The quantum nature of gravity is an enigma that has eluded even the brightest of physicists for many decades.
How can Einstein's theory of gravity be unified with quantum mechanics?
It is a challenge that could give us deep insights into phenomena like black holes and the universe's birth.
Now, the mathematical discovery could shed light on quantum gravity.
A new article recently published in Nature Communications,
written by researchers from Chalmers University of Technology, Sweden, and MIT, U.S.,
presents results that cast new light on essential challenges in understanding quantum gravity.
A grand challenge in modern theoretical physics is to find a "unified theory"
that can describe all the laws of nature within a single framework by connecting Einstein's general theory of relativity.
It represents the universe on a large scale, and quantum mechanics describes our world at the atomic level.
Such a theory of "quantum gravity" would include a macroscopic and microscopic description of nature.
Scientists strive to understand the laws of nature and the language in which these are written in mathematics.
When we seek answers to questions in physics, we are often led to new discoveries in mathematics.
This interaction is particularly prominent in the search for quantum gravity
—where it is challenging to perform experiments.
An example of a phenomenon that requires this type of unified description is black holes.
A black hole forms when a sufficiently heavy star expands and collapses under its own gravitational force
so that all its mass is concentrated in a minimal volume.
The quantum mechanical description of black holes is still in its infancy but involves spectacularly advanced mathematics.
The challenge is to describe how gravity arises as an "emergent" phenomenon.
Just as everyday phenomena, such as the flow of a liquid, emerge from the chaotic movements of individual droplets.
Scientists want to describe how gravity emerges from the quantum mechanical system at the microscopic level.
In the study, researchers showed how gravity emerges from a particular quantum mechanical system
in a simplified model for quantum gravity called the holographic principle.
Using techniques from the mathematics that have been researched before, the study managed to formulate
an explanation for how gravity emerges by the holographic principle, in a more precise way than has previously been done.
A central problem in any quantum theory of gravity is to explain the emergence of the classical spacetime geometry
in some limit of a more fundamental, microscopic description of nature.
The gauge/gravity-correspondence provides a framework in which this problem can, in principle, be addressed.
This holographic correspondence relates a supergravity theory in five-dimensional Anti-deSitter space
to a strongly coupled superconformal gauge theory on its 4-dimensional flat Minkowski boundary.
In particular, the classical geometry should therefore emerge from some quantum state of the dual gauge theory.
In the research, mathematicians confirm this by showing
how the classical metric emerges from a canonical state in the dual gauge theory.
In particular, the study obtains approximations to the Sasaki-Einstein metric underlying the supergravity geometry
in terms of an explicit integral formula involving the canonical quantum state in question.
The study shows that the results can be computationally simplified
through tropicalization in the particular case of toric quiver gauge theories.
This new study may also offer unique insight into mysterious dark energy.
In Einstein's general theory of relativity, gravity is described as a geometric phenomenon.
Just as a newly made bed curves under a person's weight, heavy objects can bend the geometric shape of the universe.
But according to Einstein's theory, even the empty space—the "vacuum state" of the universe—has a rich geometric structure.
If you could zoom in and look at this vacuum on a microscopic level,
you would see quantum mechanical fluctuations or ripples.
This new work may lead to new insights into how and why these microscopic quantum mechanical ripples arise,
as well as the relationship between Einstein's theory of gravity and quantum mechanics, something that has eluded scientists for decades.
These results open up the possibility to test other aspects of the holographic principle
such as the microscopic description of black holes.
We also hope to use these new connections in the future to break new ground in mathematics.