As written by my good friend, theoretical particle physicist Michael Park. I take zero credit for the below article. (For curious and careful readers who are not particle physicists)
In order to understand exactly what it is that the Higgs does for us, it is ﬁrst important to understand the role of symmetry in nature. What do we mean when we say “symmetry”? The more or less “mathematical” deﬁnition of a symmetry basically boils down to the property of an object that its constituent parts are related in some way. Consider for example, a circle. We can all recognize that a circle is a pretty symmetric object. But what a mathematician might mean by that, is that if you consider all of the points that make up a circle, they are all related to each other by a rotation about the center. No point is special compared to any other point from this perspective and any rotation of the circle about its center gives back the same circle. When we say that an isosceles triangle is “symmetric,” what we mean is that each point on the left side is related to some point on the right side by a reﬂection across some “axis of symmetry”. An object is symmetric if the parts that make it up, are related to some other part by some well deﬁned transformation. For a circle this transformation is a rotation (as well as a reﬂection if you think about it), while for an isosceles triangle this transformation is a reﬂection.
Now try to imagine a universe that is extremely symmetric. A universe in which each constituent is related to every other constituent in almost every way possible. When I imagine a very symmetric universe I imagine a very boring one. Perhaps it is made up of trillions of particles, but every particle has the same intrinsic properties as every other particle. There is no way to distinguish any one building block of this universe from any other building block through its properties. As a result, these particles all move at the same speed in random directions without interacting at all. There is no diversity, no structure, no life, and any sense of beauty in this universe stems from its simplicity and its symmetry.
This is not the universe we see around us. The universe we see around us is full of diversity, structure, life, and an idiosyncratic sense of beauty that humans have grown to know and love. Naively, there is no reason to think that symmetry should play any role in understanding the structure of the universe. However, the human study of physics over the last 300 years leads us to challenge this naive assumption. As the fable goes, Newton sits under a tree when an apple falls onto his head and he sparks an idea. Since there was not much to do back in those days and considering what else he accomplished, it was probably true that Newton also spent a good amount of time watching the sun rise from one part of the sky and set on the opposite side. For anyone living in those times watching apples fall from trees and stars moving across the sky, it would have been extremely far from obvious that these two phenomena could ever be described using one idea. It would have been almost impossible to imagine that there could be one underlying principle that would predict both apples falling from trees and bright lights moving across the sky. It took the genius of someone like Newton to realize that indeed, a proper theory of gravity would be capable of accomplishing this. As another example, when we see lightning strike during a thunderstorm, and magnets sticking to our refrigerators, it is far from obvious that one underlying theory could be called upon to explain both of these phenomena. But Maxwell’s theory of electromagnetism, like Newtons theory of gravity, has shown us that seemingly totally disparate phenomena can often be explained by one unifying principle. Perhaps the universe is more symmetric than we thought.
Turns out Newton and Maxwell only saw the tip of the iceberg in terms of just how powerful the use of symmetry could be in understanding the laws of nature. In the mid 1900’s, physicists started doing experiments that probed the structure of atoms by increasing the temperature until these atoms ripped apart, allowing us to study their innards. These were the ﬁrst generation of “collider” experiments. Standard Big Bang cosmology tells us that shortly after the moment of creation, the universe was tiny. Everything we see in the universe was once super condensed and as a result, super hot. The experiments being performed were interesting, not only because we were learning about the structure of atoms, but also because the conditions that we created to study these atoms (super high temperature) also mimicked the conditions that existed shortly after the creation of the universe. By studying the structure of the elementary particles that make up atoms it slowly dawned on the physicists that these elementary particles, though seemingly numerous in species, were all related to each other in very deep and beautiful ways. They realized that these elementary particles naturally fell into categories, and were related to each other through their properties in exactly the same way that the points on a circle are related to each other by a rotation about the center. It became soon obvious that the more fundamental the constituents of nature we observed, and the closer to the moment of creation we studied, the more symmetric the universe appeared to be.
Now what about the Higgs particle? The Higgs is a phenomena that happens to have a particle tied to it. Forget about the particle for now. If you make it to the end then hopefully that aspect of the Higgs phenomena will become apparent. Let’s talk about the Higgs phenomena. Recall now, the universe we imagined earlier. The perfectly symmetric one. In this universe there is only one type of particle, they all move at the same speed in random directions, and they all whizz by one another without interacting at all. This universe is perfectly simple and nearly perfectly symmetric. Imagine now that this is what our universe looked like right after it was created, when it was still super small, super hot, and super dense. Then the universe expanded, and as it expanded it cooled down; and when things cool down, symmetries break. This breaking of symmetry is what we call the “Higgs phenomena”. How does it work?
