Monday, October 12, 2015

A newly proposed table-top experiment might be able to demonstrate that gravity is quantized

Tl;dr: Experimentalists are bringing increasingly massive systems into quantum states. They are now close to masses where they might be able to just measure what happens to the gravitational field.

Quantum effects of gravity are weak, so weak they are widely believed to not be measurable at all. Freeman Dyson indeed is fond of saying that a theory of quantum gravity is entirely unnecessary, arguing that we could never observe its effects anyway. Theorists of course disagree, and not just because they’re being paid to figure out the very theory Dyson deems unnecessary. Measurable or not, they search for a quantized version of gravity because the existing description of nature is not merely incomplete – it is far worse, it contains internal contradictions, meaning we know it is wrong.

Take the century-old double-slit experiment, the prime example for quantum behavior. A single electron that goes through the double-slit is able to interact with itself, as if it went through both slits at once. Its behavior is like that of a wave which overlaps with itself after passing an obstacle. And yet, when you measure the electron after it went through the slit it makes a dot on a screen, like a particle would. The wave-like behavior again shows up if one measures the distribution of many electrons that passed the slit. This and many other experiments demonstrate that the electron is neither a particle nor a wave – it is described by a wave-function from which we obtain a probability distribution, a formulation that is the core of quantum mechanics.

Well understood as this is, it leads to a so-far unsolved conundrum.

The most relevant property of the electron’s quantum behavior is that it can go through both slits at once. It’s not that half of the electron goes one way and half the other. Neither does the electron sometimes take this slit and sometimes the other. Impossible as it sounds, the electron goes fully through both slits at the same time, in a state referred to as quantum superposition.

Electrons carry a charge and so they have an electric field. This electric field also has quantum properties and moves along with the electron in its own quantum superposition. The electron also has a mass. Mass generates a gravitational field, so what happens to the gravitational field? You would expect it to also move along with the electron, and go through both slits in a quantum superposition. But that can only work if gravity is quantized too. According to Einstein’s theory of General Relativity though, it’s not. So we simply don’t know what happens to the gravitational field unless we find a theory of quantum gravity.

It’s been 80 years since the question was first raised, but we still don’t know what’s the right theory. The main problem is that gravity is an exceedingly weak force. We notice it so prominently in our daily life only because, in contrast to the other interactions, it cannot be neutralized. But the very reason that planet Earth doesn’t collapse to a black hole is that much stronger forces than gravity prevent this from happening. The electromagnetic force, the strong nuclear force, and even the supposedly weak nuclear force, are all much more powerful than gravity.

For the experimentalist this means they either have an object heavy enough so its gravitational field can be measured. Or they have an object light enough so its quantum properties can be measured. But not both at once.

At least that was the case so far. But the last decade has seen an enormous progress in experimental techniques to bring heavier and heavier objects into quantum states and measure their behavior. And in a recent paper a group of researchers from Italy and the UK propose an experiment that might just be the first feasible measurement of the gravitational field of a quantum object.

Almost all researchers who work on the theory of quantum gravity expect that the gravitational field of the electron behaves like its electric field, that is, it has quantum properties. They are convinced of this because we have a well-working theory to describe this situation. Yes, I know, they told you nobody has quantized gravity, but that isn’t true. Gravity has been quantized in the 1960s by DeWitt, Feynman, and others using a method known as perturbative quantization. However, the result one gets with this method only works when the gravitational field is weak, and it breaks down when gravity becomes strong, such as at the Big Bang or inside black holes. In other words, this approach, while well understood, fails us exactly in the situations we are interested in the most.

Because of this failure in strong gravitational fields, perturbatively quantized gravity cannot be a fundamentally valid theory; it requires completion. It is this completion that is normally referred to as “quantum gravity.” However, when gravitational fields are weak, which is definitely the case for the little electron, the method works perfectly fine. Whether it is realized in nature though, nobody knows.

