Coffeeshop Physics
by Jim Pivarski

Long articles on this site Short CMS Results on Fermilab Today Short Physics in a Nutshells on Fermilab Today Talks and older articles

Viruses have no color

Some things are too small to see. Microscopes help us to zoom in on some of them, but only up to a point. Objects smaller than a few hundred nanometers don’t even reflect visible light: a 1,000,000× magnifying glass wouldn’t be able to show us anything, despite its magnification strength. To study the shapes of things smaller than this, scientists bounce electrons (or other particles) off of them, but this technique is a bit more like sonar than sight.

To be specific, concepts such as color have no meaning for objects this small. Color is the pattern of wavelengths of light that a substance likes to reflect— for instance, grass absorbs red light (570–750 nm) and blue light (380–495 nm) but reflects green (495–570 nm). A strawberry reflects red but absorbs green and blue. Most viruses are between 20 and 300 nm, smaller than all visible wavelengths, so they don’t reflect much visible light. They are without color in a more fundamental sense than something that is merely gray.

This may cause consternation for virologists who want to explain what the critters look like, but it derives from a deep principle of physics that relates to the bandwidths of radio stations, the Heisenberg Uncertainty Principle, and why you can put staples in the microwave.

Lost in Hyperbolia

Before I studied physics in college, I was captivated by two of the things physicists talk about: quantum indeterminacy and curved space-time. I spent a lot of time thinking about what it might mean for a particle to be both here and there, and how something as insubstantial as space could be bent up and stitched together. Even as I learned about these things rigorously, it irked me that I couldn’t visualize them.

Eventually, I came up with ways of visualizing these things that made sense of them without doing too much violence to the underlying formalism. When I talk about curved space now, for instance, I’m imagining the contorted fabric of a pair of pants I once sewed, and how they couldn’t lay flat. I presented this explanation in a previous article on this website, but the “space-time as a sheet” metaphor is an old one that might only be helpful after a course in Riemannian geometry and another in sewing.

Computers have no trouble imagining curved spaces, and multitouch devices such as iPads let the user engage the computer’s abstractions in a palpable way. So I got to thinking, what if I write a program to directly interact with curved space? This article presents the result of that tinkering: a hyperbolic portal that runs in your browser (no need to download anything), intended to give you a direct experience of spatial curvature. The code is on GitHub, and I’d love to see (and link to) anything that you might do with it.


A few weeks ago, I wrote an article for Fermilab Today about the spin of fundamental particles and the Higgs boson in particular. My cats were eager to demonstrate how photons emerge from a Higgs decay in an anticorrelated state, so I included them as Figure 1. It was wildly popular. I was even asked to present it as a talk, which gave me a chance to expand on the topics that I had raced through to stay within my 800 word budget.

Spin is interesting for a lot of reasons. At the moment, it is perhaps the most important unknown parameter of the new particle discovered last July. Spin is also at the heart of quantum weirdness, because it’s an “amount of rotation” that is somehow quantized like a light switch: on or off, and never in between. It seems like we could just put a particle on a slow enough turntable to dial up a non-quantized angular momentum, but nature has a way of enforcing its rules. Talking about spin also makes for a nice bridge between the world of subatomic particles and the world of everyday experience, since it has some macroscopic consequences.

I don’t harbor the illusion that the popularity of my article was due to anything but Cats On The Internet, however.

The bouncing baby boson

Two weeks ago, I learned something amazing and couldn’t tell anybody. I saw a plot like the one on the right: a new particle emerging from freshly unblinded data.

To avoid bias, scientists “blind” their data, hiding the most interesting part from themselves while they make sure that they understand all of the experiment’s calibrations and finalize the analysis procedure. When the physicists of the CMS Collaboration believed that the experiment was well-controlled, we all breathlessly looked at the Higgs data to see if last year’s hint might be reinforced. It was. In fact, it is now statistically robust enough to say that a new particle exists and it has some of the properties of the long-sought Higgs boson. This morning, the CMS and ATLAS Collaborations revealed their results to the world (and each other). The fact that such different experiments reached the same conclusion solidifies it: we’re probably looking at the first appearance of a particle hypothesized 48 years ago.

Why are physicists excited by one more particle? Statements like, “It gives mass to all the other particles,” are correct but beg the question, “Why should mass come from a new particle?” And what does that mean, anyway? Some physics topics are easy to motivate: a conversation about extra dimensions could begin with, “You know how there’s length, width, and height? Well, what if there are more than these three?” The Higgs Mechanism, however, solves a technical problem at the core of modern theories about matter and forces, and it requires a lot of background to even know that there’s a problem that needs to be solved. This boson’s “God Particle” epitaph hints that it plays a central role, but the name explains nothing and embarrasses physicists.

