Can We Test Quantum Gravity?

Thank you to Brilliant for supporting PBS. If we discover how to connect quantum mechanics with general relativity we’ll pretty much win  physics. There are multiple theories that claim to do this, but it’s notoriously difficult  to test them.

They seem to require absurd experiments like a particle collider the size  of a galaxy. Or we could try to physics smarter, instead of physicsing harder. Let’s talk about  some ideas for quantum gravity experiments that can be done on a non-galaxy-sized lab bench,  and in some cases already have been done.

It’s been almost right on 100 years since quantum  mechanics was discovered, and 110 since general relativity. Together these theories explain almost  everything—quantum gives us the behaviour of the subatomic world and so the building blocks of  all matter and their interactions via the quantum forces, and GR gives us the the background in  which that matter lives—space and time along with the force of gravity. Despite their incredible  successes in their own domains, the two seem to contradict each other in deep ways.

There  must be some master theory that encapsulates both and resolves these contradictions, but  in the century following the discoveries of general relativity and quantum mechanics, our  efforts to find that theory have come up short. The common approach to reconciling general  relativity with quantum mechanics has been to quantize gravity—to make the gravitational  field and so the geometry of spacetime obey the strange rules of quantum mechanics. And why not? 

It’s worked for everything else; for example we made the electromagnetic field “quantum”,  showing it was mediated by force-carrying photon—and that was a stunning success. But  quantizing gravity proved extraordinarily difficult. The hypothetical force-carrier for  gravity—the graviton—has an energy so tiny that it’s hard to even conceive of an experiment that  could detect it directly.

And then there’s the fact that the field of gravity is the fabric  of spacetime itself. We quantized the other forces of nature with respect to a continuous  background, but so far it’s been exceptionally challenging to quantize that background itself.  The most prominent approaches, like string theory and loop quantum gravity, may have made progress,  but they struggle to make testable predictions.

So what if we’ve been looking at it the wrong way  around. What if, instead of quantizing gravity, we should be trying to “gravitize the quantum”.  That is, instead of trying to give quantum properties to gravity, we should accept that  gravity is fundamentally classical and try to understand how truly quantum matter  can result in truly classical gravity.

Now we talked about approaches in which  gravity stays classical in the last episode, when we explored the new Postquantum gravity  hypothesis by Jonathan Oppenheim, in which random fluctuations in the gravitational field act on  the quantum wavefunction, causing it to collapse. We also talked about the Diose-Penrose model  a while ago, in which a superposition of different spatial distributions mass and  energy is ultimately forced to choose one such distribution consistent with  a singular gravitational field. There are compelling reasons on  both sides of the discussion, but which is it?

Is gravity quantized or is the  quantum gravitized? Unlike many questions about quantum gravity, this one may be possible  to answer with actual doable experiments. Let’s consider the two scenarios and see what predictions they make that  we might be able to test.

One: Gravity is quantum - this means gravity and  by extension the fabric of spacetime exhibit the various weird properties of quantum world,  like superposition and entanglement. If we can experimentally demonstrate one of these  things then we know gravity is quantum. Two: The quantum is gravitized - this can be  tested in the context of specific scenarios like the Diosi-Penrose theory or Oppenheim’s  Postquantum gravity.

I’m going to talk about this first because it’s shorter, then I’ll  get back to tests of actual quantum gravity. In both the Diosi-Penrose and Oppenheim  approaches, the gravitational field is responsible for collapsing the quantum wavefunction. In these  ideas, there’s only one gravitational field, only one spacetime, and quantum systems do  quantum stuff within that classical background.

One of the things quantum systems can do is  be in superpositions of states—they can exist simultaneously in multiple states at once—like  Schrodinger’s alive-and-dead cat. The job of the quantum wavefunction is to describe this range  of possible states. Measurement or observation “collapses the wavefunction” - it forces the  system to choose one state from the possibilities.

