String theory holds that what we usually consider to be individual points of spacetime, dimensionless dots with no interesting structure of their own, are actually very, very tiny multidimensional surfaces with complicated shapes. The standard analogy is a garden hose. Seen from some way off, a hose looks like a line, which is a onedimensional space - the dimension being distance along the hose. Look more closely, though, and you see that the hose has two extra dimensions, at right angles to that line, and that its shape in those directions is a circular band.
Maybe our own universe is a bit like that hosepipe. Unless we look very closely, all we see is three dimensions of space plus one of time - relativity. An awful lot of physics is observed in those dimensions alone, so phenomena of that type have a nice four-dimensional description - relativity again. But other things might happen along extra `hidden' dimensions, like the thickness of the hose. For instance, suppose that at each point of the apparent four-dimensional spacetime, what seems to be a point is actually a tiny circle, sticking out at right angles to spacetime itself. That circle could vibrate. If so, then it would resemble the quantum description of a particle. Particles have various `quantum numbers' such as spin. These numbers occur as whole number multiples of some basic amount. So do vibrations of a circle: either one wave fits into the circle, or two, or three ... but not two and a quarter, say.
This is why it's called `string theory'. Each point of spacetime is replaced by a tiny loop of string.
In order to reconstruct something that agrees with quantum theory, however, we can't actually use a circular string. There are too many distinct quantum numbers, and plenty of other problems that have to be overcome. The suggestion is that instead of a circle, we have to use a more complicated, higher-dimensional shape, known as a `bran'[43]. Think of this as a surface, only more so. There are many distinct topological types of surface: a sphere, a doughnut, two doughnuts joined together, three doughnuts ... and in more dimensions than two, there are more exotic possibilities.
Particles correspond to tiny closed strings that loop around the brane. There are lots of different ways to loop a string round a doughnut - once through the hole, twice, three times ... The physical laws depend on the shape of the brane and the paths followed by these loops.
The current favourite brane has six dimensions, making ten in all. The extra dimensions are thought to be curled up very tightly, smaller than the Planck length, which is the size at which the universe becomes grainy. It is virtually impossible to observe anything that small, because the graininess blurs everything and the fine detail cannot be seen. So 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 antiparticles 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 1/120plex units, where a unit is one Planck 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 +1/118plex 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 -1/120plex 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 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.
43
Derived from a pun: m-bran for `membrane'. Opening up jokes about no-branes and p-branes. Oh well.