We should take comfort in two conjoined features of nature: first, that our world is incredibly strange and therefore supremely fascinating . . . second, that however bizarre and arcane our world might be, nature remains comprehensible to the human mind. -- Stephen Jay Gould
This course introduces Einstein's special and general theories of relativity, and investigates how these theories have changed our understanding of space and time. These investigations illuminate questions of how scientists approach problems and the nature of scientific knowledge.
Learning goals: Through your work in this course, you will
Teacher:
Dan Styer,
Wright 215, 440-775-8183, Dan.Styer@oberlin.edu
home telephone 440-281-1348 (9:00 am to 8:00 pm only).
Instructions for meeting with me are given under "Schedule" here.
Pronouns, nouns, adjectives, and the character of science: I don't care what pronouns you use when referring to me. Similarly, you may call me "Dan", or "Mr. Styer", or "Dr. Styer", or "Prof. Styer", whichever you find most comfortable. My personal preference, however, is that you call me "Dan". In this course I will present upsetting conclusions violently opposed to our common sense and common experience. (For example: That a moving clock ticks slowly. That a moving rod is short.) I hope you'll accept those conclusions because they are based on experimental evidence and on cogent, clear, fact-based reasoning -- experiments and reasoning that you or I or anyone else could execute. If you accept those conclusions instead because I have earned the right to put a fancy shingle in front of my name, my teaching will have been an abject failure.
Course web site: http://www.oberlin.edu/physics/dstyer/Einstein
Prerequisites: This course does not assume any background in science. High school level algebra and geometry will be used as needed without apology.
Text: D.F. Styer, Relativity for the Questioning Mind. You may purchase this text, or use this link.
Tutoring: Tutors are available for this course at no charge through Oberlin College's Center for Student Success. Contact them if you would like a tutor.
Format: This course is taught in person, but all work is submitted through Oberlin College's Blackboard course management system. Class meetings are on Tuesdays and Thursdays starting at 10:00 am. I begin each class by discussing questions raised at the previous class, then I go through some new material from the textbook, and finally I use the after-class reactions (see below) to gather questions to be answered at the following class. If you understand the material well enough from the reading, then you don't need to listen to the "new material" portion of the class.
Grading: This is a first-half-of-the-semester half course, graded on a Pass/No Pass basis. It is a designated "Quantitative and Formal Reasoning" course. To receive credit, you must (1) react to classes regularly, (2) satisfactorily complete the weekly assignments, (3) pass a final examination, and (4) complete a project.
(1) How do you react to classes? By the end of the day (11:59 pm) each date when class meets, submit through Blackboard a sentence or two reacting to the state of your knowledge concerning relativity. I will use these reactions to plan the next class and the future path of this course. Your most useful reaction would be a specific question: for example, "Just because one type of clock slows down while it's moving, why does that mean that all types of clocks have to slow down while they move?" Other possible reactions would be indications of general interest ("I'd like to learn more about the pole-in-the-barn paradox.") or general questions about course material ("Why should I care about this stuff, anyway?").
The ability to answer questions is an important skill, and your work in college, including this course, gives you lots of practice to develop that skill. The ability to ask questions is an equally important skill -- Einstein said "The important thing is not to stop questioning" -- but college work typically affords less practice in this skill. This "react to classes" assignment is one way to develop your skill in question-asking. There are 13 classes for this course, and you must react to at least 10 of them.
(2) The weekly assignments are due before the end of the day (11:59 pm) on each Thursday and are set and graded through Blackboard. You may rework an assignment as many times as you wish before the deadline. In working an assignment, you may consult any written or on-line material, or you may consult your friends, but you must complete the assignment yourself . . . you may not, for example, copy answers from someone who has already done the assignment.
Because of the large number of students in this course, I can't allow exceptions to make up for missed assignments. To pass the course, you must earn at least 60% on the assignments as a whole. (I appreciate that for some of the assignments you might be sick or for other reasons not at the peak of your abilities. That's why the 60% cutoff is set so low.)
(3) The final exam will be given through Blackboard on the date of the last class meeting (18 November). I expect it will take you about half an hour to work the exam, but there is no time limit. You are not allowed multiple attempts. Nor may you consults friends, on-line material, nor any written material save your own notes that fit on both sides of one 8 1/2 by 11 inch page of paper. (I recommend that you print out this summary sheet and then add your own notes about topics that you find particularly tricky.)
To pass the course, you must earn at least 50% on the exam.
(4) The project investigates some facet of Einstein or relativity: it could be (a) the solution of a problem from the textbook, or (b) a brief (three to six page) essay, or (c) an artistic/literary project examining some aspect of relativity or its history.
(a) These textbook problems are meaty enough that solving one of them would qualify as a project: 7.6, 13.2, 13.4, 13.5, 13.6, 13.7, 14.3, 14.4, 15.4, 15.5, and any of the problems in chapter 16 except for 16.6 and 16.9.
