I Time Before Big Bang: Relational Dynamics & Singularities

[fresh_42]

I have stumbled upon this article, which sounds a bit too fantastic to me. For one, because I can't imagine others haven't tried this before, and secondly: Will there be any chance to link this with actual observations which are suited to distinguish these solutions from more common ones?

Abstract

All measurements are comparisons. The only physically accessible degrees of freedom (DOFs) are dimensionless ratios. The objective description of the universe as a whole thus predicts only how these ratios change collectively as one of them is changed. Here we develop a description for classical Bianchi IX cosmology implementing these relational principles. The objective evolution decouples from the volume and its expansion degree of freedom. We use the relational description to investigate both vacuum dominated and quiescent Bianchi IX cosmologies. In the vacuum dominated case the relational dynamical system predicts an infinite amount of change of the relational DOFs, in accordance with the well known chaotic behaviour of Bianchi IX. In the quiescent case the relational dynamical system evolves uniquely though the point where the decoupled scale DOFs predict the big bang/crunch. This is a nontrivial prediction of the relational description; the big bang/crunch is not the end of physics – it is instead a regular point of the relational evolution. Describing our solutions as spacetimes that satisfy Einstein’s equations, we find that the relational dynamical system predicts two singular solutions of GR that are connected at the hypersurface of the singularity such that relational DOFs are continuous and the orientation of the spatial frame is inverted.

The classical singularity theorems are derived from a contradiction that arises between the properties of maximal time-like geodesics in Lorentzian spacetimes and the properties of time-like (or null) geodesics that can be derived from Einstein’s equations for generic initial conditions when matter satisfies suitable energy conditions after finite proper time (or affine parameter). This leads to the conclusion that Einstein’s equations predict the breakdown of spacetime geometry. What is not implied by these theorems is that the evolution of the dynamical system that describes the physical observables has to break down.
...
We show that there exists a unique, deterministic, and entirely classical extension of Einstein’s equations through the big bang/crunch. We achieve this result without appealing to quantum effects or new ad-hoc principles. Rather, the strict insistence on describing the dynamics in terms of relational variables alone ensures the existence and uniqueness of the evolution through the apparent singularity.

https://www.sciencedirect.com/science/article/pii/S0370269318300637

 

[martinbn]

I couldn't follow it, and it seems too philosophical to me. That may be because I am not familiar at all with shape dynamics. I remember reading a book by Julian Barbour, but I didn't get much out of it, it was somewhat popular and lacked detail. Anyway their reference for shape dynamics is:

A Shape Dynamics Tutorial
Flavio Mercati
Shape Dynamics (SD) is a new theory of gravity that is based on fewer and more fundamental first principles than General Relativity (GR). The most important feature of SD is the replacement of GR's relativity of simultaneity with a more tractable gauge symmetry, namely invariance under spatial conformal transformations. This Tutorial contains both a quick introduction for readers curious about SD and a detailed walk-through of the historical and conceptual motivations for the theory, its logical development from first principles and an in-depth description of its present status. The Tutorial is sufficiently self-contained for an undergrad student with some basic background in GR and Lagrangian/Hamiltonian mechanics. It is intended both as a reference text for students approaching the subject and as a review for researchers interested in the theory.

 

[PeterDonis]

Shape Dynamics (SD) is a new theory of gravity

This is the key statement. Shape Dynamics is not a particular set of solutions to the Einstein Field Equation. It is a new theory of gravity with a different set of solutions altogether.