Scientists explore gravitational waves and the geometry of spacetime

When discussing our universe, it’s often said that “matter tells spacetime how to curve, and curved spacetime tells matter how to move.”

This idea comes from Albert Einstein’s famous general theory of relativity.

It explains how planets, stars, and galaxies move and influence the space around them.

While general relativity works well for big objects, it doesn’t fit with the rules of quantum mechanics, which describe very small particles.

For his Ph.D. research, Sjors Heefer studied gravity and its effects on our universe. His work is important for understanding gravitational waves and might help connect the big and small aspects of physics in the future.

Over a hundred years ago, Einstein changed our understanding of gravity with his theory of general relativity. “According to Einstein, gravity is not a force but comes from the shape of spacetime,” says Heefer.

“This idea helps explain phenomena like gravitational waves.”

Massive objects like the sun or galaxies bend spacetime around them. Other objects then move along the curved paths in this warped spacetime.

For example, planets in our solar system follow elliptical orbits around the sun because of this curvature.

General relativity explains many gravitational phenomena, from everyday situations to black holes and the Big Bang. It’s a cornerstone of modern physics.

However, general relativity clashes with quantum mechanics, which describes how small particles like electrons behave. “Quantum mechanics says particles can exist in multiple states at once until they are observed,” Heefer explains.

“When observed, they randomly choose a state, a process known as the ‘collapse of the wave function.'”

In quantum mechanics, a wave function describes the position and state of a particle. The square of the wave function gives the probabilities of where the particle might be found.

“All matter in our universe follows quantum mechanics’ probabilistic laws, except for gravity,” Heefer notes. “This mismatch creates philosophical and mathematical problems that are a big challenge in physics today.”

One way to solve this problem is to expand the mathematical framework of general relativity. General relativity uses pseudo-Riemannian geometry to describe spacetime.

However, recent discoveries suggest our universe’s spacetime might need a more advanced mathematical language called Finsler geometry.

To explore Finsler gravity, Heefer analyzed a field equation by Christian Pfeifer and Mattias N. R. Wohlfarth. Physicists describe nature using fields, which have values at each point in space and time.

For example, temperature is a field that has a value everywhere. The gravitational field describes spacetime’s geometry, telling us the curvature at each point, which we experience as gravity.

Heefer studied the vacuum field equation, which describes spacetime geometry in empty space. By analyzing this equation, he identified new types of spacetime geometries.

One exciting discovery involves spacetime geometries that represent gravitational waves—ripples in spacetime caused by events like neutron star or black hole collisions.

The first detection of gravitational waves in 2015 marked a new era in astronomy. Heefer’s research suggests these waves are consistent with Finsler geometry.

While Heefer’s results are promising, they are just the beginning. “The field is still young, and further research is ongoing,” Heefer says. “I’m optimistic that our work will deepen our understanding of gravity and might help reconcile it with quantum mechanics in the future.”