(b) If you write an essay, it may involve Einstein's life, or relativistic physics, or the history of our knowledge of relativity, or it may explore the effect of relativistic thought in, say, literature or sociology. Among the fine essays submitted in previous years are:
I prefer focused, analytic works to generalized, descriptive ones. For example, if you choose to write about the life of Albert Einstein, don't write about his whole life. That would be the subject for a one-thousand page book, not a three-page essay. Instead focus on his childhood, or his years in Switzerland, or his time in Princeton. Alternatively, examine Einstein's views on pacifism, socialism, or Judaism.
(c) Finally, your project may be an artistic (music, dance, sculpture, or painting) or literary (prose, verse, or drama) work inspired by the course material. It must be submitted through Blackboard --- perhaps as a photo or video. If you do choose such a project, then be sure that it contains enough relativistic content to warrant earning credit for a physics course.
It is also possible to combine these three categories of projects: One year (I am not kidding) a student submitted a series of poems that worked through the solution of problem 16.4.
Unless you use one of the textbook problems mentioned above, you must submit to me a one-paragraph prospectus of your project two weeks before the last class meeting. The project itself is due at the end of the day (11:59 pm) on Friday, 19 November.
You can track your grade status through the "My Grades" feature of Blackboard. It is easier for you to uncover your grade status than it is for me to, so if you write me asking for your grade I will not respond.
Tentative course schedule: (with assigned readings from the textbook Relativity for the Questioning Mind)
| 5 October | The Paradox of the Mirror [chap. 1] | |
| 7 October | Experiments about Light [chaps. 2, 3] | |
| 12 October | Time Dilation [chap. 4] | |
| 14 October | Length Contraction; Clock Synchronization [chaps. 5, 6, 7] | |
| 19 October | The Case of the Hungry Traveler [chap. 8] | |
| 21 October | He Said, She Said [chap. 9] | |
| 26 October | Speed Limits [chap. 10] | |
| 28 October | Speed Addition [chap. 11] | |
| 2 November | The Twin Paradox [chaps. 12, 13] | |
| 4 November | Puzzles and Paradoxes [chap. 14]; Prospectus due | |
| 9 November | Puzzles and Paradoxes [chap. 14] | |
| 11 November | General Relativity [chaps. 17, 18] | |
| 16 November | Curved Spacetime [chap. 19] | |
| 18 November | Final Exam (no class) | |
| 19 November | Project due |
Web site for NOVA program "Einstein's Big Idea".
Exhibit concerning Einstein and relativity at the American Museum of Natural History.
Interviews A and B with Alan Lightman, author of Einstein's Dreams.
Measure the speed of light using chocolate and a microwave oven.
Inside Black Holes by Andrew Hamilton.
Relativity Visualized: Space Time Travel by Ute Kraus and Corvin Zahn.
Virtual Trips to Black Holes and Neutron Stars by Robert Nemiroff.
L.D. Landau and G.B. Rumer, What is Relativity?
[Storage 530.11 231 W].
M. Gardner, Relativity for the Million [Science 530.11 175 R].
Very basic introductions. Fun to read.
D.E. Mook and T. Vargish, Inside Relativity
[Science QC173.55.M66 1987].
L.K. Barnett, The Universe and Dr. Einstein
[Science 530.11 B264 U.2].
R. Wolfson, Simply Einstein: Relativity Demystified
[Science QC173.57 .W65 2003].
General introductions.
N. David Mermin, Space and Time in Special Relativity
[Science QC6.M367 1989].
My favorite. See especially chapter 11.
Leo Sarturi, Understanding Relativity [Science QC173.55.S367 1996].
G. Gamow, Mr. Tompkins in Wonderland [Science 530.11 G148 M].
The whimsical adventures of a bank clerk who
encounters relativity
(and quantum mechanics) at first hand through a series of dreams.
B. Hoffmann, Relativity and its Roots [Science QC173.52.H63 1983].
The "roots" extend back to Copernicus.
Clear discussions of both
scientific and historic issues.
W.H.V. Reade, A Criticism of Einstein and his Problem
[Science 530.11 R227C].
An expert on Dante challenges Einstein.
J. Schwinger, Einstein's Legacy [Science QC173.59.S65S39 1986].
Clear popular account of the special and general
theories. Written by
a superb theoretical physicist, but the jokes are awful.
A. Einstein, et al., The Principle of Relativity
[Science QC6.L613 1952].
Translation of Einstein's seminal 1905 paper
begins on page 37.
M. Kaku, Einstein's Cosmos [Science QC173.59.S65 K356 2004].
Mixed science and biography.
Clifford Will, Was Einstein Right? [Science QC173.6.W55 1993].
Mostly on general relativity, but the appendix gives a quick survey of experimental
tests of special relativity.
Yuan Zhong Zhang, Special Relativity and Its Experimental Foundations
[Science QC173.65.C465 1997].
Technical but thorough treatment of experimental
tests of special relativity.
Mitchell Begelman and Martin Rees,
Gravity's Fatal Attraction: Black Holes in the Universe
[Science QB843.B55 B44 1996].
