Lunar Laser Ranging

Thibault Damour and I have just put out a new paper on using Lunar Laser Ranging to test for spatial variations of the fundamental couplings. Recently there has been a paper which claims to find a spatial gradient in the fine structure constant. If the fine structure constant has a gradient, the mass of objects will be different in different locations since the mass depends on alpha, leading to a force in the direction of the gradient. And this effect will be different for different objects because of their different compositions. Amazingly, Lunar Laser Ranging is competitive for finding the gradient in alpha by measuring the differential forces on the earth and the moon, as they can now measure the distances to millimeter level precision! This work was a quick project using our past work on composition dependence. It was fun to learn many new aspects of the orbit problem from Thibault.


I recently had some nice news – also noted here. I would like to thank all my students and collaborators for sharing their work with me, and also thank the people who nominated me for this, and those eminent folks who wrote letters on my behalf.

At the monastery

Once while visiting Fra Angelico’s cell at the Convent of San Marco, Florence, I was struck by the comparison of his cloister to offices in research institutes such as the IHES, where I am visiting now. Fra Angelico’s cloister was housed in a garden behind a high wall, and inside the monks went about their daily business, in his case producing his exquisite paintings. The IHES is in a woods behind a stone wall and big iron gate, with a central building with cells for about 40. When you arrive at the IHES you are given an empty office and the freedom to work without the usual external pressures. We filter in during the morning and the halls are remarkably quiet. At 1:00 we all go in unison for a communal lunch. After coffee it is back in the cell until tea at 5:00 – and then some more work until heading home. I am sure that for the permanent professors, and above all the Director, this is “the real world”, with pressures on fund raising, careers, politics, personalities etc. However, for the visitors, it is a remarkable opportunity for pure contemplation.

The speed of light

Mohamed and I have a new paper out on the emergence of a common speed of light in theories where different particles have different limiting speeds (the speed of the particle at very high energy). The motivation of this is that if a universal Lorentz invariance is not imposed, the wave equations of different particles will in general contain different velocities in the relation between time derivatives and space derivatives. Mohamed and I show that if the different particles are interacting, then the interactions yield a scale dependence to this limiting velocity, and the velocities approach each other at low energy. This can be a mechanism for the emergence of a universal speed of light and Lorentz invariance at low energy. There is more to the story, and it is not clear if this mechanism can be effective enough to satisfy the experimental constraints, and this is discussed in the paper.

Nature News

The journal Nature recently published an article by Davit Toms on the gravitational contribution to the running of electric charge. This got picked up by the press branch of Nature and I ended up being interviewed and quoted in the subsequent article in NatureNews. (Here is a pdf version in case the link does not work.) As can be noted, I feel that the calculation is mis-interpreted. Some of the reasons are mentioned in my paper with Mohamed and Mohamed, described in the previous post. There are possibly other reasons also. I fear that Toms, and others folks using a cutoff regularization recently, are mistaking the quadratic cutoff dependence of the coupling – which is completely unphysical – with the running of the coupling. This worry is supported by other work, some also by Toms, which finds no running in dimensional regularization. Physics cannot depend on the regularization scheme, and it is easy to understand why a quadratic dependence on the cutoff drops out when treated properly. In any case, this will be an interesting debate in the literature. In the end, I feel that the idea of gravitational corrections to running couplings is wrong.

Gravitational running couplings

Our two Mohameds and I have recently posted a paper on the gravitational effect on running couplings. There has been a lot of interest in this effect since a paper by Robinson and Wilczek. Our paper is a set of explicit calculations to see how useful the idea of a running coupling is in a well defined setting involving scattering processes. However our conclusion is that the idea of a running coupling in this setting is not useful, because even the sign of the correction can change as one goes from space-like processes to time-like ones.
Instead, the dominant physics is that of operator mixing rather than the evolution of a single coupling constant.
Our work was performed in the perturbative regime, so we had control over the techniques, and we explored a variety of possibilities for the definition of a running coupling. We note that there has been a lot of work lately on the related topic of the “asymptotic safety” program, which takes a running coupling into the non-perturbative region beyond the Planck scale. We were careful not to say anything about the asymptotic safety program, but a reader will likely recognize that our results are not positive for that research topic. We hope to address this more explicitly in the future.

Research and teaching pages for John Donoghue