Once Before Time - Martin Bojowald [11]
In reality, however, the picture is different. Only the simplest solutions of general relativity are understood, which, fortunately, suffice for many questions in physics; even the simplest and most highly symmetric solutions afford impressive insights into cosmology and astrophysical objects such as black holes. But if one tries to go only one step in complexity beyond such solutions, one encounters immense difficulties owing to the complicated form of the theory. Its equations are of a type allowing hardly any standard solution procedures to be applied. Every situation has to be analyzed anew, and only in a few lucky cases can exact solutions be found. Using computers sometimes helps, but even then the equations resist easy analysis. For these reasons, many mathematicians are interested in several issues of general relativity, and time and again they have contributed to our understanding of it. Open questions also exist, such as that of predictability (see chapter 6), that have a bearing on the foundation of physics as a whole.
A numerical analysis of Einstein’s equations—often the last hope when direct mathematical solutions turn out to be too complicated—is extremely difficult. Computational research was begun in the 1970s and received considerable support in the 1990s. Collisions of heavy stars or black holes were of particular interest because they were expected to be strong sources of an entirely new kind of signal: gravitational waves. General relativity predicts that space-time itself can be excited to vibrations, periodic ripples that then propagate in the form of waves just like those on the sea. We have strong hopes of seeing these in coming years with sensitive detectors; such developments would not only further test general relativity but also open up a new branch of astronomy. We could start to explore the cosmos not only by light or other forms of electromagnetic radiation, but also with the help of gravitational waves. It is as if we would be able not only to glance into the sky, but also to listen to it. A new sense would be opened, enabling and ennobling unprecedented experiences and insights.
To detect gravitational waves, like any new signal, one has to know what to look for: One must know the intensity of a gravitational wave as it changes in time while traveling to us, much like a wave through water, starting from its creation in a collision. Unfortunately, the mathematical equations are too complicated for a direct solution, and even computers have been of little use; frustratingly, the programs available crashed before they could show interesting results—it was like having to type a long text in a program that would quit after entering every single word. Only after intensive activity over many years, performed in several groups (whose total number is still small compared to collaborations in particle or condensed matter physics), did a breakthrough recently become possible. As first shown in the work of Frans Pretorius in 2005, stable computer programs can now be developed that are able to provide valuable insights into heavy object collision results. Just in time, the construction of gravitational wave detectors such as LIGO, a set of detectors in the states of Louisiana and Washington, GEO600 in Germany, Virgo in Italy, and TAMA in Japan is rapidly under way; the dream of gravitational wave astronomy may soon become a reality. None of this would be possible without the foundation of general relativity, as buttressed ever more firmly by continuing research.
But back to the historical developments. Einstein was certainly not working completely independently of observations, for he sought to extend Newton’s astronomically tested gravitational law. Grounding in established laws is important for any kind of progress in physics.