Science of Discworld III

there’s no hope of observing any extra dimensions directly. However, there are several ways to infer their presence indirectly. In fact, the recently discovered acceleration in the rate of expansion of the universe can be explained in that manner. Of course, this explanation may not be correct: we need more evidence.
    The ideas here change almost by the day, so we don’t have to commit ourselves to the currently favoured six-dimensional set-up. We can contemplate any number of different branes and differently arranged loops. Each choice – call it a loopy brane – has a particular energy, related to the shape of the brane, how tightly it is curled up, and how tightly the loops wind round it. This energy is the ‘vacuum energy’ of the associated physical theory. In quantum mechanics, a vacuum is a seething mass of particles and anti-particles coming into existence for a brief instant before they collide and annihilate each other again. The vacuum energy measures how violently they seethe. We can use the vacuum energy to infer which loopy brane corresponds to our own universe, whose vacuum energy is extraordinarily small. Until recently it was thought to be zero, but it’s now thought to be about l/120plex units, where a unit is onePlanck mass per cubic Planck length, which is a googol grammes per cubic metre.
    We now encounter a cosmic ‘three bears’ story. Macho Daddy Bear prefers a vacuum energy larger than +l/118plex units, but such a spacetime would be subject to local expansions far more energetic than a supernova. Wimpy Mummy Bear prefers a vacuum energy smaller than −l/120plex units (note the minus sign), but then spacetime contracts in a cosmic crunch and disappears. Baby Bear and Goldilocks like their vacuum energy to be ‘just right’: somewhere in the incredibly tiny range between +1/118plex and − 1/120plex units. That is the Goldilocks zone in which life as we know it might possibly exist.
    It is no coincidence that we inhabit a universe whose vacuum energy lies in the Goldilocks zone, because we are life as we know it. If we lived in any other kind of universe, we would be life as we don’t know it. Not impossible, but not us.
    This is our old friend the anthropic principle, employed in an entirely sensible way to relate the way we function to the kind of universe that we need to function in. The deep question here is not ‘why do we live in a universe like that?’, but ‘why does there exist a universe like that, for us to live in?’ This is the vexed issue of cosmological fine-tuning, and the improbability of a random universe hitting just the right numbers is often used to prove that something – they always say ‘We don’t know, could be an alien,’ but what they’re all thinking is: ‘God’ – must have set our universe up to be just right for us.
    The string theorists are made of sterner stuff, and they have a more sensible answer.
    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 500plexuniverses distribute their vacuum energies densely in the range -1 to +1 units. The resulting numbers are much more closely packed than the l/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