The discussion centers on the concept of dimensionality in spacetime theories, particularly in relation to the paper by Anchordoqui et al. The participants express confusion regarding the notion of a preferred frame, which suggests that spacetime dimensionality may vary depending on the observer's frame of reference. This contradicts the traditional view of dimensionality as a frame-independent property. The authors aim to address the fine-tuning problem by proposing that reducing spacetime dimensionality could resolve ultraviolet divergences in quantum field theories.
PREREQUISITESThe discussion is beneficial for theoretical physicists, cosmologists, and researchers interested in the foundations of spacetime theories and their implications for quantum field theory.
bcrowell said:They refer to this previous paper by Anchordoqui et al: http://arxiv.org/abs/1003.5914
I don't have the theory chops to understand the Anchordoqui paper in detail, but based on my limited knowledge, here's one thing that bugs me. Motion is relative, so the energy of a TeV cosmic ray is zero in the cosmic ray's own frame of reference. That makes me think that they're saying spacetime has one dimensionality in one frame, but another dimensionality in a different frame. But normally we think of dimensionality as a frame-independent property of spacetime. In GR, a diffeomorphism preserves the signature.
[EDIT] After puzzling over the paper a little more, I see that they refer to a preferred frame, which seems to be the frame of the lattice that spacetime is made out of. They also talk about some kind of violation of Lorentz invariance that somehow averages out or something. I don't really see how this can work. If there is some preferred frame, how is it determined what this preferred frame is?