This article is intended to fill in what the newspapers leave out. Without assuming technical background, I’m going to try to explain why Peter Higgs and five other (uncredited) physicists independently invented the Higgs Mechanism, what that means, and why it’s so exciting to learn that they seem to have been right. The topic ties into so many different areas of physics that I have to fight the temptation to talk about all of them. I’ll try to get at the heart of the matter, if only by cutting away the rest of the body.

The gnat who walks through walls

Imagine being invisible: what would that mean, physically? None of the skin, muscles, or bones in your body could absorb light in any way, including your eyes. Vision works because light is absorbed on the backs of your eyes, so to be invisible, you would also need to be blind.

Now imagine being intangible as well, imagine matter could pass through you as light does. You’d probably drop through the floor and orbit the center of the Earth like a yo-yo— that is, if you were insensitive to all forces except gravity. Take away gravity and there would be nothing left to tie you to this world. When light, matter, and gravity are not communicating with something, it might as well be in a separate universe. The extent of the physical world is defined by the interactions that connect our senses to phenomena: if something is truly undetectable, does it even make sense to say it exists?

Neutrinos inhabit a world that is almost, but not quite, disconnected from our own. They are insensitive to electromagnetism, the force that makes things visible and tangible, as well as the nuclear strong force that holds nuclei together in atoms. They ought to feel gravity but have so little mass that this has never been proven. We only know they exist because of their involvement in the weak nuclear force, which governs some but not all radioactive decays.

The picture above is the Earth— as seen in neutrinos. Neutrinos are emitted by uranium products in the Earth’s crust, but then pass pass through the Earth as though it were a soap bubble. The bright spots are new: they are nuclear power plants. To a weakly-interacting being who only sees neutrinos, nuclear reactors and atom smashers are the only evidence of life on Earth.

Spinning tops, protons, and planets

When I was little, I tried to make an electromagnet by winding a thin wire around a nail and connecting it to a battery. I must have seen this on Mr. Wizard’s World. But instead of magically picking up paper clips, it just got hot and wasted the battery. What I didn’t understand is that the wire must be insulated, not bare metal: instead of flowing around the nail in many circular loops, the electric current flowed through the whole thing as a bumpy metal blob.

This fact that circulating electric currents produce magnetic fields can be seen everywhere in nature. Electromagnets, whether they flip bits in a hard drive or cars in a junkyard, are essentially just (insulated) wires wound around nails. Neutron stars spin faster and faster as they collapse, generating the strongest magnetic fields known in the universe. Elementary particles such as electrons are haloed by tiny magnetic fields due to their intrinsic spin, a kind of internal rotation they can never stop. Even refrigerator magnets are not as stationary as they seem: their magnetic fields are due to a partial alignment of electron spins.

Sometimes, though, the flow can be so turbulent and complicated that its dynamics are a mystery. The underlying equations are known, but even supercomputers are not powerful enough to determine the implications of those equations. Only simplified versions of these systems can be calculated, so the predictions don’t exactly match the real systems in all their messy glory. The two examples I have in mind are a proton’s magnetic field and the Earth’s.

The discovery of rainbows

I was stuck in traffic one day when a glorious double rainbow appeared over the highway. It had been a drizzly day; the whole sky was covered with clouds except for a little gap along the horizon, and it was just about sunset. As the sun slipped between the grey above and the ground below, the Chicago skyline was briefly golden with horizontal light, and two concentric rainbow rings encircled I-290 like a kind of tunnel.

Most of the rainbows I’d ever seen were faint wisps; this was an intense glow, as bright as a flask of electrified mercury. Fortunately, the cars weren’t moving, so I got a good, long look. Rainbow-like color separation happens a lot in physics classes, and I thought I understood what caused the second rainbow. I was wrong. I was thinking about first-order and second-order rainbows from diffraction gratings. If the rainbows in the sky were due to the same mechanism, the second rainbow would have to be twice as big as the first (it isn’t) and the colors would have to be in the same order (they aren’t). I stared at that second rainbow until the car behind me started beeping. Were my eyes deceiving me? Did the colors really go in the opposite order?

When I got home, I read all about rainbows and how they work. It’s fascinating: the story of its discovery spans twenty centuries.

The crunchy star

A voyage to the sun would not be a pleasant trip. While still a million miles away, the tungsten hull of our spacecraft would start to melt. At half a million miles, it evaporates. A little farther and we’d be nothing but swirling plasma, mixing into a nuclear furnace so vast that “oceans” would be an understatement.

Though we could never touch the sun, there are stars that you can touch— former stars, anyway— and one has recently been discovered [link to paper]. It is only four thousand light-years away (16.1 years traveler time; see “We Can Get There from Here”). This star has been transformed by its neighbor into a husk of cold diamond. Since it’s solid, some astrophysicists are calling it a planet, but it’s not clear that the word applies to an object with such a bizarre history.

