One of the major issues in general relativity that separates it from other
descriptions of the universe, like quantum physics, is the existence of
singularities . Singularities are points that when mathematically described
give an infinite value and suggest areas of the universe where the laws of
physics would cease to exist — i.e. points at the beginning of the universe
and at the center of black holes.

A new paper in Nuclear Physics B, published by Roberto Casadio, Alexander
Kamenshchik, and IberÃª Kuntz from the Dipartimento di Fisica e Astronomia,
UniversitÃ di Bologna, Italy, suggests that extending the treatment of
singularities in classical physics into quantum physics could help to solve
this disparity between branches of physics.

"No description of nature is perfect and complete. Every theory has its
domain of applicability, beyond which it breaks down and its predictions no
longer make sense," Casadio says. As an example, he cites Newton's theories,
which are still robust enough to send rockets to space, but fall down when
describing the very small, or the tremendously massive.

"This is a serious issue because general relativity — the theory that best
describes the gravitational interaction at present — predicts the existence
of singularities quite generically," Casadio says. "It is like having a hole
in space, where nothing can exist, but into which observers and everything
else will fall nonetheless."

Casadio suggests that this can be envisaged as a piece of paper with a small
hole in it. "You can move the tip of your pen on the paper, which represents
the movement of a particle, but if you reach the hole your pen suddenly
stops drawing and the particles suddenly disappear," he says. "This
illustrates how singularities are theoretical obstacles preventing us from
fully understanding nature."

Casadio adds that the fact that physics ceases to exist at singularities
leads to unanswered questions such as: What really happened at the beginning
of the universe? Was everything born out of a point that never really
existed? What happens to a particle when it falls into the center of a 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:

Roberto Casadio et al, Covariant singularities in quantum field theory and
quantum gravity, Nuclear Physics B (2021).
DOI: 10.1016/j.nuclphysb.2021.115496

Tags:
Physics