If the gravitational field is not quantized, one has instead a theory known as “semi-classical gravity,” in which the matter is quantized but gravity isn’t. Though nobody can make much sense of this theory conceptually, it’s infuriatingly hard to disprove. If the gravitational field of the electron remained classical, its distribution would follow the probability of the electron taking either slit rather than itself going through the slits with this probability.

To see the difference, consider you put a (preferably uncharged) test particle in the middle between the slits to see where the gravitational pull goes. If the gravitational field is quantized, then in half of the cases when the electron goes through the slit, the test particle will move left, in the other half of cases it would move right (it would also destroy the interference pattern). If the gravitational field is classical however, the test particle won’t move because it’s pulled equally to both sides.

So the difference between quantized and semi-classical gravity is observable. Unfortunately, even for the most massive objects that can be pushed through double slits, like large molecules, the gravitational field is far too weak to be measurable.

In the new paper now, the researchers propose a different method. They consider a tiny charged disk of osmium with a mass of about a nano-gram, held by electromagnetic fields in a trap. The particle is cooled down to some hundred mK which brings it into the lowest possible energy state. Above this ground-level there are now discrete energy levels for the disk, much like the electron orbits around the atomic nucleus, except that the level spacing is tiny. The important point is that the exact energy values of these levels depend on the gravitational self-interaction of the whole object. Measure the spacing of the energy levels precisely enough, and you can figure out whether the gravitational field was quantized or not.

Figure 1 from arxiv:arXiv:1510.01696. Depicted are the energy levels of the disk in the potential, and how they shift with the classical gravitational self-interaction taken into account, for two different scenarios of the distribution of the disk’s wave-function.

For this calculation they use the Schrödinger-Newton equation, which is the non-relativistic limit of semi-classical gravity incorporated in quantum mechanics. In an accompanying paper they have worked out the description of multi-particle systems in this framework, and demonstrated how the system approximately decomposes into a center-of-mass variable and the motions relative to the center of mass. They then calculate how the density distribution is affected by the gravitational field caused by its own probability distribution, and finally the energy levels of the system.

I haven’t checked this calculation in detail, but it seems both plausible that the effect should be present, and that it is large enough to potentially be measurable. I don’t know much about these types of experiments, but two of the authors of the paper, Hendrik Ulbricht and James Bateman, are experimentalists and I trust they know what current technology allows to measure.

Suppose they make this measurement and they do, as expected, not find the additional shift of energy levels that should exist if gravity was unquantized. This would not, strictly speaking, demonstrate that perturbatively quantized gravity is correct, but merely that the Schrödinger-Newton equation is incorrect. However, since these are the only two alternatives I am aware of, it would in practice be the first experimental confirmation that gravity is indeed quantized.


  1. What about Penrose's idea that it is gravity which prevents us from observing macroscopic mixed states? Relative to this? Otherwise plausible?

    Penrose came out with this and his ideas about quantum consciousness (which I gather have been sufficiently ruled out) at about the same time, and tried to tie them together somewhat (at least talking about both in the same book). I think his ideas on consciousness have given him something of a bum rap. He certainly has had many good ideas in his career.

  2. Nice idea. Reminds me of the lamb-shift experiment. That one of course was crucial for focusing the community on QED.

  3. "For M = 10^15 u, corresponding to an osmium particle (density ρ = 22.57 g/cm^3) of diameter 5.2 µm, we predict a frequency splitting ∆f ∼ 0.1 mHz." That would be about 3.3×10^(-15) wavenumbers. It does not present as being an easy measurement.

  4. Hasn't it already been demonstrated?


  5. If gravity isn't quantized then it seems that gravitational interactions can't ever cause wave collapse. For example imagine you have a black hole in a superposition of positions. Measure the gravitational field between them and you see nothing. But even if you measure the gravitational field to one side you would still see a slightly weaker field due to the superposition of states. You cannot collapse the state with gravity alone.

