any comment on an approach to quantum gravity tried by Stephen Hawking, I think in the 1980s and 1990s, but apparently abandoned?(adsbygoogle = window.adsbygoogle || []).push({});

It was called "euclidean quantum gravity" and involved a sum over spacetimes somewhat analogous to a feynmann path integral---a spacetime being like a path.

In his 1998 review Rovelli puts Euclidean QG in the section dealing with "Old Hopes turning into Approximate Theories". he makes an interesting point that both spinfoam and dynamical triangulation simplicial QG can be seen as developing out of Hawking's initiative:

-------quote from Rovelli gr-qc/9803024--------

B. Old hopes --> approximate theories

1. Euclidean quantum gravity Euclidean quantum gravity is the approach based on a formal sum over Euclidean geometries (6):

[tex]Z = N \int D[g] e^{-\int d^4x sqrtg R[g]} [/tex]

As far as I understand, Hawking and his close collaborators do not anymore view this approach as an attempt to directly define a fundamental theory. The integral is badly ill defined, and does not lead to any known viable perturbation expansion. However, the main ideas of this approach are still alive in several ways.

First, Hawking’s picture of quantum gravity as a sum over spacetimes continues to provide a powerful intuitive reference point for most of the research related to quantum gravity. Indeed, many approaches can be sees as attempts to replace the ill defined and non-renormalizable formal integral (6) with a well defined expression. Thedynamical triangulationapproach (Section IV-A) and thespin foamapproach (Section V-C2) are examples ofattempts to realize Hawking’s intuition.Influence of Euclidean quantum gravity can also be found in the Atiyah axioms for TQFT (Section V-C1).

Second, this approach can be used as an approximate method for describing certain regimes of nonperturbative spacetime physics...

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# Hawking approach to quantizing GR

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