I hadn’t thought until recently about the fact that this year is the 100th anniversary of Einstein’s discovery of the field equations of general relativity, so there will be quite a few events taking place commemorating this (for a list of some, see here). This week’s Science magazine has a special issue on the topic. It includes news stories about LIGO and gravitational waves, new tests of the equivalence principle, and possible tests of GR from observations of the black hole at the center of our galaxy.
There’s also a review of a book from a few years ago about Einstein’s search for a unified theory, Einstein’s Unification by Jeroen van Dongen. The review addresses something I mentioned in my recent essay about mathematics and physics, that the development of GR provides a good example of a successful theory coming out of not just experiment and “physical intuition”, but motivated also by the serious use of deep mathematical ideas. According to the review:
Einstein employed two strategies in this search [for the GR field equations]: either starting from a mathematically attractive candidate and then checking the physics or starting from a physically sensible candidate and then checking the mathematics. Although Einstein scholars disagree about which of these two strategies brought the decisive breakthrough of November 1915, they all acknowledge that both played an essential role in the work leading up to it. In hindsight, however, Einstein maintained that his success with general relativity had been due solely to the mathematical strategy. It is no coincidence that this is the approach he adopted in his search for a unified field theory.
Besides the fact that Einstein said so, other evidence for the primacy of the mathematical strategy in this case is the simultaneously successful work by mathematician David Hilbert, who was definitely pursuing the mathematical strategy.
While I think there’s an excellent argument that a mathematical approach was crucial in Einstein’s discovery of the field equations, the later history this book deals with also shows the dangers this can lead to. Einstein spent much of the rest of his life on a fruitless attempt to get a unified theory by pursuing the same mathematics he had so much success with in the case of GR. It’s a good idea to keep in mind both examples. On the one hand, trying out some new deep mathematical ideas can lead to success, on a time scale of a few years. On the other, if you’ve spent 30 years pursuing a mathematical framework that has gone nowhere, maybe you should do something else. A lesson that Einstein’s successors at the IAS might want to keep in mind…
The story about new tests of the equivalence principle contains the usual nonsense about testing “string theory predictions”:
Using beryllium and titanium, they found gravitational and inertial mass equal to one part in 10 trillion, as they reported in Physical Review Letters in 2008. That’s not quite precise enough to test string theory predictions.
That “string theory predicts violations of the equivalence principle” is what used to be called a “factoid”, something not true repeated so often that it becomes a fact. It seems though that usage has changed, with “factoid” now often being used to refer to something true. A new word is needed.
Update: See here for an article by Michel Janssen and Jurgen Renn discussing in detail the question of the “mathematical” versus “physical” strategies in Einstein’s discovery of the GR field equations.