A quantum approach to a singularity problem

 

A new quantum approach to the problem of singularities could answer the question of what happens at the center of a black hole like this one found in the galaxy M87. Credit: Event Horizon Telescope collaboration et al.

The existence of singularities is one of the major concerns in general relativity that distinguishes it from other universe descriptions, such as quantum physics. Singularities are points in the universe that, when mathematically represented, have an infinite value and suggest areas where the laws of physics would cease to apply — for example, the beginning of the universe and the centre of black holes.

A new paper published in Nuclear Physics B by Roberto Casadio, Alexander Kamenshchik, and Iberê Kuntz of the University of Bologna's Department of Space & Astronomy suggests that extending the treatment of singularities in classical physics to quantum physics could help to bridge the gap between the two branches of physics.

"There is no such thing as a flawless and full depiction of nature. Every theory has a range of application beyond which it fails and its predictions become illogical "Casadio explains. He uses Newton's ideas as an example, which are still reliable enough to launch rockets into space, but fall short when describing the extremely small or extremely enormous.

"This is a big concern," Casadio says, "since general relativity — the theory that now best captures gravitational interaction — predicts the development of singularities rather generally." "It's like having a hole in space where nothing can exist except spectators and everything else will fall through nonetheless."

This, according to Casadio, can be visualised as a piece of paper with a small hole in it. "You can move the tip of your pen on the paper to simulate the movement of a particle," he continues, "but when you get to the hole, your pen stops drawing and the particles vanish." "This demonstrates how singularities are theoretical roadblocks to completely comprehending nature."

The fact that physics ceases to exist at singularities, according to Casadio, leads to unsolved problems like: What happened at the beginning of the universe? Was it all based on a point that never truly existed? When a particle goes into the centre of a black hole, what happens to it?

"We are prompted by our desire to follow this path of inquiry because of these outstanding questions," he explains. "Quantum field theory (QFT), the framework that blends quantum mechanics and special relativity and gives rise to the very successful standard model of particle physics, is widely used in our approach."

The authors built a mathematical object that can detect the presence of singularities in experimentally quantifiable variables using QFT methods. This item, dubbed the "functional winding number," is non-zero in the presence of singularities and disappears in the absence of singularities.

This method has proven that many theoretically anticipated singularities have no effect on quantities that can be tested experimentally, and thus are harmless mathematical constructions.

"If our formalism holds up to scientific scrutiny and proves to be the correct approach, it would imply the presence of a very deep physical principle, therefore physical variable choices are mostly irrelevant," Casadio adds. "This could have far-reaching implications for our understanding of physics, even beyond singularities."