beecee Posted May 30, 2019 Share Posted May 30, 2019 https://phys.org/news/2019-05-stabilizing-no-boundary-universe-quantum.html Stabilizing the no-boundary proposal sheds light on the universe's quantum origins: One idea for how the universe began is that the universe may have appeared out of nothing due to some quantum effect, such as quantum tunneling. In the 1980s, Stephen Hawking and James Hartle further elaborated on this idea by suggesting that time did not exist before the beginning of the universe, leading them to conclude that the universe has no initial boundary conditions on either time or space. The idea is called the "no-boundary proposal" or the "Hawking-Hartle state." However, precisely describing how a physical system can transition from zero size to a finite size has been challenging. To describe the quantum effects involved, physicists use the path integral formulation, which involves rewriting a single classical trajectory as an integral over many possible trajectories, resulting in a quantum amplitude. more at link..... the paper: https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.122.201302 No-Boundary Proposal as a Path Integral with Robin Boundary Conditions: ABSTRACT: Realizing the no-boundary proposal of Hartle and Hawking as a consistent gravitational path integral has been a long-standing puzzle. In particular, it was demonstrated by Feldbrugge, Lehners, and Turok that the sum over all universes starting from a zero size results in an unstable saddle point geometry. Here we show that, in the context of gravity with a positive cosmological constant, path integrals with a specific family of Robin boundary conditions overcome this problem. These path integrals are manifestly convergent and are approximated by stable Hartle-Hawking saddle point geometries. The price to pay is that the off-shell geometries do not start at a zero size. The Robin boundary conditions may be interpreted as an initial state with Euclidean momentum, with the quantum uncertainty shared between the initial size and momentum. Link to comment Share on other sites More sharing options...
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