Earlier this week I wrote an opinion piece about the difficulty and possible impossibility of a dedicated but untrained physicist discovering a revolutionary new theory or phenomenon in modern physics. In that article I made reference to several interesting open problems in modern physics, and since then several people have asked me to explain these in more detail. Today's article is the second in this mini-series, and is actually a collection of problems.

For at least thirty years, all of particle physics has been neatly combined into the Standard Model. It contains 30 particles, three forces, and includes all currently explained physics with the exception of gravity. It is considered a particularly beautiful scientific theory because it includes many symmetries, but it is still a mystery why these symmetries occur.

Most people have heard of electrons. They are subatomic particles that carry an electric charge, are stable, and are responsible for all chemical reactions and electronics. In fact they are responsible for all the properties of matter. The first interesting symmetry is called the U(1) symmetry, and essentially states that an internal property of the electron can be rotated and have no physical effect (and once more I apologize to serious scientists for this drastic oversimplification, but the point of these articles is to make these ideas as simple as possible for the general reader). By imposing this symmetry on the electron, one automatically gets all the equations of electromagnetic forces and a new particle called the photon.

Now add a second symmetry - suppose that the electron is one half of a pair of particles, and that the laws of physics are the same for both. This is called the SU(2) symmetry, and generates the weak nuclear force. The second particle is a chargeless, much lighter particle called the neutrino, while the nuclear force appears in the form of three other particles called W+, W-, and Z.

Since one and two particle symmetries produced real forces, we go further and try a three particle symmetry. This generates the strong nuclear force, along with the gluon particle with eight possible states (or eight particles depending on how they are labelled). However the electron and the neutrino are not affected by this force, but there is a similar pair called the up and down quarks which obey all three symmetries. 

So now we have four matter particles and five force carriers. But if we want to have the laws of physics behave the same when they are 'mirror reflected' (ie time is reversed, and each spatial direction is reversed) we also find a second set of particles which annihilate the first set. These are called anti-matter, and add another four anti-matter particles to the model.

And now comes the first of our big unsolved problems. 

When physicists started studying particles in accelerators or in cosmic rays, they were shocked to discover that this entire set of eight matter/antimatter particles is duplicated in an identical set of eight particles which have the same symmetries, same charges, but are much more massive. The muon is identical to the electron, but it is over 200 times as massive! Then further studies found a third complete set, with the tauon being over 3000 times as massive as the electron!

Why are there exactly three generations? Is there a fourth generation that we will discover later? The experimental bounds are already very high, suggesting that it either doesn't exist or is very massive indeed. And is there a connection between three generations of particles and three fundamental forces? Many people have tried to find an SU(4) symmetry but it just doesn't seem to work. And how does gravity fit into the Standard Model?

And even without questions of a fourth generation, there are mysteries surrounding the parameters in the model as well. Each of the 30 particles has a different mass, but so far there is no explanation for each value. The electron, muon, and tauon seem to have no internal structure, and yet their masses are related in the still unexplained Koide formula. The Higgs model of which so much has been written lately explains the source of mass, but also requires different parameters for each particle which are equally unexplained. The three forces may unify at higher energies, but we do not know what this unified theory looks like. We cannot explain why the electron has the charge that it does, but all particles' charges are related to it. There is also a set of complex numbers called the CKM matrix which describes the mixing of different generations, but it is also unexplained theoretically. And we know that some particles do not mix at all, but why are some mixing and others are not? 

The Standard Model has successfully described many phenomena, and in a beautifully symmetric manner. But it also contains many seemingly random parameters and even seemingly random numbers of particles. It is a triumph for particle physics, but there is still a long way to go.

And who knows - maybe someone reading this will be inspired to work on these problems and find the solution!