Walking through Cambridge one Friday evening, I saw a strange sight: a man praying to a Federal Express drop box. At first it seemed odd, but then I could hear the prayer in Hebrew. I looked at my watch and saw that it was 6:04 PM, the moment of sunset for Cambridge. His orientation was facing east, so clearly he was a Hasidic man praying toward Jerusalem. The initial oddity wore off as I unraveled the mystery. He must have been en route to some destination when the sunset overtook him.
I teach a course called Primitive Navigation. The subject is how navigational strategies emerged in many cultures across the earth prior to the Scientific Revolution. As part of the course, I have students identify stars and planets, and become accustomed to their motion in the sky. I track the positions of the stars and planets as a matter of course, and can even anticipate events like the backward motion of planets called retrograde motion. Currently Jupiter is executing a retrograde motion.
Now, let’s try an experiment here. Google the words “Jupiter” and “retrograde” and look at the how many hits you have to go through before you find an astronomy, as opposed to an astrology website. You’ll go through five pages of astrology hits. That’s not all. If you read one of the websites, it will tell you that Jupiter is retrograde in Taurus. But, if I look up in the sky, I don’t see Jupiter in Taurus, I see it in Aries – quite some distance away.
What’s going on?
Most people don’t care if Jupiter is executing a retrograde motion unless it tells them whether they should buy stocks or wear heels on a blind date. The scheme used by western astrologers is based on a version of the sky that was frozen in time when the ancient Greeks made observations of the sky. Since that time, the earth’s axis had wobbled to a new orientation, but, due to tradition, the astrologers use the old locations of the zodiac as a basis for the augury.
What does any of this have to do with particle physics? Clearly the two stories – the man praying at the Fed Ex drop box, and the belief in Jupiter executing retrograde motion in Taurus are matters of faith. We might scoff at these as relics from a bygone era, but we should be cautious on two accounts: 1.) descriptions of the universe at one time saw astronomy and astrology as somewhat inseparable and 2.) even modern science rests on many assumptions that to many of us have become articles of faith.
Now, you might say, “but…science has a right to examine any and all assumptions, but things like religion and astrology take all assumptions as sacred.” The problem is ‘which assumptions?’. There are so many. When I was a graduate student, I studied something called the Dirac equation. Paul Dirac was a theoretical physicist who is best known for his famous equation describing the motion of particles like electrons. He successfully combined two pillars of modern theory: quantum mechanics, which describes particles as a wave with special relativity, which takes the speed of light to be a fundamental constant of nature.
When he put these two factors together, his equation had some strange properties. At first blush, you find that electrons have this strange motion that’s called ‘zitterbewegung’; German for ‘trembling motion’. This is a very rapid oscillation of electrons at the speed of light, which doesn’t seem to really happen and would lead to odd results. This was more or less brushed under the rug.
The second problem is that there are negative energy solutions, which should be forbidden because they would violate our cherished principle of the conservation of energy. One of my friends at graduate school laughingly called these “Dirac fairy tales.” But an odd thing happened. Dirac tried to plug up the negative energy states by saying that nature somehow filled up all the negative energy solutions, leaving behind the possibility that ‘bubbles’ in the sea could be created. These bubbles would have the same mass, but opposite charge of the electron. It was an inevitable consequence of his equations, but had never been seen and he was ready to dismiss this as he had done with the zitterbewegung. He speculated that the positively charged electron might be the proton, but was dissuaded and published a prediction of a positively charged electron. In 1932, Carl Anderson discovered the positron.
So, the zitterbewegung was discarded as meaningless, but the problem of the negative energies ended up predicting the existence of antimatter.
More articles of faith: infinite energies. You might recall that the strength of the electric field gets larger as you get closer to a charged particle. In particle physics, we like to talk about ‘point-like’ particles, meaning that they have no size. In practice, this creates a problem: right at the electron, the electric field is infinite. Energy gets tied up in the electric fields, so, in principle, the energy of the electric field of the electron is infinite. This seems like a problem, since the electron seems to move quite happily around. How do physicists deal with this?
We have a process that removes the infinite energies and renders them finite. It’s called renormalization. The main idea is that we decide, somewhat arbitrarily, that our rules of physics change at very high energy scales or very small distance scales. The scale where everything changes is so remote from the scales that we’re testing that it won’t make a difference in our calculations. We ‘kill’ the infinite energies this way and make our calculations finite. This process also provides a look at particles we have yet to see that might exert a hidden influence on the strength of forces and values of masses. This process, however contrived it might seem, has given amazingly solid predictions. Yet we don’t know what it means for the physics to change at very, very short distances. It’s a matter of faith.
Theorists say that any viable theory of particles and their interactions must be of a sort that allows us to remove the infinite energies. This requirement guides theorists to root out non-conforming theories and accept theories that avoid the infinite energies. In essence, this is the role of the Higgs boson — by being the thing that makes mass, it allows our beloved Standard Model to avoid the infinite energies and does.
Physicists rarely questions these articles of faith. Sweeping zitterbewegung under the rug is fine, but what does it mean? Is there any meaning to the process that we use to kill the infinite energies, or is it just a mathematical trick that appears to work? Although they may seem like ‘fairy tales’ as my friend said, they have become articles of faith and are rarely questioned. The problem is: we don’t know whether we will be forced to reexamine some of these, or if so, which of these we have to reexamine. Until then, we have our own Fed Ex drop box where we worship.
