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The approach of quantum physics to the problem of singularity

One of the main problems of general relativity, which separates it from other descriptions of the universe, such as quantum physics, is the existence of singularities. Singularities are points that in mathematical description give infinite value and suggest areas of the universe where the laws of physics cease to exist – that is, points at the beginning of the universe and at the center of black holes.

New paper in Nuclear Physics Inpublished by Roberto Casadio, Alexander Kamenschik and Ibre Kunz of the Dipartimento di Fisica e Astronomia, Università di Bologna, Italy, suggests that extending the consideration of singularities in classical physics to quantum physics may help resolve this discrepancy between branches of physics.

“No description of nature is perfect and complete. Each theory has its own field of application, beyond which it fails, and its predictions no longer make sense, ”says Casadio. As an example, he cites Newton’s theories, which are still strong enough to send rockets into space, but fall down when describing very small or extremely massive.

The first image is a black hole

A new quantum approach to the problem of singularities may answer the question of what happens in the center of a black hole similar to that found in the galaxy M87. Credit: EHT

“This is a serious problem because the general theory of relativity – the theory that best describes gravitational interactions today – predicts the existence of singularities quite generally,” says Casadio. but which, nevertheless, includes observers and everything else. “

Casadio suggests that this can be represented as a piece of paper with a small hole. “You can move the tip of the pen on paper that reflects the movement of the particles, but when you reach the hole, your pen will suddenly stop drawing and the particles will suddenly disappear,” he says. “This illustrates how singularities are theoretical barriers that prevent us from fully understanding nature.”

Cassadio adds that the fact that physics ceases to exist in singularities leads to unanswered questions, such as: What really happened at the beginning of the universe? Or was everything born from a point that never existed? What happens to a particle when it hits the center of a[{” attribute=””>black hole?

“These open questions are the very reason we are compelled by our curiosity to pursue this line of investigation,” he says. “Our approach heavily relies on the methods of Quantum field theory (QFT): the framework that combines quantum mechanics and special relativity and gives rise to the very successful standard model of particle physics.”

The authors used the tools of QFT to construct a mathematical object that can signal the presence of singularities in experimentally measurable quantities. This object, which they have named the “functional winding number” is non-zero in the presence of singularities and vanishes in their absence.

This approach has revealed that certain singularities predicted theoretically do not affect quantities that can in principle be measured experimentally, and therefore remain harmless mathematical constructs.

“If our formalism survived scientific scrutiny and turned out to be the correct approach, it would suggest the existence of a very deep physical principle, so the choices of physical variables are rather unimportant,” Casadio concludes. “This could be consequential for our understanding of physics, even beyond the subject of singularities.”

Reference: “Covariant singularities in quantum field theory and quantum gravity” by Roberto Casadio, Alexander Kamenshchik and Iberê Kuntz, 26 July 2021, Nuclear Physics B.
DOI: 10.1016/j.nuclphysb.2021.115496



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