  6. ""They consider a tiny charged disk of osmium with a mass of about a nano-gram, held by electromagnetic fields in a trap. ""

    Why they want to use Osmium ist obvious, it is the material with the highest
    density available.
    But why a disk, not a sphere? Is some detection of the rotation of that disk intended?
    Georg (Without that closing e :=)

  7. Wow! Seriously clever. The results in the quantum gravity scenario seem well argued. But, I'm not so sure that the classical expectation is fleshed out as well.

  8. In your opinion, do the bouncer/walker experiments which reproduce 1-slit and 2-slit phenomena classically, have any role to play in deciding what fundamental assumptions are appropriate for understanding the observed results of 2-slit experiments?

    Hmmm, quantized mass. This idea was proposed before on this very blog and summarily dismissed by SH.

  9. Can you invite the authors to write a guest blog explaining simply why they think the effect is measurable now?

  10. Robert,

    This experiment has nothing to do with "quantized mass" whatever you think that means.

  11. Phillip,

    I've never managed to make much sense of Penrose's idea, and it shouldn't be confused with the framework discussed here. The semi-classical limit does not induce wave-function collapse. In a somewhat unfortunate terminology, it is sometimes said to lead to 'collapse' but what they mean is that the gravitational self-interaction can counteract dispersion. See, take an electron wave-packet for example. It doesn't normally 'interact with itself'. But in the semi-classical limit the electron sits in its own gravitational potential, which slows the spread of the wave-function. Unfortunately, this effect is too small to be measurable on electrons. In the experiment proposed here, they basically measure the deformation of the object due to this effect. Best,


  12. Joy,

    Yes, it would be totally awesome and definitely a game changer. Best,


  13. Andrew,

    I'm not sure what you mean. The scenario that they look at is the one in which gravity is classical. It basically leads to a slight deformation of the disk that doesn't come from the trapping potential but from the gravitational potential that comes from the strange self-coupling on the semi-classical limit. Best,


  14. Georg,

    I don't know for sure - actually I asked the same question. It's got something to do with the arrangement of the experiment, which isn't spherically symmetric, but cylinder symmetric (see figure in paper). They have to find a way to measure the energy levels of the system, for which they put it in a cavity and test it with a laser, and I suppose that if you have something that's flat between the mirrors the excitations are cleaner. But I'm really just guessing there. Best,


  15. Hi Sabine,
    I'm not sure why you're saying "quantum gravity test", when it is clear that gravity is purely classical. The Schroedinger-Newton idea seems rather puzzling to me, because if it is there the Schroedinger-Coulomb should be there as well, with the effect by many orders of magnitude stronger (as it seems) and apparently not observable.

  16. Druzal,

    The article you mention demonstrates that neutron is quantized in a gravitational field. I.e. the Earth's gravitational field is large enough to produce a measurable separation of energy levels. However, the gravity shows no quantum properties in that experiment - it's a potential and that's it.

    Whereas here, the question is whether gravity is just a potential indeed or it is something more complicated.

  17. Dear Sabine,

    Thanks for this very clear and understandable post on an important article. It is amazing to see that the interplay between quantum mechanics and gravity could soon be probed in experiments.

    If I may, I would like add a very short comment about quantum gravity.

    A recent series of work (in which, I must disclose, I have been partly involved) shows that there are other ways to build theories of semiclassical gravity (in the sense of quantum matter plus classical space time) which are free of self-interaction. Admittedly, you could still legitimately prefer the Schrödinger-Newton approach, but I believe this is good to know that there are other (perhaps no less appealing) possibilities with different phenomenology.

    Of course, this does not diminish the merit of the article by Grossart et al. in any way. The SN equation is now widely used and testing it would already be a significant breakthrough. I just wanted to mention that the connection with the quantization of gravity might be slightly less straightforward because of the plurality of approaches to semiclassical gravity.


  18. Antoine,

    A reference would be helpful.

