Maybe the universe isn’t rational after all
A conversation at Lunch
By Benjamin F. Plybon
Mom, dad and son always try to reach their favorite restaurant by 11:30 AM every day but today they were running late. After looking out the front door mom refused to leave home without her umbrella. The skies were darkening as clouds gather. Although not in the weather man’s forecast, rain seemed imminent. Madeline, Madge for short, with umbrella in hand felt secure and the drive began.
As expected, the lunch hour was already underway at Natalie’s when they entered the door. After a short wait, Mom, dad and son were settled at a table in the midst of the crowd of busy diners. Waitress Nadine recognized the familiar trio and quickly took orders and delivered food and drinks. Mom sipped her coca cola and began reading her selection of reading material. Son and dad were eating quietly. It would be difficult to hear conversation over the surrounding sound decibels. In a lull of the chattering voices, Son looked over at dad and broke their silence. Will dad be able to hear?
“OK dad, is the coffee good today? Is this is going to be a good day.”
“Well son, I don’t know yet”, said dad, ”It’s too hot to drink. I like hot coffee, but I’ll have to wait for this cup to cool. Do you know this stuff right out of the pot is around 180 degrees, Fahrenheit, speaking. It has to drop to 150 to be drinkable. That can take four or five minutes. Ask me again then.”
“Well, I guess, dad, we’ll just have to wait for the results. They say, no news, is good news’, so good news so far. I’m hopeful, I’m an optimist.”
No comment from mom. She is also optimistic, always. She is concentrating on her paperback and tuning out the surrounding sea of voices. Mom seemed content, quietly chewing her burger, so son smiled and turned back to his effort to communicate with dad.
Don puts down his drink, “Listen dad, you got me thinking about this particle and wave business after our discussion yesterday. The physicists I watch on my TV Science show seem to be saying we will just agree to say an electron or a photon is both wave and particle, so call it a wave-particle, briefly a wavicle, or something. Do you think that is the best we can do?”
Between bites, dad said, “That is the party line now. Did you know we have party lines in science? That is the agreed upon story we feed to the world, the people in the street as we affectionately call them, as the answer to questions about how can an electron be both a particle and a wave, simultaneously. Everyone agrees, that most of the time electrons behave like particles; but that 1924 Davison-Germer experiment did show electrons sometimes behave like waves. So we can’t say an electron is a particle, and we can’t say an electron is a wave, so let’s just agree that an electron is somehow both, a combination of particle and wave. That’s the official line now. A new kind of entity, forced on us by the quantum nature of the world. Do you have a problem with that?”
“Yes, dad, I do. It sounds like a cop-out to me. You and I have discussed this before, and you said this has something to do with Heisenberg’s Indeterminacy Principle. But I’m still not clear on that. Can you illuminate me?”
Dad chuckles, “You don’t really want me to do that. You’ve watched those films about the WWII war in the South Pacific. Many Japanese soldiers were illuminated. A marine joke. Not very funny now. Illuminate you is what they do when they strike you with a flame-thrower. I won’t do that.”
“No, dad, flame-throwers incinerate people. Not today, please. Light up my mind, and leave my body intact, breathing and able to enjoy lunch.”
“I’ll try. We tell people electrons are both wave and particle, that is the party line, but privately, physicists may have different ways to reconcile this wave vs particle problem in their own mind. I certainly have my own view of this. Christians have a similar problem deciding how to live with evolution and Genesis. Each needs to settle in their own individual minds how to reconcile Genesis with evolution. Individual Christians are free to do as they please.
But science is different. We have constraints. There is more to this matter then just picking a label. Our concepts and thoughts have to be consistent with the facts, and confirmed theories, to the best of our ability. In this case we apply what we know about Quantum Mechanics, that means Schroedinger’s Equation and Heisenberg’s Matrix Mechanics. Schroedinger’s Equation was a product of thinking about the DeBroglie suggestion, that followed the work of Davison and Germer. The Schroedinger Equation is often called the Schroedinger Wave Equation, and his work is known as Wave Mechanics. Prior to this, the mechanics of electrons, and other atomic particles, was Newtonian mechanics. But there were problems with that. Physics students learn Newton’s ideas about mechanics in a course labeled as Classical Mechanics. There is the relativistic version, based on Special Relativity, needed in the case of very high speed electrons or other particles. At speeds less than ten percent of c, the speed of light, about 3 x 1010 cm/sec., relativistic corrections were ignored. The original Schroedinger equation was a non-relativistic version. Schroedinger’s work was designed to deal with the wave property of particles like electrons.”
