- #1
Morbert
Gold Member
- 663
- 545
- TL;DR Summary
- This is a continuation of a side discussion from a recently closed thread
It is cited here, and here like so:PeterDonis said:This is not what the no boundary proposal says. It says that there is no boundary at the beginning of the universe; that means no "single point". It means the 4-D geometry of the universe at the beginning is smooth and geodesically complete and the curvature is finite everywhere, instead of the 4-D geometry being geodesically incomplete and the curvature increasing without bound as a past boundary is approached.
The paper you cited is not a paper about the no boundary proposal, but about a different proposal that is part of an attempt to develop a theory of quantum gravity.
But then what should the conditions be at the ends of space and time? Here J. Hartle and S. Hawking made a suggestion that is as radical as it is elegant [1, 2]: they proposed that there should be no such ends! In other words, they proposed that space and time should have no boundary to our past
And hereTwo leading proposals for special quantum states of the universe are the Hartle-Hawking ‘no-boundary’ proposal [20, 21, 22, 23, 24, 25, 26, 27, 28, 29]
[edit] - and hereWe calculate the probability measure on classical spacetimes predicted by the no-boundary wave function (NBWF) [1]
The full quote from the paper I cited:Considering the quantum fluctuations inherent to the universe, it is plausible that the universe originated from nothing devoid of any space-time. This idea is a cornerstone of quantum cosmology, with a long history dating back to Lemaitre [1]. The most robust formulations of this idea, such as the no-boundary proposal [2]
I don't see how this paper is not a paper about the no boundary proposal.The Euclidean four-geometries summed over must have a boundary. on which the induced metric is h,j. The remaining specification of the class of geometries which are summed over determines the ground state. Our proposal is that the sum should be over compact geometries. This means that the Universe does not have any boundaries in space or time (at least in the Euclidean regime) (cf. Ref. 3). There is thus no problem of boundary conditions. One can interpret the functional integral over all compact four-geometries bounded by a given three-geometry as giving the amplitude for that three-geometry to arise from a zero three-geometry, i.e., a single point.
Last edited: