Tuesday, March 15, 2016

Researchers propose experiment to measure the gravitational force of milli-gram objects, reaching almost into the quantum realm.

Neutrinos, gravitational waves, light deflection on the sun – the history of physics is full with phenomena once believed immeasurably small but now yesterday’s news. And on the list of impossible things turned possible, quantum gravity might be next.

Quantum gravitational effects have widely been believed inaccessible by experiment because enormously high energy densities are required to make them comparably large as other quantum effects. This argument however neglects that quantum effects of gravity can also become relevant for massive objects in quantum superpositions. Once we are able to measure the gravitational pull of an object that is in a superposition of two different places, we can determine whether the gravitational field is in a quantum superposition as well.

This neat idea has two problematic aspects. First, since gravity is very weak, measuring gravitational fields of small objects is extremely difficult. And second, bringing massive objects into quantum states is hard because the states rapidly decohere due to interaction with the environment. However, technological advances on both aspects of the problem have been stunning during the last decade.

In two previous posts we discussed some examples of massive quantum oscillators that can create location superpositions of objects as heavy as a nano-gram. The objects under consideration here are typically small disks made of silicon that are bombarded with laser light while trapped between two mirrors. A nano-gram might not sound much, but compared to the masses of elementary particles that’s enormous.

Meanwhile, progress on the other aspect of the problem - measuring tiny gravitational fields – has also been remarkable. Currently, the smallest mass whose gravitational pull has been measured is about 90g. But a recent proposal by the group of Markus Aspelmeyer in Vienna lays out a method for measuring the gravitational force of masses as small as a few milli-gram.
    A micromechanical proof-of-principle experiment for measuring the gravitational force of milligram masses
    Jonas Schmöle, Mathias Dragosits, Hans Hepach, Markus Aspelmeyer
    arXiv:1602.07539 [physics.ins-det]

Their proposal relies on a relatively new field of technology that employs micro-mechanical devices, which basically means you make your whole measurement apparatus as small as you can, piling single atoms on atoms. This trend, which has itself become possible only by the nanotechnology required to to design these devices, allows measurements of unprecedented precision.

The smallest force that has so far been measured with nano-devices is around a zepto-Newton (zepto is 10-21). That’s not yet the world-record in tiny-force measurements, which is currently held by a group in Berkely and lies at about a yocto-Newton (that’s 10-24). But the huge benefit of the nano-devices is that you can get them close to the probe, whereas the experiment holding the record relies on precisely tracking the motion of a cloud of atoms in a trap. Not only doesn’t the cloud-tracking mean that it’s difficult to scale up the mass without ruining precision. The necessity to trap the particles also means that it’s difficult to get the source of the force-field close to the probe. The use of micro-mechanical devices in contrast does not have the same limitations and thus lends itself better to the task of measuring the gravitational force exerted by quantum systems.

The Aspelmeyer group sketches their experiment as shown in the figure below

[From arXiv:1602.07539]

The blue circles are the masses whose gravitational interaction one wants to measure, with the source mass to the right and the test-mass to the left. The test-mass is attached to the micro-mechanical oscillator, whereas the source-mass is driven by another oscillator close by the systems’ resonance frequency. The gravitational pull between the two masses transfers the oscillation of the source-mass to the test-mass, where it can be picked up by the detector.

In their paper, the experimentalists argue that it should be possible by this method to measure the gravitational force of a source mass not heavier than a few milli-grams. And that’s the conservative estimate. With better detector efficiency even that limit could be improved on.

There are still a few orders of magnitude between a milli-gram and a nano-gram, which is the current maximum mass for which quantum superpositions have been achieved. But in typical estimates for quantum gravitational effects you end up at least 30 orders of magnitude away from measurement precision. Now we are talking about five orders of magnitude – and that in a field with rapid technological developments for which there is no fundamental limit in sight.

What is most remarkable about this development is that this proposal relies on technology that until a few years ago literally nobody in quantum gravity ever talked about. It’s not even that the technological development has been faster than anticipated, it’s a possibility that plainly wasn’t on the radar. Now there is a Nobel Prize waiting here, for the first experimental measurement of quantum gravitational effects.

And as the Prize comes within reach, competition will speed up the pace. So stay tuned, I am sure we will hear more about this soon.


  1. This is one of the best concise summaries I have ever read for an advanced physics experiment. And it definitely is cutting edge with respect to both theory and technological development.

  2. Very encouraging! But making the test mass to be a milligram-size and in not an eigenstate of position is going to be tricky, I expect!

    High precision measurements of G at various scales, even purely classical, should be very interesting too!

  3. "Once we are able to measure the gravitational pull of an object that is in a superposition of two different places, we can determine whether the gravitational field is in a superposition as well." How? Wouldn't the object collapse to one of the two positions, no matter if gravity is quantised or not? And even if you could somehow determine that the gravitational field is in a superposition, what would that prove exactly? As u reviewed recently, classical fields can be in a superpositions, just like quantum fields can.

  4. Maurice,

    A good question. Yes, the measurement would collapse the object (or at least decohere it to some extent, depending on what exactly you measure), but that doesn't mean that the measurement doesn't contain information about whether the state was in a quantum superposition. Basically, what you want to know is whether the gravitational field was "with" the massive object that is in a delocalized state. If you calculate the variance of the quantized system, it's characteristically different from the unquantized one, where the gravitational field cannot properly be "with" the object.

    For an earlier blogpost, I made a figure to illustrate the difference which you might find helpful.

    Yes, sorry, it should have been "quantum superposition" in that sentence. Thanks for pointing out, I'll fix that.

    The paper btw doesn't discuss testing quantum gravity. (It's remarkably un-hypey.) I am just extrapolating the possibilities based on the measurement precision, not actually proposing a specific experiment... Therefore I unfortunately can't presently lay out a detailed setting in which the difference would become obvious. Basically what you want to do is to combine this experiment with one of the previously discussed settings (see links in blogpost), but I'll have to think more about this. Having said that, once the measurement precision is there, it should become possible.



  5. "If you calculate the variance of the quantized system, it's characteristically different from the unquantized one, where the gravitational field cannot properly be "with" the object." Can you please point us to a technical discussion of this? The blog-post the figure is from does not supply such a discussion. The figure itself does not help me: why is the grav. field localised in the upper panel? The electron possesses also an electrical field which is quantised of course. Are you also claiming that the electrical field is also "fully right in 1/2 of the cases"?!

  6. The spherical ball shape of the test masses is not optimal for maximizing surface gravitation at the gap. In 2-D, then rotate about the vertical symmetry axis for the test mass (derivation is 380 words),

    Sphere, r(theta) = 2Rcos(theta)
    Shmoo, r(theta) = 5^(1/3)Rsqrt[cos(theta)]
    (6/5)[(5/8)^(1/3)] = 2.6% better

    Figure 3


  7. Maurice,

    There is no general technical discussion of this, or at least I am not aware of it. As I said this is more or less a topic nobody even thought about until a few years ago. You find some elaboration on the difference in variances in this example. I can just tell you that from various scenarios I've thought of, the variances are generally different. You can tell this also in the simple example in my figure. Just consider you scatter a particle on the potential in either case.

    Here is another paper that discusses the question, which you might find helpful. (I didn't write about this paper because I had some questions about it that I couldn't clarify in exchange with the authors. Doesn't mean it's wrong, just that there were some things I wasn't really sure I understood.)

    I was hoping it should be obvious that "fully left" or "fully right" is a way to say it's in a quantum superposition of two locations. Yes, the field which is sourced by these masses has its own quantum effects, but to first order it should just be dragged along by the sources. What it clearly should not be is being sourced by the expectation value of the source instead. Best,


  8. Uncle,

    Indeed, they also point out in the paper that a sphere is not the most optimal geometry and that this is one way to improve the efficiency.

  9. "I was hoping it should be obvious that "fully left" or "fully right" is a way to say it's in a quantum superposition of two locations." Sorry, your quoted sentence is incomprehensible, "fully left" means that there is no amplitude on the right, i.e. no superposition, isn't that correct?! Can you please clear this up and then answer my last question about the electron's electrical field? Of the two papers you quote it is the second that makes a point that seems similar to the one in your blog post, i.e. your central argument is from the paper you're not ready to write about! On further thought: even for an object with a mass of a ng its quantum gravitational field would still be in coherent state with a very large mean graviton number, right? So wouldn't its behaviour expected to be classical to extremely good precision? It's OK if these questions were still not settled, but in the second paragraph of your blog-post you clearly made it appear as if they are.

  10. Hi,

    I find it very hard to believe that the lower possibility in http://2.bp.blogspot.com/-YjhJRr_pgHg/VhkX-ooJe4I/AAAAAAAACyA/9SPZL0ykbBg/s1600/sneq.jpg could be realized as that would immediately conjure up all kinds of quantum inconsistencies.

    For example, you could send a particle been right through the center of the set up and investigate the gravitational pull on it. In the half half case, for symmetry reasons, it would not be deflected but in the other case, it would always be deflected in one or the other direction. So if you put a detector right in the middle, you could differentiate the states "left" and the superposition with 100% fidelity. But that should not be possible in a quantum theory. I leave it as an exercise to the reader to use this state differentiation machine to build a quantum cloner and using an EPR pair, faster than light signaling.

    I believe, this is pretty much the same discussion as one has to argue that you cannot couple classical gravity to the expectation value of the QFT energy momentum tensor in a consistent theory.

    Another thing, I do not fully appreciate is how this "cat state" is different from a trivial cat state: I take a radio active probe with decay rate 1/s and move the arm of a Cavendish experiment to the left if it decays in the first 500ms and to the right otherwise. True enough, decoherence leads to entanglement with all kinds of environmental degrees of freedom, but this should leave is still in a quantum superposition (of radioactive probe, Cavedish experiment, and environment) in which in half of the cases gravity is this way and half the other way.

  11. Maurice,

    "I was hoping it should be obvious that "fully left" or "fully right" is a way to say it's in a quantum superposition of two locations." Sorry, your quoted sentence is incomprehensible, "fully left" means that there is no amplitude on the right, i.e. no superposition, isn't that correct?!

    I was hoping it should be obvious that what is shown in the image and also explained in my blogpost is that the first image is to describe the state 1/sqrt(2)|left> + 1/\sqrt(2)|right>. It's a superposition of location, as I said.

    You seem to be criticizing me for not wanting to comment on a paper which I don't fully understand, which I find inappropriate. To fill you in on what it is what irks me about the paper is that I wasn't able to figure out exactly what is known about this supposed superposition state. I read several other papers about it and had an exchange with the author, but it's still not really clear to me.

    If my blogpost raised the impression that these questions are all settled, you misunderstood. I have complained many times, here and elsewhere, that there are too few people working on qg phenomenology and that there is no funding in it to hire more people. The result is, as you just notice, that the answer to basic questions such as "what is the gravitational field of an electron in a double-slit experiment in the perturbative approximation" isn't really known.

    Yes, the gravitational field has a large mean graviton number, but this isn't the point. The point is that these loads of gravitons have to go with the particle that acts as source and thus have to become delocalized. You're not seeking to measure quantum *corrections* to the gravitational potential! You just want to know if the gravitational field remains with the source - which it can't if it was classical.

    Look, think about the following situation. Schrodinger's cat is in the box and if dies it drops and the center of mass moves. If it remains alive the center of mass doesn't move. What's the gravitational field before you open the box?

    Actually, I think Claus Kiefer elaborated on this in his book on quantum gravity. (I don't have it here right now.) You can get deviations from semi-classical gravity either if you become sensitive to quantum corrections (which is what you have in mind) or if there is a sufficiently large energy in the interference terms of two sources - for which you do *not* need strong curvature effects.

    I believe the argument is originally from [what's-his-firstname] Ford, some time in the early 90s. I'll see that I find the reference somewhere.



  12. Robert,

    I've tried for like a decade to come up with any measurable inconsistency that this would result in and failed. Once you put in numbers, you always end up with something that's way smaller than anything that we could detect. Just try it... I have tried this in all kinds of scenarios, forwards and backwards, but the problem is always the same: to make this effect measurable you need to be able to measure the gravitational field *of the source mass*. This means you have to be able to bring a "heavy" object into a superposition.

    Yes, of course you can make a theoretical argument that coupling QFT to a classical theory doesn't work. As I wrote explicitly it's hard to make sense of this conceptually. But this really isn't the point. The semi-classical case only serves here as a benchmark-model. It's an example for something that you want to rule out experimentally. Best,


  13. Seem to me, that these kind of experiments may just be what the doctor order to get theoretical physics unstuck again.

  14. This means you have to be able to bring a "heavy" object into a superposition.

    I don't think this is a problem. Do the thing with the radioactive source. This creates a superposition of an object as heavy as you want. For this question, it does not matter, that its position will be entangled with all kinds of air molecules and soft photons. So decoherence does not affect this. You have 50% probability left and 50% right so the expectation value of mass density is smeared. And you should be able to detect the gravitational effect of the mass at the "other" position. Otherwise, the gravitational field is also part of the big superposition.

  15. My attempt for an intelligible explanation: the proposal (apparently from Richard Feynman) is to test if the gravitational field can entangle a system with a second system that is in a spatially dis-localised state. To entangle the systems two different gravitational fields are needed: one for each quantum-mechanical state of the second system - one field that pulls a component of the first system left and another field that pulls another component right, so to say. This contradicts general relativity because this theory describes only a single space-time. In other words: "quantum superposition" means a superposition of different states, but in GR the field can only be in a single state - i.e. indeed quantum gravity... But are u sure such a result would a ensure a Nobel prize for the experimentalist that obtained it? The comittee could internally argue that the Page/Geilker experiment was already near proof that such an entanglement must exist, no? The result would not prove that gravitons exist, right?

  16. This might be crazy, but consider this Quantum Zeno effect experiment: http://phys.org/news/2015-10-zeno-effect-verifiedatoms-wont.html.

    I quote from the article directly:

    "Previous experiments have demonstrated the Zeno Effect with the "spins" of subatomic particles. "This is the first observation of the Quantum Zeno effect by real space measurement of atomic motion," Vengalattore said. "Also, due to the high degree of control we've been able to demonstrate in our experiments, we can gradually 'tune' the manner in which we observe these atoms. Using this tuning, we've also been able to demonstrate an effect called 'emergent classicality' in this quantum system." Quantum effects fade, and atoms begin to behave as expected under classical physics.

    The researchers observed the atoms under a microscope by illuminating them with a separate imaging laser. A light microscope can't see individual atoms, but the imaging laser causes them to fluoresce, and the microscope captured the flashes of light. When the imaging laser was off, or turned on only dimly, the atoms tunneled freely. But as the imaging beam was made brighter and measurements made more frequently, the tunneling reduced dramatically.

    "This gives us an unprecedented tool to control a quantum system, perhaps even atom by atom," said Patil, lead author of the paper. Atoms in this state are extremely sensitive to outside forces,l he noted, so this work could lead to the development of new kinds of sensors."

    Could you not freaking combine this with the experiment above resulting in a much more interesting experiment? I'm asking the question . . .

    With regards,
    Wes Hansen

  17. Robert,

    Sorry, I don't know what you want to measure. For what I can tell you are proposing to let an atom decay and then measure its gravitational field. Could you be somewhat more specific? If you take an ensemble of particles that decay which is not in a coherent state you get a stochastic contribution and as a result the net gravitational field is the same as in the semi-classical case. That's why it's important that you have what they call a "Schrodinger's cat state" - one heavy state in a superposition, not an ensemble of states each of which is in a superposition. Best,


  18. Maurice,

    The Page/Geilker experiment presumes that heavy objects under question don't decohere. No, an experiment of the type I sketched here would not prove that gravitons exist. As I explained above, you do not need to detect quanta of the gravitational field to demonstrate that the field must be quantized. These are just two different things. That electron orbits are quantized is also evidence for quantization, and for this you do not need to detect photons. Best,


  19. "The Page/Geilker experiment presumes that heavy objects under question don't decohere."
    No, it does not! Rather it presumes that decoherence of heavy objects is all that there is to wave-function collapse, i.e. that there is no explicit collapse mechanism extra to the usual formalism of QM. "As I explained above, you do not need to detect quanta of the gravitational field to demonstrate that the field must be quantized." I wrote "no proof that gravitons exist" and not "no graviton detection". When you refer to "quantum gravity" you do not discriminate clearly between two completely different concepts: 1. The gravitational field is quantised in the sense that gravitons do exist in principle. 2. The gravitational field is quantised in the sense that it can exist in spatial quantum superpositions of different states. Evidence for 1. would be the sensation with a sure Nobel prize. Evidence for 2. is already at hand as per Page/Geilker under plausible (but unproven) assumptions. It is a minimal adaption of GR to make it compatible with QM, the mathematical structure of GR can remain completely intact, gravitons do not have to exist in principle. What you talk about in your post is final clinching evidence for 2. This would be a very important result (maybe, maybe even rewarded with a Nobel prize) but it would not open up any novel theoretical vistas, because the meaning of 2. is completely clear even now. On the other hand, experimental evidence for 1. would necessarily provide crucial clues on its presently unclear theoretical meaning.

