Quantum gravity could be observable in the oscillation frequency of heavy quantum states

Observable consequences of quantum gravity were long thought inaccessible by experiment. But we theorists might have underestimated our experimental colleagues. Technology has now advanced so much that macroscopic objects, weighting as much as a billionth of a gram, can be coaxed to behave as quantum objects. A billionth of a gram might not sound much, but it is huge compared to the elementary particles that quantum physics normally is all about. It might indeed be enough to become sensitive to quantum gravitational effects.

One of the most general predictions of quantum gravity is that it induces a limit to the resolution of structures. This limit is at an exceedingly tiny distance that is the Planck-length, 10^-33 cm. There is no way we can directly probe it. However, theoretically the presence of such a minimal length scale leads to a modification of quantum field theory. This is generally thought of as an effective description of quantum gravitational effects.

These models with a minimal length scale come in three types. One in which Poincaré-invariance, the symmetry of Special Relativity, is broken by the introduction of a preferred frame. One in which Poincaré-symmetry is deformed for freely propagating particles. And one in which it is deformed, but only for virtual particles.

The first two types of these models make predictions that have already been ruled out. The third one is the most plausible model because it leaves Special Relativity intact in all observables – the deformation only enters in intermediate steps. But for this reason, this type of model is also extremely hard to test. I worked on this ten years ago, but got eventually so frustrated that I abandoned the topic: Whatever observable I computed, it was dozens of orders of magnitude below measurement precision.

A recent paper by Alessio Belanchia et al now showed me that I might have given up too early. If one asks how such a modification of quantum mechanics affects the motion of heavy quantum mechanical oscillators, Planck-scale sensitivity is only a few orders of magnitudes away.

Tests of Quantum Gravity induced non-locality via opto-mechanical quantum oscillators
Alessio Belenchia, Dionigi M. T. Benincasa, Stefano Liberati, Francesco Marin, Francesco Marino, Antonello Ortolan
arXiv:1512.02083 [gr-qc]

The title of their paper refers to “non-locality” because the modification due to a minimal length leads to higher-order terms in the Lagrangian. In fact, there have to be terms up to infinite order. This is a very tame type of non-locality, because it is confined to Planck scale distances. How strong the modification is however also depends on the mass of the object. So if you can get a quite massive object to display quantum behavior, then you can increase your sensitivity to effects that might be indicative of quantum gravity.

This has been tried before. A bad example was this attempt, which implicitly used models of either the first or second type, that are ruled out by experiment already. A more recent and much more promising attempt was this proposal. However, they wanted to test a model that is not very plausible on theoretical grounds, so their test is of limited interst. As I mentioned in my blogpost however, this was a remarkable proposal because it was the first demonstration that the sensitivity to Planck scale effects can now be reached.

The new paper uses a system that is pretty much the same as that in the previous proposal. It’s a small disk of silicone, weighting a nanogram or so, that is trapped in an electromagnetic potential and cooled down to some mK. In this trap, the disk oscillates at a frequency that depends on the mass and the potential. This is a pure quantum effect – it is observable and it has been observed.

Belanchia et al calculate how this oscillation would be modified if the non-local correction terms were present and find that the oscillation is no longer simply harmonic but becomes more complicated (see figure). They then estimate the size of the effect and come to the conclusion that, while it is challenging, existing technology is only a few orders of magnitude away from reaching Planck scale precision.

The motion of the mean-value, x, of the oscillator's position in the potential as a function of time, t. The black curve shows the motion without quantum gravitational effects, the red curve shows the motion with quantum gravitational effects (greatly enlarged for visibility). The experiment relies on measuring the difference.

I find this a very exciting development because both the phenomenological model that is being tested here and the experimental precision seems plausible to me. I have recently had some second and third thoughts about the model under question (it’s complicated) and believe that it has some serious shortcomings, but I don’t think that these matter in the limit considered here.

It is very likely that we will see more proposals for testing quantum gravity with heavy quantum-mechanical probes, because once sensitivity reaches a certain parameter range, there suddenly tend to be loads of opportunities. At this point I have become tentatively optimistic that we might indeed be able to measure quantum gravitational effects within, say, the next two decades. I am almost tempted to start working on this again...