Tonight we took a 2600 year journey with Penny and Sheldon “from the ancient Greeks through Isaac Newton to Niels Bohr to Erwin Schrödinger to the Dutch researchers that Leonard is currently ripping off.”
From the Ancient Greeks: Ancient societies, including the Greeks, watched the skies carefully. Since they didn’t have Google Calendar, it was only by watching the positions of the stars each night could they mark the passing of the days and seasons and know the best time to plant crops. (It must have been a nice time to be an astronomer. If you didn’t treat your astrophysicist nicely, you might not have enough food next year.) Most of the points of light in the sky, the stars, appeared to stay in the same place with respect to each other, year after year for as long as anyone could remember. But a precious few, just five, moved relative to these fixed stars. We know them as Mercury, Venus, Mars, Jupiter and Saturn. As Sheldon explains, our Greeks forbears called them “wanderers”, or as we have derived from their language “planets”.
When you look out the side window of your car, you can see objects fixed to the ground, bushes, trees, poles etc. Those near the side of the road zip by. Objects in the distance seem to barely move at all. Although you have the same speed relative to all the fixed objects outside your car, close objects have a high angular speed and you have to turn your head fast to watch them. The far objects have a low angular speed which don’t require much tracking of your eyes. This allows us to understand the motions in the sky of stars versus the planets. The change in position in the sky is determined by their angular speed. Even though stars are moving extremely fast relative to the solar system, most faster than even the outer planets, they are so far away that changes in their position on the sky (their angular position) can only be detected with careful observation, if at all. For example, compare the farthest planet, Neptune (thanks, Pluto-haters) to the closest known star Proxima-Centauri, a little red dwarf star. Neptune is about 4,500,000,000 kilometers from Earth and moving a modest 5 kilometers per second relative to the Sun. If you watch Neptune over the course of a lifetime it will move halfway around the sky relative to the stars since it completes an orbit around the Sun every 164 years. By comparison, Proxima Centauri moves even faster than Neptune relative to the Sun but its position relative to other stars barely moves; its angular speed is tiny. The key difference is that Proxima Centauri is 40,000,000,000,000 kilometers away. Only precise astronomical measurements can see its motions, only hundredths of a degree over a lifetime.
At the other extreme, one of the fastest lights you will see move across the night sky is likely an airplane. They are moving at only 0.2 kilometers per second. But since they are close, say 100 kilometers away, they move faster on the sky than planets or stars. Galileo and Newton realized this, except for the part about airplanes. They knew that if the Earth orbited the Sun, the lack of apparent motion of the “fixed” stars meant they were extremely distant. The Universe was much larger than imagined. That story of the learning the Universe is larger than we thought is repeated many times throughout the history of astronomy. First by realizing the nearby stars are really so far away. Then by measuring the extent of the galaxy. When other galaxies were discovered our idea of the size of the Universe grew larger still. Today we do not know how large the Universe is, we only know that the speed of light is not fast enough to let us see all of it.
Through Isaac Newton: Newton explained why the planets orbit the Sun much like how a child might swing a cat by its tail over his head. If the child lets go, the cat flies off in whatever direction it was heading. In the absence of the Sun, the planets would fly off in straight lines at constant speed in one direction. Instead, the Sun pulls on the planets using gravity. The inward pull causes the planets to move in orbits around the Sun rather than straight lines. The same force of gravity that pulls objects to the ground on the surface of the Earth is what causes the planets to orbit the Sun, the Moon to orbit the Earth and what causes the Earth and Moon together to orbit the Sun together, just like the planets.
But what Sheldon was trying to get Penny to say?
Notice that the Moon and Earth go around the Sun together, even though they have wildly different masses. Objects of different masses fall at the same rate in a vacuum. Their masses don’t matter. The Sun causes objects at the same distance to move the same way. So the Earth and the Moon move around the Sun at the same rate. The Moon’s extra motion around the Earth is just a small variation in its journey around the Sun. Even the tiny International Space Station orbiting the Earth, really has its path dominated by the Sun. Its motion around the Earth is just a tiny little wiggle in its path around the Sun.
