How many quarks are there in a proton?

Murray Gell-Mann answered this question by saying 3. We now believe that the answer is slightly more complicated. It could be 3 plus infinity, that is, 3 and an infinite number of quarks and anti-quarks that appear and disappear into the vacuum with no effect ... but to change the mass of the proton. Computing things like this is another job for lattice gauge theory. In fact, if we can compute the mass of the proton, then we have calculated from quantum field theory the Avogadro number.

The mathematical theory of quarks, gluons, and their interactions is a quantum field theory named Quantum Chromo-Dynamics (QCD). This theory is worth a Nobel prize. This has been extensively tested in experiments.

 

What is the quark-gluon plasma?

In normal matter all quarks and gluons are hidden inside protons and neutrons. It is as if they are inside a locked suitcase. Normal matter is made by stacking these suitcases together to form nuclei. The quark gluon plasma can be formed by heating this stuff up so that the suitcases melt, and quarks and gluons are free to run around. A different kind of quark matter can be formed by squeezing the suitcases together so that they fuse and quarks and gluons can run through the whole volume. The temperatures and pressures at which this happens is encoded into the phase diagram of QCD.

 

Tell me really: what is lattice gauge theory?

A field theory is the mechanics of a continuous medium like air. At each point in the atmosphere the air has a certain density, chemical composition and temperature. There are mathematical relations between them which also tell how they change. These equations are not easy to solve. Weather modellers treat the atmosphere as a grid of points. At each point of the grid, one relates the density, composition and temperature to those at other points. The equations become simpler and numerical computations can tell us tomorrow's weather. Lattice gauge theory is similiar in some ways.

QCD is a field theory. At each point of space-time one specifies the values of quark and gluon fields. There are mathematical equations which say how these are related and how they change. These are mathematically intractable. Lattice gauge theory consists of treating them as points on a grid, solving the equations, and taking finer grids until the effect of gridding vanishes. The complication is that this is a quantum theory, and hence all possible fields have to be accounted for. This is like weather prediction, not only on a single earth, but an infinity of them.

 

How do you know what happened 20 microseconds after the universe was born?

Space probes have taken pictures of the universe 3 minutes after its birth (see the picture). The known distribution of chemical elements tells us about the universe about 1 minute after its birth. From there we use theory to extrapolate backwards. This theory is under continuous test at particle accelerators. This allows us to make rather clear extrapolations back to about 20 microseconds.

 

What do you have to say to experiments?

We have at least one prediction for the experiments. The "chemical" composition of the quark gluon plasma is being probed in relativistic heavy-ion colliders. In the last few years we have used a simplified version of QCD to predict the results of observations till now (see the figure at the right). One of the aims of the ILGTI is to refine this prediction by working with all the complications of QCD. Other things that we plan to compute in the near future is how fast the plasma formed in such collisions expands, how heavily its properties fluctuate from one collision to another. We may well run out of time before we run out of things to do.

 

What is in the core of a neutron star?

In order to answer this question, we need to find the "phase diagram" of QCD. This diagram tells us what pressure is required to convert normal matter to quark matter at a given temperature. When you plot this series of transition pressures, you get a "line of phase transitions", also called a transition line. The high temperature end of this line is called a "critical point". We are engaged in a friendly race with other groups around the world to find this critical point. We have an approximation to the answer, and super-computers will help us to refine it. Once we find the other end of this transition line, we will know what to expect at the core of a neutron star: normal matter or quark matter.

 

Why do you use one supercomputer and not another?

In order to select a super-computer appropriate to our needs we release a public tender. All respondents with computers which were possibly powerful enough to be useful in our project were asked to perform benchmarks by running our programs on their machines. In this way we tested several types of supercomputers. Then we chose the cheapest among the best.