Friday, December 11, 2015

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...


  1. A reflective nano-drumhead an atom or few thick quantum zero-point vibrates, then Doppler shifts laser beam interrogation. Add a phase-locked pulse train anti-phase to membrane oscillation. Heisenberg is finessed, oscillatory temperature approaches absolute zero.

    Progressively snug two such membranes in parallel and in register. Gravitation effects add a term. W, Mo, Au for density, graphene for tensile strength. Does graphene suffer patch potentials?
    Molybdenum layer
    Gold layer
    J. Phys.: Condens. Matter 27(21) 214012 (2015)
    Casimir experiment patch potentials
    Casimir experiment patch potentials

  2. Aside from everything else, such experiments sound much less expensive than one normally expects in this domain. Do you happen to know roughly what this one would cost?

  3. CW,

    Well, given that the experiment is, to my understanding, not possible with present technology, but still some orders of magnitude away, I have no clue how much it would cost.

    Doing the experiment with existing technology (then somewhat away from the Planck limit) is probably very inexpensive, provided you can convince someone with the suitable equipment to do it. In this case, it's the cost for a postdoc of maybe a year or two to run the experiment. Something like $250,000, add a little overhead and travel money.

    Buying the equipment on top of this, I don't know. I would guess it's of the order of a million or so. But it's not the kind of budget estimate I've ever had to do, so give it a large errorbar. Maybe someone more familiar with these experiments has a better estimate to offer? Best,


  4. Hi Sabine,

    let me begin by thanking you for your blog-post, it’s nice to see our paper receive attention for positive reasons!

    I have one comment and one question regarding what you wrote:

    Comment: you state “This is a very tame type of non-locality, because it is confined to Planck scale distances”. Naively one might think that this is the case, but in fact much of our interest in these models came from causal sets where the non-locality scale is (for theoretical considerations which are not watertight) much larger than the Planck (length) scale. This fact, together with the scaling of the perturbative parameter with the mass of the system, is what makes our proposal particularly promising regarding constraints/detection (btw a similar hierarchy of scales also appears in non-commutative geometry).

    Question: What do you mean when you say that Poincare symmetry is only deformed for virtual particles in the cases we consider?



  5. You say that red curve is greatly exaggerated.What is roughly numerical difference and what is the current accuracy of measuring such things? I would like to know if the difference is say 1 part in 10000 and current accuracy is like 1 part in 100 etc. Do you have such figures?

  6. If I understand the paper correctly, it implies that the interaction of a graviton with a macroscopic wavefunction can be treated in the same way as its interaction with an "elementary" wavefunction, of an electron, say. If so, why is this so ?

  7. Hi Dionigi,

    Yes, I saw that you are considering the CS case where the scale might be larger. Sorry that I forgot to mention it. I think one should just generally think of this as a parameter that is being constrained. I'd still say though the most plausible expectation is that it be somewhere at the Planck scale.

    As to the deformation of Poincare-invariance. I had an exchange with Stefano yesterday who was confused about the same thing. I didn't know that you didn't know of this.

    See, if you have a Lagrangian of the type \psi f(\box) \psi, and you interpret, as usual the thing between the fields as p^2, then p^2 is now a function of \box. The partial derivatives are elements of the tangential space and transform under local Lorentz-transformations as usual. The p, in the most general case for f, doesn't. That's how you construct DSR. You then get a non-linear transformation for the momentum, with all the problems that are related to this. The problems with DSR however all come from the modification also being present on-shell. (Ie, f is not a function of \box, but, for example, has correction terms only in the spatial components.)

    Let me put this another way. In general if you introduce this function f, then you change the size of the target space. If you normally integrate over momentum space, you integrate from - infinity to plus infinity. You can chose f so that the space is now compact (after Wick-rotation). In fact that's what you probably want, because that kills you all UV contributions. If you integrate over this space, you integrate over a finite range. How does the measure in this space transform? That's where the deformation comes in. You don't have to think of it this way. In fact you can reformulate all integrals so that you totally avoid this. But that's the way that I interpreted these modifications.

    Btw, I think the paper you should have quoted as reference [1] is this one (the one that you quote doesn't actually have anything to do with such modifications of qft). Best,


  8. kashyap,

    There are estimates in the last section of the paper. There is no figure for this. The figure in my blogpost is a plot of equation 13a with \alpha normalized to one and \epsilon b_2 ~ 0.5. I just wanted to give you a visual impression for what this modification does, and I didn't find the figure in the paper very illustrative. Best,


  9. MarkusM,

    The paper doesn't say anything about graviton interactions, I don't know what you are even referring to.

  10. MarkusM,

    I think your question has really meaning. (at different levels to begin with possible hidden premises but this is not my point.)

    I'd like to know of a theoretical reason why it would not be so?
    As far as I know, there is no known experimental difference (e.g. from double slit experiment using a particle or a large molecule). Do you know any?


  11. @akidbelle "double slit experiment using a particle or a large molecule" Diffract a resolved rigid chiral molecule. Camphor is adequate; D_3-4,7,11-trioxatrishomocubane is elegant. DOES IT RACEMIZE? Does that vary with and odd number of slits, rotational temperature, magnetic field parallel and normal to the beam? Diffraction may have footnotes.

    Adequate: 2 chiral centers/27 atoms is 7.41%
    Elegant: 8 chiral centers/19 atoms is 42.1%

    Physics' failures are grant funding as business model - verification not falsification. Theory is not shriven by observation. Get down and push.

  12. Sabine,
    "The paper doesn't say anything about graviton interactions" - Thanks for pointing to that, you are of course right. Unfortunately I had not read the paper carefully enough and so misinterpreted it - sorry.

    "I think your question has really meaning" - Maybe, but it mainly resulted from my confusion, because I was lacking enough background knowledge about cavity optomechanics. (I'm just learning that and I must say it's pretty cool physics). There have already been similar suggestions before,
    and so I presume that these kind of experiments hold water.
    "As far as I know, there is no known experimental difference (e.g. from double slit experiment using a particle or a large molecule). Do you know any?"
    No, only many theories about the "collapse of the wavefunction". It has even been outlined how to do such experiments with viruses and bacteria (but not with cats yet :-))


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