Non-Pauli Transitions From Spacetime Noncommutativity

Abstract

There are good reasons to suspect that spacetime at Planck scales is noncommutative. Typically this noncommutativity is controlled by fixed "vectors" or "tensors" with numerical entries. For the Moyal spacetime, it is the antisymmetric matrix $\theta_{\mu\nu}$. In approaches enforcing Poincar\'e invariance, these deform or twist the method of (anti-)symmetrization of identical particle state vectors. We argue that the earth's rotation and movements in the cosmos are "sudden" events to Pauli-forbidden processes. They induce (twisted) bosonic components in state vectors of identical spinorial particles in the presence of a twist. These components induce non-Pauli transitions. From known limits on such transitions, we infer that the energy scale for noncommutativity is $\gtrsim 10^{24}\textrm{TeV}$. This suggests a new energy scale beyond Planck scale.