The Higgs phenomena is actually nothing special. It occurs when water freezes and we can observe objects very similar to Higgs particles when we study ice closely. Where are they? Consider the fact that water molecules are polarized. All that means is that one way to imagine a molecule of water is to imagine it as a little arrow. A cup of water, can then be imagined as a cup of little arrows all swimming around and bumping into each other randomly and without any discernible structure. As a result, a good (pure) cup of water will have a property we call “isotropy”. What this means is that if I Honey-I-Shrunk-Myself down to molecular sizes and took a scuba expedition to the center of the cup of water, no matter which direction I look at, there will be (on average) as many arrows pointing towards me as there will be pointing away from me. No matter which direction I look, I see no direction that is special compared to any other direction as far as arrows in the water are concerned (ignoring the shape of the cup). One might say that this water has a “spherical symmetry” because every direction is the same and so they are related by spherical rotations. Now what happens when the temperature drops and the water starts to freeze? What happens is that two arrows which happen to be pointing in the same direction will eventually wander close enough to each other for their intermolecular forces to lock them into a pair. As the temperature drops further, a third arrow pointing in the same direction will come close enough to lock into the ﬁrst pair of arrows and so on and so on. After the water has completed the process of freezing, we will have large groups of arrows all locked into each other and pointing in the same direction. A new structure has formed and we call this structure a “lattice” or an ice “crystal”. By the time the water has ﬁnished the freezing process, if I am still in the middle of the cup of water, I will see every arrow now pointing in the same direction. The water (like the Higgs ﬁeld) has frozen (literally) and the spherical symmetry has been broken. Before when I looked around me there was no direction I could point out as being special. Now with all of the arrows pointing in the same direction, this special direction has become discernible, thus breaking the symmetry.
Now suppose I do this experiment again, except this time I bring with me to the center of the cup of water, two ﬁshies. One of the ﬁshies is just a regular guppy that swims through water normally. The other is a special type of ﬁsh called a “photey” that has evolved to swim unhindered through ice crystals (I know I know, just bare with me). Before the water has frozen, both the ﬁshies swim freely through the cup of water unhindered. Both ﬁshies swim at the same speed and would be neck and neck in a race through the water. If all we could measure were their speeds, there would be no way to tell them apart (one might even say that these two ﬁshies are thus related by a symmetry). But as the water starts to freeze, if the water is pure and the temperature is brought down steadily and uniformly, the ice crystals will start to coalesce uniformly throughout the cup of water. Soon the guppy will start to have trouble swimming as fast as it used to in this new environment, as it starts to bump randomly into the ice crystals. The photey on the other hand, has evolved to swim unhindered through ice crystals so it will have no problem and will continue to swim smoothly through the freezing water. By the time the water is done freezing, the guppy will be frozen in place, while the photey will continue zipping around as if nothing happened. After the water has frozen, the symmetry has been broken, and we can now distinguish the ﬁshies through their speed because of how they interact with the new environment.
Literally, the equations we use to describe these aspects of how the symmetry of water breaks as it freezes, are exactly the same equations we use to describe what happened with the Higgs ﬁeld in the early universe. In our perfectly (boring) symmetric universe full of identical particles, the particles are identical the way that the two ﬁshies were identical in speed through the melted water. If we assume that a water-like substance called “the Higgs ﬁeld” pervades the cosmos, then as the universe expands and cools, the Higgs ﬁeld freezes (literally). Some particles, like the ones that make up light (photons), do not notice the freeze out and continue to zip around at the speed of.. well.. light. Other particles, like the ones that make up atoms, notice the freeze out and react by slowing down, exactly the way the guppy became slower moving through a thick mixture of water and ice crystals. Physicists have a word to describe particles that move slower than the speed of light. We call them “massive”. These particles have now acquired “mass” through their interaction with the frozen Higgs ﬁeld. The universe is now less symmetric and more diverse than it once was. For the particles that acquired mass, it was this process that allowed them to bind together form atoms. In fact, it was the precise strength of the interactions between these particles and the frozen Higgs ﬁeld, that allowed these atoms to form in such a way that they could bond to form more complex molecules. It was the precise strength of these interactions, that then allowed these complex molecules to move about in such a way that they could attract and coalesce to form even more complex structures. As time went on, some of these structures grew exquisitely complex. After fourteen billion years, some of these structures eventually became so complex, that they began to wonder where they came from. These structures are called “humans”. This is why (to the dismay of many physicists, myself not included) people in the media often refer to the Higgs particle as “the God particle”.
