Can you tell your left from your right?

When I was three years old, I took significant pride in the fact that I could – particularly the day I discovered that many of my fellow preschoolers had not yet achieved this feat. Of course, as the years wore on and my classmates got the hang of it, I came to take the distinction for granted. It was so…pedestrian. Trivial, even.

And then a college professor showed up and left me so confused about left and right that I couldn’t fathom how anyone could rightly know which was which.

It happened in calculus class. The professor had just asked us to imagine walking along a path, keeping the path to our left. Suddenly, he paused theatrically, cocked his head, and sighed. “You know what’s always bothered me about this proof?” he interjected. “Would it work on Mars? I mean…could you explain ‘left’ to a Martian?”

The professor moved on, but his question really started to bug me. Imagine that you’d been born on the other side of Alice’s looking glass, with your entire universe a mirror image of our own. Clearly, right and left would be reversed: hearts would sit on the right, English would read right-to-left, and so on. But how would you know you were in that universe, rather than ours? Our eyes and even our brains would all be flipped, too!

This isn’t merely a question of which direction gets which label; it’s an assault on the very concepts of left-ness and right-ness. Was my three-year-old self gloating over his mastery of a vacuous, meaningless convention? We may think we know our right from our left, but does the universe agree?

In which I consult a dictionary

If you want to know what a word means, the obvious first stop is a dictionary.

Many dictionaries define “left” in terms of cardinal directions – e.g., “the side of a person or thing that is turned toward the west when the subject is facing north.”

Sadly, this definition alone won’t help us much. Just imagine the conversation with the Martian:

You: …but in Britain they’re all weird, and drive on the left side, so— Martian: Excuse me, what is left? You: Oh, left is just the side that’s turned west when you’re facing north! Martian: Ah. Um. I know that if I face the direction of my planet’s rotation, ‘west’ is the opposite direction. But what is ‘north’? You: OK, so to find north you just face west and turn right, and—oh, goddammit!

Other dictionaries exploit the convenient fact that human bodies are not symmetrical. Merriam-Webster, for example, suggests “the side of the body in which the heart is mostly located.” That definition might work here on Earth, where, by medical necessity or murderous intent, we’ve torn open enough bodies to know where hearts reside. But what would a Martian know of human anatomy?

Of course, for Mars we could simply send over a compass or a cadaver. But surely “left” ought to mean the same thing even on the other end of the universe! Besides, pointing at a physical object can’t help us distinguish our universe from its mirror image; the mirror version of us could do exactly the same thing with their mirror compasses and bodies and be equally convinced that they’d defined “left.” We need a definition that doesn’t rely on sharing physical things.

In which the universe speaks for itself

An answer finally began to emerge a few years later, when I interned at a particle physics laboratory. There I learned of “parity conservation,” a rule in physics that dictates that in a mirror-image world, objects should behave in mirror-image ways. For example, if you take a right-handed glove and turn it inside-out, a left hand ought to fit perfectly into it.

Parity conservation would dictate that, indeed, there is no physical way to define “left.” Say you tried to give a Martian an experiment to determine what left is – maybe having him spin a ball and look at which way the side facing him is moving. If parity conservation holds, the Martian could unknowingly spin the ball the other way, walk away thinking left is right, and, when he finally visits Earth, get himself killed at his first London crosswalk.

For decades, physicists believed that parity conservation was a law of the universe. But in 1956, three physicists – Chen Ning Yang, Tsung-Dao Lee, and Chien-Shiung Wu – made a startling discovery: in the world of nuclear physics, mirror-image particles don’t always do mirror-image things.

To understand their experiment, imagine that you line up 100 people front-to-back, half righties and half lefties. You give each of them a tennis ball to hold in their strong hand, and instruct them all to hurl the balls away from their bodies. What could you infer from where the balls end up?

You might see that the balls on either side of the line were, on average, thrown equally far. That’s probably the most intuitive outcome: it would suggest that a righty is exactly like a lefty, just inverted. However hard the average righty throws with her right hand, the average lefty throws exactly as hard with her left. But suppose you find a difference – the balls on the right, on average, went farther than the balls on the left. That would tell you that righties’ right hands and lefties’ left hands aren’t interchangeable. You’d know that parity conservation does not hold for righties and lefties.

This is almost identical to the physicists’ experiment, except that they used radioactive cobalt atoms instead of people. These atoms each have an inherent spin direction – they’re all either clockwise-spinners or counterclockwise-spinners. Being radioactive, they also periodically spit out electrons as they break down. Yang, Lee, and Wu oriented a bunch of cobalt atoms so that they were all spinning counterclockwise when viewed from above, and counted the number of electrons popping out above and below.

If the counts were equal, that would mean that a right-side-up counterclockwise atom was the same as an upside-down clockwise atom – parity conservation would hold true. But to everyone’s astonishment, the scientists found that more electrons came out the bottom. Somehow, nature cared whether a cobalt atom rotated clockwise or counter!

At long last, then, we can talk directions with Mars. Just get a Martian physicist on the phone and tell him to grab some radioactive cobalt. Have him orient the atoms so that their spin is in the same direction as a ball rolling towards him. Now, whichever side emits more electrons when he faces the cobalt is “left!”

In truth, it gets a bit more complicated – that definition relies on the fact that our universe consists of mostly matter, rather than antimatter, and the reasons for that remain a fundamental mystery of physics. For those details, though, I’ll have to leave you in the competent hands of Radiolab. I’m so excited that I can definitively tell my right from my left that I’ve got to share with someone. Time to go find me a Martian!