Ask Ethan: Do gravitational waves exhibit wave-particle duality?

Everything that’s inherently quantum in the Universe is both a wave and a particle. So, are gravitational waves?

“You asked me how to get out of the finite dimensions when I feel like it. I certainly don’t use logic when I do it. Logic’s the first thing you have to get rid of.” –J.D. Salinger

Now that LIGO has detected their first gravitational wave signal, the part of Einstein’s theory that predicts that the fabric of space itself should have ripples and waves in it has been confirmed. This brings up all sorts of interesting questions, including this one from reader (and Patreon supporter!) Joe Latone, who asks:

“Are gravity waves expected to exhibit wave-particle duality, and if so, have LIGO physicists already conceived of ways to test it, like the double-slit experiment?”

Wave-particle duality is one of the strangest consequences of quantum mechanics we’ve ever uncovered.

It started out simply enough: matter was made of particles, things like atoms and their constituents, and radiation was made of waves. You could tell something was a particle because it would do things like collide and bounce off of other particles, stick together, exchange energy, become bound, etc. And you could tell something was a wave because it would diffract and interfere with itself. Newton got this one wrong about light, thinking it was made of particles, but others such as Huygens (his contemporary) and then the early-1800s scientists like Young and Fresnel showed definitively that light exhibited properties that couldn’t be explained without considering it a wave. The biggest ones became evident when you passed it through a double slit: the pattern that shows up on a background screen shows that the light interferes both constructively (leading to bright spots) and destructively (leading to dark spots).

This interference is uniquely a product of waves, and so this “proved” that light was a wave. But this got more confusing in the early 1900s, with the discovery of the photoelectric effect. When you shone light on a certain material, occasionally electrons would get “kicked off” by the light. If you made the light redder (and hence, lower energy) — even if you made the light arbitrarily intense — the light wouldn’t kick off any electrons. But if you kept the bluer (and hence, higher energy) light, even if you turned the intensity way, way down, you’d still kick off electrons. Shortly thereafter, we were able to discover that light is quantized into photons, and that even individual photons could act like particles, ionizing the electrons if they were of the right energy.

Even stranger realizations came in the 20th century, as we discovered that:

• Single photons, when you passed them through a double slit one-at-a-time, would still interfere with themselves, producing a pattern consistent with a wave nature.
• Electrons, known to be particles, exhibited this interference and diffraction pattern as well.
• If you measured which slit a photon or electron goes through, you don’t get an interference pattern, but if you don’t measure it, you do get one.

It seems that every particle we’ve ever observed can be described as both a wave and a particle. Moreover, quantum physics teaches us that we need to treat it as both under the proper circumstances, or we won’t get the outcomes that agree with our experiments.

Now, we come to gravitational waves. These are sort of unique, because we’ve only seen the wave-like part of them, never the particle-based part. However, just like water waves are waves that are made of particles, we fully expect that gravitational waves are made of particles, too. Those particles ought to be gravitons (instead of water molecules), the particle that mediates the force of gravity and that’s fully expected to emerge as a consequence of gravity being an inherently quantum force in nature.

Because it’s a wave, and because that wave has been observed to behave exactly as General Relativity predicts, including:

• during the inspiral phase,
• during the merger phase, and
• during the ringdown phase,

we can safely infer that it will continue to do all the wave-like things that General Relativity predicts. They’re a little different in detail than the other waves we’re used to: they’re not scalar waves like water waves, nor are they even vector waves like light, where you have in-phase, oscillating electric and magnetic fields. Instead, these are tensor waves, which causes space to contract and rarify in perpendicular directions as the wave passes through that area.

These waves do a lot of the same things you’d expect from any sort of wave, including that they propagate at a specific speed through their medium (the speed of light, through the fabric of space itself), that they interfere with any other ripples in space both constructively and destructively, that these waves “ride” on top of whatever other spacetime curvature is already present, and that if there were some way to cause these waves to diffract — perhaps by traveling around a strong gravitational source like a black hole — they would do exactly that. In addition, as the Universe expands, we know these waves will do what all waves in the expanding Universe do: to stretch and expand as the background space of the Universe expands, too.

So the real question is, then, how do we test the quantum part of this? How do we look for the “particle” nature of a gravitational wave? In theory, a gravitational wave is similar to the earlier image that shows an apparent wave arising from many particles that move around: those particles are the gravitons and the overall apparent wave is what LIGO detected. There’s every reason to expect we’ve got a series of gravitons on our hands, that are:

• spin-2 particles,
• that are massless,
• that propagate at the speed of light,
• and that only interact through the gravitational force.

The constraints from LIGO on the second one — the masslessness — are extremely good: if the graviton does have a mass, it’s less than 1.6 x 10^-22 eV/c^2, or some ~10²⁸ times lighter than the electron. But until we figure out a way to test quantum gravity using gravitational waves, we won’t know whether the “particle” part of wave-particle duality holds for gravitons.

We’ve actually got a few chances for this, although LIGO is unlikely to succeed at any of them. You see, quantum gravitational effects are strongest and most pronounced where you have strong gravitational fields in play at very tiny distances. How better to probe this than for merging black holes?! When two singularities merge together, these quantum effects — which should be departures from General Relativity — will show up at the moment of the merger, and just before (at the end of the inspiral) and just after (at the start of the ringdown) phases. Realistically, we’re looking at probing picosecond timescales rather than the micro-to-millisecond timescales LIGO is sensitive to, but this might not be impossible. We’ve developed laser pulses that work in the femtosecond or even attosecond (10^-15 s to 10^-18 s) time ranges, and so it’s conceivable that we could be sensitive to tiny departures from relativity if we have enough of these interferometers going at once. It would take a tremendous leap in technology, including a large number of interferometers, and a significant reduction in noise and increase in sensitivity. But it’s not technically impossible; it’s just technologically difficult!

For a little more information, I just gave a live video talk on gravitational waves, LIGO and what we learned from it to the Lowbrow Astronomers at the University of Michigan, and (sorry for the Google Hangout cutouts) the full talk is online, below.

You might particularly be interested in the last question, which talks about exactly how we might be able to test the particle nature of the graviton, which would complete our picture of wave-particle duality in this Universe. We expect it to be true, but we don’t know for sure. Here’s hoping that our curiosity leads us to invest in it, that nature cooperates, and that we find out!

Submit your questions and suggestions for the next Ask Ethan here!

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