WALKING TOUR OF THE RANDOLPH COLLEGE PHYSICS MAJOR

A walking tour takes time. Learning physics well also takes time. Physics should be studied on a walking tour. Deep understanding of physics normally requires years of study. Twenty second soundbites and rapidly flashing MTV-style images just won't do the job! If you have a short attention span, physics is not for you!

The physics curriculum resembles a spiral staircase. As you circle around revisiting topics at higher and higher levels, your understanding grows. Climbing higher depends on passing the steps below in sequence. Advanced courses depend critically on their lower level prerequisites.

Let's begin the course-by-course walking tour now.

(Warning! Your guide is honest. He must sadly acknowledge that the tour now describes a past "golden age" of RMWC physics. Some of the courses below are no longer available to Randolph College students.)

INTRODUCTORY CALCULUS-BASED PHYSICS

Here you learn how and why ordinary objects move as they do. Along the way you are introduced to three extremely important fundamental quantities: linear momentum, angular momentum, and energy. The deep significance of these quantities dawns on you after you study physics for a few years.

You also study how energy is transferred by heating, how random thermal energy can be harnessed to perform useful work, and how the amount of thermal energy available for useful work is steadily diminishing.

Finally, you study the fundamental principles of electricity and magnetism, the basis for so much of modern technology.

So you start with Galileo in the 1600's, progress through Isaac Newton, and end up with James Clerk Maxwell in the mid-1800's. If this course were titled like a history course, it would be called: "Physics to the Civil War".

Algebra, trigonometry, and calculus are used without apology. If you have serious ambitions in science, you must become competent in applying mathematics to the physical world. You will get a good intellectual workout solving lots of quantitative problems!

In the laboratory that accompanies this course you will learn to include estimates of uncertainty in all your measurements. This gives you a deeper understanding of the reliability of quantitative scientific knowledge.

MODERN PHYSICS

Modern Physics is a traditional sophomore-level continuation of introductory calculus-based physics. You start with Einstein's theory of relativity, progress through an introduction to the quantum mechanics of Bohr, Heisenberg, and Schroedinger, and move on to study the fundamentals of nuclear and elementary particle physics. If this course were titled like a history course, it would be called: "Physics After the Civil War".

Relativity theory clarifies the distinction between relative and absolute. (Everything is not relative!) You learn that time elapsed between two events depends on the observer's motion! You find that matter is not conserved! You discover that energy has inertia! You learn that a general theory of relativity is also a theory of gravity! This is neat stuff!

During the introduction to quantum mechanics you learn that very small bits of matter like atoms, protons, neutrons, and electrons behave differently than large bits of matter we handle in everyday life. Atoms are not like tiny little stones. Instead, they are more like fluid wavy things that spread out through space and interact discretely with each other. Individual interactions are not completely predictable, but some interactions are more probable than others. Quantum mechanics tells you what is possible and how probable the possible is.

In an atomic nucleus energies are high, forces are strong, and relativity is important. You study the fundamentals of radioactivity, nuclear reactions, fission and fusion. You understand how chemical elements can be transmuted by means of nuclear reactions, and you begin to understand how the chemical elements we find around us on Earth are produced naturally by nuclear reactions in the cosmos as stars evolve.

The course ends along the historical path to our present understanding of the fundamental building blocks of the universe: leptons, quarks, and force-transmitting bosons.

Several assignments throughout the course will be carried out using the mathematical computing system called "Mathematica".

This course features time travel, warped space, antimatter, matter creation and annihilation, and nuclear transmutation of chemical elements. Sign up now!

THERMODYNAMICS

In this course you study thermodynamics in much more depth than you did in introductory calculus-based physics. The mathematical level is higher, and the assigned problems are more substantial.

You study ideal gas laws and the kinetic theory of gases. You learn how thermodynamic properties of the whole gas are related to the average behavior of large numbers of gas particles. You see the laws of thermodynamics applied to a variety of systems.

ELECTRONICS INSTRUMENTATION LAB

Physics is definitely not all theory and math! In fact, the majority of physicists are experimentalists who construct and use equipment to measure and explore the universe.

Almost all types of experimental work use electronics in some way. The goal of Electronic Instrumentation Lab is to teach you the basic electronics you need to function as an experimental physicist. This course is designed to take inexperienced novices as far as possible in one semester. (We do not assume you have previously repaired TV's!) You start with simple circuits you build yourself. You learn to use an ammeter, voltmeter, signal generator, and oscilloscope to probe and measure circuits. You learn to make circuits do useful things like amplify, filter, or count. You learn to solder.

The course will include lectures as well as lab work, and good technical writing in lab reports will be emphasized.

