As far as physicists have been able to determine, nature speaks two mutually unintelligible languages: one for gravity and one for everything else. Curves in the fabric of space-time tell planets and people which way to fall, while all the other forces spring from quantum particles.

Albert Einstein first spoke of gravity in terms of bends in space-time in his general theory of relativity. Most theorists assume that gravity actually pushes us around through particles, called gravitons, but attempts to rewrite Einstein’s theory using quantum rules have generally produced nonsense. The rift between the forces runs deep, and a full unification of the two grammars seems remote.

In recent years, however, a baffling translation tool known as the “double copy” has proved surprisingly adept at turning certain gravitational entities, such as gravitons and black holes, into dramatically simpler quantum equivalents.

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“There’s a schism in our picture of the world, and this is bridging that gap,” said Leron Borsten, a physicist at the Dublin Institute for Advanced Studies.

While this unproven mathematical relationship between gravity and the quantum forces has no clear physical interpretation, it’s allowing physicists to pull off nearly impossible gravitational calculations and hints at a common foundation underlying all the forces.

John Joseph Carrasco, a physicist at Northwestern University, said anyone who spends time with the double copy comes away believing “that it’s rooted in a different way of understanding gravity.”

Gravity Versus the Rest

On one side of the fundamental physics divide stand the electromagnetic force, the weak force and the strong force. Each of these forces comes with its own particle carrier (or carriers) and some quality that the particle responds to. Electromagnetism, for instance, uses photons to push around particles that possess charge, while the strong force is conveyed by gluons that act on particles with a property called color.

Physicists can describe any event involving these forces as a sequence of particles scattering off each other. The event might start with two particles approaching each other, and end with two particles flying away. There are, in principle, infinitely many interactions that can happen in between. But theorists have learned how to make frighteningly accurate predictions by prioritizing the simplest, most likely sequences.

On the other side of the divide stands gravity, which rebels against this kind of treatment.

Gravitons react to themselves, generating looping, Escher-like equations. They also proliferate with a promiscuity that would make a bunny blush. When gravitons mingle, any number of them can emerge, complicating the prioritization scheme used for other forces. Just writing down the formulas for simple gravitational affairs is a slog.

But the double copy procedure serves as an apparent back door.

Zvi Bern and Lance Dixon, later joined by Carrasco and Henrik Johansson, developed the procedure in the 2000s, advancing older work in string theory, a candidate quantum theory of gravity. In string theory, O-shaped loops representing gravitons act like pairs of S-shaped strings corresponding to carriers of other forces. The researchers found that the relationship holds for point particles too, not just hypothetical strings.

In the sum of all possible interactions that could happen during a particle scattering event, the mathematical term representing each interaction splits into two parts, much as the number 6 splits into 2 × 3. The first part captures the nature of the force in question; for the strong force, this term relates to the property called color. The second term expresses the movement of particles—the “kinematics.”

To perform the double copy, you throw away the color term and replace it with a copy of the kinematics term, turning 2 × 3 into 3 × 3. If 6 describes the outcome of a strong-force event, then the double copy tells us that 9 will match some comparable graviton event.

The double copy has an Achilles heel: Before executing the procedure, theorists must rewrite the extra kinematics term in a form that looks like the color term. This reformatting is hard and may not always be possible as the sum is refined to include ever more convoluted interactions. But if the kinematics oblige, getting the gravity result is as easy as changing 2 × 3 to 3 × 3.