Hints of dispersion (both gravity and EM waves)

[marcus]

This paper which just appeared on arxiv

http://arxiv.org/abs/0709.2365
Loop quantum gravity corrections to gravitational wave dispersion
Martin Bojowald, Golam Mortuza Hossain
27 pages
(Submitted on 14 Sep 2007)

"Cosmological tensor perturbations equations are derived for Hamiltonian cosmology based on Ashtekar's formulation of general relativity, including typical quantum gravity effects in the Hamiltonian constraint as they are expected from loop quantum gravity. This translates to corrections of the dispersion relation for gravitational waves. The main application here is the preservation of causality which is shown to be realized due to the absence of anomalies in the effective constraint algebra used."

It cites an earlier one which is not on arxiv but was published in July this year in Physical Review D and of which I obtained a paper copy. The other references are online.
http://link.aps.org/abstract/PRD/v75/e123521
Radiation equation of state and loop quantum gravity corrections
Martin Bojowald, Rupam Das
Phys. Rev. D 75, 123521 (2007) (11 pages)
(Received 16 January 2007; published 28 June 2007)

"The equation of state for radiation is derived in a canonical formulation of the electromagnetic field. This allows one to include correction terms expected from canonical quantum gravity and to infer implications to the universe evolution in radiation dominated epochs. Corrections implied by quantum geometry can be interpreted in physically appealing ways, relating to the conformal invariance of the classical equations."

 

[marcus]

I want to emphasize what it says on page 14 of the Bojowald-Hossain paper that just appeared:

"As one can see, the quantum correction function multiplies the wave number k, thus affecting the mode on all scales. Moreover, given that α > 1, the corrected group velocity due to inverse volume corrections is greater than unity. This may appear as a violation of causality since gravitational waves would travel faster than with the speed of light.

However, this refers to the classical speed of light, while a physical statement requires us to compare the velocity to the physical speed of light. This differs from the classical one because also the Maxwell Hamiltonian receives inverse volume corrections in loop quantum gravity [31]. In the regime of linear inhomogeneities such corrections have been computed in [32], and a derivation of the quantum corrected group velocity of electromagnetic waves, which we present in Sec. 6, shows that it is not smaller than that of gravitational waves. Thus, there are no violations of causality."

the reference [32] is to Bojowald Das paper of earlier this year.

Much of section 6, pages 16-20, is about this very thing and goes into more technical detail. At the end of the section, on page 20, this conclusion:

"Thus, the requirement of a closed constraint algebra, implying (68), ensures that there is no violation of causality: the corrected speed of gravitational waves agrees with the physical speed of light, which itself is subject to corrections."

It looks like we are getting away from the classical speed of light here.

 

[Entropia]

I find this paper interesting as it explores the effects of loop quantum gravity on the dispersion of gravitational waves. This is an important topic in the study of gravity and could have significant implications for our understanding of the early universe and the nature of space-time.

The authors use Ashtekar's formulation of general relativity to derive cosmological tensor perturbation equations, taking into account quantum gravity corrections in the Hamiltonian constraint. This leads to corrections in the dispersion relation for gravitational waves. The authors then demonstrate that these corrections preserve causality, which is a fundamental principle in physics.

The paper also references a related study on the equation of state for radiation in the context of loop quantum gravity. This allows for a deeper understanding of the implications of quantum geometry on the evolution of the universe in radiation dominated epochs.

Overall, this paper presents a valuable contribution to the field of quantum gravity and provides further evidence for the potential effects of loop quantum gravity on the behavior of gravitational waves. Further research in this area could lead to a better understanding of the fundamental nature of gravity and its role in the universe.