As regular readers may know, my background is in chemical engineering. Three basic concepts drive almost everything else in the field: the conservation of mass, energy, and momentum. A vast majority of problems in my field can, and are, solved using some variant of these three concepts. Sure, the mass-energy equivalence is what the universe conserves as a whole, but it doesn't affect the typical engineering designs a chemical engineer creates.
So, if a ChemE was asked to give the mass of a neutron based on the knowledge that it is composed of one up quark and two down quarks, the trivial answer would be that a neutron weighs as much as two down quarks and an up quark together. This trivial answer is off by almost 2 orders of magnitude.
Experiments have measured the mass of the up quark at between 1.5 and 3.3 megaelectron volts* (MeV); the down quark's mass is somewhere between 3.5 and 6.0 MeV. The sum of the masses of two down and one up quarks gives something between 8.5 and 15.3 MeV—but the precisely measured mass of a neutron is 939.565 MeV, meaning the quarks make up between one and two percent of its total mass. If physics, and science as a whole, is to explain the workings of our universe, we need to be able to account for this apparent discrepancy.
The nature of the various fundamental particles and three of the four fundamental forces in the universe is described by the standard model of particle physics. It's been refined since it was first proposed in the 1960s, and has now passed nearly every test that it has been put to. The standard model postulates that hadrons—protons and neutrons are the most common examples, accounting for an estimated 99 percent of the mass of the visible universe between them—are composed of three quarks. These quarks are held together by the strong nuclear force in a way that's described by a theory known as quantum chromodynamics (QCD). According to QCD, the mass of the hadrons comes from both the mass of the constituent quarks, as well as the energy holding them together, which we observe as mass.
In a paper published in last week's edition of Science, a team of scientists went back to do what we refer to as a sanity check: they attempted to calculate the masses of various light hadrons using what is known about their constituent quarks and QCD. Thanks to a property known as asymptotic freedom, problems in QCD can be solved more easily at high energies where the interactions decrease—behavior that's opposite that of many classical potential fields. At lower energies, the mathematical techniques used to solve the high energy cases no longer work and expensive computations must be carried out. To solve the low energy/low mass cases, researchers employ lattice QCD simulations.
In this computer simulation methodology, the problem is mathematically transformed into a problem that resembles a solvable statistical physics system. Space is discretized into a lattice with a fixed spacing, and the QCD potential is computed using only a handful of inputs—the masses of the constituents quarks and an external coupling constant. Since space is not actually described by a lattice, a series of simulations were carried out at smaller and smaller lattice spacings; the results show that the answers begin to converge on a continuum value, which is what we should be observing in nature.
It's not quite that simple, though. QCD is incapable of giving an exact value for the mass of a particle, as we can only calculate ratios between various masses. To tie the results back to physically measurable values, the authors of the paper used two different types of particles, the Ω and Ξ baryons. Two separate analyses were carried out, one fixing the base parameters using the Ω mass, and one using the Ξ mass. Both sets were found to predict the masses of various light hadrons to within the errors of both the stimulation and measurements of masses. The authors open their concluding paragraph, "Thus, our study strongly suggests that QCD is the theory of the strong interaction, at low energies as well [...]."
This work illustrated the fact that it's healthy for scientists and engineers to go back and reexamine our basic assumptions from time to time. In this case, one of our foundation theories appears to be correct to the level with which we can measure it. This work also does a nice job illustrating how the use of lattice QCD, and the role of simulation methods in general, can help keep us moving forward. Starting from nothing but the basics of our knowledge, researchers carried out an ab inito computation of the mass of the most important particles in our universe, and showed that theory agrees with measurements.
Science, 2008. DOI: 10.1126/science.1163233
* Weights in particle and high energy physics are often reported as equivalent energy divided by the speed of light squared, using the famous relation E=mc2. This means mass is energy/c2 but in natural units, the speed of light is often set to unity, so in mass being reported as equivalent energies.