I want to tell you about one of the most beautiful ideas that I know.

It’s a physics experiment, and it’s beautiful because in one elegant stroke, it expands our consciousness, forcing us to realize that objects can behave in ways that are impossible for us to picture (but remarkably, possible for us to calculate). It’s beautiful because it calls into question the bedrock of logic on which we’ve built our understanding of the world. It’s beautiful because it’s deceivingly simple to understand, and yet its consequences are deeply unsettling. And it’s beautiful because I refused to accept it until I ran the experiment for myself, and I distinctly remember watching my worldview shatter as the picture slowly built up on the computer monitor.

This was eleven years ago. I was a college freshman, sitting in a physics lab with all the lights turned out, staring at a blank computer screen, and for reasons that I won’t go into here, listening to a best-of compilation of 80s pop hits.

Here’s the setup. On the table in front of me there’s a box with two thin slit-like openings at one end. We’re shooting particles into this box through these slits. I did the experiment with photons, i.e. chunks of light, but others have done it with electrons and, in principle, it could be done with any kind of stuff. It’s even been done with buckyballs, which are soccer ball shaped arrangements of 60 carbon atoms that are positively ginormous compared to electrons. For convenience, I’m going to call the objects in this experiment electrons but think of that word as a stand-in for any kind of stuff that comes in chunks, really.

At the other end of the box is a CCD camera, that takes a snapshot of whatever hits it. Every time a particle makes it to the other side of the box, I see a dot light up at the corresponding point on my computer screen.

Just to be extra careful, we’ve set up the experiment so that there is only one particle inside the box at any given time. Picture, if you like, very tiny baseballs being flung into the box, one at a time. The 80s music plays on, and we sit and wait.

What would you expect to see on the other side of the box? Well, if electrons behaved like waves, you’d expect to see fringes of bright and dark bands, like ripples in a tank of water. That’s because waves can interfere with each other, canceling out when the peak of one wave meets the trough of another, and getting reinforced when the peaks line up.

But electrons aren’t waves – they come in chunks. I know this, because I can see them arriving at the screen one at a time, and they strike at a single place, like raindrops falling on dry pavement. And if electrons are chunk-like, then you’d expect to see them piling up behind the slits and nowhere else. In short, you’d expect them to behave like baseballs.

And indeed, if you do this experiment with only one slit open, they behave just like baseballs, hitting the wall in a single band behind the open slit. A reasonable prediction, then, is that when we run the experiment with both slits open, we should see two bands – one behind each slit.

So what do the electrons do?

Here, see for yourself. You can watch the electrons coming in one at a time in this video produced by scientists at Hitachi in 1989. The video has been sped up around 30X.

It takes a moment to realize just how odd this is. Somehow, the electrons created this interference pattern of bright and dark stripes. But they were sent in one at a time, so what could they possibly have interfered with? If you’re picturing the electron as a tiny baseball, you’re forced to conclude that an electron going through one slit ‘sniffs out’ that the other slit is open, and adjusts its behavior accordingly. Or that it’s somehow taking both paths and interfering with itself. This doesn’t make any kind of sense.

So let’s take a step back, and try to piece together what happened. Here’s an obvious question that you might ask. Think about an electron that arrives at the screen. Which slit did it go through?

Did the electron go through the left slit?

No! Because when you cover up the right slit, the stripey pattern disappears and you get a boring single band instead.

Did the electron go through the right slit?

No! For the same reason as above. When you cover up the left slit, instead of the stripey pattern you get a single band.

Does the electron go through both slits?

No! Because if that were true, we’d expect to see the electron split into two, and one electron (or maybe half) would go through each slit. But if you place detectors at the slits you find that this never happens. You always see only one electron at a time. It never, ever splits into two.

Did the electron go through neither slit?

No! Of course not, that’s just silly. If you cover both slits, nothing happens.

At this point you’re probably thinking that this is getting a bit ridiculous. Why can’t we just look at the damn electron and see which path it took? The problem with this idea is that looking at something means shining light on it, and shining light on it means bumping it with a photon. If you’re a tiny electron, this bump disturbs your original path.

Well, wait. Maybe you could make the bump really, really gentle, so you don’t disturb the electron much. Indeed, you can do that, but as you make the light more gentle (lower momentum), you also make it more spread out (larger wavelength), and you end up not being able to tell which slit the electron went through.

