In 2000 Bousso and Polchinski combined string theory with an earlier idea of Steven Weinberg to explain why we shouldn't be surprised that a universe with the right level of vacuum energy exists. Their basic idea is that the phase space of possible universes is absolutely gigantic. It is bigger than, say, 500plex. Those 500plex universes distribute their vacuum energies densely in the range -1 to +1 units. The resulting numbers are much more closely packed than the 1/118plex units that determine the scale of the `acceptable' range of vacuum energies for life as we know it. Although only a very tiny proportion of those 500plex universes fall inside that range, there are so many of them that that a tiny proportion is still absolutely gigantic - here, around 382plex. So a whacking great 382plex universes, from a phase space of 500plex loopy branes, are capable of supporting our kind of life.
However, that's still a very small proportion. If you pick a loopy brane at random, the odds are overwhelmingly great that it won't fall inside the Goldilocks range.
Not a problem. The string theorists have an answer to that. If you wait long enough, such a universe will necessarily come into being. In fact, all universes in the phase space of loopy branes will eventually become the `real' universe. And when the real universe's loopy brane gets into the Goldilocks range, the inhabitants of that universe will not know about all that waiting. Their sense of time will start from the instant when that particular loopy brane first 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 hidden dimensions 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 world, 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 itself in 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.
AUDITORS OF REALITY
IT WAS ONE HOUR LATER. Wizards were ranged in rows across the width of the Great Hall in a variety of costumes, but mostly in what might be called Early Trouser; despite Rincewind's view on nudity, a grubby shirt and pants would pass without comment in many ages and countries and lead to fewer arrests.
'Right, then,' said Ridcully, striding along the ranks 'We've kept all this very simple so that even professors can understand! Ponder Stibbons has given all of you your tasks!' He stopped in front of a middle-aged wizard. 'You, sir, who are you?'
'Don't you know, sir?' said the wizard, taken aback.
'Slipped m' mind, man!' said Ridcully. 'Big university, can't be expected to recognise everyone!'
'It's Pennysmart, sir. Professor of Extreme Horticulture.' 'Any good at it?'
'Yes, sir!'
'Any students?'
'No, sir!' said Pennysmart, looking offended.
'That's what I like to hear! And what will you be doin' today?' 'First, it appears, I shall be dropped waist-deep in a lagoon in the, the -' he stopped, and fumbled a piece of paper out of his pocket
'- Keeling islands, where I shall attack the sand bottom round me with this rake,' he held up the implement, 'and then return here as soon as I see any humans.'
'And how will you do that?'
'Say aloud, "Return Me, Hex",' said Pennysmart, smartly.
'Well done, good man,' said the Archchancellor. He raised his voice. 'Remember that, everyone! Exactly those words! Write them down if you can't remember them. Hex will bring you back on the lawn out side the building. There will be hundreds of you and many of you have several tasks, so we don't want any collisions! Now, if-'
'Excuse me,' said Pennysmart, raising a hand. 'Yes?'
'Why will I be standing in a lagoon flailing around with a rake, please?'
'Because if you don't do that, Darwin will tread on the dorsal spine of an extremely poisonous fish,' said Ponder Stibbons. `Now-' 'Excuse me again, please,' Pennysmart said. 'Yes?'
'Why won't I tread on this fish?'
'Because you will be lookin' where you are treadin', Mr Pennysmart,' roared Ridcully.
But a forest of other hands had gone up. About the only wizard without a hand aloft was Rincewind, who was staring gloomily at his feet.
'What's all this about?' said the Archchancellor, irritably. 'Why .have I got to move a chair six inches?'
'Why have I got to fill up a hole in the middle of a prairie?' 'Why have I got to bide a pair of trousers?' 'Why have I got to stuff a letter box full of starved snails?' Ponder waved his clipboard wildly to silence the clamour. 'Because otherwise Darwin would have fallen off a chair or been thrown from a horse or would have been struck by a stone hurled by a rioter or an unwise letter would have reached its destination,' he said. 'But there are more than two thousand tasks, so I can't explain every one. Some of them are the start of a quite astonishing causal chain.'