Thursday afternoon saw me (and my 16-year old son) at the Wellcome Collection in London for the recording of Exchanges at the Frontier. The series of talks is a partnership with the BBC World Service, and has A C Grayling (Professor of Philosophy at Birkbeck, University of London) in conversation with some of the biggest names in science, talking about the frontiers of scientific knowledge and the social impact of these discoveries.

Brian Greene (Professor of Physics and Mathematics at Columbia University, New York) is probably best known for his popular science books The Elegant Universe and The Fabric of the Cosmos, and he is a leading exponent of string theory. This conversation was fascinating and gave a useful overview of the current state of thinking on string and related theories.

The General Theory of Relativity came about because Einstein asked what was the mechanism of gravity – Newtonian physics explained *how* it worked well enough, but not *why*. Einstein’s equations explained that the objects with mass warp space-time, and other objects fall because they want to age more slowly; according to the theory this should be the same for all lengths. However, introducing Quantum Mechanics, and in particular the uncertainty principle, shows that space is not uniformly smooth at very small scales (usually the scale of particles and smaller).

The vacuum definition changes, too, if quantum mechanics is introduced. Newton thought a vacuum was an empty environment, the absence of anything in a given space; with QM a complete absence is impossible: if the electromagnetic field is zero, then the uncertainty principle says it must be changing.

Some thinkers suggest that there is no problem, and quantum mechanics and relativity don’t have to be reconciled; Brian Greene points out that to understand the origin of the universe (which was once both very massive and very small), and black holes, then there is a problem. At present the maths produces values of ∞ when both theories are used, which is a pointer to the maths breaking down. The ‘collapse’ of the uncertainty, and whether it’s stochastic or not, isn’t understood, and various suggestions have been made, e.g. parallel universes, the future affecting the past, or the collapse of the wave function.

The length scales of this measurement problem can be very small – the Planck length is assumed to be the smallest possible length, and at 10^{-33}cm that is very small: the smaller you get, the larger the uncertainty gets.

And now we got round to string theory. In the standard model particles are ‘points’, whereas in string theory these points are stretched out into filaments, either loops or with loose ends, and the string can vibrate in a different fashion to give different particles. We can’t observe these strings directly, not even in particle accelerators: the LHC can see down to 10^{-19}cm, whereas the size of the strings is nearer the Planck length.

Quantum mechanics describes every force as being transmitted by a particle: electromagnetic (photon); strong nuclear (gluon); weak nuclear (W^{+}, W^{–}, & Z particles); and gravity (graviton). String theory is the main candidate at present to unify all the forces: strong & weak nuclear, electromagnetic, and gravity, all being part of the same fundamental force (EM and weak have been united as the electroweak interaction), but a difficult thing to explain is why gravity of so much weaker than the other three forces.

String theory’s maths only works if there are more than three dimensions of space, but the extra dimensions are curled up so small that we can’t observe them. A non-mathematical analogy is a sheet of paper the surface of which has an up and down, then rolled into a tube so tightly that the circular cross-section is too small to see, although the up and down-ness of the surface is still there.

Through the early years of string theory it was thought there were six extra dimensions of space (giving 10 space-time dimensions in total), but in 1995 it was realised that a vital piece of physics had been ignored and that there should be another extra space dimension, so it is now held that there are 11 space-time dimensions in all.

This led to M-theory, which introduces the idea that some configurations of strings can have them stretched into ribbon-like structures, or membranes (or *branes*). This in turn led to the theory that our universe could be on a brane within a series of branes – analogy can be a slice of bread in a loaf. And this in turn again could explain why gravity is so weak relative to the other forces. Gravity is associated with strings with no end attached – could it be that gravity is leaking out of our brane and into adjacent ones (i.e. a parallel universe)? This is testable (with difficulty), as gravity should be stronger between two particles.

This leads to alternatives to the Big Bang theory – instead of a Big Bang there could be a ‘Big Splat’ or a ‘Big Bounce’ involving colliding branes. [a good book about this is Endless Universe: Beyond The Big Bang by Paul J Steinhardt & Neil Turok]

Someone asked: in what are the strings vibrating? Physicists take ambient space and time as axiomatic, space and time should emerge from the theory: but vibration is a change of position in space over a period of time, so some deeper definition of what the vibration is will be needed.

Questions were also asked about the whole concept’s reality in the absence of evidence. Brian Greene said that he doesn’t believe this stuff until there is some evidence, but the maths is good: for example, gravity fixes the size of the string, which then causes the maths not to produce ∞.

Are the extra dimensions are actually physical dimensions? He said this could be a problem of terminology (call them degrees of freedom?), but mathematically all the dimensions are equal (but why three are big and the rest small is not explained).

Other questions: what would it be like if we could observe these extra dimensions? Comparing this with Flatland, for example, one could see the organs inside a body without looking through the skin. Leaking gravity: this could (theoretically) be used to communicate between branes. Dark Matter: could this be leaking gravity from another brane? (nice idea, but no convincing maths yet).

Although there’s no way of proving string theory with our current technological capabilities, (the theory is not fundamentally untestable, it’s just hard to test – slamming two gravitons together in an accelerator would do it) there are experiments which would add up circumstantial evidence. For example: quantum mechanical variations in the Big Bang show up in the Cosmic Microwave Background; measuring the CMB to a finer resolution should show variations due to strings; the LHC may observe otherwise unaccountable losses of energy, or observe ‘sparticles’ (supersymmetrical particles) which are predicted by string theory; or it may be that strings are bigger than we think, and the LHC may detect them; strings may have caught on an unevenness in the inflationary early space and have been uncurled, and will be transmitting gravity waves.

The theory currently needs to address whether space and time is pre-existing; and the shape of the extra dimensions. The latter problem is a large one, as it is predicted that there are 10^{500} possible different shapes (there are 10^{88} observable photons in the universe): it may be possible to statistically analyse these to reduce the choice. It may be that the shapes of the extra dimensions influence the form of physics in any one universe, and all permutations are existing in the Multiverse.

And lastly, he said that there is no experiment he can think of that will prove string theory wrong, without it showing that quantum theory is wrong too. And we know that works.

This was a fascinating event, aided by A C Grayling’s obvious understanding of the basics of the theory, but in greatest part because of the personableness of Brian Greene. It wasn’t just interesting, it was very enjoyable. I’m looking forward to the programme’s broadcast (although it will somehow be edited down from 1¾ hours to 1 hour) on 10 November 2010. It will then be available to listen to, and available as a podcast (but both, unfortunately, edited down to 28 minutes).