Do gravitational waves exhibit wave-particle duality?

All matter particles can act like waves, and massless light waves exhibit particle-like behavior. Could gravitational waves also be particle-like?

Shown here are two black holes, each with an accretion disk, just before they collide. The announcement for GW190521 reports the discovery of the largest black holes ever detected using gravitational waves, the first time such holes have surpassed the 100 solar mass threshold. Quantum gravitational effects may be present just before and after the moment when the two central singularities overlap and the black holes merge.

The world changed forever in February 2016 when the LIGO collaboration made a revolutionary announcement that would forever change our understanding of the Universe. More than a billion light years away, two massive black holes, 36 and 29 solar masses, inhaled energy and merged. The merger created a single black hole of 62 solar masses, and the remaining 3 solar masses were converted into pure energy, according to Einstein’s formula E = mc², propagating throughout the Universe as gravitational waves. Finally, no one could doubt the physical reality of gravitational waves, including the facts that:

how they arise,
that they clearly transfer energy throughout the Universe,
and that they propagate at the theoretically predicted speed c—the speed of light in a vacuum.

Since then, LIGO has been joined by additional gravitational wave detectors like Virgo, its detection rate has grown to triple digits, and it has seen neutron star and black hole mergers with masses that vary by a factor of nearly ~100. The reality of gravitational waves has now been unequivocally confirmed, and the process of observing them is revealing an incredible amount about our universe. But all of this information is still just probing the predictions of our classical theory of gravity, general relativity.

If quantum physics is correct, then wave-particle duality should be real, too, even for gravitational waves. Here's what that means, and how we might one day test it experimentally.

This diagram, dating back to the work of Thomas Young in the early 1800s, is one of the oldest drawings showing constructive and destructive interference resulting from wave sources emanating from two points: It is physically identical to the double-slit experiment, and also works well for waves traveling through a tank. Locations labeled C, D, E, and F correspond to 100 percent destructive interference.

Wave-particle duality is one of the strangest quantum phenomena ever discovered. The independent ideas of waves and particles started out quite simply: matter was made of particles, like atoms and their constituent parts, and radiation was made of waves. You can tell something is a particle because those particles exhibit behaviors like colliding with and repelling other particles, sometimes they stick together to create composite particles, often colliding particles exchange energy and momentum, sometimes they can create bound states that result in the emission of other particles, and so on.

In the same way, you can tell that something is a wave—it will exhibit wave-like phenomena such as diffraction and interference, both with other waves and with itself. Newton was wrong about light being made of particles, but other scientists, such as Huygens (his contemporary), and then scientists in the early 1800s such as Young, Fresnel, and Arago, convincingly showed that light has properties that cannot be explained without treating it as a wave.

Perhaps the most obvious wave-like phenomenon, interference, occurs when light passes through a double slit. The pattern that appears on the background screen shows that the light interferes both constructively (resulting in bright spots) and destructively (resulting in dark spots).

The wave pattern for electrons passing through a double slit one at a time. If you measure which slit the electron passes through, you destroy the quantum interference pattern shown here. However, the wave-like behavior persists as long as the electrons have a de Broglie wavelength that is smaller than the size of the slit they pass through. This wave-like and particle-like behavior has been demonstrated for electrons, photons, and even larger composite entities.

The phenomenon of interference is a unique product of wavelike behavior. The double-slit experiment and its subsequent, more sophisticated analogues established that light is a wave. By the end of the 19th century, it was clear that some things, such as light, sound, and liquids, have wavelike properties, while others have particlelike properties.

But the distinction between these two types of behavior became even more confusing in the early 1900s, when the photoelectric effect was discovered. When you shine light on a certain material, the light sometimes “knocks out” electrons.

But the details of the photoelectric effect showed that the electron-knockout effect did not depend on the total energy (or intensity) of the light, but on the specific components of the wavelength (or energy) of the light. If you made the electron-knockout light redder than a certain threshold (and therefore lower in energy)—even if you made the light arbitrarily intense—the light would not knock out any electrons. But if you left in light that was bluer than that same certain “ionization” threshold (that would be light with higher energy), then even if you reduced its intensity, it would still knock out electrons. Soon after, we discovered that light is quantized into photons, and that even individual photons can act as particles, ionizing electrons if they have the right energy.

