Symmetric Rules for a Symmetric World

Energy can never be created or destroyed. Heard that one before, aye? This is an example of a conservation law, the statement that some quantity will not change over time. In this case, that quantity is the total energy in the universe. Physics is full of conservation laws, conservation of energy, conservation of momentum, of angular momentum, of charge, the list goes on.

Conservation laws are powerful – often all you need to know about a process is what’s being conserved in order to make predictions. Many who did physics in school will remember calculating the final momenta of two objects that smashed into each other using nothing but conservation of momentum.

It’s tempting to think of conservation laws as fundamental rules in physics – conservation of energy seems like something that just is, just like Newton’s laws or the laws of thermodynamics. But actually, if you look hard enough, you’ll find that conservation laws are a product of some much deeper facets of reality. And uncovering the hidden insights that these conservation laws betray has been indispensable to modern physics, particularly particle physics.

Conservation laws are a product of the symmetries of nature. So when we use conservation laws to make predictions, we’re actually using these symmetries.

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The Importance of Blue Skies Research

I work in particle physics. So as is natural for a researcher in such a field, I find myself often answering questions along the lines of “what’s the point of all this?” Why is so much effort poured into questions fuelled only by curiosity?

It’s a fair question. Society collectively pays for us to build big colliders and devote trillions of hours of computing time to finding the next fundamental particle. Particle physics is one of a number of fields one could call blue skies research, research that has no obvious useful application. Blue skies research mostly relies on funding from taxpayers, so in general people deserve an answer to “what is the point of all this?” The following is my attempt at an answer.

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Infinite Magnet Universe

Maths, and heavily mathsy subjects like theoretical physics, are full of seemingly unrelated ideas that are in fact deeply connected. As a consequence, there are many statements in these fields that can be expressed in radically different ways. Often throughout history, reformulating a problem into a completely new context via connections like these has been instrumental in the problem being solved.

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Through the Higgs Portal

The universe can be described by a list of particle species, and how strongly each species interacts with each of the others. For example, the electric charge of the electron, e, tells us how strongly the electron interacts with the photon. Put differently, imagining a photon flying past an electron, e tells us how often that photon will bump into the electron.

Some of the particles on this list are shy, they very rarely interact with the others. An example is the neutrino. Roughly a hundred trillion neutrinos emitted by the sun pass through your body every second. You don’t notice it because it only extremely rarely interacts with what you’re made of, i.e., the electrons, protons and neutrons that make up the atoms and molecules that make up you. It may very occasionally bump into an electron in one of your atoms, making it do a little wobble, but this happens so rarely that it has an imperceptible overall effect.

What else could be going through you right now? Maybe there are other things we haven’t discovered yet, because they’re so difficult to detect. The following is my attempt at an answer.

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Clever Demons and Hungry Black Holes

The French scholar Pierre-Simon Laplace once told the story of a demon. The demon knows all the laws of physics, and is so smart that he can do an infinite number of calculations in his head. If you told him the exact state of the universe at one point in time, then he would be able to predict with certainty the exact state of the universe at some later time. He would always win bets.

He could also use his physics knowledge to turn the clocks back, and deduce, given the state of the universe at some time, the state it had at some earlier time. If you wanted to destroy a document containing information you’d rather no one ever find out, and, say, burned it, you still wouldn’t be safe. The demon could look at the smoke coming off the flames, and use it to deduce what was on the page.

Laplace told this story in order to convey the idea that

“We may regard the present state of the universe as the effect of its past and the cause of its future.”

This seems like a pretty sensible way to view nature to most physicists. The universe is in principle predictable. If it wasn’t the case, what’s the point in physics?

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