It's been a while since I did any ResearchBlogging posts, because it turns out that having an infant *and* a toddler really cuts into your blogging time. Who knew? I keep meaning to get back to it, though, and there was a flurry of excitement the other day about a Nature Physics paper proposing a way to search for quantum gravity not with a billion-dollar accelerator, but with a tabletop experiment. There's a write-up at Ars Technica, but that comes at it mostly from the quantum gravity side, which leaves room for a little Q&A from the quantum optics side.

**Wait a minute, you said this is in Nature Physics? I don't have access to that.** You're in fine company, because neither do I. Thanks to the arxiv, though, you can read a preprint for free, and that's what I'll be working from.

**OK, so what's the deal with this quantum gravity stuff? Are you telling me they can make a black hole with lasers, now?** No, there aren't any black holes involved, even though black holes are the canonical example of a system where you need quantum gravity to understand what's going on. Black holes are rather difficult to work with, though, so people who want to look for a quantum theory of gravity try to find other ways to see its effects.

In this case, they make use of the fact that most theories of quantum gravity involve a minimum length scale. That is, there's a minimum length below which you can't talk about distances in any sensible way.

**Wait, what? What does that even mean?** It's an almost inevitable consequence of trying to merge general relativity with quantum mechanics. General relativity is a theory of space and time, while quantum mechanics takes its name from the fact that energy only comes in discrete amounts. A quantum theory of gravity, then, will almost certainly involve space and time coming in discrete amounts.

**So, what, it's like the universe is put together with teeny-tiny Lego blocks, and you can't have anything smaller than a single block?** That's not a bad analogy. Something sorta-kinda like that, yes-- the exact details depend on the particular version of quantum gravity you favor, but in general, most of them require the rules to change dramatically at very small distances.

**So, this paper is about a way to scatter light off the Lego blocks and see them directly?** Well, no. The distance at what the rules have to change is something like the "Planck length," which is 10^{-35}m. If you could magnify a single atom to appear the size of the entire solar system, the Planck length would be around the size of a single atom on the screen you used to project the image of the atom. There's no way to see that directly.

**But how can you measure anything about physics at teeny-tiny length scales if you can't see things that small?** I said that the rules change dramatically when you get to that length scale. Long before that, though, a quantum theory of gravity would make really small modifications to the basic rules of physics. And if you're clever enough, you can measure those small effects.

**So, this paper is by some really clever guys who measured those effects?** No, because it's a theoretical paper. They haven't measured anything yet. But it is by some really clever physicists, at the quantum optics institute in Vienna, who came up with an idea that might let somebody else measure the effects, and see signs of quantum gravity.

**And how do they propose to do that?** Well, like all quantum optics measurements, it ultimately comes down to an interference measurement. They plan to bounce light off a small object, and look for the small "phase shift" that quantum gravity produces by interfering the reflected light with light from the original laser.

The key, here, is using a small enough object and just the right technique so that the shift is big enough to detect.

**How small an object are we talking about, here?** Really small. They run the numbers for an object that is about 10^{-11} kg. That's really small, but in the range of microfabricated membranes and mirrors that people use for cavity optomechanics. And, in fact, this is a proposal for a cavity optomechanics experiment: they want to use one of these tiny little mirrors as part of an optical cavity, where its motion gets coupled to the light bouncing back and forth inside the cavity.

**That Ars Technica piece talks about the Heisenberg uncertainty principle. Are they measuring the position and momentum of the tiny little mirror?** Not directly, no, because that would be unbelievably tedious to try to map out. Quantum optics people are much too clever for that.

Instead, what they're doing is measuring a phase shift, represented schematically by the diagram at right. Physicists love to draw little pictures to represent what's going on, and in this case, you can represent the state of a pulse of light by a little arrow like the hand of a clock. As time goes on, the arrow rotates in a circle, and the angle that it rotates through is referred to as the "phase" of the pulse.

Any time you have a pulse of light interact with something, that shifts the phase of the light. If you bounce the pulse off a cavity containing one of these micro-mirrors, you expect that to produce a phase shift, moving the arrow from its initial position (pointing directly to the right, at the purple circle) to the dashed arrow on the diagram. Quantum gravity introduces an *extra* shift, though, which would take the actual state to the red arrow pointing to the purple ellipse. The difference between the dashed arrow and the red arrow is the "phase shift," which you can measure by taking the shifted pulse and interfering it with some light from the initial laser pulse.