This graph of photon energy versus electron energy for an electron bound in a zinc atom shows that below a certain frequency (or energy), photons do not escape from the zinc atom. This is independent of intensity. However, above a certain energy threshold (at short enough wavelengths), photons always eject electrons. As the energy of the ionizing photons increases further, electrons are ejected at an increasing rate.

An even stranger realization came in the 20th century when we discovered that:

Single photons, if passed through a double slit one at a time, will still interfere with each other, creating a pattern that corresponds to a wave nature.
Electrons, which are known to be particles, also exhibit this interference and diffraction pattern.
Compound particles and even tiny living organisms can interfere with each other when you pass them through a double slit.
However, if you measured which slit a photon or electron went through, you wouldn't get an interference pattern at all. You'd only get one if you didn't make any measurements.

It seems that every particle we have ever observed can be described as both a wave and a particle. The big lesson of quantum physics is not that things are inherently either “waves” or “particles,” but that we need to treat all objects as waves and/or particles, depending on the physical circumstances of the scenario in question. If we insist on treating a phenomenon as a “wave” or a “particle” 100% of the time, we simply won’t get results that agree with our experiments.

The signal from the gravitational wave event GW190521, as seen by all three gravitational wave detectors active at the time: LIGO Hanford, LIGO Livingston, and Virgo. The entire signal was only ~13 milliseconds long, but it represented the energy equivalent to 8 solar masses converted into pure energy using Einstein's formula E = mc². It is one of the most massive black hole-black hole mergers ever directly observed. The raw data and theoretical predictions, shown in the top 3 panels, match incredibly well, clearly showing the presence of a wave-like structure.

Now, finally, we are ready to look at gravitational waves. These waves are unique in physics because we have only seen the wave part of them, but never the particle part. This is because, although we have often assumed that reality is quantum in nature, we have never been able to test gravity to see if it exhibits this inherent quantum behavior or not.

But just as water waves are made of particles, we can reasonably expect gravity waves to be made of particles, too. When you see ripples on a pond, waves in the ocean, or ripples from someone jumping into a pool, you are clearly observing a wave-like phenomenon on a macroscopic scale. But microscopically, water is made of individual molecules—lots of them—that interact with each other. It is only from their combined motions, added together, that wave-like behavior emerges.

In gravity, the particles that form gravitational waves, unlike water waves, should not be water molecules, but gravitons – particles that transmit the force of gravity within the framework of all known ideas that the quantum theory of gravity can give. It is quite expected that gravitons will appear as a consequence of the fact that gravity is a quantum force inherent in nature, and just as light is made of photons, gravitational waves should be made of gravitons.

A series of particles moving in circular paths can create the macroscopic illusion of waves. Similarly, individual water molecules moving in a particular pattern can create macroscopic water waves, individual photons create what we perceive as light waves, and the gravitational waves we see are likely composed of the individual quantum particles that form them, called gravitons.

Because it is a wave, and because this wave has been observed to behave exactly as predicted by general relativity, including:

during the convergence of bodies in a spiral,
during the fusion phase and
during the final moments of the merger, when the black holes vibrate and distort,

we can safely conclude that it will continue to do all the wave-like things that general relativity predicts. In detail, they are a little different from other waves we are familiar with: they are not scalar waves, like water waves, or even vector waves, like light, where there are in-phase, oscillating electric and magnetic fields.

Instead, it is tensor waves that cause space to compress and expand in mutually perpendicular directions as the wave passes through that region, as shown in the following video.

These waves do many of the things you would expect any wave to do, including

they propagate at a certain speed through their medium (at the speed of light, through the very fabric of space),
they interfere with any other pulsations in space both constructively and destructively,
these waves “travel” over any other, already existing curvature of space-time,
and if there were a way to make these waves exhibit diffraction—perhaps by bending around a strong gravitational source such as a black hole—they would do just that.