  20. Maurice,

    Sorry, I don't know what you mean about the Page/Geilker experiment. To test quantum gravity, they were assuming that the quantum superpositions from some radioactive decay transfer over to massive balls. Clearly nobody in their right might would explect that. When I say quantum gravity, I here mean the perturbative quantization of quantum gravity. If you think that all I say is wrong and indeed believe that Page and Geilker have already found evidence for the perturbative limit of qg, why then do you think people are still trying to find evidence for it? Best,


  21. Sorry Sabine, apparently you really do not understand Page/Geilker. I recommend Kiefer's discussion of their experiment in the Intro p.17-18 of his textbook (edition 2006), which concludes, quote: "This experiment [Page/Geilker] ... demonstrates convincingly that (1.34) [semi-classical expression with expectation value of stress-energy tensor] cannot fundamentally be true." Certainly Kiefer would not write this if their conclusion would depend on assumptions that "nobody in her/his right mind would make". So you are certainly wrong on Page/Geilker, please take your time with answering, read Kiefer carefully first ;-). "[Do you] believe that Page and Geilker have already found evidence for the pertubative limit of qg[?]" No! Pertubative gravity is what I meant with statement 1. above (gravitons exist in principle). As I explained in my previous comment Page/Geilker is only evidence for statement 2. (the grav. field can be in quantum superpositions). Sigh, your question unfortunately indicates that you are really confused about the difference between statement 1. and 2., it's not only a problem of sloppy wording.

  22. Maurice,

    Tell me how you want to bring the gravitational field into a quantum superposition without at least perturbatively quantizing it. And then tell me what about Page and Geilker's experiment you cannot explain in the semi-classical treatment.

  23. "Tell me how you want to bring the gravitational field into a quantum superposition without at least pertubatively quantizing it." By assumption. Why would this assumption require that gravitons exist? "And then tell me what about Page and Geilker's experiment you cannot explain in the semi-classical treatment." That's becoming embarrassing. Page & Geilker's experiment is really "QG pheno 101". The quote in my previous comment clearly indicates that Kiefer's Introduction contains the answer to your question. The Intro chapter is free on google books, just check it out.

  24. Maurice,

    Yes, it's embarrassing indeed that you cannot answer my questions after you've made such a lot of noise in pretending you know more about qg pheno than I. It is also astonishing that you seem to assume I know neither Page & Geilker's experiment (which I have both written about on my blog and have also covered in those QG 101 lectures you didn't attend) nor Kiefer's argument, which you first try to use in an appeal to authority, but then cannot explain why it's relevant.

    I think it's time I disengage from this fruitless exchange. You just continue to demonstrate your inability to understand even simplest explanations. (Hint "by assumption" is not a consistent theory.) You have wasted enough of my time and of my reader's time. Good bye,


  25. Wow, this is exciting stuff. We're only three (or so) orders of magnitude off which is pretty amazing.

  26. I checked out your "lecture" on Page & Geilker from Jan. 2012. You called their experiment a laughing matter and then Giotis made you aware of the fact that your lecture is in contradiction to Kiefer's Intro because he takes the experiment quite seriously. Now that's serious because it means that either Kiefer or you have misunderstood some very elementary concept, right? I think your misunderstanding shows up when you answered Giotis on Jan 23, 2012,3:34: "It seems to me there is some implicit assumption here that because the gravitational field is not
    quantized, there are not 'many' versions of it. I don't see however why this has to be the case. You can have many versions of classical fields, corresponding to different classical solutions." That's wrong in my opinion: in GR spacetime has to
    have a unique metric, there is no sense in which it can have two metrics, one that describes a pull to the left and another in which it describes a pull to the right.I even addressed this point in some detail on March 17 12:31 pm, so in a reasonable exchange you should have contradicted me there and told me in which sense there can be two versions of the field in classical GR. Let us assume for a moment Kiefer (and Page, Giotis and I) are wrong. Even then it also looks pretty bad! How could you have left such a crucially important point for over 4 years without clearing it up in a publication that would have been very important,
    because clearly everybody who is confused about such an elementary point, will not be able to contribute anything of real worth to the QG problem, right?!

  27. Maurice,

    The sentence you quote from me that you think is "wrong in your opinion" was explicitly referring to the MWI. Just that you left out this part of the quote. I hope that this misquote was an accident and not deliberate.

    If you read it again you might note that I didn't and don't disagree with the point about the MWI that Giotis and Kiefer were making. I just disagree with you. I'm not a many-worlds fan and don't bother with that. My sarcastic remark about "nobody in their right mind" was obviously totally lost on you.

    And I was not referring to writing blogposts when I said that I on occasion give lectures about qg phenomenology. Apparently it hasn't even occurred to you that I might indeed be working in the field, has it? I wonder why that is.

    Look. I have in this blogpost pointed out to my readers a development that I think is interesting. I find it totally bizarre that you apparently try to argue there isn't anything new to this and the people who have worked on the half-a-dozen studies that I've now quoted (none of which I personally was involved in btw) are all idiots and you understand it better. Ok, all right then. I've tried my best but I don't think I can help you.