by Shane L. Larson
The Cosmos is a stunning and beautiful place that inspires unabashed awe in many of us. The story of understanding the Cosmos and what makes it tick is what science is all about. But there is an extra dimension to these tales of discovery, and that dimension is the personal stories of the scientists who have wrested utterly amazing secrets from Nature.
The human stories wrapped around science stories touch each one of us on a deep level because we can identify with the uniquely human response to difficulties, to friendships and collaborations, to confusion, to success and elation, and sometimes to tragedy. Can you imagine Galileo’s astonishment when he saw craters on the Moon through his little telescope, something no one had ever seen before? Can you feel the elation Henrietta Swan Leavitt must have felt when she discovered she could measure the distance to the stars? We can sympathize with the colleagues of physicists Henry Daghlian and Louis Slotin, both of whom died from radiation exposure in accidents at Los Alamos during the Manhattan Project. We are horrified by the unexpected death of Emmy Noether, one of the greatest mathematical physicists of the early 20th Century, who died suddenly from complications after an operation.
The stories of the scientists at the heart of discovery remind us that science is an all together human endeavour; we are the only species, so far as we know, to systematically explore and understand the Cosmos. We are one of the few species that use an understanding of the Cosmos to improve our lives. Mixed in with the biographies and well documented histories of science, there is also a bit of folklore — funny tales and anecdotes that capture the endeavour in small vignettes. I think sometimes we tell these bits of folklore, whether they are true or not, because they often capture some of the ephemeral emotions that we all feel when faced with the Big Questions in the Cosmos. One of my favorite examples of this kind of folklore has to do with the realm of the atoms, quantum mechanics, and Albert Einstein.
In the early part of the 20th Century, physicists were trying to understand the discrete colors of light emitted and absorbed by hydrogen atoms. All atoms have a unique and discrete spectrum of light they emit — a spectral fingerprint that identifies precisely what kinds of atoms you are working with. Hydrogen, being the simplest of atoms, was the focus of everyone’s attention, in the hopes it would be the easiest to understand. There was an empirical formula for the hydrogen spectrum — a simple formula that was worked out from observations — but no one knew why the formula worked. It just did!
The first clue as to what was going on came from Danish physicist, Neils Bohr, who proposed something we now call “the Bohr Model of the Atom” in 1913; it is just the classic picture of an atom that we are all taught in grade school. Bohr’s colleague, Ernst Rutherford had shown in 1911 that the atom was comprised of two parts — a small, hard center called “the nucleus” and an outer cloud where the electrons resided. Bohr discovered that if the electrons are required to reside on orbits — circles of specific size — he could predict exactly the spectrum of colors emitted by hydrogen. The Bohr Model was one of the early discoveries that helped drive the emerging branch of physics called “quantum mechanics,” which was concerned primarily with how the world behaves on the smallest scales imaginable.
One of the interesting features of the Bohr-Rutherford atom is that it is mostly empty space. The nucleus is only about a femto-meter across. That’s one-billionth-millionth of a meter, 0.000 000 000 000 001 meters. By contrast, the electron cloud is about a million times larger, about a tenth of a nano-meter across. That’s only 0.000 000 000 1 meters. That means the atom is mostly empty space. Now think about that for a minute. That sounds crazy, because if atoms are mostly empty space, then you are mostly empty space, and so is everything else!
That notion certainly doesn’t jive with your everyday experiences. When you fall off your mountain bike, you most certainly collide with the ground and stop! If you and the ground were both mostly empty space, shouldn’t you just pass right through each other? It would be a lot less painful! It turns out that electrons dislike being around one another — they are “electrically repulsive.” The reason you and the ground bounce off of one another is because the electrons in the ground repulse the electrons in you. But if the electrons are on little orbits, wouldn’t they still usually miss each other? As it turns out, the little orbits picture isn’t the right picture to carry around in your head; the sub-atomic world is much stranger than that.