If gravity is classical, then the superposition  of its contents shouldn’t cause a superposition of the gravitational field. A superposition  might involve different distributions of mass—which normally would mean different spacetime  curvatures—perhaps a superposition of spacetimes. But if gravity is classical then there’s only one  spacetime regardless of its contents.

This could lead to a tension between the gravitational  field and the matter producing that field. The Diosi-Penrose approach says that  when this tension gets too large, the wavefunction collapses. Another way  to think about it is that the fuzziness in the matter distribution is within a certain  range of matching a single spacetime curvature And in that case it can stay in superposition. 

But  if the distribution of matter strays outside that range then the superposition collapses  into a well-defined matter distribution. Oppenheim’s postquantum  gravity is slightly different: it states that the gravitational field  contains random fluctuations—called gravitational diffusion—that mess up quantum  superpositions, causing them to collapse. Both the Oppenheim and Diosi and  Penrose make a similar prediction: that there should be a stochastic quality  to the gravitational force or its effect.

This gravitational diffusion might be the most  straightforward thing to test if it exists. It would imply that there’s a fundamental limit  to the precision with which any mass can be measured. So if we can build a set of scales  with a certain very high precision, and if the weights it measures appear to fluctuate outside  that precision, it may suggest an intrinsic uncertainty in the gravitational field.

The most  accurate experiment measuring a mass conducted so far has led researchers to rule out versions  of the theory with rapid spacetime diffusion, implying that any gravity-induced collapse from  this mechanism is very weak. Oppenheim and team propose other tabletop experiments that  could constrain this better in the future. Rather than look for the funky  behavior of the gravitational field we can also approach this from the other  side—by trying to see when the collapse of the wavefunction happens.

If we can see where  quantum superposition gives way to classical matter we may be able to figure out  if it's gravity causing that collapse. Both the Oppenheim and Diosi-Penrose models,  as well as any of the family of models known as objective collapse theories predict that  wavefunction collapse becomes increasingly likely as an object grows in size or mass. If  any of these ideas are correct, there should be a limit to how large an object we can put into  superposition for any appreciable amount of time.

So far we haven’t found such a hard limit,  but we’ve been able to put some pretty big things in superposition—for example, getting  interference patterns from large molecules in double-slit experiment. Based on the largest  systems that have been put in superposition, we can rule theories where the  gravity-induced collapse is very strong. So we have some constraints on these ideas  where a classical gravity is influencing the quantum wavefunction of matter, and  more advanced tests are being planned that may turn up something.

Of course, it  may be that gravity really isn’t classical in the way these theories propose. It may  be that gravity really is quite quantum, just like matter. If that’s the case then, we’ll need different experiments.

Two of the strangest properties of quantum  objects are superposition—which we just talked a lot about—and entanglement.  Quantum entanglement is when you have two quantum systems that each may  be in a superposition of states, but the systems are also correlated so that the  state of one depends on the state of the other. For example, if a “quantum coin” was in  a superposition of both heads and tails, while a pair of quantum coins could be both in  superposition, but also be entangled so be in the opposite state to each other.

Even though  each of the coins is fundamentally undefined in its state. If the first coin is measured so that  it’s wavefunction collapses to either heads or tails, its entangled partner’s wavefunction  will immediately collapse to the opposite. Quantum entanglement sounds like an exotic  phenomenon, but it’s not; quantum particles are constantly getting entangled with each other. 

In fact, every interaction between particles generates entanglement, even if it doesn’t last  very long. We’ve observed these entanglements when the interaction happens via the quantum  forces—for example, when particles interact by exchanging the photons of the electromagnetic  force. So what if we could cause particles to become entangled by a gravitational interaction? 

As I’ll try to convince you, this would mean that the gravitational field itself has to be  part of the entanglement of those objects and spacetime has to be in a superposition of states.  Which would mean spacetime has to be quantum. One particular proposal for this type of  experiment has recently been put forward, known as a Quantum Gravity-induced Entanglement  of Masses, QGEM, experiment.

