Multi-folds, Non-Commutative Spacetime, Spin, and All That
Creators: name: Maes, Stephane
Publisher: name: Zenodo
Year: 2022
Subjects: subject: Multi-fold
subject: 2D
subject: boson
subject: fermion
subject: Weinberg-Witten
subject: E/G conjecture
subject: Entanglement
subject: fractal
subject: General Relativity
subject: Gravity
subject: Higgs Boson
subject: jumps
subject: multi-fold theory
subject: multi-fold universe
subject: multi-fold W-type hypothesis
subject: non-commutative
subject: multi-fold spin model
subject: toy model
subject: non-commutative spacetime
subject: spacetime
subject: location
subject: Pauli exclusion principle
subject: Quantum gravity
subject: Quantum Physics
subject: FOS: Physical sciences
subject: random walk
subject: spin
subject: spin statistics theorem
subject: support domain
subject: wavefunction
subject: size
subject: zitterbewegung
subject: supersymmetry
subject: spin 2
subject: spin 3/2
subject: higher spins
subject: integer
subject: half integer
subject: Compton wavelength
subject: Qball

description: 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.
description: Cite as: Stephane H. Maes, (2022), “Multi-folds, Non-Commutative Spacetime, Spin, and All That”, https://doi.org/10.5281/zenodo.11114501, https://shmaesphysics.wordpress.com/2022/12/31/the-principles-of-quantum-mechanics/, December 31, 2022. Also as https://shmaesphysics.wordpress.com/2022/12/31/multi-folds-non-commutative-spacetime-spin-and-all-that/, (osf.io/au7wc, viXra:2405.0022v1).