INTERMEDIATE PHYSICS LAB

This is a junior level lab where you perform a variety of experiments from different areas of physics. The particular experiments chosen depend on the interests of the instructor and students. They could include experiments from classical mechanics, thermodynamics, electromagnetism, optics, and, certainly, modern physics. Some of these experiments will let you practise the skills you learned in Electronics Instrumentation Lab, including computer interfacing.

Lab reports will include advanced techniques of data analysis as well as continued emphasis on good technical writing.

MATHEMATICS AND COMPUTER SCIENCE

Let's take a brief pause in the walking tour of physics. We'll sit here on this bench and talk about how math and computer science intertwine with the physics major.

Physics majors take lots of math because math is the language of physics. The universe is filled with changing quantities. Many things depend on the rate at which other things change. Calculus allows you to precisely describe these changes and relationships. Three semesters of calculus are needed to master differentiation, integration, and working with quantities that depend on more than one variable.

Since almost all important laws of physics are mathematically expressed as differential equations which you must solve to find the knowledge you desire, a course in differential equations is a prerequisite for upper level physics courses. The concepts and skills learned in Linear Algebra are the "basis" for understanding the mathematical formulation of quantum mechanics.

The tour guide is often asked, "Why do physics majors need so many courses?" The tour guide responds, "Because physics is not trivial"!

The more math you can manage to take, the better educated you will be. Courses in Discrete and Combinatorial Math and Mathematical Statistics will help you count possible quantum states and compute probabilities. They will also help you understand statistical methods used to analyze experimental data. A course in complex variables strengthens your ability to work with complex functions which are ubiquitous in physics.

Since mathematics incorporates universal logic, it is relevant to more than physics. People with physics backgrounds often end up applying their analytical skills to other disciplines ranging from the world of finance to biological research.

Computer skills are also vital for a physics major. Computers control experiments, gather data, and analyze data. They don't do this on their own! Somebody has to set them up and program them. Experimental physicists often do this. Theoretical physicists also frequently use computers because consequences of the fundamental laws of physics can usually be determined only by approximate computer calculations. So physics majors should take as many computer science courses as possible. Computer expertise not only makes you a better physicist, it also makes you employable in many areas outside of physics.

Now it's time to get up and resume the walking tour.

CLASSICAL MECHANICS

Here you study classical laws of motion in depth at the junior-senior level.

The course begins with brief mathematical excursions into matrix representation of three dimensional rotations and index notation. At this point you have climbed far enough along the spiral staircase physics curriculum to study Newton's laws of motion at a higher level. You see that Newton's second law is really a set of differential equations. You solve these equations exactly for several important types of motion, including motion through a resisting medium, damped driven oscillation, and classical rocket motion. After studying these exactly soluable motions, you realize the vast majority of motion is too complicated for such exact treatment. You learn to analyze these complicated motions by means of approximate computer calculations. Then you study Newton's classical law of gravity, gravitational multipoles, and tidal forces.

The second half of the course covers one of the most important topics in theoretical physics, the Lagrangian/Hamiltonian formulation of laws of motion. This formulation is equivalent to Newton's laws of motion, but is expressed in terms of energies instead of forces. Objects move according to Newton's laws if the difference between their kinetic and potential energies is minimized. This is the starting point for modern formulations of field theory. Along the way you learn about the calculus of variations which allows you to find relationships that maximize or minimize quantities. You then apply the new formulation to several types of motion including classical planetary motion.

After an interesting look at Newtonian motion in accelerated reference frames, the course winds up with studies of rigid rotation and coupled oscillation.

STATISTICAL MECHANICS

Statistical mechanics is the branch of physics that analyzes how large scale behavior of a collection of pieces depends on the behavior of the constituent pieces.

Here's an example: Gas is a collection of atoms. Gas pressure depends on the behavior of gas atoms. Gas pressure on the walls of a container is caused by the average force gas atoms exert as they collide with the container walls. Statistical mechanics leads to a quantitative relation between gas pressure and atomic properties.

In this course statistical mechanics is applied to two important cases. One is an "electron gas". The "electron gas" models properties of electrons which conduct electricity through wires. The other is a "photon gas" which models properties of light created by incandescent bodies.

The principles of statistical mechanics can be used to derive thermodynamic equations of state. They also lead to profound insights into the meaning of thermodynamic quantities like temperature and entropy. When you study statistical mechanics on the spiral staircase physics curriculum, you return to thermodynamics at a higher level.

ELECTROMAGNETIC THEORY

Your upward journey along the physics curriculum spiral staircase has brought you to electromagnetism at the junior-senior level. This course is definitely not volts for dolts!

Electromagnetic fields are vectors which vary in complicated ways through space and time. The laws of electromagnetism, which describe these fields, are all expressed in terms of vector calculus. Therefore, the course begins with a rigorous section on vector calculus and its application in different coordinate systems.