So how can ﬁshies like us deduce that something like the Higgs ﬁeld permeates through all of space? Let’s go back to the water example, since for all intents and purposes, it is a mathematically perfect analogy. In the universe today, the “water” is frozen. The symmetries are broken, which means that every little arrow is already locked into place pointing in the same direction. There isn’t much concrete evidence that it was ever melted and that ﬁshies ever swam through it at the same speed. But maybe, just maybe, we could prove that the arrows are capable of moving freely like the arrows in water at high temperatures, if we can just jiggle one of the arrows enough to break it free momentarily. The diﬀerent ways in which these arrows can jiggle can be broken down into two basic categories. To understand the diﬀerence between them, imagine an arrow like the kind people used to use to hunt. Suppose I take the arrow and stick it into the ground with the arrow head pointing upwards. If the position of the arrow is ﬁxed, then there are only two basic ways I could jiggle this arrow. I could twirl it around like a drill like I was trying to start a ﬁre, or I could take the arrow head and swing it back and forth. The arrows that make up the ice crystal are the same way, but notice that these two types of jiggles are not of the same nature. If I jiggle the arrows in the ice crystal like a drill, every arrow still points in the same direction. This “drill type” of jiggle does nothing to restore the symmetry that has been broken. But if I jiggle the arrow heads to and fro, this is a special type of jiggle that restores just a little bit of the freedom that made the water symmetric in the beginning. Let’s call this kind of jiggle, “a Higgs jiggle”. Maybe, if I ﬂick one arrow head hard enough side-to-side, it could knock into the one next to it, and that one could knock into the one next to it, causing a chain reaction sending a vibration that travels across the ice crystal for some distance. Maybe, if we can ﬂick the Higgs ﬁeld hard enough, we could knock one of its arrows hard enough to send a “Higgs vibration” through the space in which it permeates. This “Higgs vibration” is what we call “the Higgs particle”.
When it was shown that the Higgs phenomena could be relevant to nature 40 years ago, physicists immediately incorporated it into their theory. But how could we ever hope to jiggle the Higgs ﬁeld hard enough observe it? We could do what we’ve always done to understand the structure of matter and to recreate the conditions of the early universe. Take two particles and smash them together at extremely high energies (high temperatures, early universe, you know the drill). We’ve never stopped trying to build bigger and bigger particle colliders for curiosity sake. But since the development of the Higgs theory, it has always been a goal to build one big enough to smack the Higgs ﬁeld hard enough to prove that this is the reason why some particles (like the ones that make up atoms) have mass and others (like the ones that make up light) don’t. In the 1980’s, physicists celebrated around the globe at the discovery of the “drill type” jiggles we talked about earlier. These “drill type” jiggles, according to the theory, were responsible for why radioactivity behaved the way that it did. When they measured the precise properties of these “drill type” jiggles, they found that they matched perfectly with our observations about radioactivity, if the theory was correct. Conﬁdence in the Higgs theory got a second wind, but in order to be totally sure that the Higgs theory was true, they’d have to produce the real symmetry-restoring “Higgs jiggles”.
The problem is that it didn’t take long to understand the theory well enough to know exactly what it said about the Higgs jiggles and what they should look like. The theory indeed conﬁrmed that Higgs jiggles should propogate through space, if the arrows could be ﬂicked hard enough. But it also said explicitly that they wouldn’t live for more than a tiny fraction of a second before dispersing. In particle language, this means that it would indeed be possible produce the Higgs particle at a collider, but it would decay to other particles almost immediately. The other problem was that the theory also said explicitly, that only one out of a trillion or so collisions would produce a Higgs particle on average. It soon became clear that ﬁnding the Higgs would be similar to ﬁnding a needle in a large warehouse full of haystacks. The only thing working to our advantage was that the theory also predicted exactly how the Higgs particle must decay. Some of these decays were such that no other particle could perfectly mimic. In other words, the Higgs particle had a few “smoking gun” decay signatures that we could exploit in order to ﬁnd it. At this point, the story becomes messy and complicated. I cannot begin to estimate the outrageous number of working hours that went into developing the techniques and the technology to carry out this impossible search. To do so, physicists at the European Center for Nuclear Research (CERN) built the largest machine ever made by mankind (yes really) and cooled it to a temperature colder than any other place in the universe (no joke). To make a long story short, last week the scientists at CERN announced that they had analyzed and collected enough trillions of trillions of collisions to discern the existence of a new type of jiggle that no one had ever seen before. This jiggle so far, has every single property that the Higgs particle should have. Is it really the Higgs? Well if you were going to place a bet, now you know where the smart money should go.
Thanks to Simon Knapen for proofreading and helpful suggestions Brian Soames for asking curious questions that inspired a lot of this story
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