Gauge Theories 2. From Athens 300 BC to Geneva 2011 AD2.1 Atoms-A Mystery of Two Millenia Humankind’s serious quest to understand our nature dates back at least to ancient Greece when came out a unique group of people who not merely gazed at the stars in the vast sky or watched the people and things around them but also pondered the reason behind the mystery of those remote objects, conjectured the inner structure of various kinds of matter around them and tested new forms of state management. Along the way, they developed the logic system, axiomatic mathematics, astronomy, physics and democracy among other great achievements. Some of them such as logic, number theory and geometry are taught and practiced today almost in exactly the same way as over 2000 years ago. Ancient Greek civilization is a rare bout of intellectual explosion in the history human evolution. To me it is a huge mystery how they could reach such a highland of intelligence and rationality. We are exceptionally blessed to have such a golden time in our history and should feel eternally grateful for their contributions to the entire humankind. It is a great comfort to see their spirit perpetually planted in our minds and more and more people becoming the spiritual descendants of the ancient Greeks. Of their great achievements, relevant to this series is that they hypothesized the existence of atoms, the tiny, unbroken components of all matter. Different combinations of atoms create different forms and kinds of matter. It is a tremendous simplification of our nature. One can never overestimate the influences of this philosophy on the people who set out to search for the answer to a natural phenomenon. In fact, it has become the most important drive of modern science and technology.
With that said, atomic theory of ancient Greece largely remained a pure speculation for more than 2000 years. Alchemists may protest this assessment, but their contributions are limited to the synthesis of some new compounds only. Fancy and useful these things may be, the significance to the understanding of the structure of matter is null. No substantial progress was made until the age of industrial revolution of 18th-19th century. The indisputable, quantitative evidence of the existence of atoms was provided by a colorblind British, John Dalton. The chemical reactions he performed may be called trivial even in his time, but his capacity of logic inference can only be called genius. In a few years, his theory was warmly accepted and applied by the mainstream of science. A few decades later, a Russian named Dmitri Mendeleev tabulated the elements that had been discovered. The table reveals a hidden, astonishing simplicity, i.e., all elements are somehow related to each other and form a hierarchical family. Elements sharing physical or chemical properties such as density, color, luster, conductivity, reactivity etc can be grouped into rows and columns, called periods and groups, respectively.
It would take the world another over 100 years to have a full understanding of the significance of the periodical table. Indeed, there are still many puzzles about the table today. Mendeleev’s periodical table was accepted almost immediately because new elements that were predicted by his table were found with exactly the same properties as predicted. Unlike the ancient Greek’s atoms, Dalton’s atoms have many kinds, each element having its own atoms. Like ancient Greek’s atoms, Dalton’s atoms are unbroken. This property, however, with the efforts of great scientists such as Svante Arrhenius, James Thompson, was found to be untrue. Atoms do have their own internal structure. The description and explanation of atomic structure are the major tasks of the physicist and chemists of the early 20th century. With a very simple apparatus called cathode ray tube, Thompson discovered electrons and measure its charge/mass ratio. He further built up an atomic model in which the negative and positive charges are more or less uniformly mixed together to form a tiny ‘jelly’. In less than 20 years, this model was overthrown by Ernest Rutherford who proved that there is a tiny but massive nucleus in the atom. His atomic model is like a tiny solar system in which the heavy ‘sun’ is positively charged and the light ‘planets’ are negatively charged. While the stability of our solar system is maintained by the gravitation attraction between the sun and the planets, the stability of the atom is maintained by the electric attraction between the ‘sun’ and the ‘planets’. This model is still used in high school and college textbooks today. Like the solar system where inner planets have lower energies and hard to leave the sun, the electrons closer to the nucleus have lower energies and harder to leave the atom. Unlike the solar system where each planet runs on its own orbit (we never observe a planet make a change of their orbit), the electrons in an atom may make a jump, or transition, i.e., they may change their orbits. When an electron gets extra energy from, e.g., light, that may move to an orbit of higher energy. On the other hand, an electron in the orbit of higher energy may jump ‘down’ to lower orbit by emitting light (photon). With this ‘dynamic planet’ model, the mysterious spectrum can be understood. The answer to questions such as “why does sodium, when burned, emit its characteristic yellow color while magnesium emits a different, bright white color?” becomes obviously clear.
Things looked perfectly simple and fine. People started to give a sigh of relief. The atoms are tiny solar systems and our solar system has many tiny kids or grandkids, isn’t it a beautiful picture? The sensitive reader may see a kind of gauge symmetry here. If we make a scale change, or gauge transformation, our solar system becomes an atom or vice versa. Physical theories work the same way in different scales (gauges). (caution: we know that theories with this kind of gauge symmetry is rare because energy scale and size scale are related to each, that is why we do not see tiny solar systems very often. You see gauge has to have something more than ‘scale’. ).
However, the tiny solar system model, or planets model, was found to be erroneous. As a well-known phenomenon, if a charge has acceleration, it will emit electromagnetic wave and loses energy. For example, the arctic lights are the consequence of charged particles accelerated by the earth’s magnetic field. An electron moving in a circular orbit certainly has acceleration. According to classical electromagnetism, then, an electron has to emit light and lose its energy and finally it would crash into the nucleus. That is to say, the planet model cannot explain why the atoms are stable. Electrons are there moving around the nucleus but they do not lose energy and swirl into the nucleus.
It took about 10 years to solve the problem. To get the answer, a new kind of physics, suitable (and maybe uniquely applicable) in the microscopic scale, was established. It is a rare kind of revolution in science, a revolution that puts giants like Newton, Maxwell and Einstein in an embarrassing situation. That is quantum mechanics. Initially, it was built to answer a very specific, important but not that earth-shaking, question of the stability of atoms, but its consequence is epoch. You may find quantum mechanics book thick and frightening, but it can be summarized into a single, short sentence: quantum mechanics says that the order of making two (hence more) measurements matters. You may get a different result if you change the order of two measurements. It sounds odd, you may say, how does it relate to the question of the stability of atoms? You may also protest, why is it such a big deal? We all know that the order of dating and making love are very important, does that make us a quantum mechanical object?
I think it’s a good time for both you and me to say “給我一個突破”. See you next week.