So, today’s BMC post is a bit of a historical interlude, with a healthy dose of quantum mechanics. Don’t worry, that doesn’t mean this will be a particularly complicated or long post, as the concepts are surprisingly simple.
It’s 1927, do you know where your electrons are?
By the beginning of the 20th century, a number of experiments were beginning to show the confusing and seemingly contradictory quantum nature of matter. In 1900, a huge paradox was facing physicists: the ultraviolet catastrophe. The equipartition theorem (see past BMCs for more info on it) stated that the energy distributed through each degree of freedom. For an electromagnetic wave, these degrees of freedom are the available frequencies. Because the number of modes of vibration in a 3-dimensional cavity is infinite, and each mode carries an amount of energy proportional to the temperature, the power radiated by a cavity at any non-zero temperature should be infinite, as there are infinite degrees of freedom available to the electromagnetic waves in the cavity: We should see ovens blasting deadly x-rays and gamma radiation out of them whenever some poor unsuspecting chef opens it. Clearly, we don’t. This was solved by quantizing the energy of the electromagnetic radiation into discrete packets, also allowing Einstein’s famous solution to the photoelectric effect (he won his Nobel prize for this, not anything relativity related). This was a weird solution, as other experiments clearly show light to behave like a wave, doing wave-y things like diffracting and interfering. It also heralded the idea that ultimately became the even weirder solution to another problem.
The problem that this quantum interpretation was used to solve was the Rydberg energy levels found in the hydrogen atom. The electrons orbiting a hydrogen atom classically should be able to have any arbitrary orbital radius, and thus any arbitrary energy level before being ionized. Instead, by examining the spectrum of the hydrogen atom, we found electron energies to lie in specific values, and electrons to orbit only at certain radii. Louis de Broglie, owner of a tremendous name (his full name was Louis-Victor-Pierre-Raymond, 7th duc de Broglie!), decided to take the solution for the quanta of light, and apply it in the opposite direction. If light waves acted particle-y, then perhaps matter particles acted wave-y. Using the relation for the energy and wavelength of light, de Broglie applied the same equation to electrons. The result gave the discrete energy levels as a nice side effect of the modes of vibration for the orbiting matter waves about a hydrogen nucleus. His hypothesis was directly confirmed in 1927 by firing electrons through a crystal and viewing the resulting diffraction pattern (caused by the self-interference of the matter waves). This is even weirder than particulate light: matter is a wave, and can interfere with itself and other matter. This has been confirmed for particles as large as metal nuclei, and will likely be tested on living viruses in the near future. What does it mean for life if living things can exist in superposition states?
What does this mean?
Well, for one thing it means it is rude to tell someone they have an abnormally small wavelength! But it also tells us something important about the world we see. The reason the quantum nature is so counterintuitive is that our senses give us data directly that tell us the world is classical. We never see cars interfering with each other instead of crashing, or baseballs occasionally quantum tunneling through bats. The De Broglie wavelength helps explain why. Because the De Broglie wavelength is proportional to Planck’s constant, it tends to be tiny. Planck’s constant, in units of Joules, is about 6.6 divided by 10 to the 34th power, or a 1 followed by 34 zeros (I don’t know why I just said that, I really hate the 1 followed by N zeros popular science meme.) Because the De Broglie wavelength is inversely proportional to the momentum of the object, unless an object has absolutely minuscule mass or velocity (or temperature!), the wavelength is too small to have any observable effect. When you get down to particles smaller than atoms, the wavelength blows up, and the scales become big enough to have an effect on the particles themselves. This is one of the reasons the “big” world seems classical, when deep down it is quantum. I’m sure if I was a sentient electron writing this, I would be telling you the exact opposite, why those weird huge things don’t act all wave-y like us.