Has Loop Quantum Gravity Been Disproven by Recent Observations of Gamma-Ray Bursts?

Recently, there has been a buzz among academic YouTubers in the West about whether "Loop Quantum Gravity (LQG)," one of the candidates for a theory of quantum gravity, has been disproven by observations of gamma-ray bursts.

The background to this commotion stems from a previous discussion by Lee Smolin, an expert in LQG theory, regarding the observational testability of the theory.

LQG theory has various possibilities, and in one version, Lorentz symmetry is slightly broken. Smolin argued that by observing light from distant celestial bodies, it would be possible to confirm whether relativistic Lorentz symmetry is broken. In other words, he claimed that LQG is a scientific theory that is falsifiable.

Specifically, if LQG theory breaks Lorentz symmetry, it is predicted that light with high frequencies would travel slightly slower. However, the magnitude of this effect is extremely small, making it almost impossible to detect in standard particle accelerator experiments. Yet, as light emitted from distant celestial phenomena like gamma-ray bursts travels over cosmic distances, this minute effect could accumulate, potentially becoming a signal of observable magnitude by the time it reaches Earth.

Recently, a verification of Lorentz symmetry breaking, including the LQG theory proposed by Smolin, was conducted. The results are documented in the paper below by the LHAASO group.

This paper claims that no Lorentz symmetry breaking was observed. This result became a major topic, and YouTube programs titled "LQG, the rival of string theory, is dead!" were created, attracting public interest.

However, Carlo Rovelli, another prominent expert in LQG theory, points out that there is a misunderstanding here. He emphasizes in the program below that even after the recent gamma-ray burst observation results, LQG theory itself has not been disproven and remains a valid theory.

According to Rovelli, there are various approaches and different ways of thinking within LQG theory, and the consensus in the field is that the Lorentz symmetry breaking proposed by Smolin does not actually occur. In this article, I would like to introduce a simple part of that logic.

First, LQG theory is a different theory from string theory. In this theory, spacetime is not continuous from the beginning, but is described as a network-like structure of vertices and links connecting them. This is called a "spin network." This structure is discrete, and its typical scale is considered to be around the "Planck length," which is approximately 10 to the power of minus 35 meters.

LQG theory is, so to speak, an extension of lattice field theory used in numerical calculations, attempting to capture quantum spacetime.

For example, let's simplify the space of LQG theory for intuitive explanation and depict it as a quantum object with a discrete lattice structure at the micro scale, as shown in Figure 1. Each circle drawn in this figure represents an "atom of spacetime," and we consider these to be connected to form spacetime.

This discrete spacetime with a lattice spacing of about the Planck length also behaves as a continuous spacetime in regions where the wavelength is much longer than the lattice spacing. This is the same as how water behaves as a continuous fluid when viewed on a large scale, despite being made up of individual water molecules.

When calculating the propagation speed of light in a discrete spacetime like Figure 1, the speed of low-frequency light (light with long wavelengths) almost matches the speed of light c in classical relativity. However, it is known that the speed of high-frequency light (light with short wavelengths) becomes slightly slower than c. For example, blue light would be slightly delayed compared to red light. This speed difference is extremely small, but for light from distant celestial bodies, the effect should accumulate during the long-distance travel, resulting in an observable difference when it reaches Earth.

The target of this observation was light from a gamma-ray burst named "GRB221009A." As a result, it was confirmed that the light reached Earth simultaneously, regardless of frequency, which disproved Smolin's prediction.

There is no doubt that this result is very important. This is because, even if it was disproven, the fact that a certain type of quantum gravity theory was verified through observation is an achievement that overturns some criticisms that "quantum gravity is untestable and not science."

So, has the entire LQG theory been disproven by this observation result? According to Rovelli's argument, only one of Smolin's models was disproven. Rovelli's view is that standard LQG theory maintains Lorentz symmetry and is not inconsistent with these observation results.

Rovelli first cites the example of the spin angular momentum of an electron. Its value is discrete, but the continuous rotational symmetry of its dynamics is preserved. Using this example, he emphasizes that even if physical quantities are discrete, it does not deny continuous symmetry. He argues that the same applies to Lorentz symmetry.

In a discrete lattice structure like Figure 1, spatial continuous translational symmetry other than lattice-dependent discrete transformations is broken. Similarly, Lorentz symmetry would also be broken. However, in quantum mechanics, linear superposition of states is possible. By preparing states of the lattice shifted little by little as shown in Figure 2 and linearly superimposing them, continuous translational symmetry is restored.

Furthermore, according to Rovelli, Lorentz symmetry is restored in LQG theory as well, through the mechanism of state superposition. Therefore, he argues that the standard LQG theory remains unaffected and intact in light of the recent gamma-ray burst observation results.

On the other hand, Sabine Hossenfelder, an academic YouTuber known for her book "Lost in Math: How Beauty Leads Physics Astray," disagrees with Rovelli's opinion. She pointed out that the concept of "minimum area," a characteristic feature of LQG theory, contradicts Lorentz symmetry.

In Hossenfelder's view, LQG theory posits that there is a minimum unit called the "Planck area" for areas such as the event horizon of a black hole. However, Hossenfelder criticizes this, arguing that if Lorentz symmetry exists, such a minimum unit of area cannot exist. This is because, under Lorentz symmetry, the measured value of an area can contract continuously and indefinitely depending on the observer's state of motion, making it impossible to define a fixed minimum unit.

For this reason, Hossenfelder argues that LQG theory, which assumes a minimum area, cannot maintain Lorentz symmetry, and that LQG theory has been disproven by the recent gamma-ray burst observation results.

However, Rovelli counters that Hossenfelder misunderstands LQG theory. It is true that LQG theory is characterized by the quantization of area through the Planck area. This theory includes the concept of an "area operator," and its eigenvalues are given by the following formula.

Here, the quantum number j takes non-negative integer values or positive odd half-integer values.

What Rovelli emphasizes in particular is the case where j=0. In this case, the eigenvalue of the area operator becomes zero. In other words, in LQG theory, it is possible for the area to be zero. He states that the minimum area at the event horizon of a black hole should be interpreted as a quantum mechanical expectation value.

Therefore, if the non-vanishing values of the state vector coefficients are concentrated at j=0, the expectation value can become arbitrarily small.

Thus, it is permitted in LQG theory to Lorentz-transform a black hole as shown in Figures 4 and 5, and to continuously contract its area.

In this way, Rovelli argues that Hossenfelder's criticism of LQG theory is off the mark because she does not correctly understand the fundamental structure of the theory.

In conclusion, while some LQG theory models by Smolin were disproven by the observation results using gamma-ray bursts by the LHAASO group, the standard LQG theory that possesses Lorentz symmetry remains valid and survives. Similarly, string theory, which preserves Lorentz symmetry, was not particularly restricted by these observations.