Gravitational bar detectors set limits to Planck-scale physics - Really?

Contains 10^-31% juice.

Three weeks ago, Nature Physics published, to my surprise, another paper on quantum gravity phenomenology:

Gravitational bar detectors set limits to Planck-scale physics on macroscopic variables
By Francesco Marin et al
Nature Physics (2012), doi:10.1038/nphys2503

The appearance of the word “macroscopic” in the title should be a warning sign.

As we discussed previously, there are recurring attempts in the literature on quantum gravity phenomenology to amplify normally tiny and unobservable effects by using massive systems. This is tempting because in macroscopic terms the Planck mass is 10^-5 g and easy to reach. The problem with this attempt is that such a scaling-up of quantum gravitational effects with the total mass of a system isn't only implausible as an amplification, it is known to be wrong. Next two paragraphs contain technical details, you can skip them if you want.

The reason this amplification for massive systems appears in the literature is that such a scaling is what you, naively, get in approaches with non-linear Lorentz-transformations on momentum space that have been motivated by quantum gravity. If Lorentz-transformations act non-linearly the normal, linear, sum of momenta, this linear sum is no longer invariant under Lorentz-transformations and thus does not constitute a suitable total momentum for objects composed of many constituents.

It is possible to introduce a modified sum, and thus total momentum, that is invariant. But this total momentum receives a correction term that grows faster than the leading order term with the number of constituents. The correction term is suppressed by the Planck mass, but if the number of constituents is large enough, the additional term will become larger than the (normal) leading order term. This would mean that momenta of macroscopic objects would not add linearly, in conflict with what we observe. This issue has been called the “soccer ball problem”; accepting it is not an option. Either this model is just wrong, or, as most people working on it believe, multi-particle states are subtle and the correction terms stay small for reasons that are not yet well understood. To get rid of these terms, a common ad-hoc assumption is to also scale the Planck mass with the number of constituents so that the correction terms remain small. Be that as it may, it's not something that makes sense to use for “observable predictions”.

Earlier last year, Nature published a paper in which the questionable scaling was used to make “predictions" for massive quantum oscillators. Since this prediction is not based on a sound model, it is very implausible that anything like this will be observed.

The authors of the new paper now propose to precisely measure the ground state energy of a gravitational wave detector, AURIGA. In theories with a modified commutation relation between position and momentum operators, this energy receives correction terms. Alas, such modified commutation relations either break Lorentz-invariance, in which case they are very tightly constrained already and nothing interesting is to be found there. Or Lorentz-invariance is deformed, which leads to the necessity to modify the addition law and we're back to the soccer-ball problem.

So you might suspect that the new paper by Marin et al suffers from a similar problem as the previous one. And you'd be wrong. It's much better than that.

The authors explicitly acknowledge the necessity to understand multi-particle states in the models that they aim at testing, and present their proposal as a method to resolve a theoretical impasse. And while they talk about very massive objects indeed (the detector bars have a mass of about 10⁵ kg), they do not scale up the effect with the mass (see eq 4). Needless to say, this means that the effect that they get is incredibly tiny, about 33 orders of magnitude away from where you would expect quantum gravitational effects to become relevant. They modestly write “Our upper limit... is still far from forbidding new physics at the Planck scale.”

Here's the amazing thing. For all I can tell, not knowing much about the AURIGA detector, the paper is perfectly plausible and the constraint makes indeed sense. I have nothing to complain about. In fact they even cite my review in which I explained the problem with massive systems.

The only catch is of course that the limit that they obtain really isn't much of a limit. If Nature Physics was consistent in their publication decisions, they should now go on and publish all limits on Planck scale physics that are less than 34 orders of magnitude away from being tested. I am very much looking forward to this. There are literally hundreds of papers that compute corrections due to modified commutation relations for all sorts of quantum mechanics problems. I should know because they're all listed and cited in my review. Expect an exponential growth of papers on the topic. (I am already dreading the day I have to update my review.) Few of them ever bother to put in the numbers and look for constraints because rough estimates show that they're far, far, away from being able to test Planck scale effects.

The best constraints on these types of models is, needless to say, my own, which is a stunning 56 orders of magnitude better than the one published in Nature.

So it seems that for once I have nothing to complain. It's a great paper and it's great it was published in Nature Physics. Now I encourage you all to compute Planck scale corrections to your favorite quantum mechanics problem by adding an additional term to the commutation relation, and submit your results to Nature. How about the g-2, or the Casimir effect? Oh, and don't forget that somebody should think about the soccer-ball problem...