Whether you’re laughing right now—or staring at your screen in confusion—hinges on how much you know about one of the foundational ideas in quantum physics: Heisenberg’s uncertainty principle.
In its most basic and commonly known form, the uncertainty principle says that the more precisely you know the position of a particle in a quantum system, the less well you know its momentum (and vice-versa). The principle also applies to other pairs of characteristics in quantum systems, like energy and time. But every physics graduate first starts to unpack this concept through the lens of position and momentum, so we will, too.
If this was all Heisenberg’s uncertainty principle said, it probably wouldn’t have been profound enough to weave its way into pop culture in the form of mugs, T-shirts, and cartoons—let alone place its pioneer as an alias for an infamous meth-cooking chemistry teacher.
German theoretical physicist Werner Heisenberg first introduced his uncertainty principle in a 1925 paper. It’s special because it remains intact no matter how good our experimental methods get; this isn’t a lack of precision in measurement. It doesn’t matter how smart you are, or how sophisticated your equipment, is you can’t think your way past it. It’s a fact of nature.
Legendary physicist and master bongo player Richard Feynman put it like this: “The uncertainty principle ‘protects’ quantum mechanics. Heisenberg recognized that if it were possible to measure both the momentum and the position simultaneously with greater accuracy, quantum mechanics would collapse. So he proposed that must be impossible.”
Reality is telling us that we can have our quantum cake, but we can’t eat it, too.
What Is the Heisenberg Uncertainty Principle?
Chad Orzel is an associate professor in the Department of Physics and Astronomy at Union College in Schenectady, New York, who is also the author of several books that explain often complicated and esoteric ideas to a layman audience. In his book, How to Teach Quantum Physics to Your Dog, he covers Heisenberg’s uncertainty principle.
The origin of the uncertainty principle is found in the duality of particles in quantum physics; depending on what they’re doing, they can be described as either a particle or a wave, Orzel tells Popular Mechanics.
At the turn of the 20th century, physicists were engaged in a heated debate regarding the nature of light, and whether it exists as a particle or a wave. Thanks to a pioneering test known as Young’s Double-Slit experiment, physicists discovered the answer was “Door No. 3” as Orzel puts it. That is, light isn’t a particle or a wave—it has properties of both. And, shockingly, particles of matter like electrons also demonstrate this particle-wave duality.
“So every particle in the universe—or every kind of object that we know of in the universe— has this combination of properties we associate with waves, and properties we associate with particles; they’re a third kind of object that isn’t really one or the other,” Orzel says. “And it’s because of that you can’t get rid of the Heisenberg uncertainty principle with a better experimental technique, because it’s really fundamental to that dual nature.”
He continues by explaining the fact that you need to have both wave-like properties and particle-like properties, meaning you can’t measure either of them perfectly.
“Being able to have both requires that each be imperfect, in a way, and there’s just no way around that,” Orzel explains. “We know from experiments that things that we think of as particles, like an electron, would have a well-defined position, but they also have a wavelength associated with them, and that wavelength is related to the momentum.”
When the particle is moving, it’s doing “wavy stuff” that has a characteristic wavelength associated with it—and that length, it turns out, is inversely proportional to the momentum. This means the faster the particle is going, the shorter the wavelength, and the slower the particle is going, the longer the wavelength.
“You need to have both of these things if you want to have the position well defined and momentum well defined,” Orzel says. “It has to have both a position in space that you can point to and say ‘it is right here.’ And it has to have a wavelength with some characteristic length associated with it. And those things are incompatible.”
Think of the momentum of a traveling particle as a wave; the peaks of the wave represent the probability of the particle’s position. One infinitely long wavelength represents a very precise momentum. Problem is, with that single infinite wavelength, there is an infinity of peaks, thus the momentum is precisely known, but the position is completely unknown. The particle could be anywhere. That means in that situation, you’ve got an exact momentum, but no clue about location.
To get a read on the particle, what we could start doing is stacking different wavelengths, each representing different momentums for the particle. Where a peak meets a trough, you get “destructive interference,” and the wavelength is flattened. Where the peaks meet, you get an increased peak, and thus an increased probability of finding the particle.
Add enough wavelengths and birth enough constructive and destructive interference, and you’ve got a single peak and close to a definite position for the particle. In the process of creating this peak, you’ve also destroyed the wavelength, meaning you now know zilch about the momentum—you’ve sacrificed it for certainty about the position.
“The best you can do is create a wave packet, which is flat, and then you have some waves that get bigger and bigger and they come to a peak and then they get smaller on the other side, sort of tapering off on either side,” Orzel says. “You can look at that region of space and say, here are the peaks, and I’ve got so many here. We also have a wavelength giving the momentum, but the region in which that’s happening is relatively confined and can be quite small.”
That means momentum and a position can be given for a system using this wave packet, but crucially there’s an uncertainty to both measurements. We’re all clued in on the joke now, but there’s still the question of what makes it ludicrous.
Why Don’t We See the Heisenberg Uncertainty Principle on Everyday Scales?
Obviously, a car—whether it’s driven by one of the founders of quantum mechanics or not—isn’t a “quantum object.” It doesn’t travel like a wave, meaning your car can’t diffract around corners, and thus it isn’t governed by the rules of the subatomic or the uncertainty principle; nor are tennis balls, or comic books, or squirrels. The reason you can’t find your keys every morning isn’t that you know their momentum precisely and thus can’t possibly know their position—so no more using that as an excuse for being late for work.
The big question is: why doesn’t the Heisenberg uncertainty principle affect “everyday” or “macroscopic” objects?
The answer lies in the equation that describes the phenomena.
The generalized form of the Heisenberg uncertainty principle says that if you measure the momentum of a particle with uncertainty Δp, then this affects the uncertainty of the position Δx, which can’t be any less than ℏ/2Δp.
The whole equation looks like this: Δx ≥ ℏ/2Δp. It’s the ℏ (pronounced “H-bar”) element we’re interested in here.
This is known as the reduced Planck’s constant, and the thing about it is . . . it’s small, very small, and it constrains the values of the uncertainties of our two properties and makes them small, too.
“The uncertainties are so small for macroscopic objects that if you have an object that’s one kilogram, moving at one meter per second, its wavelength would be 10-34 meters, [that’s zero, a decimal point followed by another 33 zeroes], which is a distance that’s so small, it doesn’t really make sense to talk about,” Orzel explains. “Then the uncertainty in the position is going to be some smallish multiple of that, which is just so tiny it’s ridiculous. So, you can’t see the uncertainty principle with ordinary macroscopic objects.”
You can see that uncertainty with subatomic objects like electrons, however, when the wave properties become apparent; that’s because their wavelengths are long enough. As Orzel points out, that’s also when you can measure that uncertainty.
Exactly where the line between quantum and non-quantum behaviors lies is currently a hot research topic in physics, with scientists discovering quantum effects in particles as large (and even larger) than Carbon-60 atoms, also known as “Buckyballs,” because of their resemblance to the hexagonal egg carton-like architecture of Buckminster Fuller.
As for why the uncertainty principle is so captivating, Orzel explains:
“It’s telling us something fascinating about the universe, which is that at a very deep fundamental level, the nature of reality is such that there will always be some uncertainty and that it is impossible, even in principle, to know certain things about the world or certain combinations of things about the world.”
Oh, and it makes for great jokes, too.
Robert Lea is a freelance science journalist focusing on space, astronomy, and physics. Rob’s articles have been published in Newsweek, Space, Live Science, Astronomy magazine and New Scientist. He lives in the North West of England with too many cats and comic books.