Suppose that we take the 16-year trip to visit this world: what would it look like? Could we really stand on the heart of a dead star?

We can get there from here

“Have you heard about this? Opera says neutrinos travel faster than light!”

I was in a conversation at Fermilab yesterday when I first heard about it. “Is that like one of those things where astrophysicists say that quasar jets travel faster than light, but only because they’re leaving out some projection effect?” I said.

“No, this is for real. Except— I think so. I can’t really tell; the article doesn’t say very much.”

I shrugged. I have no nose for news. It was only when my wife asked me about it that I knew it was a big story. She usually hears too much physics from me, so she doesn’t actively seek it out. By that point, it was in all the newspapers, the experimenters made their paper public, and CERN’s director general sent out a general e-mail.

If it’s true that neutrinos travel faster than light, it would be a huge upset. Some may take it to mean that relativity is overturned, Einstein rolls in his grave, and there’s no longer any limitation on the speed of future spaceships: we can get to distant stars in weeks, rather than decades. However, the implications run a lot deeper than that.

Relativity is a fact of life, as much as falling or heat and cold. We may not experience relativity in everyday things, but particle physicists encounter it daily. It’s not a small effect, something that might be a mirage. In fact, in the conversation at Fermilab I was learning about special techniques to measure particles that travel significantly slower than the speed of light: those are the oddballs. If this new observation about neutrinos is true, then it would have to fit into the constant stream of other observations. The new data would have to augment relativity— they can’t overturn it.

Quirky science fiction

I like old science fiction. The stories from the first half of the twentieth century didn’t always get the science right, but they incorporated a lot of the latest ideas of their time. For example, When Worlds Collide, a 1934 novel about the Earth colliding with a roving exoplanet, had this description of the rocket that would save a remnant of humanity:

“Each of these tubes generates the rays that split atoms of beryllium into their protons and nuclei. The forces engendered in the process, which is like a molecular explosion, but vastly greater, together with the disrupted matter, is then discharged through this gun...”

Splitting atoms? Vast forces? They’re talking about nuclear energy ten years before the world knew about the atom bomb. But more surprisingly, the authors knew that beryllium might be a good atom to do it. Leó Szilárd’s secret patent two years later was based on the idea that beryllium or uranium might start a chain reaction— beryllium didn’t work, but uranium did.

Why did the authors, Balmer and Wylie, think that beryllium might be a good ingredient for a nuclear rocket? At the time, beryllium was used as a neutron source, and neutrons were known to increase the radioactivity of normal matter— but the neutron had only been discovered three years prior. Did they read scientific journals? Were these ideas “in the air,” known to a literate public?

Today’s science fiction usually doesn’t follow science this closely. Much of what I find in the modern stories is based on scientific ideas or discoveries that are at least fifty years old, like wormholes, antimatter, and parallel universes. If telepathy was ever considered scientific, then it was in the hyper-empirical environment of the 1920’s and 30’s, yet mind-readers are still ubiquitous in sci-fi. Did the science in science fiction congeal half a century ago?

Leprechauns and laser beams

My fourth grade teacher was a child of Irish immigrants, and sometimes he told stories in class. My favorite went like this: leprechauns are bound by a law that obliges them to do whatever you say if you catch them. One day, a man caught a leprechaun and ordered him to reveal the location of his pot of gold. The leprechaun was furious, but he had no choice. He led the man through the forest to an old tree and said, “There. Me treasure is under the roots of that tree,” and that was the truth.

The man needed an axe and a shovel to get at the gold, so he tied a ribbon around the tree to mark it while he went back to town for some tools. He commanded the leprechaun not to take down the ribbon or move his gold or anything like that. The leprechaun, still under obligation, grumbled but agreed. When the man returned with his tools, the tree was still marked by its ribbon, but so was every tree in the whole forest. He never found that treasure.

The beauty of the leprechaun’s trick is that a completely ribboned forest has exactly as much information as an unribboned forest. A ribbon on every tree except one would convey as much as a ribbon on one tree. This “amount of information” is called entropy, and it is as much a physical quantity as length, voltage, and temperature. In fact, I think that entropy is a more fundamental concept than temperature— knowing about entropy makes it easier to understand what temperature is.

A stitch in time

I never really understood General Relativity until I learned to sew, just as I never really understood thermodynamics until I learned to cook. As with cooking, I was driven to sewing by necessity: my jeans didn’t fit. The first modifications were small ones: darts here and there to pull in material, later I added elastic waistbands, then suspenders.