**So, what does this have to do with the uncertainty principle?** Well, if you just did the simplest thing you could imagine and bounced a single pulse off the cavity, the phase shift would depend on, say, the position of the movable mirror, which wouldn't help you much. If you're a clever quantum optician, though, you can do a multi-step measurement that causes the phase shift to depend on both the position and the momentum of the mirror. In fact, it depends on a combination of the two that is, mathematically, exactly the thing that gives you the uncertainty principle.

**So, you use four pulses of light?** No, you use one pulse four times. The scheme looks like this:

You send a pulse of light in from the left, which passes straight through some optics on the way to the cavity, where it interacts with the moving mirror. On the way back out, it passes through an optical element that rotates its polarization, so rather than passing back out the way it came in, it gets reflected by a polarizing beamsplitter (the bluish square thing), and reflected downwards. On the lower path, it goes through a delay line, just a long bit of fiber optic, then goes to the other beamsplitter, where it's reflected again. On the second pass, it goes through an electro-optic modulator (EOM) that rotates its polarization so it passes straight through the beamsplitter into the cavity again. And the whole process starts over.

After it's bounced off the cavity four times, the EOM setting is changed to have the polarizing beamsplitter reflect it up to a detector where it interferes with a bit of the original pulse that has just been going through a big delay line, waiting for the measurement.

**OK, that seems awfully complicated. What's the point of all that?** Well, the delay line at the bottom of the figure is chosen to make sure that the pulse hits the cavity at exactly the right points in the oscillation of the moving mirror (which is wiggling back and forth the whole time, at a particular frequency that depends on the properties of the microfabricated mirror). If the four interactions are spaced just right over one full out-and-back oscillation of the mirror, you find that, mathematically, the phase shift depends on both position and momentum in just the right way.

So, rather than needing to make a whole bunch of position and momentum measurements, mapping out the tiny modification of the uncertainty principle caused by quantum gravity, you get a single phase shift measurement that depends on the strength of the quantum gravity effects in a simple and elegant mathematical way.

**That's pretty clever, dude.** Yeah, it is. That's why quantum optics is awesome. We have the ability to measure phase shifts to really good precision using interference effects, and if you're sufficiently clever about it, you can turn almost anything you'd like to know about into a phase shift.

**So, you just bang this together, and it tells you right off whether quantum gravity exists?** Well, it's a lot more subtle than that. The uncertainty principle limits your ability to measure the phase shift-- that's what's represented by the purple circle and oval in the diagram above-- and if you want to make a good measurement of the strength of quantum gravity, you need to make sure that the width of the oval at the end of the arrow representing your pulse is less than the phase shift. That requires some balancing of the various parameters you can change, to find values where you can reasonably expect to measure something.

In the paper, they run the numbers for three different types of quantum gravity theories, to check the plausibility. For the one that would make the biggest shift, the parameters you would need to have (the reflectivity of the mirrors, the intensity of the laser pulse, the vibration frequency of the mirror, the laser wavelength, and the number of times you need to repeat the measurement) are pretty reasonable. The one that makes the smallest difference is pushing the limits of current technology a bit, but not completely unreasonable.

**Awesome! So, when can we expect the experimental results? Is next week too soon?** Much too soon. The basic numbers aren't unreasonable, but that doesn't mean it'll be easy. This also requires that the mirror be very, very "cold" in the sense of not vibrating very much, which is fairly challenging. Either you need to do the whole thing in a dilution refrigerator at temperatures of a tenth of a degree above absolute zero, or you need to do something really clever to eliminate the vibration of the mirror. Those are both possible, and indeed there are groups working very hard on doing exactly this kind of thing, but it's not a trivial experiment. You're probably looking at several years before anybody could do a really good measurement, though with this proposal out there, you can bet that experimental groups are thinking of ways to do intermediate steps as soon as possible.

This does, however, provide a great example of the potential power of quantum optics to explore new physics in experiments that fit within a single large-ish laboratory, and don't require billions of dollars. This might be the best way we have to get information about how physics works all the way down at the Planck length. And that's pretty amazing.

