Almost all relevant physical systems are pretty complicated. One I am working on is how the interior of so-called neutron stars look like. Neutron stars is what is left of stars somewhat heavier than our sun, but not too heavy, after they became a supernova. In a neutron star the atoms collapse due to the strong gravitation. Only the atomic nuclei remain, and are packed very densely. Neutron stars have roughly one to two times the mass of our sun, but have a radius of only about ten kilometers, barely larger than a small city. These star remnants are very interesting for astronomy and astrophysics. But I am more interested what happens in their most inner core.
Deep inside the neutron star, everything is even more packed. In fact, even the atomic nuclei are no longer separated, but are mashed into a big mess. Because their are so densely packed, even the nucleons are overlapping. Thus, the substructure of them, the quarks may become the most important players.
But this nobody knows yet for sure. It has been a challenge to understand such matter since more than thirty years. It is a joint effort of theoreticians, like me, people smashing atoms on each other in accelerators, so-called heavy-ion experiments, and people observing actual neutron stars with telescopes of many kinds.
In general, if quarks come into play, very often simulations have been very helpful. But it turns out that we are not (yet) clever enough to simulate a neutron star's interior. The algorithms, which we have developed to deal with single nuclei are just too inefficient to deal with so many nuclei. For technical reasons, this is called the sign problem, denoting the particular technical problem involved. This obstruction is also known since decades, without us being able so far to remove it.
An alternative have been other methods and models, but we would like to have a combination, to be more sure of our results.
One possibility has been to circumvent the problem. We have looked at theories which are similar to the strong nuclear force, but slightly modified. The modification were such that numerical simulations were possible. We made this detour for two reasons. We hoped that we could learn something in general. And we wanted to use these results to provide us with tests for our models and other methods. In a way we cheated: We evaded the problem by doing a simpler problem. And hoped that we would learn enough by this to solve the original problem or get a new insight.
However, so far our detours had serious drawbacks. The replacement theories were only able to solve some problems, but never all at the same time. Some had the problem that the mass creation by the strong force did not work in the right way. This would yield wrong answers for size and mass of a neutron stars. Or the nucleons were not repellent enough, so that all neutron stars would collapse further to so-called quark stars, much smaller than neutron stars and made from quarks.
And here comes my own research into play. Just recently we found another theory, which we call G2-QCD for very technical reasons. Irrespective of the name, it has neither of these problems. However, it is still not QCD. E. g., it has besides the nucleons further exotic objects flying around. But it is anyway the theory closest to the original one so far investigated. And we can actually simulate it. That is something we just done very recently. The results are very encouraging, though we are yet far from a final answer for neutron stars. Nonetheless, we have now an even stronger test for all the models and results from other methods available. This should provide even more constraints on our understanding of neutron stars, though still an enormous amount of work has to be done. But this is research: Mostly progress by small steps. And we thus continue on with this theory.
And this is just one example in my research where it is worthwhile to take a detour, and this is true for physics in general: Often the study of a simpler problem helps to reveal the solution of the original one. Even if we did not (again yet) succeeded, we made progress.