Modern space-time and undecidability
  The picture of space-time that Minkowski created in 1907 has been followed by two important developments in physics not contained in the original picture: general relativity and quantum mechanics. We will argue that the use of concepts of those theories to construct space-time implies conceptual modifications in quantum mechanics. In particular one can construct a viable picture of quantum mechanics without a reduction process that has outcomes equivalent to a picture with a reduction process. One therefore has two theories that are entirely equivalent experimentally but profoundly different in the description of reality they give. This introduces a fundamental level of undecidability in physics of a kind that has not been present before. We discuss some of the implications. 
Rodolfo Gambini and Jorge Pullin