What is reality? Mathematics and cosmology

Originally published in The Scotsman newspaper 6th October 2008 and ©yright; The Scotsman

This week marked the end of Sir Michael Atiyah's presidency at the Royal Society of Edinburgh (RSE). Michael Atiyah is one of the world's most eminent mathematicians. His work has been influential on modern theoretical physics. He used his leaving speech at the RSE to pose deep questions: What is reality? Is the universe built using the "fantastically intricate mathematics" of String Theory? Or do we await a new Newton or Einstein to simplify the picture?

Although 79, Sir Michael Atiyah remains full of energy. Born in England to a Lebanese father and Scottish mother, he now lives in Scotland where he holds an honorary professorship at the University of Edinburgh. Atiyah made profound connections between research in advanced geometry and the physics of Quantum Mechanics. He is a mathematician rather than a physicist, but has worked closely with leading physicists in Quantum Mechanics and String Theory. He has received numerous awards and honours, including the Fields Medal in 1966 - the mathematics equivalent of a Nobel prize - a knighthood in 1986 and the prestigious Order of Merit in 1992.

The main issue in modern physics is how to resolve two conflicting theories: the Standard Model of Quantum Mechanics, and Einstein's theory of General Relativity. Quantum Mechanics describes the very small - an exotic zoo of sub-atomic particles. These can be in several states at once, leading to the strange quandary of Schrodinger's cat who is both alive and dead at the same time. Meanwhile, General Relativity describes the very big - with the force of gravity acting as a distortion of time and space. Both theories have been thoroughly tested in experiments, but attempts to combine them are problematic. This has set physicists since Einstein searching for the elusive "Theory of Everything", a theory which will explain both Quantum Mechanics and Relativity as two views of one underlying truth. String Theory is the best candidate for that.

String Theory considers all particles to be made up of tiny vibrating strings. The length and vibrations of these strings determine their behaviour, like notes interacting in a guitar chord. Bizarrely, the theory suggests that space has more dimensions than we commonly observe. We are aware of 3 dimensions of space, and time is counted as the fourth dimension. But attempts to apply String Theory in 4 dimensions lead to problems. So if String Theory is correct, there are other dimensions that must be invisible to us. Scientists believe the extra dimensions exist as tiny subatomic tubes.

The problem with String Theory is that it is not one clean theory, but a family of possible theories. There are no experiments to test which of these are correct - if any. The new giant collider at CERN may find evidence that lends weight to String Theory, but it is not expected to settle the question. However progress is being made. Led by American professor Edward Witten, physicists and mathematicians are discovering that what they thought were completely different theories, are in fact different ways of looking at the same theory.

Atiyah pointed out that there can be many "correct" ways to view the world. As an example, consider a simple stone. We see a stone as a lump of solid rock. To a chemist, it is a collection of atoms. To a physicist, those atoms are mostly empty space criss-crossed by force-fields. To a mathematician, those fields are a set of equations. Perhaps, Sir Michael suggested, the equations are the true reality.

Though he helped develop modern theories, Atiyah does not believe they are the final answer. We may be making the same mistake as the ancient Greeks, who thought the planets moved in circles. Since this did not match observations, the Greek astronomoer Ptolemy added extra circles rolling on the first circles (epicycles), and then extra circles again were added - wheels within wheels. The result explained the experimental data of the time, but it was overly complicated - and wrong. That model was eventually blown away by Johannes Kepler and Isaac Newton's insights, which revealed a simpler more elegant world.

When Atiyah was a young man, the great logician Kurt Godel complained to him that physicists had given up on understanding, and were now focused only on description. Michael Atiyah has striven for understanding, following Poincare's view that science is no more a collection of facts and proofs, than a house is a collection of bricks. Atiyah is still hopeful that behind the complexity of current String Theory there may be revealed a universe we can understand. tags: physics maths