The highlight of Maths Week Ireland (see post below) was the Hamilton lecture, a public lecture at Trinity College presented by the Royal Irish Academy in conjunction withThe Irish Times and Depfa Bank. The lecture was Warped Passages: Unraveling the Mysteries of the Universe’s Hidden Dimensions’, by Lisa Randall, Professor of Particle Physics at Harvard. Prof Randall needed no introduction to the physicists in the audience – a particle theorist, comsologist and string theorist, she is currently one of the most cited physicists in the world, not least due to the Randall-Sundrum model of a higher dimensional universe. She has also just published a highly successful book on the RS model for the general public, and this was the topic of the lecture.
It was obvious from the start the lecture was going to be exceptional. The very first point Prof Randall made was her belief in the role of experimental verification in science, citing the role of experimentation in the optics and mechanics of Hamilton as an example (this is an important point for string skeptics, who worry that some aspects of string theory may not be falsifiable/verifiable above the Planck scale). A second point in the introductory remarks concerned her philosophical approach to theoretical physics – that models and theories are avenues to be explored, which may or may not turn out to represent nature.
The lecture proper started with a highly succinct introduction to the world of particle physics (the atom, the nucleus, the proton and the quark were dealt with in one slide). The next slide covered the fundamental forces and the Standard Model. The audience was then treated to an introduction to the rise of string theory as an attempt to reconcile general relativity and quantum physics, with higher dimensions arising naturally from the equations. There was a lovely flashback to the work of Kaluza and his attempt to unify gravity and electromagnetism by writing the equations of general relativity in five dimensions (rather than the four of Minkowski spacetime), and the subsequent proposal of compactification by Einstein and Klein (compactification is the idea that we do not percieve the 5th dimension simply because its rolled up on a tiny scale).
In the second part of the talk, Randall went on to give an outline of modern string theory, from the proposal of eleven dimensions to brane theory. The crux of the talk was a description of how, in her model, branes might provide an a solution to the hierarchy problem (i.e. the relative weakness of gravity relative to the other three fundamental interactions), if we dispense with compactification. As I understand it, the basic idea is that the non-gravitational particles and interactions could be trapped on a 3D brane, with gravity not confined – in which case the familiar particles would experience a reduced gravity due to their separation from it and a warping of that spatial separation by the energy of the universe. In the two-brane model for example, it is proposed that gravity resides on a different brane, its influence on our ‘home’ brane hugely reduced by the warping of space between the two branes.
Image from NYT via Cosmic Variance
The lecture concluded with an overview of testable consequences at the LHC. First, it was suggested that higher dimensions might be detectable as missing energy, as Kaluza-Klein particles produced in high-energy interactions escape into higher dimensions. Even better, KK particles of the RS model should be clearly distinguishable from the compactification model (and from supersymmetric particles) by their decay mechanisms, mass-spectrum and spin. She amplified further on this point in answer to a query of mine – indeed question time was excellent , with clear answers to all questions.
Overall, this was a super talk on an extremely hot topic. The main themes I took out of it were
(i) an emphasis on the possible verification/falsification of modern concepts in string theory at the LHC
(ii) an emphasis on ‘it might be wrong’
(ii) disappointment at the unavailability of energies that could have been seen at the cancelled SCC– often forgotten in Europe.
Two great quotes were
‘I don’t believe in any particular theory – I have often worked simultaneously on theories which are mutually incompatible’
‘When dealing with higher dimensions, a word is worth a thousand pictures’
If you want to more about this topic buy the book. Alternatively, there are some great articles on the topic on the Randall website.
Postscript: On the journey back to Waterford last night, it struck me that the real ‘out-there’ proposal on the dimensions of the universe remains that of Enstein and Minkowski. The idea that time is simply another dimension, equivalent to the three spatial ones was truly extraordinary – evidenced by the interplay between temporal and spatial dimensions for bodies travelling at high speed (special relativity) or in strong gravitational fields (general relativity). I’ve never understood the public amazement at the idea of multi dimensions in space – if anything, I find the idea a bit trivial once compactification is added to the mix. So the RS model is a welcome change from that. But here’s a really shocking proposal – what if we live in a universe with extra dimensions, but the extra dimensions are non-spatial? Imagine if spin (which we don’t really understand) is a dimension rather than a parameter? Or colour, charm, strangeness, parity and all those other quantum properties that are really just labels? Hmm…daft thought for the day
Antimatter 