Don interrupted, “Whoa, pause for a moment before we get too deep into this. You remind me of a bit of wisdom I once heard. There is a way you can always recognize university professors at social gatherings. Ask a man a question and if he is a professor he will not just answer your question he will give you a lecture. You are doing that, dad. Old habits are hard to shake. I know there is a lot of mathematics in this and we can’t get into that sitting here. You once showed me the Schroedinger equation and what the solutions look like. For some reason you have the Schroedinger Equation written on your desk pad, along with some incomprehensible scribbling. Something you were thinking about. I use napkins as scratch pads, myself. That works for me. Can you tell me, how particles can also be waves, without getting into a lot of math, a la Schroedinger, Heisenberg and Bohr? Is there a shorter answer?”
“Sorry”, dad says, “Mathematics is my second language and I feel handicapped trying to talk about matters like quantum mechanics and relativity without chalk and blackboard. I became a mathematician because I realized that modern physics is highly mathematical. I don’t think it is possible to have more than a superficial understanding of most modern physics with all mathematics stripped away. The Schroedinger Equation is a Partial Differential Equation and Heisenberg produced Matrix Mechanics. To one unfamiliar with Partial Differential Equations and Matrices, their work becomes incomprehensible. But, it is a good exercise for me to try to extract the essential physical ideas in this work without the mathematics. There is always the danger of distorting such theories when trying to describe them to non mathematicians. That is done in some popular science books and articles.”
A thought occurred to Don, “I see a parallel in translating poetry from one language to another. Have you ever tried to translate a German poem to English? Or a French poem to English?”
“Yes”, said dad, “I have. When I was a college student I had a German Professor direct from Berlin, after WWII. We read some German poetry in class. Our professor gave us English translations. Somehow the poetry was lost. We had prose translations of poetry. I read well enough to read in German. Some was beautiful in German, but the translations were not. Yes, you have the idea.”
“OK, I thought you would agree. As you have stated, mathematics is a kind of language. Translating can be as difficult as translating Arabic poetry”.
Dad agreed and noted, “We also have another problem. Some things can be said in mathematics that have no accurate, non mathematical translation, using only words. Here is where important physics ideas get lost in popular versions. But, as our English friends say, ‘Let’s give it a go’. Let’s return to your question about Indeterminacy in this problem. Heisenberg managed to prove it is impossible to measure precisely, simultaneously, the position of an electron and it’s momentum. Newton’s particle was a point mass in his mechanics. His mechanics depended upon, at least theoretically, knowing the exact position and momentum of a particle at a given precise time. From that information Newton’s mechanics allows us to compute future positions of that particle. Celestial Mechanics is built on that idea. Heisenberg said, it is not even theoretically correct to apply Newton’s ideas to an electron. Strictly speaking there are no particles in the atomic world, particles as in Newton’s physics. Particles such as Newton envision don’t exist in the world of atoms, because of the indeterminacy principle. Newton’s particles are not physically possible. In brief, an electron is neither a particle nor a wave. Ponder on that.”
Incredulous, Don says, “Are you telling me an electron is not a particle? Not a wave either? From bad to worse it seems. In current physics they tell me an electron is both a particle and wave. You tell me an electron is both not a particle and not a wave. Wow! Do other physicists know that.”
“Well they do and they don’t. They know all that I have told you, but I think they have missed the point. I am considering writing an article called ‘Pointless Matter’. It is concerned with this problem with the particle idea. I have written a draft of that article. You can read the whole thing later, if you wish. Point is a geometrical idea. It is an abstraction of the concept of ‘location’ of an object in geometry. Geometry, Euclidean and non-Euclidean, is based on the two concepts: points and lines; suggested by the everyday ideas of location and direction. A location is represented by a point, a direction is represented by a line. A Newtonian particle is a point with mass. A meaningful Newtonian particle is a point, a precise location at a given time. Heisenberg says, precise measurement of location rules out precise knowledge of momentum, the representation of motion. An electron at a precise location would be a particle with unknown motion. A particle with known momentum must have an unknown location. Sounds like nonsense doesn’t it?”
