The post below made reference to the theory of supersymmetry and this weblog is long overdue a post on the subject. However, as supersymmetry is proposed as an extension of the Standard Model (SM) of particle physics, we’d better have a few words about the SM first…
As we said before, one of the big discoveries of 20th century physics is that there exist only four independent forces or interactions. These are gravity, electromagnetism (the unification of electricity and magnetism achieved by Maxwell in the 19th century), the strong nuclear force (that holds the protons and neutrons together in the nucleus), and the weak nuclear force (responsible for nuclear decay and radioactivity).
Physicists have long suspected that the four fundamental forces are not truly independent, but deeply connected. The idea is that at the tremendous energies of the Big Bang, a single superforce existed, which gradually split off into the four seperate entities we see today as the universe cooled. This idea received a great boost in the 1970s, when Salaam, Weinberg and Glashow established a strong theoretical connection between the electromagnetic and the weak nuclear interactions, using the methods of gauge symmetry. The theory predicted the existence of new 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.
Shortly before this, the first comprehensive theory of the strong nuclear force had also emerged – the key idea being Gellman’s prediction that the nuclear particles (protons and neutrons) are in fact made up of quarks, and the strong nuclear force is really an interquark force. This was verified by scattering experiments at Stanford in 1979, and the theory of the strong interaction is now known as quantum chromodynamics
Putting the two theories together gave rise to the Standard Model – a model that has been fantastically accurate at predicting the masses and properties of all particles discovered so far. However, the model contains several shortcomings
– there is no real unification between the electro-weak and strong interactions, they are treated in parallel
– gravity doesn’t appear at all
These shortcomings led to new theories that attempted to unify the strong nuclear force with the electro-weak interaction (known as Grand Unified Theories), and even more ambitious attempts to unify all three with gravity (Theories of Everything). To accomplish either of these, some new mathematical approaches would be needed….see next instalment…
Update
I forgot to mention another shortcoming of the Standard Model – namely that one particle, necessary to the model, has never been observed (thanks, tankers!). The Higgs boson plays a central role in the SM as the Higgs field gives the mechanism for other particles to acquire the masses we observe. Unfortunately, no evidence of the Higgs particle has been seen in accelerator experiments so far. Most theoreticians are convinced this is simply because we need higher energies than currently available to create it (i.e. it has a large mass), and expect to see evidence of Higgs bosons in the next round of accelerator experiments due to begin at the new accelerator in CERN next year – the Large Hadron Collider.
The alternative is that we’ll see something quite different, which would be even more interesting!
Antimatter 
A big problem comes from the Abelian U(1) electromagnetic theory, e.g. the Weinberg mixing angle.
U(1) has 1 charge and 1 gauge boson and it is supposed to model electromagnetism, while SU(2) has 2 charges (two isospins) and 3 gauge bosons (neutral, positive and negative in charge) for the neutral currents and W+/- bosons of the weak force.
But the observable gauge boson of electromagnetism and the observable Z_0 of the weak neutral currents, are not adequately modelled by U(1) and SU(2) respectively, so an ad hoc mixing of the two is needed. So neutral gauge bosons B and W_0 from U(1) and SU(2) need to be mixed together to produce something modelling the observable photon and observable Z_0 gauge boson.
This is an entirely empirical correction, with the Weinberg mixing angle coming not from theory but from adjustment to make the theory model the observables. It makes the U(1) x SU(2) a very complex and inelegant theory of electroweak phenomena, even before you get into discussing the Higgs mechanism you need to break the symmetry and make it consistent with observations.
I think that a much better model would be to change the Higgs mechanism and just use SU(2), so instead of the Higgs mechanism giving mass to all of the gauge bosons at low energy, it only gives mass to some of them, allowing only left-handed spinors get to interact with weak gauge bosons.
The rest of the W_+, W_-, and W_0 gauge bosons of SU(2) remain massless, and we observe them as electromagnetic (massless W_+ and W_-) and gravitational (massless W_0) gauge bosons. The extra polarizations of the gauge boson photon (it has 4, rather than the usual 2 polarizations for photons) come from the electric charge carried. Normally massless radiation can’t propagate it it has an electric charge, due to the infinite magnetic self-inductance which would result, but that is cancelled out in the case of exchange radiation, because the magnetic field curls cancel out between each oppositely-directed flow of gauge bosons from one charge to another and back. This scheme allows a full causal mechanism of exchange radiation causing electromagnetic and gravitational forces, predicting the coupling parameters.
When you think about U(1) for electromagnetism, it is an extremely problematic theory. You have only one electric charge, so opposite charge must be considered to be charge going backwards in time. Then you only have 1 type of gauge boson, with 4 polarizations and no explanation of what the additional 2 polarizations are, beyond the fact that you need them to allow repulsion as well as attraction forces. It is possible to remove U(1) and extend the role of SU(2) to include electromagnetism and gravitation, simply by modifying the Higgs mechanism so that it allows some massless versions of SU(2) gauge bosons to exist at low energy. This makes new checkable predictions, and is consistent with the observationally checked aspects of the existing Standard Model.
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The Higgs Boson has been found and confirmed as of 2013.
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