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.
https://www.sciencedirect.com/science/article/pii/S0370269318300637The 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.
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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.
martinbn said:Shape Dynamics (SD) is a new theory of gravity
The Big Bang theory is the prevailing scientific explanation for the origin of the universe. It states that around 13.8 billion years ago, all matter and energy in the universe was concentrated into a single point, known as a singularity. This singularity then began to rapidly expand and cool, eventually resulting in the formation of galaxies, stars, and planets. The Big Bang theory is important because it helps us understand the fundamental laws and processes that govern the universe, and has been supported by a vast amount of scientific evidence.
Currently, it is impossible to determine what happened before the Big Bang with any certainty. The laws of physics as we know them break down at the singularity, making it difficult to make accurate predictions about the state of the universe before the expansion began. Some theories, such as the cyclic model, propose that the universe goes through a series of cycles of contraction and expansion, but this is still a subject of much debate and further research is needed.
The concept of time before the Big Bang is a highly debated and complex topic. Some theories suggest that time did not exist before the Big Bang, as it is a product of the expansion of the universe. Others propose that time existed in a different form or dimension before the expansion began. However, due to the limitations of our current understanding of the universe, it is difficult to make definitive statements about the concept of time before the Big Bang.
Singularities are points in space-time where the laws of physics break down. In the context of the Big Bang, the singularity refers to the extremely dense and hot state in which the universe existed before the expansion began. It is important to note that the singularity is not a physical object, but rather a mathematical concept used to describe the beginning of the universe. Our current understanding of the universe suggests that the singularity was the starting point for the expansion and subsequent evolution of the universe.
Currently, the concept of time before the Big Bang is purely theoretical and has not been supported by any concrete evidence. The limitations of our current technology and understanding of the universe make it difficult to gather evidence from before the Big Bang. However, scientific theories and models, such as the cyclic model and the concept of a multiverse, continue to be explored and may provide further insights into the concept of time before the Big Bang in the future.