Anyone Can Understand Quantum Physics: Part Two, The Uncertainty Principle
Hello everyone, and welcome to part two of my series titled ‘Anyone Can Understand Quantum Physics’. If you missed part one, ‘Wave-Particle Duality’, you can find it here. Not to plug myself, but I’d recommend reading it first before continuing here as this post will build on and expand on the topics discussed in part one (experiments and calculations by Thomas Young, Max Planck, Albert Einstein, and Louis de Broglie, which opened the doors to our current understanding of waves and particles, and their intertwined nature). As I said in part one, it is my strong belief that science should be accessible to everyone. So, to carry out that belief, I’m here to describe the fundamentals of quantum physics in a way that, hopefully, anyone can understand. Feedback is welcome and encouraged from everyone, whether you are a non-scientist, an expert in string theory, or somewhere in between. With that, let’s talk about our second topic: Heisenberg’s Uncertainty Principle.
You might only know Heisenberg as Walter White’s alter ego on ‘Breaking Bad’, but German physicist Werner Heisenberg was no kingpin in the drug game. At least, if he was, he did a fantastic job of keeping it a secret. He worked for the Nazi party on their nuclear weapons research and development, but there’s speculation that he may have been secretly derailing Hitler’s whole thing. It’s controversial. In his earlier years as a scientist, Heisenberg studied theoretical physics with Niels Bohr in Copenhagen. He won the 1932 Nobel Prize in Physics “for the creation of quantum mechanics”; imagine winning the Nobel Prize for literally creating a field in physics. This dude is the real deal. His scientific magnum opus was titled ‘The Actual Content of Quantum Theoretical Kinematics and Mechanics’; in this, he makes his famous claim that became known as the Heisenberg Uncertainty Principle. His principle is misquoted about as often as Darth Vader in The Empire Strikes Back — students often memorize it as “one can never know a particle’s position and momentum at the same time”. His principle does apply to position and momentum, but the context was a little broader.
“[C]anonically conjugated variables can be determined simultaneously only with a characteristic uncertainty.” — W. Heisenberg, 1927
Basically, Heisenberg’s Uncertainty Principle puts a limit on the certainty with which we can find the values of two complementary variables (variables that inherently go together, like energy and time, or position and momentum). While his principle can definitely apply to position and momentum, he wasn’t specifically talking about these two variables. The mathematical definition of the Uncertainty Principle, when applied to position and momentum, wasn’t even derived by Heisenberg, but by another physicist named Earle Hesse Kennard. The inequality Kennard derived expresses the standard deviation of position and momentum to be greater than or equal to half of the reduced Planck constant. In simpler words, Kennard showed mathematically that when the uncertainty of either the position or momentum goes down, the uncertainty of the other variable goes up. The closer we get to accurately determining the position of a particle, the further we get from finding the momentum.
This seems kinda counterintuitive. Take, for example, the momentum and position of a baseball. The equation to find the linear momentum is p=mv, where p is momentum, m is mass, and v is velocity. Even without knowing the exact position of the baseball, you can find its momentum; the only pieces of information needed are the mass and velocity. Velocity is the derivative of position, though, so they are inherently related. This equation works in classical physics because we consider the baseball to be an object with its center of mass existing at a specific point in space. In quantum physics, this begins to fall apart. Why? Because, remember, every particle exhibits properties of both particles and waves. The equation works if the particle is simply treated as such, but the wave properties of a particle make the Uncertainty Principle true.
In a wave, you can point to specific positions on the wave, but you can’t really define a specific location of a wave since it is spread out over space — the wave occupies a range of positions. To point at one specific position, there couldn’t be a definite wavelength or momentum. Because the wave oscillates, it essentially has to be ‘paused’ to say with certainty that it occupies a certain position. This is further proven by de Broglie’s equation, which shows that the wavelength is equal to h/mv. Remember that mv is equal to momentum, so de Broglie’s equation can be rewritten as λ=h/p. Without a defined wavelength, there can be no defined momentum. This can be reversed, too: knowing the momentum with some certainty means that there is definitely a wavelength, so the position becomes uncertain.
In application, measuring the position or the momentum of a particle is impossible without interacting with it. For example, you can find the position of an electron by shining light (aka blasting photons) at it. Momentum is transferred when the photon hits the electron, so you want to use light at a low-energy wavelength to be more certain of the electron’s momentum. Low-energy waves have a long wavelength. To decrease uncertainty in position, however, you need to use light with the shortest wavelength possible, which increases the energy. The more specific you are with one variable, the less specific you can be with the other.
Heisenberg made other contributions to quantum physics beyond his principle, most notably his matrix mechanics formulation with Max Born and Jordan Pascual. According to the matrix mechanics Wikipedia page, he came up with this formulation while frolicking on an island, reading poems and exploring nature. I have no idea whether this story is true (we all know how reliable Wikipedia can be), but I sincerely hope it is. BRB, gonna go read some Goethe on an island and hope I have a scientific breakthrough. Just following in Heisenberg’s footsteps…
Anyway, that’s really all there is to it. The more confident you are about a particle’s position, the more uncertain you become about its momentum. The more certain you are about a particle’s momentum, the less positive you can be about its position.
Part 3 of my series ‘Anyone Can Understand Quantum Physics’ is coming soon. Follow me on Twitter for updates and to stay connected!
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