Studying the double-copy nature of gravity

Both quantum mechanics and Einstein’s theory of gravity are needed to improve our understanding of the beginning of the Universe and the microscopic structure of spacetime. But the two theories are in conflict with each other in the research field of particle physics. Henrik Johansson is studying a new aspect of quantum gravity, and is searching for new formulas capable of reconciling the theories.

Henrik Johansson

Associate professor in Particle Physics

Wallenberg Academy Fellow 2013

Uppsala University

Research field:
New mathematical descriptions to unify quantum mechanics and the general theory of relativity.

Henrik points out that social skills and the ability to cooperate are essential for those researching in the field of particle physics.

“You can’t be a lone wolf. I get my best ideas when I talk to other researchers,” he says, greeting some colleagues sitting on a sofa and talking outside his office at the Ångström Laboratory.

Henrik’s research deals with nature’s most fundamental forces. Among other things, he is interested in a complex problem that has frustrated physicists for many years: trying to reconcile Einstein’s general theory of relativity with quantum mechanics. These two successful theories collide, which makes it difficult for scientists to explain the processes involved when the Big Bang created the universe.

“I have always been fascinated by the general theory of relativity, which Einstein formulated to explain gravity. Much remains to be resolved in this field. Part of my project is about understanding gravity on very small length scales – quantum gravity – where the theory of relativity and quantum mechanics are in conflict with each other.”

Collisions of particles

Following his admission as a Wallenberg Academy Fellow, Henrik returned home to Sweden in the fall of 2014 after 11 years abroad. He moved to Uppsala from Geneva in Switzerland, where he had been a postdoc at CERN, the world’s largest particle physics laboratory.

While studying for his PhD at the University of California, Los Angeles (UCLA), Henrik made a discovery that simplifies computations of the probability that particles will collide and interact.

“New formulas of this kind may be of use in calculations needed to interpret experimental data, for example from the particle accelerator at CERN. It is essential to compute these probabilities in order to obtain new information about elementary particles and their properties.”

“Like most physicists, I dream of future achievements that will add to our understanding of the Universe. I see this award as a fantastic opportunity to try to realize that dream. Now I can also achieve my goal of building up a research team striving for international excellence.”

Looking for a finite theory

The general theory of relativity, which will be 100 years old in November 2015, has important applications in astronomy, cosmology, and other fields. It is used, for instance, to predict planetary motions, black holes and the behavior of the universe on large distance scales. But quantum mechanics governs forces and interactions between the very smallest particles, such as atoms, protons, neutrons, and elementary particles like quarks and gluons.

Henrik explains that there are a number of problems that cause this conflict between quantum mechanics and relativity theory. The main one is that attempts to combine the two in mathematical calculations yield infinite answers to otherwise sensible questions.

“If calculations yield the answer infinity, they are unreliable. It is impossible for an experiment to produce infinity as the result. So if a theory yields infinity as the result, this means there is something wrong with the theory, and a new theory must be found that provides a finite answer.”

Everyone in the world of physics dreams of finding a theory capable of combining quantum mechanics with Einstein’s theory of gravity. During 2007 – 2009 Henrik and his colleagues at UCLA performed successful computations of a theory of quantum gravity called “supergravity”. Simply put, it is Einstein’s theory with the addition of extra particles, creating a special kind of symmetry called “supersymmetry”.

“Our calculations did not yield infinity, and other researchers after us who studied the theory using other methods confirmed that this is an unusually well-behaved theory. We are now going on to see whether this is the theory we are looking for.”

New algebra

During the computations needed to analyze the supergravity theory Henrik discovered an interesting structure in the results: a previously unknown duality between the “quantum color” of particles and movement data, or kinematics. He writes a series of formulas on the blackboard to demonstrate.

“This duality means that we can mathematically describe gravitons, the elementary particles that carry the force of gravity, as double copies of gluons – the carriers of strong nuclear force. Since then we have found that all theories of gravity we have examined have this characteristic double-copy nature. This is an important step in understanding the quantum version of Einstein’s theory.”

Although there is strong evidence for the duality between quantum color and kinematics, no complete description exists of the mathematical basis of the phenomenon. But this is what Henrik and his research team are trying to achieve with the help of the Knut and Alice Wallenberg Foundation.

“It is an enormous challenge. We know that the mathematics of this duality should be described by a special Lie algebra, named for the nineteenth century Norwegian mathematician Sophus Lie, and used in all modern physics.”

Henrik has no problem finding motivation, even though individual computation stages in the systematic puzzle he is trying to solve can sometimes take a very long time, and he does not know whether they will find a solution in a month, a year or 10 years.

“No – I am studying fantastic things, so I find no shortage of inspiration.”

Text Susanne Rosén
Translation Maxwell Arding
Photo Magnus Bergström