The Lisi story below is a good hook for a post on the theory of everything…so here goes.
One of the big discoveries of 20th century physics is that there exist only four independent forces or interactions. These are gravity (known since Newton), electromagnetism (the unification of electricity and magnetism achieved by Maxwell in the 19th century), the strong nuclear force (that holds the protons together in the nucleus), and the weak nuclear force (responsible for nuclear decay and radioactivity).
Einstein always suspected that these interactions were not truly independent and spent most of the latter part of his life trying to achieve a unified theory that could describe both gravity and electromagnetism (a program that became known as unified field theory, initiated by Kaluza and Klein). Einstein failed in this program, not least because we now know that gravity is the hardest nut to crack (we have no satisfactory quantum theory of gravity, while all the others interactions can be described in terms of quantum theory).
Nowadays, unified field theory works from the oposite direction. Using the methods of gauge symmetry, theoreticians in the 1970s established a strong connection between the electromagnetic and the weak nuclear interactions. The theory predicted the existence of unkown particles (W and Z bosons), which were subsequently discovered in high-energy experiments at CERN in the 1980s…ever since we talk about the electro-weak interaction as a single entity.
One of the giant particle detectors at CERN
This success of electro-weak unification resulted in furious attempts to extend the unification program to include the strong interaction (a program known as Grand Unified Theory) . However, the GUT program soon ran into serious trouble, with a clutch of ‘no-go’ theorems showing that such unification was mathematically unsound (see the O’ Raifeartaigh theorem and the Coleman-Mandula theorem). Various novel ideas to circumvent this problem gradually emerged in the 1970s, the most promising of which is probably the theory of supersymmetry. Anyway, there now are strong hints of connections between the electro-weak and the strong interactions at high energies. Most ambitious of all is the prospect of a unified theory that also includes gravity i.e. that describes all four interactions in a single framework – the so-called theory of everything.
All the above is really boils down to the simple idea of a single super-force existing at the tremendous energies of the Big Bang, which gradually split off into the four seperate entities we see today as the universe cooled…pretty neat eh? The problem is that the mathematics of such a theory of everything (TOE) remains elusive – the leading candidate is string theory – yep, the famous string theory that is controversial because it is so mathematically abstract that it makes almost no predicitions that can ever be verified/falsified by experiment…..but that’s a separate story!
Suffice it to say that Einstein’s famous quest for a theory that incorporates a description of the elementary particles and all their interactions, now continues under the title Theories of Everything, and is still the Holy Grail of theoretical physics. As regards Garrett Lisi’s paper, part of the unification program inviolves the description of all the elementary particles using the mathematical theory of groups. (For example, Gellman’s classification of the known particles in the 1960s using group theory led to the prediction of a deeper layer of matter making up most particles – the quarks, later detected experimentally). Lisi’s paper purports to show that a particular mathematical group, the E8 group, may offer a very useful way of decribing all of today’s known particles, in a very simple framework…hence the interest. Plus, he’s an excellent surfer!