Pikovski, I., Vanner, M., Aspelmeyer, M., Kim, M., & Brukner, ï¿½. (2012). Probing Planck-scale physics with quantum optics Nature Physics DOI: 10.1038/nphys2262

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A quantum theory of gravity, then, will almost certainly involve space and time coming in discrete amounts.

Sadly, no. Discreteness at the Planck scale would mean breaking of Lorentz symmetry, which is tested to absurdly high precision. There are relevant or marginal operators associated with this symmetry breaking, which means the effects don't actually disappear at much longer distances and we should have already seen them. So any sensible theory of quantum gravity has to avoid this constraint and will definitely not show up in this kind of experiment. (String theory, for instance, makes no such prediction of discrete space and time.)

Okay, if somebody has to be the ass to tell everybody they're getting excited about nothing, I will: The authors of this paper are using an approach to the minimal length with modified commutation relation. That's the best trodden path. The problem is, if you introduce a minimal length as a spatial distance then that's not Lorentz-invariant. Lorentz-invariance violation (LIV) is extremely tightly constrained already. You'd hope that their experiment tests something new.

To avoid the constraints on LIV, you can go and modify the Lorentz-transformations too. In fact, that's what is most often implicitly assumed in these approaches, though often not explicitly stated. Then, you are no longer breaking Lorentz-invariance and have a chance of testing something new. This is known as a deformation of the Poincare symmetry or deformed special relativity, just to give you some keywords. However, this comes at a price to pay. This only works if the momentum transforms non-linearly. As a consequence, the linear sum of momenta is no longer Lorentz-invariant. To maintain Lorentz-invariance, you have to introduce a new addition law. And if you do that, you run into what's known as the "soccer-ball problem." That problem is that the effect you get scales up with the mass of the object you are considering. That's a problem because for large masses you have to reproduce the normal addition law.

Now, the authors of this paper are completely ignorant of this issue altogether. If you look into the appendix, they happily sum momenta linearly. This would break Lorentz-invariance, and thus their theory is subject to constraints on LIV. They mention in the passing "Finally, we note that theories with a modified commutator have an intrinsic ambiguity as to which particles or degrees of freedom of a composite system the deformations should apply to." Right. Unfortunately, that's a bug, not a feature.

That having been said, the authors are dealing with an ansatz that is insufficiently specified (one doesn't know what the transformation behavior is), and by virtue of this are able to ignore the problems with defining multi-particle states. They aren't the first to do that, btw, people have repeatedly tried use the fact that the modification of the commutation relation becomes more relevant with the mass to make exciting predictions for composite systems, by virtue of ignoring the question of transformation behavior.

This paper should not have been accepted for publication on the ground that the authors have not sufficiently specified the model, and either don't know or willing ignore the known problems.

If you want to know some more, have a look at this http://arxiv.org/abs/1202.4066, at the paper I am commenting on, and the references therein.

Meanwhile, there's a fascinating idea about how AMO physics can probe really fundamental and important physics we can't probe in other ways, which is infinitely more plausible than getting evidence for quantum gravity effects.

There is nothing inherently quantum gravitational about some energy reaching the Planck scale, that statement is not even Lorentz invariant. Quantum gravitational effect become important when some Lorentz Invariant quantity with dimensions of energy becomes of the order of the Planck mass, which does not happens in the situation described here.

This is a trivial fact which has nothing to do with any mysterious or conjectural physics. In exactly the same way, there is also no strong interaction effects coming into play when the centre of mass energy of some object reaching 1GeV, and nuclear physics is not required to discuss length measurement with precision of one Fermi (which can be achieved easily by repeated mesurements). It is somewhat surprising that such simple confusion is so prevelant.

Seems similar to the MichelsonâMorley experiment--with similar out come I am guessing. But I am skeptical for another reason. Most people think that QM is the most fundamental treatment of the microscopic. To me it is a theory of measurement only with the Heisenberg relations giving a limit of measurement. I believe that below measurement there are properties that are simply washed out in the quantum ensemble. That is structure that might exist for one particle(that makes up that ensemble) cannot be observed because the act of observing will change it. For example, spin emerges from the Dirac equation,but only if you include a magnetic probe. That probe changes the symmetry of the environment and the spin that is measured could very likely be different from the spin not measured (former will tend to align with the probe and produce a vector).