Considered one of the largest unsolved challenges in modern physics is bringing together two powerful theories that describe very different parts of reality. Quantum theory explains the behavior of extremely small particles with remarkable precision. Einstein’s general theory of relativity, then again, describes gravity and the motion of planets, stars, and galaxies. Yet despite their success, these two frameworks still don’t fully align.
Physicists have proposed several possible ways to merge them right into a single theory. Ideas equivalent to string theory, loop quantum gravity, canonical quantum gravity, and asymptotically protected gravity all try to bridge the gap. Each approach has benefits and limitations. What researchers have lacked to this point is a transparent observable effect that experiments could measure to find out which theory best reflects how nature actually works. A brand new study from TU Wien may represent a step toward solving that problem.
Trying to find the “Slipper” of Quantum Gravity
“It is a bit just like the Cinderella fairy tale,” says Benjamin Koch from the Institute for Theoretical Physics at TU Wien. “There are several candidates, but only one among them might be the princess we’re on the lookout for. Only when the prince finds the slipper can he discover the actual Cinderella. In quantum gravity, we’ve unfortunately not yet found such a slipper — an observable that clearly tells us which theory is the correct one.”
To discover the correct “shoe size,” meaning a measurable approach to test different theories, the researchers focused on a central concept in relativity called geodesics. “Practically every little thing we learn about general relativity relies on the interpretation of geodesics,” explains Benjamin Koch.
A geodesic describes the shortest path between two points. On a flat surface, that path is solely a straight line. On curved surfaces, the situation becomes more complicated. As an example, traveling from the North Pole to the South Pole along Earth’s surface follows a semicircle, which represents the shortest possible route on a sphere.
Einstein’s theory connects space and time right into a single 4 dimensional structure called spacetime. Massive objects equivalent to stars and planets curve this spacetime. In accordance with general relativity, the Earth circles the Sun since the Sun’s mass bends spacetime and shapes the trail the Earth follows into an orbit.
Making a Quantum Version of Spacetime Paths
The precise shape of those paths relies on something called the metric, which measures how strongly spacetime is curved. “We will now attempt to apply the foundations of quantum physics to this metric,” says Benjamin Koch. “In quantum physics, particles have neither a precisely defined position nor a precisely defined momentum. As an alternative, each are described by probability distributions. The more precisely one among them, the more fuzzy and unsure the opposite becomes.”
Quantum theory replaces precise particle properties with mathematical objects often known as wave functions. In the same way, physicists can attempt to interchange the classical metric of relativity with a quantum version. If this happens, spacetime curvature is not any longer perfectly defined at every point. As an alternative, it becomes subject to quantum uncertainty.
This concept creates extremely difficult mathematical problems.
Benjamin Koch, working along with his PhD student Ali Riahinia and Angel Rincón (Czech Republic), managed to quantize the metric using a brand new method for a selected but vital case: a spherically symmetric gravitational field that continues to be constant over time.
Such a model can describe systems just like the gravitational field of the Sun. The researchers then calculated how a small object would move on this field when the metric itself is treated as a quantum quantity.
“Next, we desired to calculate how a small object behaves on this gravitational field — but using the quantum version of this metric,” says Koch. “In doing so, we realized that one needs to be very careful — for example, whether one is allowed to interchange the metric operator by its expectation value, a type of quantum average of the spacetime curvature. We were capable of answer this query mathematically.”
The team derived a brand new equation called the q-desic equation, named in reference to classical geodesics. “This equation shows that in a quantum spacetime, particles don’t all the time move exactly along the shortest path between two points, because the classical geodesic equation would predict.” By examining how freely moving objects travel through spacetime (equivalent to an apple falling toward Earth in outer space), scientists could potentially detect quantum features of spacetime itself.
Tiny Differences and Cosmic Scale Effects
How different are these quantum paths from those predicted by classical relativity? If researchers consider only peculiar gravity, the difference is incredibly small. “On this case, we find yourself with deviations of only about 10-35 meters — far too small to ever be observed in any experiment,” says Benjamin Koch.
Nonetheless, Einstein’s equations also include one other factor often known as the cosmological constant, often related to “dark energy.” This component is chargeable for the accelerating expansion of the universe on the biggest scales. When the researchers incorporated the cosmological constant into their q-desic equation, the outcomes modified dramatically.
“And after we did that, we were in for a surprise,” reports Benjamin Koch. “The q-desics now differ significantly from the geodesics one would obtain in the same old way without quantum physics.”
The expected deviations appear each at extremely small distances and at very large cosmic scales. The small scale differences are likely unimaginable to measure. But at distances around 1021 meters, the consequences could change into substantial.
“In between, for instance in relation to the Earth’s orbit across the Sun, there may be practically no difference. But on very large cosmological scales — precisely where major puzzles of general relativity remain unsolved — there may be a transparent difference between the particle trajectories predicted by the q-desic equation and people obtained from unquantized general relativity,” says Benjamin Koch.
A Potential Method to Test Quantum Gravity
The research, published within the journal Physical Review D, introduces a brand new mathematical framework for connecting quantum theory and gravity. More importantly, it might offer a path toward comparing theoretical predictions with real observations.
“At first I might not have expected quantum corrections on large scales to provide such dramatic changes,” says Benjamin Koch. “We now need to research this in additional detail, in fact, however it gives us hope that by further developing this approach we are able to gain a brand new, and observationally well testable, insight into vital cosmic phenomena — equivalent to the still unsolved puzzle of the rotation speeds of spiral galaxies.”
Returning to the Cinderella analogy, physicists may finally have identified a measurable clue that can assist distinguish between competing theories of quantum gravity. The slipper could have been found. The subsequent step is determining which theory it truly suits.