To Niels Bohr: Theorists had tried many models to explain the architecture of the atom. But it was only once the experimentalist Ernest Rutherford scattered charged particles from gold foils that it became clear that a central positive charge, an atomic nucleus, was surrounded by distant electrons with negative charge. The motion of the planets around the massive central Sun served as a convenient model. First the Japanese physicist Hantaro Nagoka (1904) proposed the electrons formed rings much like the dust surrounding Saturn. Rutherford himself proposed a planetary model (1911), just as planets orbit the Sun under the force of gravity, Rutherford proposed electrical forces kept the electrons in orbit around an atomic nucleus. Yet even at the time, physicists knew this could not work, since electrons moving in a circle mut radiate light, lose energy, and fall inward, crashing into the nucleus. The Danish physicist Niels Bohr (1913) took the planetary model, but proposed that only certain distances from the nucleus were allowed, i.e. that the energy levels were quantized. Such quantization had previously served Planck and Einstein to describe the behavior of light. Now, Bohr gave birth to a quantum mechanical view of matter, the branch of physics necessary to explain atomic and molecular structure and upon which much of modern technology is based.
To Erwin Schrödinger: Bohr’s model was inspirational, but still didn’t work so well. For example, all electrons in this planetary picture would carry angular momentum around the nucleus, but many do not. The predicted intensity of radiation from atoms did not match the data. In 1926, Erwin Schrödinger developed a more rigorous description of quantum mechanics and the atom. Rather than thinking of electrons like planets, it is because of Schrödinger we think of the electrons being distributed in regions around the atom. Electrons are more or less likely to be found in any one place given by a mathematical function resembling a wave. Schrödinger therefore called it the “wave-function” and in quantum mechanics every particle has one.
To the Dutch researchers that Leonard is currently ripping off: Wave-functions behave counter-intuitively. Perhaps because our intuition was developed more while running across the African Savannah than while orbiting an atomic nucleus. One particularly counter-intuitive behavior of the wave-function is the Aharohnov-Bohm effect featured so prominently in this episode. The effect describes what happens to the wave-function near a magnetic field. It isn’t surprising, perhaps, that if your particle, described by its wave-function, crosses a region with a magnetic field that something about it might change. What Yakir Aharonov and David Bohm predicted using Schrödinger’s wave-function description is that you could have an effect by just going around, but never sampling directly, a magnetic field. Specifically, if electrons follow two different paths around a region of magnetic field and come together, they will have changed in different ways: While one wave-function might be at the crest of its wave, another might be at its trough. Putting the electrons together after their separate journeys, makes the “interference pattern” that Bernadette so rightly admired because they can be beautiful. The effect was predicted and subsequently observed with magnetic fields decades ago.
The Dutch researchers Leonard was ripping off have seen the effect now with electric, not just magnetic fields. The Dutch researchers accomplished it using electrons naturally moving around their sample, through a process called diffusion. Leonard was trying it even more directly by passing a beam of electrons through a sample. You may have noticed they added a vacuum pipe carrying an electron beam into Leonard’s lab. (The end of the pipe is covered in aluminum foil, to keep the flange clean while being built.) The small nan0-fabricated rings would keep all their electric field inside and he would steer his electrons around either side and create an beautiful interference pattern.
I leared something new hearing Penny describe the whole thing to Leonard. Before she said it to the live audience, I never realized the Aharonov-Bohm effect was so funny. I bet we could have had them rolling in the aisles if we mentioned the Stern-Gerlach effect.
P.S. Easter Egg alert. You can see your science consultant in tonight’s episode sitting across from an actual UCLA graduate student in theoretical physics, our very own Sheldon. (He is even working on one of the same problems: N=8 Supergravity.) A gold star to the first person who identifies which scene it is. Scenes are rehearsed several times and then run through several times in front of the camera to get it right. Luckily the props department gave us an interesting little book on quadrupole moments of nuclei from the 1960s to read. Most of the books you see around the apartment and on the sets are real physics books, some very interesting, so there is always something good for us to read between takes.