There’s no way to win here. Any scheme that you can invent to determine which route the electron took will also destroy the interference pattern.

To summarize, we’ve arrived at a pattern of fringes that’s built up one particle at a time. But when you try to work out exactly how those particles got there, you find that they didn’t take the left route, they didn’t take the right route, they didn’t take both routes, and they didn’t take neither routes. As MIT professor Allan Adams puts it, that pretty much exhausts all the logical possibilities!

An electron is not like a wave of water, because unlike a wave, it hits a screen at a single location. An electron is not like a baseball, because when you throw in a bunch of them through a double slit, they interfere and create patterns of fringes. There is no satisfying analogy that anyone can give you for what an electron is. As Allan Adams points out in his introductory lecture on quantum mechanics,

These electrons are doing something we’ve just never thought of before, something we’ve never dreamt of before, something for which we don’t really have good words in the English language.

Apparently, empirically, electrons have a way of moving, [..] a way of being, which is unlike anything that we’re used to thinking about.

And so do molecules.

And so do bacteria.

So does chalk.

It’s just harder to detect in those objects.

Physicists have a name for this new mode of being. We call it superposition.

It’s sometimes useful to think of an electron as behaving like a particle, and it’s sometimes useful to think of an electron as behaving like a wave. But these are just conveniences of language, and they’re both incomplete pictures. An electron is neither a wave nor a particle. An electron is an electron. The same goes for a photon, an atom, a buckyball, a giant molecule, or what have you. (The larger the object, the harder it is to see these fringes.)

Werner Heisenberg, one of the creators of quantum mechanics, understood this clearly. In 1930, he wrote,

The solution of the difficulty is that the two mental pictures which experiment lead us to form—the one of the particles, the other of the waves—are both incomplete and have only the validity of analogies which are accurate only in limiting cases. [..] the apparent duality arises in the limitations of our language.

As Heisenberg and others taught us, although language fails us, it’s possible to come up with rules that correctly predict how tiny things behave. Those rules are quantum mechanics. You can learn these rules for yourself by reading Richard Feynman’s classic book QED, or watching his lectures on the subject. Using these rules, physicists can throw around fancy sounding sentences like ‘the electron wavefunction is in a superposition of going through the left slit and going through the right slit’. These sentences have well defined mathematical meanings, and they make predictions that match the data. But what’s missing here is a coherent picture that you can hold in your head that will explain which path the electron took, and what’s more, we can be fairly confident that such a picture can never exist.

It’s perhaps not surprising that our ape-brains, which evolved in a middle-sized world throwing rocks and spears, can’t visualize the behavior of very small things. What’s surprising to me is that even though we’re unable to picture this quantum world, we’ve managed to work out the rules of the game.

References

This post has largely been inspired by watching Allan Adams’s excellent introduction to quantum physics made available by MIT OpenCourseWare. The first lecture is an fascinating and often hilarious look at the principle of superposition explained in a non-technical way. I highly recommend checking it out – he’s a very engaging lecturer.

The story is about the nature of light and matter. And it is driven by a fervent battle of ideas between some of the greatest minds in science. It begins at the turn of the eighteenth century.

By then, Isaac Newton had already made a name for himself as the biggest badass in science. He invented calculus (edit: although the origins of calculus are somewhat mired in controversy), devised the law of gravity and formulated the laws that govern how things move. That’s pretty eventful for a few decades (in fact, he did much of this work in a single year), and it’s almost inhuman that all this came from a single person.

And things were just getting started. By the turn of the century, Newton had turned his considerable attention towards the problem of light. How does it work? What is it made of? Using a series of simple, methodical experiments, he argued that if you stripped light down to its tiniest constituents, you would end up with particles that he called corpuscles. This idea was widely adopted, and became the mainstream scientific opinion for over a hundred years.

There were always doubters to this idea, but they weren’t many of them, and they weren’t popular. It was another brilliant English scientist, Thomas Young, who would take the next step in understanding light.

Young was quite the Renaissance man. In addition to being a physicist, he made significant contributions to fields as diverse as music, language (he compared the vocabulary and grammar of 400 different languages), Egyptology (he partly deciphered Egyptian hieroglyphics from the Rosetta stone) and the physiology of vision.

But what Young considered his greatest achievement (and he had a few) was overthrowing Newton’s century-old notions of light. In its place, he argued that light was not made up of particles, but was instead a wave, quite like the ripples on the surface of water.