  19. Druzal,

    As Kyrylo says, the experiment you refer to has nothing to do with quantum gravity. It's about quantum properties in a classical gravitational potential (which is not the potential of the quantum system itself). We wrote about this a long time ago. Best,


  20. In addition to (hopefully) answering the old quantum vs. classical question about gravity, it seems to me like this experiment might actually enable us to determine one more somewhat *CRITICAL* component/attribute of gravity:

    IT'S SPEED. Is it == c? Is it > c?! [I would absolutely *LOVE* to learn one day that gravitons actually have negative mass, hahah!], OR- maybe the speed of gravity actually depends on the strength of the gravitational field? But what if it was c/2? Or 2c? Or [pi*e*sqrt(2)/2]*[c/G]??


    ...for some reason I'm imagining there are black holes in which photons are becoming entangled with gravitons... though my lay brain is unable to imagine what that would/could/might entail :(

  21. Jerzy,

    I'm saying quantum gravity test, because I don't expect such an experiment to find any evidence for the SN equation... As I wrote in the last paragraph, ruling out the SN isn't the same as demonstrating a quantized gravitational field, but I don't know a third option. Antoine in a comment above seems to know of one, but honestly I'm not very convinced. (Yes, I know, I wrote a paper saying that gravity might be neither classical nor quantized, but in the low energy limit it's still just perturbative qg.)

    Regarding your question, it's addressed in this paper, see page 6 ("Finally we wish to come back to the fundamental issue..."). I don't see why Schrödinger-Newton implies Schrödinger-Coulomb. Best,


  22. LarchOye,

    I don't know what you mean, how do you want to measure this? There's no time-dependence in this setting. Yes, you can entangle gravitons (if they exist). Best,


  23. Sabine,

    Sorry for the lack of references, I did not want to exploit this comment section of your blog to advertise my own work but this may have made my contribution unnecessarily vague.

    The preprint I have recently coauthored with Lajos Diosi and which might be relevant is this one
    Similar ideas have been explored earlier by Kafri et al. in the context of a toy model (open access).
    The idea is to suppose that the mass density of everything behaves as if it were continuously monitored (i.e. weakly measured) and that the information extracted from this monitoring were used to source the gravitational field as in a feedback scheme. This allows to preserve the linearity of quantum mechanics at the master equation level and does not give rise to gravitational self interaction terms. I have no idea if the physical world actually behaves this way, and if I had to bet money on it, I would probably bet that it does not, or at least not exactly this way. Nevertheless, it shows that semi-classical gravity can be approached in many different nonequivalent ways.

    I should mention that the latter approach can be seen as an extension of spontaneous localization models (a la Ghirardi, Rimini, Weber, Pearle, Diosi, Penrose and others..), models which are usually not very popular. However, even if you strongly dislike this approach and see it as an admittedly ad-hoc solution to the measurement problem, you may still find some interest in it for the general problem of classical/quantum coupling.



  24. But why a disk, not a sphere?

    I thought their paper said that (the first paper linked in Bee's post; around equation 8) that in 3 dimensions, the gravitational shift is independent of the principle quantum number of the orbit. This would be impossible to measure. So, "For now, consider only the case where the trap frequency is lowered in one dimension, but the wavefunction is kept narrow in the remaining two." This results in the frequency shifts of equation 10a and 10b. Now the frequency shift of two transitions can be compared accurately, and so there is an experimentally measurable effect.

    "A fully three-dimensional analysis, giving up the approximation of a wavefunction that
    is narrow in two dimensions, can only be obtained numerically. For an axially symmetric wavefunction that is in the ground state for the transverse directions the details can be found in App. A of Ref. [23]. There it has been shown that the e ect stays the same in quality and order of magnitude also in this three-dimensional situation."

    "The Schrodinger{Newton e ect will be probed with the longitudinal motion (x
    -direction in Fig. 3) of the trapped osmium microdisc."

    x is perpendicular to the plane of the disk.

