• Corpus ID: 238634742

1 2 O ct 2 02 1 A sign of the times

@inproceedings{Magueijo202112O,
  title={1 2 O ct 2 02 1 A sign of the times},
  author={Jo{\~a}o Magueijo},
  year={2021}
}

• J. Magueijo
• Published 2021
• Physics

We examine in greater detail the recent proposal that time is the conjugate of the constants of nature. Fundamentally distinct times are associated with different constants and we should select the one related to the constant dominating the dynamics in each region or epoch. We show in detail how in regions dominated by a single constant the Hamiltonian constraint can be reframed as a Schrodinger equation in the corresponding time, solved in the connection representation by outgoing-only monochromatic plane waves moving in a “space” that generalizes the Chern-Simons functional. We pay special attention to the issues of unitarity and the measure employed for the inner product. Normalizable superpositions can be built, including solitons, “light-rays” and coherent/squeezed states saturating a Heisenberg uncertainty relation between constants and their times. A healthy classical limit is obtained for factorizable coherent states, with classical cosmology seen through the prism of the connection (the comoving Hubble length) rather than the more conventional expansion factor (metric). A brief discussion of the arrow of time within this framework is included. In this multi-time setting we show how to deal with transition regions, where one is passing on the baton from one time to to another, and investigate the fate of the subdominant clock. For this purpose minisuperspace is best seen as a dispersive medium, with packets moving with a group speed distinct from the phase speed. We show that the motion of the packets’ peaks reproduces the classical limit even during the transition periods, and for subdominant clocks once the transition is over. Strong deviations from the coherent/semi-classical limit are expected in these cases, however. Could these be a “sign of the times”, accessible notably in the transition period (from matter to Lambda domination) we live in?