The grand task of modern theoretical physics is to find a “unified theory” that could describe all laws of nature in a unified structure, combining Einstein’s general theory of relativity, describing the universe on a large scale, and quantum mechanics, describing our world at the atomic level. The theory of “quantum gravity” must include both macroscopic and microscopic descriptions of nature.
A black hole is formed when a heavy star expands and collapses under the action of its own gravitational force, so that all its mass is concentrated in an extremely small volume. The quantum mechanical description of black holes is still in its infancy and requires the help of higher mathematics.
“We seek to understand the laws of nature – and the language in which they are written is mathematics. It is in it that we find the answers to the questions we seek in physics. This interaction is particularly prominent in the search for quantum gravity – where it is extremely difficult to do experiments,” explained Daniel Persson, professor in the Department of Mathematical Sciences at Chalmers University of Technology.
“The challenge is to describe, the emergence of gravity as an ’emergent’ phenomenon. Just as everyday phenomena emerge from the chaotic motions of individual droplets, we want to describe how gravity emerges from a quantum mechanical system at a moment in time at the microscopic level,” said Robert Berman, professor in the Department of Mathematical Sciences at Chalmers University of Technology.
Persson and Berman, along with Tristan Collins of the Massachusetts Institute of Technology in the United States, showed how gravity arises from a special quantum mechanical system in a simplified model of quantum gravity called the holographic principle.
“Using methods of mathematics that I researched previously, we were able to formulate an explanation of how gravity arises according to the holographic principle in a more precise way than has been done before,” Berman added.
The scientists’ study offers a new understanding of dark energy. In Einstein’s general theory of relativity, gravity is described as a geometric phenomenon. Just as a newly made bed bends under the weight of a person, heavy objects can warp the geometric shape of the universe. But according to Einstein’s theory, even empty space-the “vacuum state” of the universe-has a rich geometric structure. If we could zoom in and look at this vacuum on a microscopic level, we would see the quantum mechanical fluctuations or pulsations known as dark energy. It is this mysterious form of energy, from a broader perspective, that is responsible for the accelerated expansion of the universe.
“Our results open up the possibility of testing other aspects of the holographic principle — for example, the microscopic description of black holes,” Daniel Persson concluded.
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