Multi-folds, Non-Commutative Spacetime, Spin, and All That

Abstract

In the original multi-fold paper, we provided a review of lesser known details on spin, leading to the insights that spin is not a relativistic concept, even if naturally best modeled with relativity and Poincaré symmetries, and that it could also be seen as a rotation of energy, plausibly associated to rotations of the wave function. A toy multi-fold mechanism for these rotations was suggested, as food for thoughts. The multi-fold W-type hypothesis can be added to the picture as an additional source for angular momentum to potentially explains why the rotation f the wave function carries angular momentum..In the present paper, we revisit these results and concepts. Then we discuss additional little known insights about spin. In particular, how fermions imply non-commutative spacetime, and conversely; while bosons do not. Then, we show that any theory with fermions, e.g., quantum theory, implies a non-commutative spacetime in a range of small spatial scales. Then we discuss how one can see that quantum Physics, considered fermionic, and gravity or general relativity, considered bosonic, conventionally and in multi-fold universes. In particular we link spacetime non-commutativity, zitterbewegung with the notion of fermions and bosons, and the spin statistic theorem; providing a new derivation of the latter. Accordingly, massive fermions have sizes that feels the spacetime non-commutativity which results into zitterbewegung at energies where they are massive and transversal momentum uncertainties of the non-commutative spacetime when massless. On the other hand, bosons, massive or massless, have sizes that hide the spacetime non-commutative effects. In multi-fold universe, spacetime is non-commutative in a spatial scale range, and this interpretation directly aligns with the toy multi-fold spin model. The paper introduces new, but equivalent definitions for fermions and bosons, and a versions of the Weinberg-Witten theorem, that now more explicitly hints at unphysicality of gravitons.