The Bohr-Rutherford model of the atom was one of the central starting points in the development of quantum mechanics, the branch of study concerned with understanding the interactions and dynamics of particles on the scales of atoms. Over the course of two decades following Bohr’s model, all the major tenets of quantum mechanics were discovered. The cacophony of quantum effects that were amassed and tested in this time were triumphant revelations about the world of small things, but they all smacked of absurdity because they almost always clash with the direct sensory reality of what goes on in the macroscopic world.
One of those discoveries was that the position of tiny particles, like the electron, were not so easy to nail down. In fact, the electron was known to inhabit areas around the nucleus of an atom that we now call “orbitals” — extended regions of space where we are “most likely to find the electron” if we go looking for it. The reality of “position” was suddenly replaced by the idea of probability and statistics. There was no definitive answer anymore to the question of “where is the electron?” A new mathematical entity was discovered to describe this idea, called a “wavefunction.”
So what’s going on? We said Bohr’s model completely and accurately described the spectrum of hydrogen by imagining the electron was a little ball going around a fixed orbit. How can that be right, AND this electron probability cloud be right? Insights into the physical world often capture precisely the correct physics, but the picture we carry around in our head or the words we use to describe what has been captured in the mathematics are incomplete. This is the case of the Bohr atom. Bohr’s mathematics was correct, and explained the behaviour of the hydrogen atom, but the picture of an electron going around on a little orbit was not the correct picture, because it didn’t capture one important aspect of the physics, namely why only certain orbits were allowed. The reason was a discovery of one of Bohr’s contemporaries, and points the way to wave mechanics.
Louis Victor deBroglie proposed in his 1924 PhD thesis that all matter behaves like waves, including electrons. This idea is known as “wave-particle duality.” The idea was so radical, his graduate committee didn’t know what to make of it. They passed the work on to Einstein, who supported it whole-heartedly, and deBroglie was awarded his PhD. Five years later, deBroglie was awarded the Nobel Prize in Physics for his discovery. How did this connect the Bohr atom to wave mechanics? deBroglie suggested that if the electron were a wave, the only Bohr orbits that were allowed were those which perfectly fit an electron wave around it. Thus the electron was not a particle located somewhere around the orbit, rather it was the entire wave that covered the entire orbit.
The reality of the wavefunction idea was born out in experiments time and time again, forcing physicists to accept that the microscopic world was truly different than the world of Big Things like ping pong balls, Yugos, hedgehogs and popsicles. But there are certain implications of accepting the wavefunction idea that are even weirder than not knowing where the electron is. One of those things is quantum tunneling.
Imagine I caught an electron and am keeping it as a pet in an aquarium in my living room. According to quantum mechanics, if I go looking for my electron, I am most likely to find it in the aquarium. But the wavefunction extends oustside the aquarium, and that means there is a teeny-tiny probability that the electron will be found OUTSIDE the aquarium. If I do find it there (sneaky little quantum jailbreaker), we say that the electron “tunneled” through the barrier of the aquarium wall.
This really happens. If it didn’t, you wouldn’t be reading this blog post, because modern microchips work on the premise that electrons can tunnel their way through barriers; this is one of the operational principles behind transistors and diodes, which make up a significant fraction of the guts of your computer.
And this brings me back to our starting point: folklore. There is a story that Einstein was so uncomfortable with this idea of tunneling, that he took to wearing gigantic shoes around his house (I imagine them to be kind of like giant clown shoes), in order to inhibit his feet from tunneling through the floor while he was walking around! Now, this story about Einstein is almost certainly false; Einstein was perfectly aware of the fact that quantum effects are not important on the scales of the macroscopic, and he was certainly capable of computing the probability of his feet tunneling through his floor!
But we tell this tale tale anyhow, not because it is funny, but because quantum mechanics IS disconcerting! Quantum tunneling makes NO SENSE, especially if you are used to thinking about hacky-sacks, pomegranates, and freight trains. We use this story to tell ourselves that Einstein was uncomfortable with this idea, thus reassuring us that it is okay for us to be uncomfortable too.
And it is okay to be uncomfortable. Discomfiture over cherished ideas being challenged and overturned is the bread and butter of science. This is how our knowledge grows, and how our understanding of the Cosmos evolves to be more complete. We abandon old beliefs, no matter how cherished, if we find them to be unworkable in the face of new data and new knowledge.