The structure of the cosmos is rooted in symmetry. As first demonstrated by Emmy Noether in 1918, for every physical law of conservation in the Universe, there is a corresponding physical symmetry. For example, all other things being equal, a baseball hit by a bat today will behave exactly the same as it did yesterday. This symmetry of time means that energy is conserved. Empty space is the same everywhere and in all directions. This symmetry of space means that there is conservation of linear and rotational momentum. On and on. This deep connection is now known as Noether’s Theorem, and it is central to all of modern physics.
Where Noether’s Theorem really shows its power is in particle physics. Although the mathematics of particle physics is complex, the underlying symmetries govern what can happen when particles collide. So, conservation of charge means that when a particle collision creates a shower of new particles, the total charge of all the particles must equal the total charge of the particles before the collision. Another basic symmetry is parity, also known as mirror symmetry. If you stand in front of a mirror and raise your right hand, your mirror image will raise its left. If you spin a ball toward your left, the mirror ball will spin to the right. Since elementary particles have an inherent rotation or spin, this means that particle showers should appear in rotational pairs.
One way to test the laws of physics is to see where certain symmetries are broken. In particle physics, an important symmetry is the combination of charge and parity, known as charge-parity, or CP symmetry. CP symmetry is what requires that for every matter particle, there must be a corresponding antimatter particle. For a long time, it was thought that CP symmetry was conserved, which was a problem for cosmologists since our Universe is made almost entirely of matter, not a mix of matter and antimatter. But in the last half of the 20th century, we found examples of CP violations, which led to a revolution in our understanding of the standard model of particle physics.
Although it isn’t mentioned as much, the same symmetries apply to general relativity. In fact, Einstein’s equations can be derived by applying the physical symmetries seen in Newtonian physics while dropping the requirement that space be Euclidean. Technically, the principle of equivalence Einstein used to derive relativity is a consequence of symmetries, not the other way around. So what if we used these symmetries to test relativity the way we do in particle physics? One way to do this would be to look at the mergers of black holes, which is the point of a recent study in Physical Review Letters.
In this work, the team looked at the gravitational waves generated by the mergers of stellar black holes. Specifically, they focused on the polarization of the gravitational waves. Since gravitational wave polarization is connected to the rotation of the merging black holes, this allowed the team to test parity conservation. Under the standard model of general relativity, parity should be conserved, and this is precisely what the team found. To the limits of observation, black holes don’t violate parity. That said, we should note that the observational limit is pretty weak. We simply haven’t observed enough mergers to conclusively prove black holes obey parity, though we expect that they do.
The team also looked at the recoil effect of black holes in a second paper. When two black holes merge, the resulting black hole can get a gravitational kick that sends it flying off from its point of origin. If spatial symmetry holds, then the recoil of black holes shouldn’t show any bias, such as having more of them speed away from us than toward us. Again, the team saw no violation of symmetry, in agreement with general relativity.
Neither of these results are strong enough to be conclusive, and since both results are what we expect, there’s nothing surprising in this work. But studies such as this are worth doing as we continue to gather data. We know that somehow general relativity and quantum theory must combine into a general theory of quantum gravity, and we know that quantum theory violates some of the symmetries of general relativity. A big question is whether quantum gravity violates any symmetry as well. In time, studies such as these could give us the answer.
Reference: Calderón Bustillo, Juan, et al. “Testing mirror symmetry in the Universe with LIGO-Virgo black-hole mergers.” Physical Review Letters 134.3 (2025): 031402.
Reference: Leong, Samson HW, et al. “Gravitational-wave signatures of mirror (a) symmetry in binary black hole mergers: measurability and correlation to gravitational-wave recoil.” arXiv preprint arXiv:2501.11663 (2025).