The Conjecture That Gravity Might Always Be Weak

In 2006, a group of physicists proposed a bold idea: that gravity must be the weakest force in any consistent theory of quantum gravity. Almost twenty years later, this so-called Weak Gravity Conjecture remains unproven, but the research it inspired continues to raise deep questions.

Did you know that gravity is the weakest known fundamental force?

That may not be obvious. Gravity seems like the strongest force in our day-to-day lives, a force which pulls against us every time we walk up a flight of stairs. But on the level of individual particles, gravity is extraordinarily weak. We are used to the gravity of the entire Earth, around 10^50 atoms, conspiring to pull us towards the Earth’s core. Compare that to a static charge: rub a balloon on your sweater, and the few electrons it picks up can easily attract stray pieces of paper or lift your hair, resisting the gravitational pull of the entire planet.

For a particle physicist, gravity’s extreme weakness is puzzling. It makes quantum gravity uniquely hard to study. The particles in particle colliders simply aren’t influenced by gravity enough for gravity’s subtle quantum effects to be noticeable. Even the next-weakest force—the weak nuclear force—is vastly stronger. That’s why colliders have thoroughly explored the weak nuclear force in detail, while gravity remains elusive, despite shaping space and time.

Maybe gravity’s weakness is just a coincidence, a quirk of our universe. But maybe not.

The Origins of the Weak Gravity Conjecture     

In 2006, four physicists at Harvard—Nima Arkani-Hamed, Luboš Motl, Alberto Nicolis and Cumrun Vafa— found a plausible reason. Their idea, called the Weak Gravity Conjecture, suggests that gravity must always be the weakest force: in any possible universe with quantum gravity, there must be some particles that, like electrons, obey a different force, one stronger than gravity. Their argument, based on a thought experiment involving black holes, spawned a wave of research. Though the conjecture remains unproven, it seems deeply linked to some of the most fundamental concepts in physics.

From Strings to the Swampland

In the early 2000’s, string theorists had a problem. The proposal they worked on, that particles are actually tiny strings traveling in a curled-up ten-dimensional space-time, had a lot of advantages. It would allow gravity and quantum mechanics to work together in a way that is challenging to reproduce for less exotic theories, and what’s more, it would link gravity with nature’s other particles and forces, turning them all into different configurations of the same fundamental strings. But this link would turn out to be less useful than hoped. 

String theorists had hoped that by linking together all the particles of nature, they could make predictions for undiscovered particles. But these predictions depended on how the extra dimensions of space-time were “curled up”, and it had become clear that there was an enormous number of ways this could be done, a metaphorical “landscape” of different possibilities each making different predictions. 

In response, some theorists wondered if there were universal features to the many predictions of the landscape. They proposed the idea of a “swampland”, an area outside of the landscape populated by predictions that are impossible according to string theory, and perhaps according to any other consistent theory of quantum gravity. Some features of the swampland were guessed from string theory calculations. Others emerged from general principles or thought experiments.     

A Venn diagram showing how the swampland encompasses the landscape. The standard model is located within the landscape.

Depiction of the Swampland (Credit: Cosmic Predictions from the String Swampland, Cumrun Vafa, Physics 12, 115; artist Alan Stonebraker)

The Thought Experiment at the Heart of the Conjecture

The Weak Gravity Conjecture is based on one such thought experiment, featuring a charged black hole.

According to Einstein’s equations, a black hole is inescapable: anything that falls past a critical distance, called the event horizon, will never be seen again by the outside world. This is true even if you feed the black hole a diet of electrons, giving it a negative charge. That charge will be detectable from the outside: the black hole will repel other electrons just like a negatively charged balloon. But the electrons that fell in will remain.