Eventually I got so fed up with the bad fit that I decided to make my own jeans from scratch. I bought a few yards of fabric, wrapped it around myself, and started cutting. Mistakes weren’t a problem: I knew how to patch and I figured I would just keep cutting and patching until the thing fit around my body. It took about a week for the carpet to slowly evolve into pantaloons. I finished them just in time to wear them when my wife came home from a conference, whereupon she exclaimed, “They’re purple!” Pants 1.0 have been described as part-Joker, part-Catwoman, and they lasted about a year.

Spending all that time with fabric forced me to think a lot about topology and curvature. I had to somehow reproduce my own curvature in cloth: too much curvature and it would bulge, too little and it would be tight. The most difficult part is the crotch, which bends upward in the front and back, but downward toward the legs. “Oh,” I realized, “That’s what it means to be negatively curved!” Zero and positive curvature are easy to understand from textbooks, but negative curvature is always drawn as a twisted bit of graph paper, mysteriously called a saddle-point. “Of course it’s a saddle,” I said to myself. “What else are saddles meant to fit?”

What is the sound of two electrons clapping?

Paszenko the Cat is a music critic. I don’t say that just because he looks for a better place to nap whenever I play my cello— I wouldn’t blame any creature for that. It’s because he seeks out good music. He sits attentively, ears forward, whenever the music is harmonious and full of pentatonic intervals. But he has no patience for anything as modern as a diminished fifth.

My cat made his tastes obvious one day when a tutor came to give me cello lessons. The cellos came out of their boxes and Paszenko casually left the room. But when my teacher began to play, he came back. He got closer, sniffed the strange cello, and hopped into the teacher’s lap while he was still playing. And purred.

What colors a sound most is the path that it takes to get into our ears. From cello string to bridge to chamber to cat’s body sounds different than it would if it had bounced around the room before reaching Paszenko’s eardrums. As the waves flow from one object to another, they excite resonances whose frequencies depend on the shapes of those objects— the fancy curves in a cello’s body are not merely decorative. Remote as it may seem, the creation and destruction of subatomic particles works the same way. This is more than an analogy: it is one of the ways nature repeats herself at vastly different scales.

To see the world in a cup of coffee, and eternity in an hour

(This was the original “about page,” but I have converted it into a full-length article.)

I used to hate coffee. Though I knew that it’s an acquired taste, I couldn’t understand why anyone would want to acquire that taste: it was like drinking ink.

My wife tried to introduce me to the joys of coffee the way she had been raised: creamer first. When she was young, she sipped the little cups of creamer with one drop of coffee added to each, then gradually increased the ratio. I tried some coffee ice cream, but it seemed like a waste of good vanilla.

My conversion, however, was inevitable: I’m a particle physicist, and the two things that particle physicists do socially are drinking coffee and skiing. Many important physics conversations happen over coffee, the way that tobacco presided over Native American covenants. One day at CERN, a Swiss colleague offered me a cup while we worked out the details of some project, and I said, “Sure, thank you,” to be polite.

He hesitated for a moment, then asked, “Do you take it with or without pollutants?”

Nukes = Booze

“The ‘burning’ of uranium in an atomic furnace is so strange an affair that to get a picture of it at all we must overturn our familiar ideas about the behavior of fuel.” This is the beginning of a 1952 Scientific American article on Nuclear Chemistry by John F. Flagg and Edwin L. Zebrowski. “Imagine a lump of coal in which only a tiny proportion of the lump (one part in 140) is combustible. The combustible atoms are scattered all through the lump. As each burns, it gives off sparks that ignite the others, and the burning proceeds by a chain reaction. But the ashes of the burned atoms, deposited throughout the lump, soon begin to absorb some of the sparks and smother the fire.”

Something about this metaphor seemed wrong to me when I read it. Perhaps I should call it an anti-metaphor because the point is how uranium is unlike coal. I later came across the following quote from Ernst Rutherford, interviewed a year before nuclear chain reactions were first proposed. He said, “Anyone who expects a source of power from the transformation of these atoms is talking moonshine.”

That’s exactly it! Nuclear energy is just like moonshine!

Talking to physicists at parties

“So, what do you do?”

“Me? I’m a physicist.”

“Hey, isn’t that a coincidence? I hated physics!”

“Really? Wow.”

“I was so terrible at it in school, and my teachers were simply awful. But you must be a genius!”

“Um... actually...”

“Oh, hi! Nice to meet you. A mathematician? I was so bad at math...”

That exact conversation is more common than you might think. I’m sure that lawyers get evil-lawyer jokes and accountants get some variant of, “Gee, that’s boring,” but physicists are told that their passion is dreadful in a way that’s supposed to be a compliment. It would be easy to slip into the conceit that what we’re doing is so esoteric and so painfully difficult that we are modern-day wizards, but that would be a lie.