Mathematical discovery may shed light on the mysteries of the universe

(ORDO NEWS) — How to combine Einstein’s theory of gravity with quantum mechanics? This task can give us a deep understanding of phenomena such as black holes and the birth of the universe.

A new paper in the journal Nature Communications, written by researchers at Chalmers University of Technology (Sweden) and the Massachusetts Institute of Technology (USA), presents results that shed new light on important problems in understanding quantum gravity.

The grandiose task of modern theoretical physics is the search for a “unified theory” that could describe all the laws of nature in a single framework – to combine Einstein’s general theory of relativity, which describes the Universe on a large scale, and quantum mechanics, which describes our world at the atomic level.

Such a theory of “quantum gravity” would include both macroscopic and microscopic descriptions of nature.

“We strive to understand the laws of nature, and the language in which they are written is mathematics. When we look for answers to questions in physics, we are often led to new discoveries in mathematics.

This interaction is especially noticeable in the search for quantum gravity – where it is extremely difficult to conduct experiments,” explains Daniel Persson, professor in the Department of Mathematical Sciences at Chalmers University of Technology.

An example of a phenomenon requiring this kind of unified description is black holes. A black hole is formed when a sufficiently heavy star expands and collapses under its own gravitational force, so that all of its mass is concentrated in an extremely small volume.

he quantum mechanical description of black holes is still in its infancy, but includes some impressive advanced mathematics.

Simplified model of quantum gravity

“The challenge is to describe how gravity arises as an ’emergent’ phenomenon. Just as everyday phenomena – such as the flow of a liquid – arise from the chaotic movement of individual drops, we want to describe how gravity arises from a quantum mechanical system on microscopic level,” says Robert Berman, professor of mathematics at Chalmers University of Technology.

In a paper recently published in the journal Nature Communications, Daniel Persson and Robert Berman, along with Tristan Collins of the Massachusetts Institute of Technology in the US, showed how gravity emerges from a particular quantum mechanical system, in a simplified model of quantum gravity called the “holographic principle.”

“Using methods from mathematics that I have explored previously, we have been able to formulate an explanation of how gravity occurs using the holographic principle in a more precise way than has been done before,” explains Robert Berman.

Dark energy fluctuations

The new paper could also provide new insights into the mysterious dark energy. Einstein’s general theory of relativity describes gravity as a geometric phenomenon. Just as a freshly made bed sags under the weight of a person, heavy objects can bend 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 you could zoom in and look at this vacuum at a microscopic level, you would see quantum mechanical fluctuations or ripples known as dark energy.

It is this mysterious form of energy that, from a broader perspective, is responsible for the accelerated expansion of the universe.

This new work could lead to new insights into how and why these microscopic quantum mechanical pulsations occur, as well as relationships between Einstein’s theory of gravity and quantum mechanics that have eluded scientists for decades.

“These results open up the possibility of testing other aspects of the holographic principle, such as the microscopic description of black holes. We also hope that in the future we will be able to use these new connections to make new discoveries in mathematics,” says Daniel Persson.

The scientific article “Emergent Sasaki-Einstein Geometry and AdS/CFT” was published in the journal Nature Communications and was written by Robert Berman, Tristan Collins and Daniel Persson from Chalmers University of Technology, Sweden, and Massachusetts Institute of Technology, USA.


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