Don shaking his head said, “It certainly does. Only a physicist would be able to understand this mess. What about the rest of us? Everyone I know thinks electrons are just charged particles. What is the correct way to think about electrons?”
Dad snorts, “Blame Werner Heisenberg. It began with a paper he published in July, 1925. The paper was motivated by his concern that classical mechanics, that is Newton’s mechanics, was being applied in researching electrons and atomic structure. He stated bluntly, that is a mistake. This was even before he produced the Indeterminacy Principle. At this time he centered on the fact that the mechanical theorizing treated electrons as if they could be observed, much like astronomers watch Mars moving in its orbit. He demanded that our theories must involve only observables. The position and movements of particles such as an electron cannot be observed. He developed physics not dependent upon variables that are unobservable, or measurable; these numbers can only be known approximately. That requires abandon of Newton type particles. After Heisenberg nothing remained but the label particle for something that is not a particle. A different kind of physical object. Does that make sense to you?”
“I think I get the gist of the idea. We certainly can’t observe an electron and watch it move. But how do we do the physics without classical mechanics?”
“That has been a problem. Heisenberg produced his Matrix Mechanics that did fit his prescription. He made no use of unobservables. His work was accepted as theoretically correct, but it turned out to be too complicated to use on typical problems of interest. The problem, most important at that time, was determination of the structure of the simplest atom, the hydrogen atom. Bohr gave his solution in 1913, but there were many problems with his ideas. His model pictured the atom as a miniature solar system. To even present a picture was taboo to Heisenberg. Soon after Heisenberg did his work, Bohr agreed with him. Schroedinger’s solution produces wave functions, a purely mathematical representation of an atom. Neither Schroedinger Wave Mechanics nor Heisenberg’s Matrices produces a picture of a Hydrogen atom. Both reveal the structure in terms of possible energy levels, and an array of possible quantum states. From this mathematical structure, physicists can obtain a greal deal of information about atomic structure, and predict results of experiments.
“In 1959, Heisenberg published a small book called The Philosophy of Physics. In this book he discusses a problem confronted by modern physicists. He points out, our language, and the associated concepts of physics, were designed to talk about the macro world of normal size objects. Classical Mechanics was designed for that world, and it works beautifully. At the atomic level classical mechanics does not work, and the concepts don’t fit. We need a new language. The language of mathematics can be used, but the English language words like particle, momentum, energy, and so on, do not fit exactly; but we continue to use the words. So today we are forced to use the word particle for objects that are not particles, wave for something that is not quite a wave like water waves, and the language problem goes throughout all of our atomic and sub-atomic physically thinking. We have invented new terms like Quarks and described them with words such as charm, or color, suggesting properties like charge; suggesting electrical charges, but are not. I fear the language of mathematics may be the only language that truly fits the physics studying today. How do we describe the results to non mathematicians? Big problem.”
Don says, “I think I’ve been sufficiently confused for one day. Good try, dad, but I guess I’ll have to learn more mathematics if I want to understand modern physics. Maybe, tomorrow we can discuss the physics of playing pool. That I understand.”
Dad, laughed. “Pool you do know. A long time ago a physicist named Coriolis used his mathematics and physics to analyze the motion of pool balls. You would have to know mathematics to understand his view of pool. Do you really want to discuss that tomorrow? Probably not, son. Maybe we should start with Calculus and get you up to Partial Differential Equations by next Spring? We’ll need a year or two to do Tensor Analysis and Relativity. Does that sound OK to you?”
“Ready to go, mom? I think dad has become irrational. Was that Irish coffee today, dad?”
Mom nods, “Yes, Don, I’m ready. Next lunch can you talk about something besides particles and waves and weird people like Heisenberg, Dirac and Schroedinger?”
Dad said as rising from the seat, “Sure we can, mom, but those were fascinating people. Those were my gods before I became a Christian. I exchanged my old gods for a new God, the real God. Right, reverend mom? Do you remember when the kids, and some adults, in the churches called you that? You’re still my favorite preacher, rev mom. Was your book interesting?”
(Copyright © 2015 Benjamin F. Plybon. All rights reserved.)