W.J. Kaufmann, Black Holes and Warped Spacetime
[Science QB843.B55 K38].
I. Nicolson, Gravity, Black Holes and the Universe
[Science QC178.N5 1981].
J. Gribbin, Unveiling the Edge of Time: Black Holes, White Holes, and
Wormholes
[Science QB843.B55 G75 1992].
Kitty Ferguson, Prisons of Light
[Science QB843.B55 F54 1996].
Igor Novikov, Black Holes and the Universe
[Science QB843.B55 N6713 1990].
Kip S. Thorne, Black Holes and Time Warps: Einstein's Outrageous
Legacy
[Science QC6.T526 1994].
Seven books on general relativity, cosmology,
and black holes. (Many students have written final essays on
these subjects.)
A. Pais, "Subtle is the Lord . . .": The Science and Life of Albert Einstein
[Science QC16.E5 P26].
Exhaustive biography. The sections on Einstein's
science assume
technical training, but the biographical sections are accessible
to anyone.
Dennis Overbye, Einstein in Love: A Scientific Romance
[Science QC16.E5 O9 2000].
Despite the coquettish
title, this is a reliable biography of both the personal
and scientific aspects of Einstein's first forty years.
Fred Jerome, The Einstein File: J. Edgar Hoover's Secret War Against the World's Most Famous Scientist [Science QC16.E5 J46 2002].
G. Holton, Einstein, History, and Other Passions [Mudd Q173.H7342 1995].
A book about the character of science and scientific
creativity
as exemplified by the life and work of Einstein.
J. Renn and R. Schulmann, eds., Albert Einstein/Mileva Maric--The Love Letters [Science QC16.E5A4 1992].
P. Galison,
Einstein's Clocks, Poincaré's Maps: Empires of Time
[Science QB209.G35 2003].
How did Einstein get these strange ideas, anyhow? It's impossible to be certain, but
Galison speculates.
G. Holton and Y. Elkana, eds., Albert Einstein: Historical and Cultural
Perspectives [Science QC16.E5 J48 1979].
L.P. Williams, Relativity Theory: Its Origins and Impact on Modern
Thought [Science QC 173.58 W54 1979].
Iain Paul, Science, Theology, and Einstein [Mudd BL240.2.P3].
David Cassidy, Einstein and Our World [Science QC16.E5C37 1995].
Four good sources of ideas for
your essay.
J. Renn, ed., Albert Einstein: Chief Engineer of the Universe,
volume 1 Einstein's Life and Work in Context,
volume 2 One Hundred Authors for Einstein. (Weinheim: Wiley-VCH, 2005.)
[Science Oversize QC16.E5 A6583 2005, vol. 1 and vol. 2].
A large number of brief essays, which might inspire your essay!
A.P. French, ed., Einstein: A Centenary Volume [Science QC16.E5 E37].
Reminiscences, biographical essays,
excerpts from Einstein's writings.
Paul J. Nahin, Time Machines: Time Travel in Physics, Metaphysics, and Science Fiction [Mudd PS374.S35N34 1993].
Alan Lightman, Einstein's Dreams [Mudd PS3562.I45397 E38 1993].
"An elegant wisp of a novel that imagines
Einstein pondering the nature
of time as he works as a patent clerk". . . New York Times,
23 Dec 1992, p. B2.
Arthur I. Miller, Einstein, Picasso: Space, Time and the Beauty that Causes Havoc [Art N72.S3 M55 2001].
C. Lanczos, The Einstein Decade [Science QC16.E5L33 1974].
See especially "Conceptions and Misconceptions"
on page 21.
P.A. Schilpp, ed., Albert Einstein: Philosopher-Scientist
[Science QC.E5 S3 1970].
Einstein's autobiography and selected critical essays.
Fred Jerome and Rodger Taylor, Einstein on Race and Racism [Science QC16.E5 J466 2005].
A. Einstein, Essays in Science ( The World as I See It)
[Science QC71.E515].
A. Einstein, Einstein on Peace (O. Nathan and H. Norden, eds.)
[Mudd JX1952.E44 1968].
A. Einstein, The Fight Against War (A. Lief, ed.) [Storage 172.4Ei68].
A. Einstein, Out of My Later Years [Science QC16.E5 A3 1950b].
J. Bernstein, "Besso", The New Yorker, 27 Feb. 1989, page 86.
R. Schwartz, "The FBI and Dr. Einstein", The Nation, 3 Sept. 1983.
J. Bronowski, "The clock paradox'', Scientific American,
208 (February 1963) 134-144.
(We refer to this effect as the "twin paradox".)
Julie M. Johnson, "The theory of relativity in modern literature",
Journal of Modern Literature, 10 (June 1983) 217-230.
Paul Laporte, "Cubism and relativity with a letter of Albert Einstein",
Leonardo, 21(3) (1988) 313-315.
Marlin Thomas, "Albert Einstein and LD",
Journal of Learning Disabilities, 33 (March/April 2000) 149-157.