For many years now the consensus in a dominant part of the theoretical physics community has been that the center of attention should be on the problem of quantizing gravity, and that conventional notions of quantum theory and space-time geometry need to be abandoned in favor of something radically different. The slogan version of this is “Space-Time is Doomed.”
Ever since my student days long ago, I’ve spent a lot of time looking into the problems of quantum gravity and what people have tried to do to address these problems. The highly publicized attempts to get known physics out of radically different degrees of freedom that I’ve seen haven’t seemed to be making any progress, remaining very far from anything like known physics. In the case of string theory, which also claimed to be able to get particle physics, there was at one point a (highly over-hyped) relatively well-defined proposal that one could discuss, but that’s no longer the case.
Recently things have changed as I’ve become convinced of the promise of certain specific ideas about four-dimensional geometry involving twistors and Euclidean space-time signature. I’ve written about these here and on the blog, and have given some talks (see here and here). These ideas remain speculative and incomplete, but I think they provide some new ways of thinking about the problems of quantizing gravity and unifying it with the other forces.
The existence of a yearly essay competition gave me an excuse to write something about this which I just finished yesterday and sent in, with the title Is Space-Time Really Doomed?. After spending some time on a diversion into arithmetic geometry, I’ve been getting back to seriously thinking about this topic, looking forward to having time in coming months to concentrate on this. I hope the essay will encourage others to not give up on 4d geometry as doomed and unquantizable, but to realize that much is there still waiting to be explored.
Update: The essay is now on the arXiv here.
Update: Awards for this announced here. I got an honorable mention.