Once Before Time - Martin Bojowald [147]
Hence one can first infer the dependence of principles, as well as theories constructed upon them, on the existence of traditional streams in physics research. At its frontiers, after all, physics is never secure in the sense that all researchers involved would agree with all developments at all times. The emphasis on some principles as opposed to others is dependent on researchers’ preferences. Willfulness can find here an especially easy entrance, particularly since concrete motivations arise not just purely intellectually, but all too often, unfortunately, from research-political considerations or even personal differences and vanity.1 Moreover, inertia adds to this tendency: Once a decision on certain principles has been made, it is sometimes difficult to distance oneself from them even if their inadequacy has been recognized. Also, research life has accelerated; a reorientation would cost too much time and make one fall behind hopelessly in the competition for publications, research funds, and jobs. In the end, old principles are often defended for their own sake, and actual science is lost sight of.
These considerations mean that the uniqueness of theories is always conditional, for the underlying principles must first of all be accepted. Despite the claimed uniquenesses of theories, very different candidates with the same aim but different principles can easily coexist. Quantum gravity, with string theory, loop quantum gravity, and several other alternatives, is one example. While their shared ambition is clear, their foundations are not. Such theories are growing toward the end of their viability: They are plants whose seeds have fallen among the rubble, tasked to grow up toward the light. Especially when there is no glimmer of observation to show the way, this can be a long, roundabout way through a vast dark maze. Wander there too long, and the plant will become etiolated and may not survive to reach the light.
In order to bring within reach the question of a theory’s uniqueness, a decisive mathematification is initially a strength. It allows a very precise formulation and a clear decision about uniqueness. To gain knowledge of nature, however, this process poses a disadvantage, for observations enter only indirectly via principles employed by the theory. Once a foundational decision about principles has been made to construct a theory and its mathematical apparatus, nature is no longer consulted in the uniqueness analysis. Even if a mathematically unique theory were to arise in this way, what would this mean for Nature ignored in the process? As quoted in the introduction, it is not up to physicists to impose laws on Nature, as mathematically elegant as they may seem.
Once mathematics is put to the task, allowed reformulations are always equivalences. The result does not mean less and it does not mean more than the assumptions, even though they always look surprisingly different. To exaggerate, all mathematical theorems are trivialities. The result is already contained in the assumptions, if often very veiled. In the unveiling, the high art of mathematicians shows itself, along with the importance of mathematical results in numerous applications. But by itself mathematics is no good as a model of nature. For this, observations remain necessary to crystallize a theory, be it a mathematically unique consequence of certain principles or not. No mathematics of a “theory of everything,” however sophisticated, can replace this.
ONE THEORY, ONE SOLUTION?
BE CAREFUL WHAT YOU WISH FOR
Thou’rt like the spirit, thou dost comprehend.
—GOETHE, Faust
The ideal would be a unique theory with a unique solution. If