    "Longitudinal frequency can be orders of magnitude lower than the transverse [31, 32], which accurately embodies our theoretical description that the wave function remains narrow in two dimensions"

    This would say that one must use a disk, not a sphere?

  25. Direct quotation from SH: "If the gravitational field is not quantized, one has instead a theory known as “semi-classical gravity,” in which the matter is quantized but gravity isn’t. Though nobody can make much sense of this theory conceptually, it’s infuriatingly hard to disprove."

    The experiment described in the blog posting may not directly test semi-classical gravity, but failure to find evidence for quantized gravity would certainly have a bearing on the matter, so to speak.

    I think we could easily "make sense of [semi-classical gravity]" if we wanted to. But, of course, that would require abandoning a half-century of prejudice. This would probably require empirical forcing of a high order.

  26. Robert,

    You're more than welcome trying to construct a consistent theory of semi-classical gravity. I am sure you'll be the one to succeed where 80 years of work by the brightest minds on the planet have failed. Good luck!

  27. @antoine tilloy "the mass density of everything behaves as if it were continuously monitored" "the information extracted from this monitoring were used to source the gravitational field as in a feedback scheme"

    What of an isolated uncharged point particles' gravitational mass, especially neutrinos and "dark matter" with near zero scattering cross-sections? Se-72 to As-72 half-life is 8.4 days, electron-capture decay. Fully ionized Se-72 is stable. What interrogates a neutrino in vacuum free fall? If inertial and gravitational mass can diverge, the Equivalence Principle is violated and GR fails.

    @Arun The disk is a mirror that couples to the cavity. A sphere would be isotropic and self-cancelling. Osmium has the smallest [2(pi)][sqrt(B)], thus the object appears to have structure. That is footnote [22] and Table 1.

  28. “To see the difference, consider you put a (preferably uncharged) test particle in the middle between the slits to see where the gravitational pull goes. If the gravitational field is quantized, then in half of the cases when the electron goes through the slit, the test particle will move left, in the other half of cases it would move right (it would also destroy the interference pattern). If the gravitational field is classical however, the test particle won’t move because it’s pulled equally to both sides.”

    That result would confirm classical gravity and psi-ontology. *shudder*

  29. I'm having trouble understanding the results of the double slit experiment. If gravity is quantized, and moves in a superposition through both slits at once, wouldn't this be the scenario that leaves the test particle unmoved? And with classical gravity, forcing a movement through one slit or the other would shift the particle? I feel like I must be missing something.

  30. Paul,

    Right, that's an interesting point, I hadn't thought about this!

  31. Planx,

    Forget about the double-slit that causes interference for a moment, it makes things more complicated than they need to be. Just consider a state that is in a superposition of left and right without the later interference. If gravity is in a superposition, what happens is that this superposition affects the test-particle which also gets into a superposition - that is, until you measure it, in which case it collapses. If you consider only the 'left' wavefunction, it pulls the particle left, if you consider only the 'right' wavefunction, it pulls the particle right. If you measure then both the particle and the test particle, their momenta will add up, but they will have moved either way. This isn't the case in the semi-classical picture (it can actually violate momentum conservation, but this effect is tiny and vanishes if you take averages). It's an unstable and thus unrealistic situation of course, but if you place the test-particle exactly in the middle, it won't do anything.

    If, in classical gravity you 'force a movement through one slit or the other', then, yes, you move the particle, but that isn't the double-slit experiment - for that you really need both slits.

  32. Sabine,

    Thanks for the link and your thought-provoking posting.

    My concern is that I don't see a thorough "engineering" analysis of the overall signal-to-noise ratio for this setup. The frequency shift can be induced by perturbing variables that have nothing to do with gravitational self-interaction, such as, but not limited to:

    - variations of the material constant B with geometry of the crystal, temperature fluctuations, local pressure effects and fabrication stresses,
    - misalignments of the levitating disc, concave mirror and front lens,
    - gravitational effects related to the mass of all trap components,
    - inhomogeneity and internal structure defects of the front lens, deviations from its ideal reflectivity...and so on.

