Garrett Lisi: This surfer is no Einstein...
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No Einstein...but behind Garrett Lisi's 'theory of everything' lies an amazing idea, says Marcus du Sautoy Two months ago, the physics world was buzzing with the news of a new Einstein. Garrett Lisi, an unemployed physicist with no university affiliation who spent his time surfing in Hawaii, had come up with the Holy Grail of science: a theory unifying quantum physics and Einstein's theory of relativity.
The media went wild. However, in the last few weeks several physics blogs have uncovered a problem with Lisi's idea: it doesn't work. But to understand why, it is necessary to explore the fascinating concept the 39-year-old based his theory on - symmetry. Lisi was attempting to bridge quantum physics - which works for very small things, like electrons and protons - and relativity - which works for very large things, like galaxies and stars. advertisement
At the moment, we can't fit the two into one coherent model that accurately describes the world we see. Yet the idea of symmetry is vital to both. Quantum physicists can explain the menagerie of fundamental particles we observe - quarks, gluons, fermions, bosons and more - as different facets of a symmetrical object. Relativity, too, works so beautifully because of the symmetries that exist between space and time: Einstein's famous equation E=mc2 is essentially expressing a symmetry between mass and energy. Symmetry is part of the language of nature: many animals and plants exploit symmetrical shapes as a way of standing out against the chaos of the landscape. Symmetry also underlies the molecular world. Diamond gets its strength from its crystal structure, which binds the carbon atoms together. Viruses such as polio and HIV exploit the symmetry of the icosahedron, a 20-sided dice made up of triangular faces. Because of the simplicity of this shape, viruses find it easier to replicate. It is also important in the arts. From the Moorish painters in the Alhambra, to Bach's work, symmetry is a crucial ingredient. Although we have been playing with symmetrical objects since the first dice were thrown, it is only in the last two centuries that a true understanding has evolved - thanks to French mathematician Evariste Galois. Before his death in a duel in 1832, Galois created a language called group theory that shifted attention from the symmetries of objects to the ways they interact. If I place a 50p piece on the table, I can count the number of symmetries by seeing how many times I can twist or flip it to end up with the same outline. Just as the number seven is not a concrete thing, but a concept that can be applied to seven cats or seven cups, so Galois realised that the symmetries that describe the coin could describe those of another object. This language, of talking about "groups" of symmetries, lets us prove that the vast number of designs on the walls in the Alhambra are examples of only 17 patterns. One of Galois's most stunning breakthroughs was the realisation that there are fundamental symmetrical objects which act as building blocks for all others. The first on his list were the rotations of coins with a prime number of sides - like the 50p piece (those with six, or eight, or nine sides were not "indivisible" - for example, the rotations of a 15-sided figure can be built out of the rotations of a triangle and a pentagon). But there were others - the rotations of a football, for example, with its patchwork of hexagons and pentagons, are one of the atoms of symmetry. The greatest achievement of 20th-century mathematics has been to complete Galois's project. We now have a list of all the building blocks of symmetry - but although they were christened "simple groups", they are far from it. In particular, there are some very strange designs that don't seem to fit in, known as "sporadic" or "exceptional". The title of Lisi's paper - An Exceptionally Simple Theory of Everything - does not describe how easy his theory is, but refers to his use of one of these groups, called E8, as the key to his idea to unify quantum physics and relativity into a theory. E8 can be thought of as the symmetries of a huge snowflake living in 248-dimensional space. Lisi believed that inside this he could bind the symmetries of the quantum world and relativity. Unfortunately, the consensus, after investigation, is that it is impossible to use E8 in the way Lisi was hoping and produce a consistent model that reflects reality. Lisi has been riding a wave - but it is time to knock him off his board and recognise that we are still waiting for the next Einstein to span the gap between the symmetries of the very small and the very big.
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