A general approach to a quantum theory of gravity has found a surprising relationship between the quantum fields of massive particles.
BY DEBDUTTA PAUL
The study of black holes, now routinely observed and also imaged, is fraught with challenges. The black hole information paradox is one of them, which Stephen Hawking formulated.
Theoretical physicists have proposed various solutions, one of them being the principle of holography of information. It says the information about the black hole’s interior, or ‘bulk’, resides on its boundary. “The wavefunction in the exterior has complete information about the interior,” said Suvrat Raju from ICTS-TIFR. Hawking’s error was to apply the intuition developed from classical physics, developed by Isaac Newton and refined by Albert Einstein, to a quantum process. In classical physics, the region outside a black hole contains no information about its interior except for its total mass, charge, and angular momentum. However, Suvrat and his colleagues have shown that in quantum theory, just the opposite is true: sufficiently precise observations of its exterior can bring out all details about its interior.
The principle applies not only to black holes but to all things around us. For example, Suvrat explained that the same is true for hard disks, which contain information we access via computers.
In principle, then, it would be possible to conduct extremely precise measurements outside the hard disk to figure out its contents. The measurements need to be so precise that it’s practically easier to read the hard disk with the help of a CPU. However, theoretical physics often delves into the in-principle questions because their answers can uncover deep truths about nature. Answers to such questions lie in the mathematics of physical theories.
Quantum Field Theories and Quantum Gravity
Physicists use quantum field theories to explain the physics of fundamental particles. In these theories, quantum fields pervade time and space, and their interactions give rise to the particles making up our universe. The fields’ behaviour explains the particles’ mutual interactions, including collisions and scattering. In this way, quantum field theories describe the blocks building up our universe like a jigsaw puzzle.
Usually, quantum field theories do not include gravitation, which is the weakest interaction in the universe. According to Einstein’s general theory of relativity, a classical theory, gravitation is caused by the bending and buckling of spacetime itself. Instead, in quantum field theories, spacetime acts like a fixed arena on top of which the quantum fields function. So, specifically those quantum field theories that include gravitation are called quantum gravity theories. String theory (according to which all particles are tiny strings) is one such theory.
Physicists had first postulated the principle of holography within string theory. However, we do not know the string theory that describes our world. The recent work on holography of information demonstrates, starting from the basic principles of gravity and quantum mechanics, that a version of holography should hold in all theories of quantum gravity even if we do not know all the details of these theories.
Holography of information
The idea of holography isn’t new. Dennis Gabor first developed the technology of holograms and received the 1971 Nobel Prize for this invention. It uses information stored in the phase of electromagnetic waves to create three-dimensional illusions.
In string theory, holography was originally posited to hold in a universe with a negative cosmological constant. However, our universe is not like that. Since its expansion accelerates, the cosmological constant is positive. But, since its value is very small, physicists take it to be zero, and the resulting spacetime describes our universe accurately. The resulting spacetime is ‘flat’.
In spacetime with negative cosmological constant, the arguments developed by Suvrat and his collaborators reproduce the results from string theory. A few years ago, a group at ICTS-TIFR and their colleague at the Chennai Mathematical Institute formulated the holographic principle in flat spacetime.
However, the group made a simplifying assumption in their argument. They assumed a universe that had gravity and only massless matter. But the real world also contains massive particles. So, a group at ICTS-TIFR has been working to incorporate massive particles in this story.
Scattering, wavefunctions, and probabilities
As a first step, this group developed a new framework to describe massive particles in quantum field theory without gravity. To do this, they studied the scattering of particles against each other, similar to what experiments at CERN can probe.
“In a scattering process, particles come from an early time, interact, and go away to [a] very late time,” explained Priyadarshi, one of the authors of the new study. Physicists call these very far past and future the ‘infinities’. But, the infinities are different for massless and massive particles because massless particles (photons) travel at the speed of light. “If one waits long enough, in the past or the future, then massless particles go infinitely far away,” explained Suvrat.
The collision of massive particles is a mathematical nightmare because of their complex interactions, but a careful analysis can offer meaningful clues. Theoretical physicists need to accurately predict the probability of various scattering processes between these massive particles. “The mathematical description of scattering involves how particles at early time and late time are related to each other,” said Priyadarshi.
Priyadarshi and his collaborators asked whether one could find a different way of understanding the interactions of massive particles. In quantum mechanics, particles are never exactly localised at one point. They are described by wavefunctions, which relate to the probability of finding them. These wavefunctions always persist out to long distances. What if one keeps track of the behaviour of these tails over time? Since these regions are far from where the particles interact, it provides theorists with a neat mathematical way to describe the results of observations an experimentalist could perform on the particles. In mathematical parlance, these observations are said to be performed at “spatial infinity”.
The group at ICTS-TIFR found that it was possible to use observations at spatial infinity to describe the interactions of massive particles.
A particular consequence of these relationships has surprised the team. The observables which describe the massive particles at spatial infinity are the average of the quantum fields very early and late times before and after the scattering.
The path ahead
The next step is to understand how to incorporate gravity into the same mathematical framework. The researchers hope that this framework will eventually connect with gravitational theories, completing the missing element in the story of holography in flat space. “The full program is the holography of flat spacetime: that’s the bigger goal,” said Athira P V, one of the authors of the new study.
To know more, read the following papers by the authors.
- Anupam A. H, P.V. Athira, Priyadarshi Paul and Suvrat Raju: Interacting Fields at Spatial Infinity
- Alok Laddha, Siddharth G. Prabhu, Suvrat Raju and Pushkal Shrivastava: The holographic nature of null infinity
The author thanks Priyadarshi Paul, Athira P V, and Professors Loganayagam R and Suvrat Raju, ICTS-TIFR, and Professor Nirmalya Kajuri, IIT-Mandi, for discussions.