Here's a bit from the Conclusion section of the April 2006 Rovelli et al paper(adsbygoogle = window.adsbygoogle || []).push({});

http://arxiv.org/abs/gr-qc/0604044

==quote==

7 Conclusion

We have computed a first and a second order term in the expansion in λ of the diagonal components of the graviton propagator, in a large distance regime, starting from a background–independent formulation of quantum gravity.

The result has the 1/|x−y|^{2}dependence on the distance expected from the linearized quantum theory, the expected dependence on the physical constants, and the numerical

proportionality constants can be fixed as a condition on the semiclassical boundary state.

The main tool we have used is the definition of general covariant n-point function, given in (49). Many issues remain open. Among these are: the calculation ofnon-diagonalterms in the propagator [47];...the physical interpretation of the numerous subdominant terms, and their relation with the relativistic and the quantum corrections to theNewton law[9]; ...

In our opinion, the interest of the calculation is not so much in the final agreement with the linearized expression or in the details of the model used, but rather in the fact that it shows how somelow-energy quantities with a transparent physical meaning can be computed, starting from the abstract context of a background independent formalism.

The specific choices of ingredients used for the calculation is therefore of lesser interest, in our opinion, that the display of the feasibility of calculations of this sort.

==endquote==

This is the result which Rovelli paraphrased informally sometime later by saying

We have calculated Newton's Law starting from a world with no space and no time.

I realized recently that this particular statement could sound extravagant to someone encountering it unprepared, but in fact this is exactly what was done by starting from a background independent formalism. Since there is no prior background geometry, there is no space and time as we know them. It is not immediately obvious how to describe even the simple situation where there are two points a certain distance apart.

However this was done, and much more. So since it is a recent development, which may strike those unfamiliar with the business as surprising, I will list some of the landmark papers. The paper just quoted was:

Graviton propagator in loop quantum gravity

Eugenio Bianchi, Leonardo Modesto, Carlo Rovelli, Simone Speziale

41 pages, 6 figures

published in Class.Quant.Grav. 23 (2006) 6989-7028

(Submitted on 10 Apr 2006)

"We compute some components of the graviton propagator in loop quantum gravity, using the spinfoam formalism, up to some second order terms in the expansion parameter."

**Physics Forums | Science Articles, Homework Help, Discussion**

Dismiss Notice

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Newton's Law starting from no background spacetime

**Physics Forums | Science Articles, Homework Help, Discussion**