I’ll describe the original version proposed by Sougato  Bose and collaborators in 2017. It uses a Stern-Gerlach interferometer.  This is the device that first demonstrated the existence of quantum spin back in the  20s.

The original version used silver atoms, which have a single unpaired electron in  their outer shell, so the atom takes on the quantum spin of that lone electron. That  gives the atom a tiny dipole magnetic field. This causes the atom to be deflected when it  passes through the external magnetic field of the Stern-Gerlach device.

It’s deflected upwards  if  its spin axis is point up and downwards if its spin is down. Because quantum spin is  quantum, all atoms will be measured to have either spin fully up or spin fully down (reflected  all the way up or reflected all the way down)— there are no in-betweens for  quantum properties like this. If the atom starts in a superposition state of  being both spin-up and spin-down then it’ll end up in a superposition state of being physically  up or down just before it hits the detector screen.

So we've turned a spin superposition  into a spatial superposition. At the screen, the superposition collapses  into one or the other location. But we can also remove the screen and  use more magnets to bring the spatial superpositions back together, in which  case we turn the spatial superposition back into a spin superposition.

Now  if we measure that spin we should find it collapses completely randomly  into 50-50 spin up or spin down. If we were to run a second Stern-Gerlach  interferometer next to the first, the spins we’d measure at the end of the second device  would have no relationship to the spins measured at the end of the first. Atoms in the different  devices are uncorrelated—they are not entangled.

But now let’s move the devices really,  really close together. The spin-up path of interferometer one is right alongside  the spin-down path of interferometer two. Let’s pretend for a moment that the silver  atoms can interact gravitationally.

The spin-up-one and spin-down-two atoms  tug on each other ever so slightly, while the other paths are too far for the atoms  to interact. Remember that the spin measurements at the output of interferometer one versus two  used to be random—uncorrelated. Up-up, down-down, up-down, down-up should all be equally likely.

Any  quantum interaction should generate entanglement, so now, if gravity is quantum, the outputs  of the two interferometers are entangled and correlated. For example, depending on how this is  set up you may find that that the interferometers produce opposite spin results to each other very  very slightly more often than same spin results. Now single atoms are way too light to produce  a measurable entanglement.

But what if we could do this with many atoms? Specifically,  with a nanodiamond. These are tiny diamonds with widths measured in nanometers.

A little  defect inside the diamond crystal structure can be created by removing one carbon atom and  replacing it with a neighbouring nitrogen atom. This leaves an unpaired electron which  gives the nanodiamond a net spin. The same technology is actually a candidate  for qubit storage in quantum computers.

So we create nanodiamonds and put their  unpaired electrons in a spin superposition, then shoot them through the pair of Stern-Gerlach  devices. In principle we should get a spatial superposition of these relatively massive  crystals, and if gravity is quantum, we should get entanglement between the devices that will be  reflected in correlations in their final spins. What would all of this mean if it proved to work?

Well from the point of view of particle  physics, the masses get entangled when gravitons are exchanged between the two masses.  This is just like in electromagnetism, where photon exchange leads to the electromagnetic  force, and sometimes entanglement. We’ve made a video before on how hard it is to  detect single gravitons even in principle, so this entanglement between the two masses in  the QGEM experiment might be considered indirect evidence for the existence of gravitons—the  hypothetical quantum carrier of gravity.

From the point of view of general  relativity, the superposition of gravitational forces could be interpreted as  a superposition of spacetime geometries. So, spacetime itself would be exhibiting one of  the most quantum of all properties. In general, a positive QGEM result would be strong  evidence that gravity is indeed quantum.

These are just some examples of experiments that  have been proposed—or actually conducted—to test some of these ideas about the link between  quantum mechanics and gravity. Whether to find quantum effects in the gravitational field,  or to show that gravity doesn’t even need to be truly quantum. There are lots of other  ideas and efforts in progress beyond these, and there’s a good chance that some  will bear fruit—perhaps finally unlocking that century-old mystery  of the quantum nature of spacetime.

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