Albert Einstein was the first to speak of gravity in terms of the curvature of spacetime when formulating his theory of general relativity. Most theorists assume that gravity also operates through particles called gravitons, but attempts to rewrite Einstein's theory using quantum rules have generally led to nonsense. The division between the forces is profound, and the possibility of completely unifying the two grammars seems remote.

"There is a gap in our image of the world, and this is closing it," says Leron Borsten, a physicist at the Institute for Advanced Study in Dublin.

Although this mathematical relationship between gravity and quantum forces is not proven or has a clear physical interpretation, it allows physicists to perform almost impossible gravitational calculations and suggests the existence of a common base underlying all the forces.

On one side of the dividing line in fundamental physics are the strong, weak and electromagnetic forces. Each of them has its own mediator particle (or several of them) and some property to which that particle is sensitive. Electromagnetism, for example, uses photons to shake electrically charged particles, while the strong interaction is transmitted by gluons that act on those particles that have a property called color.

Physicists can describe any process in which these forces intervene from a series of particles that are dispersed among themselves. For example, the process can start with two particles moving closer and end with two particles moving away. In between, in principle, infinite interactions can occur, but theorists have figured out how to make extremely accurate predictions by prioritizing the simplest and most probable sequences.

On the other side of the dividing line is gravity, which does not lend itself to this kind of treatment.

The gravitons interact with each other, and that generates loops of equations with a complexity typical of Escher's works. They also proliferate with a promiscuity that would make a rabbit blush. When gravitons mix, any number of them can emerge, complicating the prioritization scheme used with the other forces. Just writing the formulas for a simple gravitational process is hard work.

Zvi Bern and Lance Dixon, later joined by Carrasco and Henrik Johansson, developed the procedure in the 2000s, building on some earlier work in string theory, a possible quantum theory of gravity. In string theory, O-shaped loops representing gravitons act as pairs of S-shaped strings, which correspond to mediators of other forces. And the researchers found that the relationship also holds for point particles, not just hypothetical strings.

In the sum of all the possible interactions that can occur during a particle scattering process, the mathematical term that describes each interaction is divided into two parts, in the same way that the number 6 is divided into 2 × 3. The first part reflects the nature of the force in question; in the case of the strong interaction, that term is related to the property called color. The second term expresses the motion of the particles, that is, the "kinematics."

The idea of the double copy is to discard the color term and replace it with a copy of the kinematic term, thus converting 2 × 3 into 3 × 3. If 6 describes the result of an event mediated by the strong interaction, then the method of the double copy tells us that 9 will correspond to some event comparable to gravitons.

The double copy has an Achilles heel: before carrying out the procedure, theorists must rewrite the additional kinematic term so that it resembles the color term. That rephrasing is difficult and may not always be feasible, as the sum is refined to include increasingly intricate interactions. But if the kinematics helps, getting the gravitational result is as easy as going from 2 × 3 to 3 × 3.

The procedure does not make much physical sense, since, strictly speaking, gravitons are not pairs of gluons. However, it is a powerful mathematical shortcut. Since he developed the double copy method, Bern has taken advantage of the savings

The procedure does not make much physical sense, since, strictly speaking, gravitons are not pairs of gluons. However, it is a powerful mathematical shortcut. Since he developed the double copy method, Bern has taken advantage of his savings to challenge the widely held view that all particle theories of gravity produce absurd and infinite answers.

Supergravity, which balances the gravitons by adding new "companion" particles in a mathematically appropriate way. Using double copying, they have made increasingly precise calculations within the framework of that theory.

Although supergravity is too symmetrical to reflect our world, its simplicity makes it the lowest apple in the tree of possible particle theories of gravity. Bern and his collaborators hope to translate their computational successes into more realistic theories.

As is well known, black holes bend spacetime to the extreme of catching light, and spinning holes carry warped spacetime with them. The equations are tremendously complicated, so much so that if one looks at the equations of a rotating black hole

The researchers divided the spacetime warped by the black hole into two parts: the flat spacetime and a term that represented a strong deviation from flatness.

And it turns out that it is. Both static and spinning black holes act like double copies of charged particles,

Black holes are not literally two copies of electrons. But that mathematical relationship is reducing the total dominance that Einstein's theory of relativity exercises in the gravitational realm.

Recently, experts in the double copy procedure have begun to address gravitational wave astronomy, the new discipline that detects distant objects and events from the waves they generate in spacetime.

The double copy has revealed a hidden and simpler side of gravity, but even theorists who have dedicated their careers to exploring that relationship wonder what the origin of simplicity is.

The researchers note that electromagnetism, the weak and the strong force are derived directly from a specific type of symmetry (a transformation that leaves everything the same, such as turning a square 90 degrees).

Interestingly, when rewriting it using the double copy, gravity seems to obey a symmetry similar to that of the other three forces.

The road to a complete theory of quantum gravity is long and uncertain, and the double copy may not get us there. But his ability to find a shortcut between calculative verbiage gives theorists hope that the two seemingly incompatible formulations of modern physics are not the last word.

/ Photo by Samuel Velazco / Quanta Magazine.org /

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