Monday, April 29, 2019

Motivic Gravity

One of my regular readers, M.D. Sheppeard, has published a fascinating new paper in the Journal of Physics, entitled "Constraining The Standard Model In Motivic Quantum Gravity", which is open access. The abstract is as follows:
A physical approach to a category of motives must account for the emergent nature of spacetime, where real and complex numbers play a secondary role to discrete operations in quantum computation. In quantum logic, the cardinality of a set is initially replaced by a dimension of a linear space, making contact with the increasing dimensions in an operad. The operad of associahedra governs tree level scattering, and is closely related to the permutohedra and cube tiles, where cube vertices can encode components of a spinor in higher dimensional octonionic approaches. A study of rest mass generation begins with the cosmological infrared scale, set by the neutrino masses, and its related see-saw mechanism. We employ the anyonic ribbon spectrum for Standard Model states, and consider its relation to magic star algebras, giving a context for the Koide rest mass phenomenology of charged leptons and quarks.
At a "forest" level, the paper looks at how select structures in abstract algebra can yield a framework in which the particles of the Standard Model fit nicely. It isn't so much about motivic quantum gravity itself, as it is about how the logic of motivic quantum gravity can be generalized to provide a new perspective on Standard Model physics.

The article isn't very computationally intense, but does require a firm and broad understanding of abstract algebra concepts and terminology, as well as some familiarity with the prior works referenced in the paper. This is a paper that builds on prior work that is prerequisite to understanding it, rather than being an introductory review of the theory.

The motivic descriptor basically (and other feel free to correct me if I haven't gotten it quite right for an educated layman's level description) means starting with amplitudes and then examining those amplitudes to determine the nature of space-time in an emergent manner. This logic is then applied on a more general basis to the issues addressed in this paper. 

The paper also builds to a significant extent on prior work by Brannen and Koide regarding the relationships between the masses of the Standard Model particles.

Mitchell Porter discusses the paper further at the Physics Forums. He explains an important feature of the type of amplitude analysis done in the paper. "[P]olytope methods obtain the scattering amplitudes through constructions that don't involve space-time", rather than using the Feynman path integral approach which has a more obvious connection to a physical description of what is going on in the calculations, at the cost of being much more computationally intense.

1 comment:

Mitchell said...

Urs Schreiber remarks that the mainstream use of motives in amplitudes is just technical and algebraic - motivic theory has produced some useful identities. The attempt to guess why motives are relevant leads to more high-flown speculations by Connes and others (e.g. Kontsevich).

Within string theory, getting space-time from motives is particularly the purview of Ralf Schimmrigk.