know it, the vacuum energy has to lie in the Goldilocks zone where everything is just right. And there are so many loopy branes that a huge number of them must have vacuum energies that fall inside it:
    Vastly more will fall outside that range, but never mind.
    The theory has one major advantage: it explains why our universe has such a small vacuum energy, without requiring it to be zero – which, we now know, it isn’t.
    The upshot of all the maths, then, is that every stable universe sits in some valley of the branescape, and an awful lot of them (though a tiny proportion of the whole) lie in the Goldilocks range. But all of those universes are potential, not actual. There is only one real universe. So if we merely pick a loopy brane at random, the chance of hitting the Goldilocks zone is pretty much zero. You wouldn’t bet on a horse at those odds, let alone a universe.
    Fortunately, good old quantum gallops to our rescue. Quantum systems can, and do, ‘tunnel’ from one energy valley to another. The uncertainty principle lets them borrow enough energy to do that, and then pay it back so quickly that the corresponding uncertainty about timing prevents anyone noticing. So, if you wait long enough – umptyplexplexplex years, perhaps, or umptyplexplexplexplex if that’s too short – then a single quantum universe will explore every valley in the entire branescape. Along the way, at some stage it finds itselfin a Goldilocks valley. Life like ours then arises, and wonders why it’s there.
    It’s not aware of the umptyplexplexplexplex years that have already passed in the multiverse: just of the few billion that have passed since the wandering universe tunnelled its way into the Goldilocks range. Now, and only now, do its human-like inhabitants start to ask why it’s possible for them to exist, given such ridiculous odds to the contrary. Eventually, if they’re bright enough, they work out that thanks to the branescape and quantum, the true odds are a dead certainty.
    It’s a beautiful story, even if it turns out to be wrong.
    1 To see why, double it: the result now is 2 + 1 + ½ + ¼ + ⅛ ++ … which is 2 more than the original sum. What number increases by 2 when you double it? There’s only one such number, and it’s 2.
    2 If you’ve never encountered the mathematical joke, here it is. Problem 1: a kettle is hanging on a peg. Describe the sequence of events needed to make a pot of tea. Answer: take the kettle off the peg, put it in the sink, turn on the tap, wait till the kettle fills with water, turn the tap off … and so on. Problem 2: a kettle is sitting in the sink. Describe the sequence of events needed to make a pot of tea. Answer: not ‘turn on the tap, wait till the kettle fills with water, turn the tap off … and so on’. Instead: take the kettle out of the sink and hang it on the peg ; then proceed as before. This reduces the