Symmetry is beautiful, but asymmetry is why the Universe and life exist

Symmetry is beautiful, but asymmetry is why the Universe and life exist

The Universe has asymmetries, but that’s a good thing. Imperfections are essential for the existence of stars and even life itself.

Many theoretical physicists are fascinated by symmetry and feel that equations should reflect this beauty. The presence of anti-matter was successfully predicted by mathematical equations based on symmetry. However, there is a risk in equating truth and beauty with symmetry. The Universe, like living creatures, is not completely symmetrical.

We left-handed people are a minority among humans, with roughly a 1:10 ratio. But make no mistake: the Universe, from subatomic particles to life itself, loves left-handedness. In fact, if Nature did not have this basic asymmetry, the Universe would be a completely different place – bland, primarily filled with radiation, and empty of stars, planets, or life.

Nevertheless, there is a popular aesthetic in the physical sciences that promotes mathematical perfection — expressed as symmetry — as Nature’s blueprint. And, as is often the case, we get lost in a falsely fabricated duality of having to choose camps: are you for “all is symmetry” or are you an imperfection iconoclast?

Antimatter: why physicists love symmetry

“Beauty is truth, truth beauty,” as Keats famously said. However, if you insist on equating Keats’ beauty with mathematical symmetry as a path toward discovering “truth” about natural laws — which is quite common in theoretical physics — the danger is that you relate symmetry with “truth” in such a way that the mathematics we use to represent the Universe through physics should reflect mathematical symmetry: the Universe is beautifully symmetric, and the equations we use to describe it must reveal this beautiful symmetry. Only then will we be able to approach the truth.

Quoting the great physicist Paul Dirac, “It is more important to have beauty in one’s equations than to have them fit an experiment.” If any other less well-known physicist said that, they would be laughed at by colleagues, branded a crypto-religious Platonist, or a quack. But it was Dirac, and his beautiful equation, based on symmetry concepts, did predict the presence of anti-matter, the fact that every particle of matter (such as electrons and quarks) has an anti-particle companion.

That is an incredible achievement – the mathematics of symmetry, applied to an equation, guided humans to find a whole parallel realm of matter. It’s no surprise Dirac was so devoted to the god of symmetry. It directed his thoughts toward an incredible discovery.

It is important to note that antimatter does not have the strange meaning that it appears to have. In a gravitational field, anti-particles do not rise. A few of their physical features, most notably electric charge, are reversed. As a result, the positron, the anti-particle of the negatively charged electron, has a positive electric charge.

We owe our existence to asymmetry

But here’s the issue that Dirac was unaware of. The laws that dictate the behavior of the fundamental particles of Nature predict that matter and anti-matter should be equally abundant, that is, that they should appear in a 1:1 ratio. One positron for every electron. However, assuming this perfect symmetry held, matter and antimatter should have annihilated into radiation fractions of a second after the Big Bang (mostly photons). That, however, was not the case. As an excess, around one in a billion (roughly) particles of matter survived. And that’s a wonderful thing, because everything we see in the Universe — galaxies and stars, planets and moons, life on Earth, every form of matter clump, alive and nonliving — emerged from this small excess, this fundamental asymmetry between matter and antimatter.

Despite the cosmos’ expected symmetry and beauty, our research over the last few decades has revealed that the laws of nature do not apply equally to matter and antimatter. One of the most important unsolved questions in particle physics and cosmology is what mechanism might have caused this little excess, this imperfection that is ultimately responsible for our existence.

There is an internal symmetry operation that converts a particle of matter into one of antimatter in the language of internal (“internal” as in changing a particle’s property) and external (“external” as in spinning an object). The operation is represented by the capital letter C and is known as “charge conjugation.” The observed matter-antimatter asymmetry implies that Nature lacks charge-conjugation symmetry: particles and their antiparticles cannot be transformed into one another in some cases. C-symmetry is specifically violated in the weak interactions, which are responsible for radioactive decay. The culprits are the neutrinos, the strangest of all known particles, affectionately called ghost particles due to their ability to go through matter practically undisturbed. (There are about one trillion neutrinos per second coming from the Sun and going through you right now.)

To understand why neutrinos violate C-symmetry, we need to consider another internal symmetry known as parity, which is represented by the letter P. A “parity operation” turns an object into its inverse. You are not, for example, parity-invariant. The heart is on the right side of your mirror image. Parity, like tops, is connected to how particles spin. However, particles are quantum objects. This implies they can’t merely spin in any direction. Their spin is “quantized,” which means they can only spin in a few ways, similar to how old-fashioned vinyl records could only be played at three speeds: 33, 45, and 78 rpm.

One rotation “speed” is the least amount of spin a particle may have. (Very roughly, it’s like a top rotating straight up. It may turn clockwise or counterclockwise when viewed from above.) Electrons, quarks, and neutrinos are examples of this. They have spin 1/2, which can be either +1/2 or -1/2, corresponding to the two rotating directions. Curling your right hand around with your thumb pointing up is a good way to notice this. Positive spin is counterclockwise, while negative spin is clockwise.

We should receive a left-handed anti-neutrino if we apply the C operation to a left-handed neutrino. (Yes, even if the neutrino is electrically neutral, it does have its anti-particle, also electrically neutral.) The issue is that Nature contains no left-handed anti-neutrinos. There are only neutrinos that are left-handed. The weak interactions, which are the only interactions neutrinos experience (apart from gravity), break charge conjugation symmetry. That’s a problem for those who love symmetry.

CP violation: asymmetry wins

But let’s take it a step further. When we apply C and P (parity) to a left-handed neutrino, we should get a right-handed anti-neutrino: the C converts the neutrino to an anti-neutrino, and the P converts the left-handed neutrino to a right-handed neutrino. Anti-neutrinos, by the way, are right-handed! We appear to be in luck. Although the weak interactions violate C and P separately, they appear to satisfy the combined CP symmetry operation. In practice, this means that left-handed particle reactions should occur at the same rate as right-handed anti-particle reactions. Everyone was relieved. Nature seems to be CP-symmetric in all known interactions. Beauty was back.

The excitement didn’t last long. In 1964, James Cronin and Val Fitch discovered a minor violation of the combined CP-symmetry in the decays of a neutral kaon, identified as K0. Essentially, K0 and their anti-particles do not decay at the pace anticipated by a CP-symmetric theory. The physics community was shocked. Beauty has gone. Again, it has never fully recovered. CP violation is a naturally occurring phenomenon.

So many asymmetries

CP violation has a deeper and more mysterious implication: particles choose a preferred time direction. The asymmetry of time, the trademark of an expanding Universe, happens also at the microscopic level! This is enormous. It’s so big, in fact, that it’ll need its own essay soon.

And here is another explosive fact about imperfection that we will address. Life is also “handed”: the amino acids and sugars found in all living things, from amoebae to grapes to crocodiles to humans, are left- and right-handed. We generate 50:50 combinations of left-handed and right-handed molecules in the lab, but this is not what we see in nature. Life likes left-handed amino acids and right-handed sugars almost exclusively. Again, this is a large open scientific subject on which I have spent a considerable amount of time working. Next time, let’s go there.

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