Furthermore, we know that as the universe expands, these waves will do what all waves in an expanding universe do: stretch and expand as the background space of the universe expands.

As the universe expands, the wavelength of all radiation also stretches. This applies to both gravitational and electromagnetic waves; every form of radiation stretches its wavelength (and loses energy) as the universe expands. As the fabric of the universe expands, the wavelength of all radiation also stretches. This causes the universe to become less energetic, and many high-energy processes that spontaneously occur at early times become impossible in later, colder epochs. It takes hundreds of thousands of years for the universe to cool enough for neutral atoms to form.

So the big question is, how can we test the “quantum” part of this idea? How can we look for the “particle-like” nature of the gravitational wave?

Theoretically, a gravitational wave is like the previous image, which shows an apparent wave arising from many particles moving around: these particles are gravitons, and the overall apparent wave is what LIGO detected. There is good reason to believe that we are seeing a sequence of gravitons – these are:

particles with spin 2,
massless,
which spread at the speed of light,
and interact only through gravitational force.

LIGO's constraints on the second property of gravitons, their masslessness, are extremely good: if the graviton has a mass, it is less than 1.6 x 10-22 eV/c², or about ~10^28 times lighter than an electron. But until we find a way to test quantum gravity using gravitational waves, we won't know whether the particle part of the wave-particle duality holds for gravitons.

There are actually several possibilities for such a test, although LIGO and other gravitational-wave observatories are unlikely to be able to conduct any of them in their current incarnation. You see, quantum gravity effects are strongest and most pronounced where there are strong gravitational fields at very short distances. What better way to probe this regime than with a black hole merger?

When two singularities merge together, these quantum effects — which must be deviations from general relativity — will manifest themselves at the moment of merger, as well as just before merger (at the end of the inspiration phase) and just after merger (at the beginning of the descent phase). In reality, we are talking about probing picosecond time scales, not the micro- and milliseconds that LIGO is sensitive to, which will require a huge advance in the sensitivity of gravitational wave experiments on the time scale.

Is it physically impossible? Not necessarily. LIGO, remember, works by using lasers that pass through vacuum cavities, bounce off mirrors thousands of times, and then have their light reconstructed and put back together. Now consider this: we have developed laser pulses that operate on femtosecond or even attosecond (10^-15 s to 10^-18 s) timescales, and so it is entirely possible that our equipment is sensitive enough to tiny deviations from relativity if we have enough of these interferometers operating simultaneously. This would require a huge leap in technology, including many interferometers, a huge reduction in noise, and an increase in sensitivity. But it is not technically impossible, it is just technologically difficult!

Starting with a low-power laser pulse, you can stretch it by reducing the power, then amplify it without destroying the amplifier, and then compress it again to create a more powerful pulse with a shorter period than would otherwise be possible. We have now moved from the femtosecond (~10^-15 s) era to the attosecond (10^-18 s) era of physics when it comes to lasers.

While we have good reason to believe that gravitational waves are simply the quantum analogue of electromagnetic waves, unlike the detection of the electromagnetic photon, we have not yet met the technological challenge of directly detecting the gravitational particle that is the opposite of gravitational waves: the theoretical graviton. While current gravitational wave detectors do not yet have sufficient time-domain sensitivity to probe the quantum gravitational effects that might occur on either side of the precise moment of a black hole-to-black hole merger, this is not a technological or theoretical impossibility: it is simply a huge challenge.

Theorists are still calculating the unique quantum effects that should arise and working with experimentalists to develop tabletop tests of quantum gravity, while astronomers studying gravitational waves are puzzling over how a future-generation detector might one day reveal the quantum nature of these waves. Although we expect gravitational waves to exhibit wave-particle duality, until we detect it, we cannot know for sure. Let’s hope that our curiosity will lead us to invest in it, that nature will cooperate, and we will know the answer once and for all!