    Ervin Goldfain

  33. Would detecting a change in gravity give you info about which slit (or r and l) and decohere superpositions?
    Is it just a detail that grav waves are from quadrupoles? Or Lorentz invariance is enough for the discrepancy to show?


  34. As an aside, WOW...I've been discovering Neil Turok. He's the only scientist I've come across whose views about the state of science strongly reflect my own.

    How comes no one has blogged about it? I mean, he is being really scathing. Is it because he's being iced out? it because he's the boss at Perimeter and no one wants to burn their bridges.

    Or is because, he's got a knock down argument and everyone on some level knows it.

  35. Chris,

    I haven't had time to look the lecture and I haven't heard anything that has convinced me it would be worth the time. I read a summary that said something to the extent the universe is simple. To which I can only say it isn't. So I'm not sure what that's supposed to knock down. Best,


  36. If you have 100 minutes to spare:

    Let me know what he says in 140 characters or less ;)

  37. After Turok noted that simplicity appeared to dominate on both the largest and smallest scales, hinting that some unknown possible connection relates the two, a questioner asked him whether fractals might be a useful tool since its self-similarity relates the small and the large.

    Turok looked a bit uncomfortable and then said something like 'I don't know anything about fractals so I cannot comment on that'.

    Very amusing and informative.

  38. That would be UV/IR mixing, not fractals.

  39. Sabine hi - 140 words or less would be it's not really about simplicity as such, but what is discovery/science, in terms of what are the 'good to haves', the 'need to haves' and the 'must not haves'. It's not going to say what one does not already know. But definitely one of things needing hearing again on a regular basis. Particularly now.

  40. Hi Robert - fractals are like this 'woo woo' subject.

  41. My 2c (so IMO), Turok's talk has been misrepresented. The talk, ending at the "Thank You" slide, is not nonsense. But also not news to many readers of this blog, and certainly not to you, B. The Q&A was nonsense & fluff. Except the one report at the beginning of a possible advance: shocks arising amid the primordial acoustic waves. In the Q&A he makes a wild guess that this may help us understand the matter-antimatter asymmetry. Frankly, I'd keep my distance from the latter idea.

  42. Thanks for the summaries :) It's somewhere on my list, maybe next time I have the flu and can't do much else, I'll have a look at this...

  43. Re: "Thanks for the summaries but Naaaa"

    If only I'd spent a little longer sayin' it better

  44. Chris,

    It's got nothing to do with Turok - I just generally don't like watching recorded lectures, I much prefer reading.

  45. Bee, thanks for your unusually clear exposition of the issues regarding the quantization or not of gravity.

    So if this or some other experiment demonstrates that gravity is quantized along with matter, then the issue would become, just exactly HOW is gravity quantized?

    And what would this proposed experiment have to do with psi-ontology?


  46. Michael,

    Right, that would give rise to the next question of course, how it always goes in science. But you have to see this in the historical perspective: measuring effects of quantum gravity was simply believed to be impossible for the last 80 years. Now look, certainly this proposed experiment is a challenge, and maybe they'll not be able to measure the frequency finely enough to make a conclusive statement, but this isn't off by 30 orders of magnitude, it's down to one or two orders of magnitude.

    About the psi-ontology. If you'd measure the shift from the SN equation, this would mean that the wave-function must be "real" (in the sense of existing, not being real-valued) because it directly gives rise to the gravitational potential in this equation. Now you can go and complain that the gravitational *potential* isn't directly measurable either (you actually measure the gradient), but that would move a rather philosophical debate onto a much more concrete level. Best,



COMMENTS ON THIS BLOG ARE PERMANENTLY CLOSED. You can join the discussion on Patreon.

Note: Only a member of this blog may post a comment.