Previously, we said that the strong force was the most difficult to calculate. We showed the equations associated with the strong force. Scientists have difficulty measuring the strong force because it is impossible to isolate a quark. For example, scientists measuring the strength of attraction between magnets simply test this in a lab with two magnets. Scientists measuring the attractive force of two quarks are stymied because when one tries to separate a quark from a proton or neutron ends up with the original particle plus a meson (quark-antiquark pair). The meson is created from the extra energy used to pry the quark out of the proton or neutron. The illustration below might help in understanding.
In this illustration two quarks are being ripped apart by some force. What you can see is that as the quarks separate there is an energy field that grows as the distance between the quarks becomes larger. It is this energy field that contributes to forming a meson. Nature has decided that, rather than allowing the extra energy between the quarks, it is easier just to turn the extra energy into a meson.
One has to wonder, why is there so much energy within these strong bonds. Let's take a look at the relative strengths of our four forces. Maybe then you will see why the strong force is so different than the other forces.
This means that the strong force is 10^38 times as powerful as gravity. This is a 1 with 38 zeros behind it. This is an incredibly powerful force. Let’s compare this to something from our environment. Suppose you held a one pound weight in your hand. This would show a gravitational force of 1 pound. If we wanted to show the pull of the strong force, you would need to hold 100,000,000,000,000,000,000,000,000,000,000,000,000 one pound weights. This would be 77 trillion times the weight of the Earth. This is where the energy comes from when quarks are ripped from protons and neutrons.
This also explains why the strong force is so hard to calculate. Scientists have developed something called perturbation theory to help them with intense calculations. When dealing with numbers that are very small, scientists can simply skip steps because those steps do not affect the final calculation(s).
When scientists are dealing with numbers as big as 10^38 they cannot afford to skip any steps, called a non-perturbative equation. Thus the equation for the strong force, shown previously has to be carried out to its end. This necessitates computers that can do millions of calculations per second.
Why is it so hard to calculate?
In order to determine why QCD is so hard to calculate, we first have to understand why we would want to sort these fiendishly hard equations in the first place. Scientists believe that the universe, including all of its matter, was created during the Big Bang. Scientists also know that when matter is created, anti-matter is also created. So why is it that the universe “decided” to create more matter than anti-matter?
Massive particles are the answer. Physicists have found that massive particles will decay, asymmetrically, into matter instead of anti-matter. If scientists can study these large particles, they will be able to determine why there is so much matter in the universe.
But wait a minute. We cannot simply tear protons and neutrons apart and throw their respective quarks on a scale. Quarks do not appear alone, they are always with a partner antiquark. This combination is called a meson. Mesons are very short lived particles, living only about 6 microseconds. This is far too short of a time to measusre the mass of the quark, much less try to subtract the weight of the attached antiquark.
ADDITIONALLY, there are gluons that attach the quark-antiquark pair in a meson. If these were virtually weightless particles, (similar to photons in QED) their weights could be ignored. But gluons contain a huge amount of energy, thus they weigh more, thus they have to be included in the equation.
FINALLY, gluons are not just simple connections. They are more than small bottles of Elmer’s glue. Gluons have a property called colour charge (GLOSSARY). This is very different from the electromagnetic charge of protons and electrons. Colour charge allows gluons to exchange other gluons. An analogy would be to think of a band versus a one man band. Within a band there are sections of instruments. There is a woodwinds section, a brass section, and a percussion section. A one man band plays multiple instruments at the same time. So if one were to ask a band member what instrument they played it would be easy for them to name their instrument. If one were to ask the same question of a one man band, he/she would reply with multiple instruments, not one instrument. In the same way, gluons can be many "colors" without being any one color as well as changing their number. This means that the amount of gluons in a meson cannot be measured because it is constantly changing.
P.S. Quark-antiquark pairs are always appearing and disappearing within the cloud of gluons. These fleeting pairs of quarks and antiquarks also have to be accounted for within scientists equations.
So what can we do? Scientists have always known that to calculate the position of every meson and gluon would be impossible, so they cheated. They ignored the mesons, but this produced results that were far from experimental results. Then the idea was brought up to consider everything in a four dimensional grid of space time (four axis, x, y, z, time). If scientists put everything at the intersection of a grid, they would know exactly where to find the particle and be able to measure its qualities. Then they could make the grid smaller and smaller until their calculations were very precise. This would be similar to finding the area under a curve. If we use smaller and smaller rectangles, we can approximate the area to a greater and greater accuracy. This can be illustrated in the animation below.
This is the theory of lattice quantum chromodynamics. If you are interested in learning about how LQCD calculations are made at Fermilab, click the link below