At first, he met with huge resistance to his ideas. But in 1803, Young convinced his skeptics with a simple, game-changing experiment.

Here is how it works. Imagine light is composed of tiny particles, like droplets of water, that are being spit out from a lamp. If this light falls on a barrier that has two thin slits sliced into it, it will shine through these slits. If this ‘garden hose’ theory of light is correct, you would expect to see something like the following picture.

What you see here is the drops passing through the slits and striking the wall in basically two places. At the right is a plot of how many drops hits the wall, and there are two piles of water drops that are directly behind the two slits.

Now imagine the same experimental setup, but instead of spraying droplets, we fill the room ankle-deep in water. Things now look something like this:

At one end, you start sending out ripples in the water. Just like when you drop a pebble into a pond, these ripples move rhythmically outwards in circles, peak followed by trough followed by peak.. and so on. When the ripple hits the barrier, you now have two ripples coming out, one from each slit.

And as these ripples start moving towards the screen on the right, something entirely new happens – they interfere. That is, there are places on the screen where the crest of one wave hits the trough of another, and the two waves cancel each other out. And there are other places where two peaks or the two troughs line up – the waves reinforce. If you were to look along the screen, you would find places where the water stays completely still, next to places where it splashes wildly.

If you wanted, you could do the same experiment with sound. Instead of slits, you could have two speakers. Sound is a wave, it’s a vibration in the air that wiggles our eardrums. As you move your ear along the screen, you would find places where the two sound waves reinforce, and you would hear a louder sound. And there would be also places where you would hear nothing as the sound waves cancel each other out (no vibration). The overall picture you get is this striped interference pattern shown above, of alternating highs and lows.

So Young performed this experiment with light. To everyone’s surprise (but his), he found that light doesn’t act like the bullets of a machine gun. What he saw on the screen was an interference pattern – alternating bands of light and dark. The interpretation was unambiguous – light behaves like a wave, not like a bunch of particles.

And for the next century, the wave theory reigned supreme, until no less a figure than Albert Einstein came onto the scene. In his amazing year 1905, Einstein explained a famous experiment – the photoelectric effect – by invoking the idea that light is made of particles that carry energy. He would later win the Nobel Prize for this achievement. Somewhat embarrassed by Newton’s corpuscles, physicists rebranded these particles with a new name – photons.

And soon after, engineers were building devices that could make noises whenever they detected light. Rather than hearing some kind of continuous splish-splosh that you may expect from a wave, they would hear a sound like individual raindrops – tick, tick, tick. Each of those ticks was a photon striking the detector.

Now, if you’re with me so far, this is a point where you can stop and scratch your head. On the one hand, Young proved that light is a wave. But then you have Einstein and these detectors. They’re practically screaming in our ears that light is a particle. So what’s really going on here?

This is the dilemma that gave rise to quantum mechanics – depending on what experiment you do, light seems to behave like a wave, or like a particle. It turns out, as physicists later discovered, that this is true for any kind of stuff, not just light. If you take atoms or electrons and send them through the double slit, they’ll behave like the interfering ripples, not like water drops.

My teachers made a big deal about this in high school, and I used to always wonder what the fuss is all about. After all, water ripples are waves, but water is made of particles (H20 molecules). No one talks about the wave-particle duality of water. What’s different about these subatomic particles?

Well, I’m going to tell you now what my school teachers never taught me, but I learned from popular science books instead. Let’s say you’re a rogue physicist, and you think that everyone’s having you on with all this wave-particle mumbo jumbo. Here’s a simple experiment you can perform to prove them wrong. What if you repeat the double slit experiment, with one small change – this time, you send stuff in one particle at a time. Before you read on, take a minute to think about what you would expect to see on the screen.

If you haven’t come across this before, then your intuition is probably telling you that the particle couldn’t possible interfere, because there aren’t any other particles around to bump into.

Now, here’s what actually happens. Remember, at any given time there is only one particle in the picture. (the video you’re seeing was done for electrons, but the same thing happens for light)

How wild is that? Our rogue physicist’s idea fell flat. Even though you send in the electrons one at a time, they still manage to interfere. If they behaved like billiard balls, they would be going through one slit or the other, in which case you would just see two bright bands that are behind the slits. Instead they produce these alternating dark and light bands. How could this be?

