I woke up hungover and needed aspirin, coffee, and greasy food. There were potatoes in the cabinet, so a hash brown was in order. I ground up the spuds, drenched them in olive oil, and lit the stove’s burner.
The tricky part is timing the flip to fry both sides. There’s some magic moment when the bottom pieces crust together into a half-cooked hash brown, but potato shreds will fly everywhere if you flip before they’ve become cohesive. This destroys the structure and leaves you with fragments that won’t cook evenly.
The uncooked pile of potato has a symmetry reminiscent of the Taoist’s uncarved wood. It can end up as a well formed hash brown or as a Humpty Dumpty’d mess. But once it’s crusted or prematurely flipped, there’s no going back – you’re stuck with what you’ve got.
The 25 cent term for this phenomenon is Spontaneous Symmetry Breaking (SSB), which occurs when a system loses some of its internal symmetries. In the hash brown example, the symmetry consists of having more than one possible outcome. Yet at some point, this is broken and only one option remains.
Models incorporating SSB are used to describe many aspects of the physical world, ranging from superconducting materials to quantum chromodynamics to magnet.1 One of these models is the mechanism that gives particles mass, the Higgs Boson.
Before delving deeper into the physics, let’s re-examine the cooking equipment and my attempt to eat a balanced breakfast.
I’ve taken a bowl and placed it upside-down in a pan, creating a pan-bowl.2 Gravity’s pull makes it incredibly difficult to balance the orange on top of the pan-bowl. Any small disturbance will cause it to tumble to the low ground – the intersection of the bowl’s rim and the pan, highlighted below in green – which I call the Goldilocks Trench. This is another instance of SSB and the shape traced by the pan-bowl is the phenomenon’s signature pattern.
Originally, the orange is in a central, symmetric position, allowing it to move in any direction. But once it’s fallen into the Goldilocks Trench, the orange is constrained to roll in one of only two directions – clockwise or counterclockwise. As in the hash brown example, the fruit and pan-bowl system starts out with many options that disappear once the symmetry is broken.
The orange’s gravitational potential energy – which increases with its height – directly corresponds to its distance from the origin. If it’s near the center, the orange has an excess of gravitational energy and rolls outwards to lose it. Likewise, going too far out causes the same problem and the orange retreats inwards.3
But in the Goldilocks Trench, the distance from the center is juuuuuust right because the gravitational energy is minimized. In other words, the lowest height is paired with a unique distance from the center – the only stable combination.
The SSB of the fruit and pan-bowl is comparable to how the Higgs Boson gives particles mass. Instead of considering the gravitational potential of an orange, we’ll examine how strongly a particle interacts with the Higgs. The strength of this interaction determines the particle’s mass.
If the particle interacts strongly with the Higgs, it has a high mass; if it doesn’t, it has a low mass. To visualize this, let’s consider a loose analogy, bearing in mind that mass is a measure of how much effort it takes to cause an object to accelerate.
Imagine you’re getting coffee and across the table is either a friend or a narcissist.4 If you’re dining with a friend, it’s easy to hang around for a long conversation because you have rapport and bounce ideas off each other.
But the narcissist ignores your interests to rant about themselves. Though there’s plenty of talking, there’s little interaction, making it more likely that you’ll suddenly remember to “check the oven” or “feed the cats.”
In this example, you’re the Higgs Boson, your partner is a particle, and the quality of your conversation is how strongly the Higgs and the particle interact. It’s harder to part ways with your friend in the same way that it’s difficult to accelerate a particle that interacts strongly with the Higgs – that is, the particle is quite massive.
Each type of particle interacts with the Higgs in a characteristic manner – just like how our conversations vary based on our company. Physically, this is manifest through the dimensions of the pan-bowl.
Nature alters the curves so that each type of particle has a unique pan-bowl configuration describing how strongly it interacts with the Higgs.5 Every Goldilocks Trench will be a different distance from the center, which uniquely defines the particle’s mass. The further it is from the center, the higher the mass.
This is also why SSB is essential for giving particles mass in the first place. Without its signature pan-bowl shape, particles could remain at the symmetric “position” for mass – zero. Breaking the symmetry enables interaction with the Higgs, driving particles to nonzero mass, just as heat and spatulas force the fate of fried potatoes.
This is what keeps the world from being too light a place! Speaking of that, it’s way too bright outside. But the hangover’s easing its grip; food and physics always help.
1. Yes, Insane Clown Posse, that’s how they work.
3. Let’s pretend that my pan has much higher walls. Besides, this wouldn’t really be a physics discussion without bizarre approximations.
4. They’re not mutually exclusive, but you should reevaluate your life if these categories’ Venn diagram resembles a single circle.
5. This is our basic model, though it has some problems that require further testing (warning: maths and fancy words). Despite the need for fine tuning, many aspects won’t change too much – similar to how this banana and hat system still resembles our previous pan-bowl combos.
Many thanks to Sean Downes, Autumn Rizzo, Dominic Collins, and Pops for feedback!