# Hawking approach to quantizing GR

1. May 29, 2004

### marcus

any comment on an approach to quantum gravity tried by Stephen Hawking, I think in the 1980s and 1990s, but apparently abandoned?
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):

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

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. The dynamical triangulation approach (Section IV-A) and the spin foam approach (Section V-C2) are examples of attempts 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...

------end exerpt----

Last edited: May 29, 2004
2. May 29, 2004

### marcus

this is the thread and post that I intended, I somehow accidentally entered the other (fragmentary) one a minute earlier, which I would appreciate if a mentor would delete so there wont be the apparent duplication

3. May 31, 2004

### meteor

This from J. Baez:
http://math.ucr.edu/home/baez/week67.html
"Hawking likes the "Euclidean path-integral approach" to quantum gravity. The word "Euclidean" is a horrible misnomer here, but it seems to have stuck. It should really read "Riemannian", the idea being to replace the Lorentzian metric on spacetime by one in which time is on the same footing as space. One thus attempts to compute answers to quantum gravity problems by integrating over all Riemannian metrics on some 4-manifold, possibly with some boundary conditions. Of course, this is tough --- impossible so far --- to make rigorous. But Hawking isn't scared; he also wants to sum over all 4-manifolds (possibly having a fixed boundary). Of course, to do this one needs to have some idea of what "all 4-manifolds" are."

BTW, the Euclidean path integral is also known as Hawking integral
In fact, Hawking wrote a book about EQG,this
http://www.amazon.com/exec/obidos/tg/detail/-/9810205155/103-5096705-4815848?v=glance
if you want to pay the 113 \$!

Last edited: May 31, 2004
4. May 31, 2004

### TeV

Smells like Hawking is heading to Strings@Branes theories math tools to deal with the PROBLEM

5. Jun 3, 2004

### jnorman

i personally find hawking to be nearly incomprehensible. after reading "the nature of space and time", the series of essays by hawking and penrose, i was able to follow penrose with little difficulty, whereas EVERY essay by hawking seemed convoluted, confused, very poorly written, almost to the point where i had to assume hawking didnt understand the concept himself, much less being able to convey his thoughts in anything resembling a coherent fashion. it was as if he was more concerned with sounding super-intelligent than with addressing the subject matter in a clear way - like 20 pages of spinfoam instead of just saying straight out, "i dont know". i was reminded of feynman's comment that he always believed that if he was not able to explain something to a freshman, it meant that he(feynman) did not understand the concept well enough himself.