Is Dimensionality Frame-Dependent in Spacetime Theories?

[J.F.]

Detecting Vanishing Dimensions via Primordial Gravitational Wave Astronomy
http://prl.aps.org/abstract/PRL/v106/i10/e101101

 

[bcrowell]

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?

 

[J.F.]

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?

I see that authors aspire to resolve the fine tuning problem. They refer to school boy idea:
"lowering the dimensionality of space-time universally cures ultraviolet divergences in practically all of the quantum field theories".