Undergrad Does Planck time violate Lorentz-invariance

[kodama]

I am well aware that spatial discreteness is in conflict with Lorentz-invariance.

If there were a theory of QG that proposed Planck time as the smallest interval of physical time, would that be in conflict with Lorentz-invariance?

 

[MPBenowitz]

I am well aware that spatial discreteness is in conflict with Lorentz-invariance.

If there were a theory of QG that proposed Planck time as the smallest interval of physical time, would that be in conflict with Lorentz-invariance?

Discreteness is a property of a mathematical structure. Properties by themselves do not violate Lorentz-invariance. As far as I am aware of there is no reason to believe there can't exist mathematical structures that are both discrete and obey Lorentz-invariance. Just because Lorentz-invariance has a representation of SO(1,3) which is a group of continuous actions doesn't necessarily mean there cannot exist an underlying discrete space. One can imagine, for example, having spatially discrete degrees of freedom with a continuum of rotational degrees of freedom, e.g. a complex phase.

 

[julian]

I am well aware that spatial discreteness is in conflict with Lorentz-invariance.

Hang on, is distrceteness of angular momentum in conflict with rotational invariance in ordinary qunatum mechanics? No, in the sense that the angular momentum operator's eigenfunctions (with discrete angular momentum eigenvalues) in one frame tramsform into a quantum superposition of the angular momentum operator's eigenfunctions in the rotated frame. It is the expectation value that transforms conitinuously under rotations.

Are eigenvectors of a length operator with disctrete eigenvalues in conflict withe Lorentz invariance? No, in the sense that length operator's eigenfunctions (with discrete length eigenvalues) in one frame tramsform into a quantum superposition of the length operator's eigenfunctions in the Lorentz transformed frame. It is the expectation value that transforms conitinuously under Lorentz transformations.