Impossible Rotation

There is no evidence that the universe as a whole is spinning, putting a damper on Gödel’s rotating universe. Still, most celestial objects, comets, planets, stars, galaxies and even black holes seem to be endowed with a certain amount of spin. 


At the other end of the spectrum, the lightest everlastingly stable charged particle—the electron—is also endowed with spin. It is both convenient and misleading to suppose that the quantum mechanical spin of a particle is the angular momentum arising from the rotation of a body around its own axis, in analogy with classical spinning motion about a point.

Though helpful in justifying why charged particles with spin also posses an intrinsic magnetic moment, picturing spin as a true classical motion analogue for point size particles with no corpuscular extend is intractable. Classical considerations—such as assigning mechanical rotation to the electron—lead directly to paradoxes and superluminal speeds. 


Classical rotation for particles is quite impossible.  


Yet all particles are inevitably endowed with irremovable and unchanging integer spin (bosons) or fractional spin (fermions). The electron—the first subatomic particle to be discovered—is over a century old in our books, and indeed we owe most modern technological advances to harnessing the power of this poorly understood particle. Though probing electrons and the atomic nuclei they orbit seems no longer in the forefront of research. In pursuit for a unifying perspective in quantum gravity, particle physicists are studying the world of the very tiny with particle colliders, and astronomers are peering into the cosmic microwave background radiation, both in search of underlying patterns. Recent efforts have revealed a Higgs particle and gravitational waves. Since Feynman, very few physicists seem to be writing up on their wall the fine structure constant let alone staying up and worrying about it at night. The invention of the multiverse has taken focus away from invariant and low-energy features of our Universe. Yet, we can hardly claim to have a solid grasp of mundane species such as electrons and atomic nuclei. Nuclei incarnate Nature’s experiments in containing matter and energy; they shape the boundaries where all four forces of Nature are present. 

Taking cues from extremes in nuclear stability and instability a simple symmetry crystallizes. This new proposed geometric pattern is successful at predicting numerical ratios in both small and large structures. With no adjustable parameters this pattern can unapologetically retrodict ingredients that make up the cosmological soup in a geometric fashion, which is quite amenable to visualization. Algebraic formulas are notoriously hungry and consume part of the big picture; therefore, though equations are provided in the Appendix, most relationships are rather best relayed in this book in pictures or 3D-interactive models. When this simple geometric pattern is used, the relationships evoked, are—without adjustable parameters—within 1% of the fine structure constant, the mass ratio of the proton to the electron and particle mass ratios for every elementary particle and even composite particles such as the particles of the retired Eightfold Way. Along with a simple way of explaining the awkward parameters of the Standard Model, the new geometric pattern seems to seep out to all facets of spacetime.