On the Symmetry of Objects

Author: Himangshu Kar

Collected from: Facebook post

The concept of symmetry in physics is extremely important. In fact, it’s so crucial that without the idea of symmetry, it’s impossible to understand why a universe like ours would exist at all. But the interesting thing is, you don’t need to know complex equations to grasp the idea of symmetry. If an object keeps a certain property unchanged even after some kind of transformation, that’s called symmetry. The more types of transformations an object can withstand without changing, the more symmetric it is. Let’s explain visually. Take a square, for instance. If you rotate this square 90 degrees, it looks exactly as it did before. If the square was drawn correctly, no matter how hard you try, you wouldn’t be able to tell the difference between the original and the square after a 90-degree rotation. Every time you rotate it 90 degrees, you get an identical square. This inability to distinguish between states is a kind of symmetry.

Now imagine a circle. Whether you rotate it by 1 degree or 100 degrees, it remains exactly the same. There’s absolutely no way to notice a difference. Since in the case of a square, it only returns to its original state after each 90-degree rotation, but for a circle, you’re free to rotate it by any angle, that means the degree of freedom (for symmetry) is greater for the circle. So a circle has more symmetry than a square.

You might be thinking—so what? Well, it matters. In reality, symmetry imposes constraints and sets limits. That’s the power of symmetry. For example, if you tell me, “I’ve drawn a figure on paper that looks exactly the same no matter how you rotate it,” I can tell you right away that you must have drawn a circle. Because apart from a circle, you can’t draw anything that possesses such a strong property. In other words, the more symmetry increases, the fewer possibilities remain for anything to happen. This is how, due to powerful symmetries, rules get established. That’s what happens. Gauge symmetry, for example, is the origin of nature’s four fundamental forces. This is the core idea of quantum field theory. Physics discusses many different types of symmetry. Perhaps, another day, we can talk about the diversity among them.

Modern physics talks about three types of spatial symmetry: reflection, rotation, and translation symmetry. The fundamental particles we know obey rotational and translational symmetry but not reflection symmetry. We all know this reflection symmetry as P-symmetry or parity symmetry. Among the four fundamental forces, only the weak nuclear force violates this reflection symmetry, while the other three uphold it. The problem arises only in the case of the weak force.

It was the American scientist Lee and Chinese scientist Chen-Ning who first suspected that reflection symmetry is not conserved in weak force interactions. That was back in 1956. They designed several experiments to test their hypothesis. About six months later, experiments confirmed that the weak force indeed does not obey reflection symmetry.

There are various explanations for this symmetry breaking, but one of them is a rather strange theory. According to this theory, every fundamental particle has a mirror counterpart. In other words, that particle would be the mirror image of our familiar particle—its right side would become the left side. If a universe were made up of these particles, it would be the opposite of our world. Strange as this theory may sound, it is certainly fascinating. However, we do not know if it is correct.

Recently, scientists have proposed two ways to test this theory in New Scientist. I’ll mention one of them here. In this experiment, neutrons will be used. Neutrons are quite stable when inside an atom. But if you remove a neutron from the atom and let it be alone, it becomes unstable. The neutron then decays into a proton, an electron, and an electron antineutrino. This is called beta decay. Depending on how this decay is measured, scientists find two different neutron half-lives. One method yields 14 minutes 48 seconds; the other, 14 minutes 39 seconds. The two methods give different results. In one, the neutrons themselves are counted; in the other, the protons produced from the decayed neutrons are counted. But in both cases, the results should be the same. Scientists suggest that this nine-second discrepancy is mainly due to mirror neutrons. If a neutron transforms into its mirror counterpart between emission and detection, the proton count could be skewed. Since one method involves counting neutrons and the other protons, the results will differ. That’s the reason for the nine-second difference. In the presence of an electromagnetic field, the probability of such mirror transformation increases slightly, and a weak type of electromagnetic field was used in the experiment. Scientists have now designed another experiment to determine if this really happens. Let’s see if neutrons actually turn into mirror versions. Of course, none of this really affects us. Even if neutrons transform into mirror versions, the common people in our country will remain barbaric, and Facebook intellectuals will stay sycophantic and without self-respect. But to live, one must do something—so I wrote, and you read. That’s it!!