Physics 109b: Chaos and Quantum Physics
Predictability in Science - 1999

Jerry P. Gollub

Course description

            Brief:  Two revolutions that both limit and extend the deterministic paradigm of modern science.  Following a brief review of the central ideas of classical physics, the basic features of chaotic dynamics and quantum physics will be explored, to understand the extent to which predictability is possible for physical systems that are either nonlinear or very small.  Not open to students majoring in Physics, Chemistry, or Mathematics. No prerequisite, but high school physics and a basic grasp of elementary calculus (even if rusty) would be helpful.  NA

            Extended:  The Newtonian paradigm of the "clockwork universe" is often presumed to be typical of science.  In fact, the idea that science has as its goal complete prediction of the future is unrepresentative.  This course explores two important scientific revolutions that changed our understanding of the role of prediction:  nonlinear dynamics and chaos; and quantum physics.  Each involves a mixture of prediction and limits on predictability.  Several weeks will be spent on needed background material in classical physics so that these developments can be understood and appreciated.  Students will be expected to achieve a basic understanding (quantitative to a limited extent) of the fundamental concepts of each area, through readings, exercises, and computer simulations.  By the end of the course, the case studies will be used to achieve a deeper understanding of the nature and significance of prediction for assessing scientific progress. 

            The course format includes three lecture/discussions per week, classroom demonstrations and computer simulations, regular readings and written assignments,  and three exams.  There is an optional short paper on a topic of the student's choice.

Who should take this course:

            This course is intended for students who have not taken a college level physics course (or more than 1 semester of astronomy) and are not majoring in physics, chemistry, or mathematics.  If you have declared (or are likely to declare) a major in any of these disciplines, or if you have taken physics or more than one semester of astronomy at Haverford, you may not take the course, except with the instructor's permission.  This restriction is necessary so that the course may be effectively tailored to the needs of its intended audience


            The course does not require mastery of calculus, but an understanding of the basic ideas of integration and differentiation at the level of Math 113a is desirable.  We will be expressing physical ideas in mathematical form, and I will assume basic skills in algebraic manipulation and quantitative reasoning.  Many of the ideas in the course are intellectually deep, and you will need to invest serious intellectual effort in the course.  If you have not taken high school physics, you may need to invest extra effort, but this will be taken into consideration in evaluating your work (see below).


            The following sources will provide primary readings, and should be purchased in the bookstore:

            1.  From Alchemy to Quarks;  The Study of Physics as a Liberal Art by Sheldon L. Glashow.  This is broad based physics survey designed for the core curriculum at Harvard.  We shall use the part of the book that is concerned with quantum physics, nuclei, and elementary particles, after a limited discussion of classical physics.

            2.  The Essence of Chaos, by E.N. Lorenz.  This is a very nice introduction to the ideas of chaos by a prominent meteorologist and one of the pioneers in the subject.  He will help us to understand the extent to which the weather and other physical systems are predictable.

Additional objectives

            --  To understand some of the major concepts and ideas in twentieth century physics (and also to some extent the classical ideas that underlie them);

            --  By studying several scientific revolutions, to gain an understanding of the process and development of science, and the motivations of its participants;

            --  To understand and reflect upon the successes and limitations of scientific knowledge;

            --   To acquire the tools needed to follow future developments in physical science intelligently.

Course requirements

            I ask for serious engagement by all participants.  This means:  coming to class reliably, doing the assigned readings and homework in a timely manner, participating in class discussions to the extent that the size of the class allows and reviewing carefully for the exams (review questions will be provided). 

            1.         Regular class attendance.  It is important that you come to all classes in order to profit adequately from this course and to fulfill your responsibilities as a participant.  You are expected not to miss more than two classes for any reason (including athletic events, oversleeping, etc.), other than illness.  If you anticipate difficulty in meeting this requirement, please do not take the course.  Excessive absences can result in a grade of incomplete.

            2.         Readings and assignments.  You are expected to do the assigned readings (weekly) and about 8-10 brief written assignments.  You are responsible for reviewing the sample solutions, which will be posted in Stokes Library.

            3.         Three exams, including a (non-cumulative) final.  Review questions will be provided to guide your studying.

            4.         A short paper on a topic of your choice is optional (see below).


            The average course grade is likely to be around 3.2, depending somewhat on class performance.  If you have not taken high school physics, there will be a "handicap" of about 0.3 (i.e. one grade step) in the final evaluation of your work to reflect the extra effort you may need to invest. The following weights will apply to the various components of your work:

                                                                                                Without paper              With

                        Weekly Assignments                                         25%                             20%

                        Three exams,                                                    75%                             60%

                        Short paper                                                      0%                               20%

            Homework assignments are expected on time, except in case of illness.  You may also have one no-penalty extension for up to a week in case you are swamped with work due simultaneously in different courses.  Just turn in a note in place of the assignment indicating that you wish to take advantage of this policy.  Beyond that, it is still worthwhile to turn in late homework for about half credit, but it will not be graded.  (You will benefit from staying up to date.)

            Absences (for reasons other than illness) will lead to a grade point penalty of about 0.1 grade point per absence if more than two were noted.  In extreme cases, a student may be dropped from the course or given an incomplete. 

Honor code

            Students sometimes find it helpful to discuss homework together.  This is encouraged, but your written work should be your own and should not be copied from that of a study partner.  Two assignments that have substantially identical wording or equations would be presumed in violation of the honor code.  Assistance and sources must be acknowledged.

Interacting with Jerry Gollub

            Electronic mail (sent to jgollub) is always welcome.  I will occasionally send you mail and announcements. 

            Phone: You may phone my office at 896-1196.  Please leave a message if I'm not there, along with your number and a suggested time in the evening when I can return your call.

            Office:   I have found that the best way to get together is to arrange (after class) a mutually agreeable time.  You are also welcome to drop in (Room 113 or 18); afternoons are best.  Please do not hesitate to contact me; no question or topic is too small.  If you are having a lot of trouble with the homework, be sure to come to see me as soon as possible. 

            Feedback:  If you have concerns about the course or ideas about how to make it better, you should let the me know immediately, either in person or by e-mail.  Don't wait!


Physics 109b99 Outline

Week of

Jan 18              Describing motion; Newton's Laws.

Jan 25              Gravitation; prediction using computers.

Feb. 1              Energy; momentum; statistical prediction.


Feb. 8              Chaos:  unpredictable algorithms (mappings). Exam #1 due Feb. 17.

Feb. 15            Chaos continued; Routes to chaos; the weather.

Feb. 22            Complexity; fractals; frontiers.


Mar. 1              Oscillations and waves.

Mar. 8              BREAK

Mar. 15            Electromagnetism and light; quantum nature of radiation.


Mar. 22            Wave-particle duality;  concepts of quantum physics.

Mar. 29            Exam #2 due March 31.  Uncertainty principle; tunneling microscope.

Apr. 5              Understanding atoms.


Apr. 12            Nuclear phenomena and radioactivity.

Apr. 19            Particles: fundamental constituents of matter.

Apr. 25            Particles (cont.); summary of the course.

Exam #3; optional paper (due during finals period).