Vortices, topology and time
arXiv:2311.11160 · doi:10.1016/j.physletb.2024.138810
Abstract
We relate physical time with the topology of magnetic field vortices. We base ourselves on a formulation of unimodular gravity where the cosmological constant appears as the canonical dual to a variable which on-shell becomes four-volume time. If the theory is restricted to a topological axionic form (viz. a parity-odd product of an electric and a magnetic field), such a time variable becomes the spatial integral of the Chern-Simons density. The latter equates to helicity, so that unimodular time is transmuted into the linking number of the vortices of the topological magnetic field, times their flux. With the added {\it postulate} that this flux is a universal constant, the flow of time can thus be interpreted as the progressive weaving of further links between magnetic field vortices, each link providing a quantum of time with value related to the fixed flux. Non-abelian extensions, and targetting parameters other than are briefly examined, exposing different types of vortices and a possible role for inter-linking leading to new phenomenology.
References in corpus (12)
- Forks in the Road, on the Way to Quantum Gravity
- The quantization of unimodular gravity and the cosmological constant problem
- Sequestering the Standard Model Vacuum Energy
- On the cosmological constant problem
- A Manifestly Local Theory of Vacuum Energy Sequestering
- Unimodular loop quantum gravity and the problems of time
- Cosmological time and the constants of nature
- New Weyl-invariant vector-tensor theory for the cosmological constant
- Instantons and unitarity in quantum cosmology with fixed four-volume
- Losing the trace to find dynamical Newton or Planck constants
- Polynomial Duality-Symmetric Lagrangians for Free p-Forms
- Towards a third-order topological invariant for magnetic fields