Initially, it makes sense to study electric and magnetic effects separately. This wisely postpones the full complexity of electromagnetism. Purely electric effects are studied first. While you learn about electric fields you also encounter lots of applied math. You solve partial differential equations to find electric potential. You use Fourier series to match electric potential to boundary conditions. A series expansion is used to derive expressions for electric multipoles which give insight into the fundamental nature of electric sources.

Pure magnetic effects are covered next. Then you come to the general electromagnetic laws known as Maxwell's equations. Maxwell's equations describe what happens when both electric and magnetic fields are present in general circumstances. You now know enough to follow in the footsteps of James Clerk Maxwell who made one of the greatest scientific discoveries of all time. You will solve Maxwell's equations and find that light is an electromagnetic wave!

During the remainder of the course you study the properties of electromagnetic waves. You learn about polarization, and how simple optical laws, like the laws of reflection and refraction, can be derived from electromagnetic theory. If time allows, you also study how accelerated electric charges create electromagnetic radiation.

Several assignments throughout the course will be carried out using the mathematical computing system called "Mathematica".

QUANTUM MECHANICS

Senior physics majors reach the top of the undergraduate spiral staircase. They've worked hard to climb so high. They've solved many problems and learned lots of math. They've earned the ability to study senior level quantum mechanics.

Quantum mechanics accurately describes the unfamiliar microscopic world of atoms and subatomic particles. Since we have no direct experience of this microscopic world, and since the microworld behaves very differently than the macroscopic world we occupy, we have no intuition about how the microworld should work. Our only guide is mathematics. (The situation is analogous to our inability to easily visualize four-dimensional space. We directly experience the three-dimensional world we live in, but most of us cannot understand four-dimensional space without the help of mathematics.)

Quantum mechanics contains a set of fundamental postulates. These postulates specify "rules" for gaining information about the microworld. The postulates are abstract at first sight. They often need to be encountered again and again before they begin to make sense. Quantum mechanics requires patience and perseverance.

The course begins exploring the fundamental postulates by describing the simplest possible system: a free "particle" in one dimension. A good part of the first semester is spent in one dimension. There is a lot to learn here, including how "particles" respond to forces, quantization, radioactive alpha-decay, tunneling, and the uncertainty principle.

A good deal of time is spent learning the mathematical formalism of quantum mechanics, including matrix notation and Dirac notation. You study the properties of operators which represent observable properties. You learn the profound relation between symmetry, conserved quantities, and quantum numbers. You work in infinite dimensional space! It is truly amazing how these extremely abstract topics begin to make sense after a while! But you have to put in the work and "pay dues" before things come together.

During the second semester you study harmonic oscillation, angular momentum, the hydrogen atom, spin, identical particles, and, if time allows, perturbation theory. Several assignments throughout the course will be carried out using the mathematical computing system called "Mathematica".

This is a challenging course. It is serious business for serious students.

SENIOR RESEARCH

Seniors use the skills they've obtained to carry out a substantial research project. First, a research topic of interest to both the student and instructor is chosen. It may be a topic not covered in the regular curriculum, or the project might be a deeper investigation of a previously studied topic. The project may be experimental or theoretical.

Students normally take one semester to carry out this project. (A more extensive two-semester "honors" project is also possible for interested students whose high grades make them eligible for this option.)

Students do most of the work themselves with guidance from the instructor. Student and instructor meet regularly throughout the project so progress can be assessed.

Students then write a paper on their project. For most students the paper is almost as much work as the project itself. The instructor works very closely with the student on the paper, giving advice and constructive criticism through the inevitable and numerous revisions. Finally, the student gives an oral presentation before an audience of faculty and students. Students usually practice their talks beforehand so the instructor can make useful suggestions about the organization and presentation.

After the talk, we all go out to dinner and blow off steam.

The walking tour now ends. The weary tour guide is asked once again, "Why does the physics major require so many courses?"

The tour guide patiently responds, "Because the RMWC physics department offers a quality major! Less is not more! Less is, simply, less!"

(The guide used to be proud of the quality RMWC physics major. Now he says, "We do the best we can with the resources we have. Less is simply less.")

"The physics curriculum was not designed to pile on credits and make more work for everyone. It was designed to teach the topics national organizations like the American Association of Physics Teachers agree constitute a solid physics major. It was designed to cover topics that appear on the Graduate Record Exam. It was designed to provide solid physics education. Students earning the B.S. physics degree have plenty of room in their schedules for all the required courses outside of math and physics, and they will have a strong liberal arts education. Remember, liberal arts does not equal only humanities! Science and math are part of the liberal arts!"

Check out some contributions of 20th century women to physics.

Trying to offer a rigorous quality physics major at RMWC:

BACK TO TOM'S HOMEPAGE
RANDOLPH COLLEGE HOMEPAGE