Einstein’s equations, however, have a blind spot: they don’t take quantum mechanics into account. In 1974, Stephen Hawking tried to figure out what would happen to quantum particles near a black hole. What he found was that the extreme way that black holes curve space and time changes the rules, letting particles pop into existence outside the event horizon and escape. This effect, later dubbed Hawking radiation, lowers a black hole’s mass. It happens very slowly for large black holes, and more quickly as they shrink. The same process can lower a black hole’s charge in the same way, carrying charged particles away.

On the left, vacuum fluctuations from the infinite past—depicted as waves—approach the black hole. As these fluctuations encounter the intense curvature of spacetime near the event horizon, they become distorted. This distortion alters the vacuum state, causing some fluctuations to appear as real particles to a distant observer. For one of these particles to be detectable—escaping as Hawking radiation—it must carry away energy. That energy is effectively drawn from the black hole’s gravitational field, resulting in a net loss of mass. These escaping particles, shown as large sets of orange lines on the right, stream into the infinite future as Hawking radiation. While nothing that crosses the event horizon can escape, this quantum process occurs just outside the horizon, allowing black holes to gradually lose energy and mass over time—ultimately leading to their evaporation.

Arkani-Hamed, Motl, Nicolis, and Vafa imagined a black hole that had swallowed a large number of charged particles, slowly evaporating due to Hawking radiation. If the repulsive force between charged particles is strong enough, then the radiation will on average, decrease the black hole’s charge. Eventually, the black hole will become neutral and will radiate away much of its remaining mass as light, eventually vanishing entirely.

If the forces between charged particles are too weak, though, something else happens. The charged particles won’t escape the black hole on average, and the black hole’s charge will not fall. The black hole will not vanish, but will remain, filled with however much charge it had to start with, a “remnant” that continues to flit around the universe.

Because black holes can hold different amounts of charge, there would be many different types of remnants. The remnants would be new kinds of particles, in a sense, ones that could come in an infinite variety of charges. That isn’t contradictory, per se, but it’s odd.     

So the group took a leap, and guessed that remnants like these are impossible. In order for that to be the case, there would have to be at least one type of charged particle with a low mass, light enough that the repulsive force between two of them from their charge was stronger than the gravitational force pulling them together. They conjectured that such a particle always exists, and this was called the Weak Gravity Conjecture.

What Do You Do With a Guess?

A conjecture is just a guess, in the end, albeit an educated guess. What matters is what people do with it.

In the case of the Weak Gravity Conjecture, people did quite a lot. It turned out to be a simple idea with surprisingly sophisticated consequences. 

Some worked on checking the conjecture, finding examples in string theory that pushed the limits. When they couldn’t find examples that broke the rules, they started checking stricter conditions. A few surprisingly strict rules seemed to hold, requiring the existence of not just one charged particle, but an infinite number of combinations of those particles bound together, each with energy low enough that its electromagnetic force is stronger than its gravity.

Researchers also found that the idea was deeply tied to more fundamental principles. By asking for basic requirements like cause and effect, signals not going faster than light, and probabilities being smaller than one, they found rules like the Weak Gravity Conjecture emerged from only a few other assumptions. In recent years, people have used these principles to investigate how the equations of black holes might change when quantum effects are taken into account.

They also explored what consequences the conjecture might have for other forces and particles. Physicists investigated consequences for axion-like-particles, types of very light particles that might explain dark matter, and for the quantum fields that might drive the process of cosmic inflation, a hypothetical event in the early universe which caused very rapid expansion. 

What started with a simple idea and a provocative thought experiment has blossomed over time. Today, more than a thousand papers have cited the Weak Gravity Conjecture, many of them with a few thousand citations of their own. The conjecture is still unproven. But it has been fruitful nonetheless. It drove research into the swampland of impossible quantum gravity theories, into the basic principles of physical reality, and into possible explanations for cosmic phenomena. And all of that research continues to this day.

Matt von Hippel is a science journalist based in Copenhagen with a background in particle physics. He blogs weekly at 4gravitons.com, and has written for Quanta Magazine, Scientific American, and Ars Technica.