# Finding the pattern in all matter

## The search for symmetries leads to a deeper understanding of nature, says Katie Mack.

**To a physicist,** the highest form of praise for a theory is to say it is “beautiful”. Such a theory is not only logical and precise, it reveals deep fundamental truths about nature in the form of new patterns.

The search for patterns has always been the bedrock of science. When Dmitri Mendeleev put together the periodic table of elements, he didn’t know about electrons and their orbitals, but he could see patterns in how elements behaved. So he grouped them by their masses and properties: the noble gases that did not react with other elements were on the right-hand side of the table, while the alkali metals, that were never found in isolation, were on the far left.

Mendeleev knew the patterns hinted at something deeper, so he stuck with the system, even when it left gaps in the table. Eventually, other scientists determined that an element’s propensity to interact, and thus its place in the table, came down to the arrangement of the atom’s electrons. When new elements, such as gallium, were discovered, they slotted nicely into the vacant spots.

The table paved the way for quantum mechanics and for a simpler, more beautiful world: instead of dozens of unique elements, there were now three building blocks – protons, neutrons, and electrons. Their arrangements determined their interactions and explained chemistry.

In everyday life, we consider an object to be symmetrical if it looks

the same after a transformation of some kind.

Major discoveries in science almost always come from identifying patterns, followed by theories to explain them. In particle physics, the patterns usually display symmetries.

In everyday life, we consider an object to be symmetrical if it looks the same after a transformation of some kind. Reflection symmetry means an object looks the same when it is reflected in a mirror. An object has rotational symmetry if it looks the same when you turn it.

In physics, the concept of symmetry is sometimes purely mathematical. If an equation describing a physical system stays the same even when you perform an operation on it (like changing coordinates or adding a number), that means the system has a symmetry. For instance, when calculating the equation for a swinging pendulum with no friction it doesn’t matter whether the start time is now or 10 years in the future – the equation has a time-translation symmetry.

German mathematician Emmy Noether showed every symmetry comes with a conservation law. So in the case of the swinging pendulum, time-translation symmetry means the system’s energy is conserved forever. Other kinds of symmetry lead to other conserved quantities.

Noether’s theorem connects symmetries we can observe in nature to fundamental rules about how physics works. And in much the same way that Mendeleev’s patterns of elements predicted gallium, we can use the symmetries of particle physics to predict new particles, such as the Higgs boson.

The physics of the subatomic world can be divided into theories of three basic forces of nature: the strong force that binds the nucleus together, the weak force that governs radioactive decay, and the electromagnetic force that attracts electrons and protons to each other. (Gravity, the fourth basic force, is extremely weak on these scales.)

In the 1960s, scientists discovered dozens of new particles with atom-smashing machines. Their interactions via these fundamental forces could be laid out in patterns in a microscopic-scale analog to the periodic table. These patterns led scientists to develop what we now call the standard model of particle physics, and once again it broke down the dozens of exotic particles into a few fundamental pieces: quarks, leptons and bosons. But, like Mendeleev’s table, something was missing – in this case a boson with particular interactions that should slot into a specific spot, completing the picture. It was the Higgs boson, found by the Large Hadron Collider (LHC) in 2013.

While the standard model has been successful, we know it’s not the final theory. Problems in our picture of the fundamental forces hint at a deeper symmetry we have yet to uncover. This is the basis for the theory of supersymmetry, which adds a new symmetry to the standard model, and gives each particle a “superpartner” particle at a higher mass. If supersymmetry is correct, the LHC might find evidence for it. If not, we’ll develop a new model, guided by Noether’s theorem as we use new results to construct theories with more perfect symmetries. That, to my mind, is beautiful.

Also in Cosmos: The woman who invented abstract algebra

This article appeared in Cosmos 66 - Dec-Jan 2016 under the headline "The pattern of matter"

*Katie Mack is an astrophysicist at the University of Melbourne.*