What if gravity is actually a double copy of other forces?

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

Albert Einstein first spoke of gravity in terms of curves in space-time in his general theory of relativity. Most theorists assume that gravity actually pushes us through particles, called gravitons, but attempts to rewrite Einstein’s theory using quantum rules have generally generated shocks. The fracture between the forces is deep, and a complete unification of the two grammars seems far apart.

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

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

While this unproven mathematical relationship between gravity and quantum forces has no clear physical interpretation, it allows physicists to pull out almost impossible gravitational calculations and hints at a common foundation underlying all forces.

John Joseph Carrasco, a physicist at Northwestern University, said anyone who spends time with double copying comes to believe “that it is rooted in a different way of understanding gravity.”

Gravity Towards Rest

On one side of fundamental physics is divided 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 to which the particle responds. Electromagnetism, for example, uses photons to push around charged particles, while strong force is transmitted by gluons that act on particles with a property called color.

Physicists can describe any event that involves these forces as a sequence of particles spreading out. The event could start with two particles approaching each other, and end with two flying particles. There is, in principle, infinitely much interaction that can occur between mediums. But theorists have learned to do it frighteningly accurate predictions from the priority of the simplest and most probable sequences.

On the other side of the division lies gravity, which rebels against this type of treatment.

Gravitons react by themselves, generating looping, Escher-like equations. They also proliferate with a promiscuity that would make a rabbit blush. When gravity mixes, any number of them can emerge, complicating the priority scheme for other forces. Just writing the formulas for simple gravitational pull is a slog.

But the double copy procedure serves as the 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 rings representing gravitons act as pairs of S-shaped strings corresponding to carriers of other forces. The researchers found that the relationship is also valid for point particles, not just for hypothetical strings.

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

To make the double copy, discard the color term and replace it with a copy of the kinematic term, transforming 2 × 3 into 3 × 3. If 6 describes the result of a strong force event, then the double copy tells us that 9 will correspond to some compared gravitational event.

The double copy has an Achilles heel: Before performing the procedure, theorists must rewrite the kinematic term further into a shape that resembles the color term. This reformulation is hard and perhaps not always possible since the sum is refined to include increasingly complicated interactions. But if the kinematics require it, obtaining the result of gravity is as easy as changing 2 × 3 to 3 × 3.

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