Where quantum theory and the theory of relativity meet

Physics has a problem—their key models of quantum theory and the theory of relativity do not fit together. Now, Dr. Wolfgang Wieland from Friedrich-Alexander-Universität Erlangen-Nürnberg (FAU) is developing an approach that reconciles the two theories in a problematic area. A recently published paper that was published in Classical and Quantum Gravity gives hope that this could work.

There are four fundamental forces in the universe: gravity, electromagnetism, the weak and the strong interaction. While general relativity describes gravity, quantum theory deals with the other three forces. This creates a problem: “As early as the 1930s, it was recognized that the two theories do not fit together,” explains Dr. Wieland, who leads a Heisenberg project on this topic at the Chair of Quantum Gravity at FAU.

Usually, this has no major consequences: general relativity is mainly used to calculate the behavior of large masses in the universe. Quantum theory, on the other hand, focuses on the world of the very smallest things. However, to better understand key phenomena such as the Big Bang or black holes, a model is needed that unites both concepts—quantum gravity. General relativity states that all matter in a black hole is united at one tiny point. It is therefore important to understand how gigantic gravitational forces act in the microcosm, although this is where the laws of quantum mechanics actually apply.

Concepts of cause and effect do not apply in black holes

The theory of quantum gravity could turn our concept of causality under extreme conditions on its head: “Time determines the relationship between cause and effect—causes lie in the past, effects in the future,” explains Wieland. “This assumption is firmly embedded in quantum mechanics. However, general relativity predicts that large masses bend spacetime due to their gravity. In a black hole, this effect is so extreme that the terms ‘before’ and ‘after’ have no meaning. This has enormous implications for our understanding of cause and effect.”

For decades, research has been trying to find a theory of quantum gravity that allows statements to be made under such extreme conditions. One problem is that in quantum theory, energy is divided into the smallest possible packages, the quanta. Observables such as energy or angular momentum can only take discrete values, not continuous ones. This also affects the electromagnetic, weak, and strong interactions, they are also “quantized.”

Gravity cannot be simply broken down into quanta, but since it arises from the curvature of spacetime according to the theory of relativity, a detour could be possible. “Our approach is that space and time themselves are not continuous but consist of small portions,” explains Wieland. “If this thesis is correct, then gravity can also be described with the help of quantum theory.”

Is spacetime granular?

In a quantized spacetime, we cannot move a cup by any arbitrary distance, only by fixed steps. Likewise, there is no clock that divides the passage of time into arbitrarily fine intervals—it progresses in steps, like the second hand of an analog clock. In the macroscopic world, these steps are not observed because they are extremely small.

An important role in this concept of quantized spacetime is played by the Planck units coined by Max Planck. These are a fundamental system of units that can be constructed solely from the speed of light and the natural constants of gravity and quantum theory. Another constant, the Planck power, can be calculated from the Planck units. Wieland’s current publication focuses on the Planck power.

“Our current understanding is that power—that is, the amount of energy that can be emitted per unit of time—can become infinitely large in our universe,” he explains. “This leads to some of the partial equations in a quantum theoretical description of gravity becoming unsolvable.”

In the study, Wieland shows that in a quantized spacetime, there is an upper limit for power. This limit, which, like the speed of light, cannot be exceeded, is the aforementioned Planck power. It is unimaginably large at 10⁵³ watts—but still limited.

“If my theoretical considerations prove true, it will be possible to break down the power of gravitational waves into the smallest quanta,” explains Wieland. In his Heisenberg project, he will not only address this problem but also the question of how gravity influences the causal structure of the world.