Physics - Spring 1998

Physics 2 ("Physics and the Quantum Enigma") focusses on the mysteries of quantum mechanics. It satisfies Q and IN requirements. It is readily accessible to non-science majors. It has no prerequisites. (But some physics majors also take it because it covers material too strange for our regular physics curriculum.)

Quantum mechanics, the most battle-tested of all theories, is basic to every science. It is required for the understanding of atoms, the Big Bang, molecules, lasers, and transistors. But it presents us with an enigma--a crazy puzzle.

Issues once considered beyond the domain of physics are forced upon us by quantum mechanics. Demonstrations in the laboratory display aspects the nature of physical reality, universal connectedness, and perhaps even human consciousness that, at first sight, seem ridiculous. On more careful examination they seem even more ridiculous.

To understand these issues, we start with several lectures on ordinary (classical) physics--though we present them with an historical and philosophical emphasis. Two lectures on Einstein's Theory of Relativity then follow--as psychological preparation for quantum mechanics. (Relativity is almost impossible to believe, so thinking about it is good practice in believing impossible things--a skill essentially required in order to appreciate the quantum enigma.) Then, after a fairly standard introduction to quantum mechanics, we go on to the enigma: "physics' skeleton in the closet."

There are about 30 lectures, and a weekly discussion section. There is weekly homework, a midterm, and a final exam. The title of each lecture follows with a few words of description.

PART ONE: Classical Physics: Our Intuitive Worldview

Setting the Scene for Science:

Ancient Greek science, which became the science of the Renaissance. This is what Galileo's method for science overturned.

A Method for Science:

Galileo's new approach to science. It started the "Age of Reason" or "The Enlightenment." It is the foundation of all modern science and technology.

Motion:

We start science (as Aristotle taught us to) with the simplest aspects of Nature.

The Newtonian Synthesis:

Newton's F = Ma, the "universal equation of motion," and his law of universal gravitation. Putting the heavens and the earth together.

Our Newtonian Legacy:

The philosophical (and the psychological and social) impact of Newton's physics.

Energy:

What energy is, and the forms it can take.

The Electric Force:

The force with which we see, hear, taste, and-- maybe--the force we think with.

Waves:

Waves of water, sound, electric field, and--we'll see--waves of matter.

PART TWO:

Einstein's Relativity:

Psychological Preparation For Accepting Something "Impossible"

Relativity I:

Einstein's postulate, the universal speed limit, E = Mc2.

Relativity II:

The slowing of time in moving systems (why you can become older than your mother).

PART THREE:

Quantum Mechanics:

Confronting the Enigma

A Logical Parable; Quantum Mechanics Overview. An overview of what's to come.

Light:

Wave or Particle? The first (gentle) taste of the enigma.

The Real Nature of Atoms:

A double entendre: what atoms are really like, and a "demonstration" that they are physically real things.

A Quantum Atom:

Bohr's early quantum description of the atom. Spectra "explained"! But strange problems arise.

Matter: Wave or Particle?

The second (a bit less gentle) taste of the enigma.

Schrödinger's Equation:

The new fundamental law of Nature.

The Skeleton in the Closet:

The enigma: what happened to physical reality? What's going on?

The Uncertainty Principle and Complementarity:

The craziness has protection and organization.

Schrödinger's Cat:

The story Schrödinger told to show that his quantum mechanics is absurd.

The Copenhagen Interpretation:

The standard defense of the craziness, the "official dogma," a new philosophical stance for science.

Quantum Mechanics Applications:

Too much philosophy! Quantum mechanics is practical--it makes money: lasers, superconductivity, transistors.

Objections to the Copenhagen Interpretation:

The Einstein-Bohr debate, Einstein's concession.

The EPR Paradox:

Einstein's demand for physical reality.

Introduction to Bell's Theorem:

What must be true in a reasonable world.

Bell's Inequality, its Tests, and Implications:

The proof that our world is surely unreasonable--whether or not quantum mechanics is correct!

Alternative Interpretations Of Quantum Mechanics :

Interpretations even more bizarre than Copenhagen.

Quantum mechanics and Consciousness

Every interpretation of quantum mechanics forces us to say something about consciousness--and it's something strange.

Epilog: Where does this leave us?

Nature seems to be telling us something: something about the nature of reality, a universal connectedness, and consciousness. It's something we still do not understand. We just know it's strange.

The idea of this course is to learn ways in which computers might be useful to physicists. Our main focus will be on a discussion of algorithms for solving a number of generic problems, and trying out our ideas on a few specific problems. We will have good practice in learning to implement simple algorithms by writing and testing programs in C, with a few techniques of C++ being used occasionally. It will help if you know how to do some programming, although not necessarily in C. Our assignments will require the implementation of our algorithms through the writing of short, simple C programs, for which I will be the guide for those who need it.

Here is a list of possible topics, not in any special order:

• Differentiatiion of a function
• Integration of a function--that is, numerical quadrature.
• Monte-carlo integration
• Extrapolation and interpolation
• Finding roots
• Solving ordinary differential equations (along with this might be some discussion on how to make keyboards interactive, at least on UNIX)
• Techniques for making and displaying graphs
• Fitting curves to data
• Inverting a matrix?

These are some ideas. We may alter or amplify the list, depending on the wishes of those attending the class. For example, some of those in the class may have senior thesis problems that could serve as jumping-off points for our discussions.

The "text" is Numerical Recipes in C (second edition), by William Press et al, which is an excellent book. It has much more than we need in it, but it also has much that we will use. Although it is not a formal text book (it is more properly classified as a reference book), it is a fine book to learn from, and will be useful long after this class is over.

Good books from which to learn C programming include The C Programming Language (second edition), by Brian Kernighan and Dennis Ritchie. Ritchie designed the language in the 1970s, so this is the authoritative book. It's a little terse, however. A more wordy book (and one with excellent problems) is A Book on C, by Al Kelley and Ira Pohl. There is a fourth edition now. The third edition, if still available, is also excellent. I use both Kernighan and Ritchie, and Kelley and Pohl.

There will be a single exam, at the end of the course. In addition, I will assign a few problems each week for the homework. In all, it should be a lot of fun.

Most of my experience relates to solving problems in nonlinear dynamics. For example, I know some neat examples involving the Mathieu Equation. I have also written several C programs that are used in our upper division physics lab courses, such as the nonlinear least-squares curve fitting program that we use in 133 and 134, along with a useful program that produces graphs. No doubt we'll discuss them. For additional information, questions or suggestions about this course, feel free to call me (my home number is 423-0796; my office is 459-2405) or send me email (drip@cats.ucsc.edu)

-- Peter Scott

Revised 7/14/04.