“Aha!”, says the rogue physicist. “I’ve figured out what must be happening. The reason I was thwarted is because I must have been wrong about the electron in the first place.”

“Maybe what’s really happening is that the electron somehow splits into two pieces, goes through both slits, and then interferes with itself.” And so the physicist hatches a plan to vindicate their idea.. by looking to see which slit the electron really goes through.

And here comes the mind-bogglingly bizarre thing about quantum mechanics. Let’s say you shine light on the electron to see which slit it goes through. What you see is that it always goes through one slit or the other, nothing weird is going on. But, once you do this, the interference pattern disappears and instead you get just the two bands!

If you detect which slit the electron goes through, then it behaves like a plain-old billiard ball. But when you turn off the light, and can’t tell which door the electron goes through, it interferes and you get the pattern of light and dark fringes. So, just by looking at the particles, we are changing the outcome of the experiment.

There is no picture that you can hold in your head that will explain these results. It’s not like a billiard ball with some strange gears and clockwork inside it. It’s something fundamentally different.

But they have gotten used to the idea that measurements matter. In the quantum world, a measurement fundamentally alters the thing that you are studying.

Rather than finding this strangeness unsatisfying, I find it incredibly exciting. In a way, I feel that we’ve been pretty lucky so far. Our brains have evolved to understand the African jungles and savannah in which we grew up. Everything that makes sense to us is not too alien from this environment. But when we start to push our understanding to this sub-atomic level, there is no good reason for our macroscopic intuition to apply here. Like Alice’s looking glass, these two slits are our door into a strange new world.

And if you thought things couldn’t get any weirder, you’re wrong. Here’s the clincher. Let’s say you repeat the double slit experiment, but this time you put a detector only behind one slit. So I know if the electron goes through slit B, but not if it goes through slit A. What would you expect to happen now?

What happens is not that you get half an interference pattern. Instead, this is no different from the previous experiment with two detectors. The electrons pile up behind the slits.

Think about what this means. If you are still clinging in your head to a picture of an electron as a ball flying through one of the slits, then you are forced to conclude that the electron going through slit A somehow knew about the detector in slit B, and decided not to interfere. This is absurd (even by quantum standards) and many a crackpot have travelled down this road. Instead, what we should learn from this experiment is that our classical picture is fundamentally broken. The electron does not behave like a ball, or anything else we can readily imagine.

Well, then, what the hell is it? To find out, tune in to part 2 of a tale of two slits.

That’s it for now. I’ll let this madness settle in. In part 2 of this post, I will explain the rules of the new game in town: quantum mechanics. I’ll revisit the double slit experiment, but this time I’ll describe the elegant methods that physicists use to make predictions in the quantum world. And I’ll comment on an interesting new experiment that revisits the double slit.

References:

If you want to understand how quantum mechanics works without getting into the mathematical details, you could do no better than read Feynman on the subject. His book QED: The Strange Theory of Light and Matter has my vote for one of the finest popular science books of all time.

Richard P. Feynman (1988). QED: The Strange Theory of Light and Matter Princeton University Press ISBN-13: 978-0691024172

Young, T. (1804). The Bakerian Lecture: Experiments and Calculations Relative to Physical Optics Philosophical Transactions of the Royal Society of London, 94, 1-16 DOI: 10.1098/rstl.1804.0001

The experiment that I mentioned with a detector behind just one slit is a special case of the Quantum Eraser experimental setup.

Here’s the writeup by Hitachi that goes along with the video embedded above.

After being very pleased with myself for coming up with  ‘a tale of two slits’, I googled it to find that it had already been coined. However, my mild annoyance quickly turned to delight as I started reading Ethan Siegel’s excellent and entertaining blog.

Edit: Richard Dawkins has a way with words. In this fascinating TED talk from 2005 (one of the first talks on TED.com), he speaks eloquently about the idea that our brains have evolved to find the universe intuitive at a given middle-sized scale. He calls this our Middle World, and we can step out of middle world by looking at things that are at a different scales in size and speed.

Footnotes:

I remember that the double slit experiment, one photon at a time, is the first experiment I ever did in college. It was my first semester, and at the time, I didn’t expect it to work. It just seemed too far out to be true. Sitting in that dark room watching the interference pattern slowly build up on the computer screen essentially shook the classical physics out of me.