COURSE: MATH 4900/5900-001

TIME AND PLACE: 11:15-12:35 TR in Sam Wilson Hall 322

INSTRUCTOR: Dr. Robert Gardner

OFFICE HOURS: TBA

OFFICE: Room 308F of Gilbreath Hall

PHONE: 439-6979 (308F Gilbreath), Math Department Office 439-4349

E-MAIL: gardnerr@etsu.edu

WEBPAGE: http://www.etsu.edu/math/gardner/gardner.htm (see my webpage for a copy of this course syllabus, copies of the classnotes in PDF and Postscript formats, and updates for the course).

TEXT: The Special Theory of Relativity, A Mathematical Exposition, by A. Das. New York: Springer-Verlag, 1993.

COURSE OUTLINE: We are going to "play by ear" the outline of this course. I want to capitalize on the presence of Dr. Martin Hendry in the Department of Physics, Astronomy, and Geology. He is teaching Astrophysics (ASTR 3415) which will emphasize applications to cosmology (see http://www.etsu.edu/math/Einstein/cosmology.htm for details). We will cover, as planned, special relativity in commemoration of the centennial of Einstein's "miraculous year," both in a physics setting and in the setting of a mathematical exploration of spacetime as a vector space. We will also explore rudimentary general relativity in an attempt to synchronize with Dr. Hendry's Astrophysics class. The general relativity will be a bit more informal (of necessity, due to your instructors knowledge [or lack thereof]). We will "roll with the punches" as best as possible and take advantage of the presence of this prestigious scientist (Dr. Hendry is visiting ETSU as the Basler Chair of excellence).

CLASSNOTES. The classnotes I plan to follow are available online in PDF and PostScript formats. See http://www.etsu.edu/math/gardner/SpecialRelativity/notes.htm.

GRADING. Your grade will be based on assigned homework problems. Undergraduate and graduate students will have different expectations.

HOMEWORK

NOTE. This class is offered in commemoration of the 100th anniversary of the publication of Einstein's 1905 paper "On the Electrodynamics of Moving Bodies" (Zur Electrodynamik bewegter Korper, Annalen der Physik, 17, 1905). This paper was completed on June 30, 1905.

EINSTEIN'S MIRACULOUS YEAR. ETSU will have a number of other events, including public presentations and special university classes, to commemorate Albert Einstein's annus mirabilis, or "miraculous year." Einstein completed six papers in 1905. Each was published by the prestigious German journal Annalen der Physik. Four of the papers were published in 1905 and the other two in 1906. The papers fall into three general categories:

• The light quanta and photoelectric effect,
• Brownian motion, and
• special relativity.

1. "On a Heuristic Point of View Concerning the Production and Transformation of Light," completed March 17, 1905. This appeared in Annalen der Physik, volume 17, pages 132-148. This work includes the light quanta hypothesis and study of the photoelectric effect. This was fundamental in the development of the quantum theory and was the basis of the justification for Einstein receiving the Nobel Prize in physics in 1921.
2. "On the Motion of Small Particles Suspended in Liquids at Rest Required by the Molecular-Kinetic Theory of Heat," completed in May 1905. This appeared in Annalen der Physik, volume 17, pages 549-560. This paper on Brownian motion helped explain the agitated random motion of particles suspended in a liquid.
3. "On the Electrodynamics of Moving Bodies," completed in June 1905. This appeared in Annalen der Physik, volume 17, pages 891-921. This is probably the most famous of Einstein's 1905 papers. It is this paper that founded the special theory of relativity.
4. "Does the Inertia of a Body Depend on Its Energy Content?," completed in September 1905. This appeared in Annalen der Physik, volume 18, pages 639-641. This is a follow-up to the special relativity paper in which Einstein presents a preliminary version of the equation E=mc².
5. "A New Determination of Molecular Dimensions," completed April 30, 1905 and revised on August 19, 1905. This appeared in Annalen der Physik, volume 19, pages 289-305 in 1906. This is Einstein's Ph.D. dissertation work from the University of Zurich. It contains a new method for the determination of molecular sizes and of Avagadro's number.
6. "On the Theory of Brownian Motion," completed December 19, 1905. This appeared in Annalen der Physik, volume 19, pages 371-381, in 1906. This is a second paper on Brownian motion.

ETSU EVENTS FOR FALL 2005: Some of the planned events to commemorate this year include the following:

1. An ETSU Planetarium show entitled "Albert Einstein - A Centennial Celebration of his Miraculous Year," will be presented during the class and as a public planetarium show on September 15. An online version is available at http://www.etsu.edu/math/gardner/einstein/intro.htm.
2. A special Fall 2005 offering of Cosmology and General Relativity (ASTR 3415), taught by the 2005 Basler Chair recipient, Dr. Martin Hendry. For an advertisement of the class, see http://www.etsu.edu/math/Einstein/cosmology.htm. The syllabus of the class is here.
3. Several public presentations by Basler Chair Dr. Martin Hendry. For initial details, click here. The presentations will include:
   • ET Life: Is There Anybody Out There? (Saturday, September 24, 2005 at 8:00 p.m. at the ETSU Harry D. Powell Observartory) This short talk on the prospects of finding life on other planets will be presented as part of a Star Party/Observatory Open House, during which participants may, weather permitting, view celestial objects through the observatory's telescopes. The Powell Observatory is located above campus off Narrow Lane.
   • How Scotland Changed the World. (Thursday, September 29, 2005 at 7:00 p.m. in the D.P. Culp University Center's Martha Street Culp Auditorium) A personal reflection on 5,000 years of Scottish history, science and culture, complete with musical accompaniment.
   • Einstein's Dreams. (Thursday, October 20, 2005 at 7:00 p.m. in the D.P. Culp University Center's Martha Street Culp Auditorium) We will celebrate the centennial of the theory of relativity and explore how Einstein's theories shape our modern understanding of the universe.
   • Did We Really Land On the Moon? (Thursday, December 8, 2005 at 7:00 p.m. in the D.P. Culp University Center's Martha Street Culp Auditorium) Hendry says that 36 years after Neil Armstrong first stepped on the moon, many still believe the Apollo landings were fake, and in this lecture, he invites members of his audience to review the evidence for themselves.
4. A technical planetarium show on general relativity and black holes. This show was given September 8, 2005. For an online version of the show, see http://www.etsu.edu/physics/plntrm/relat/relatabs.htm.
5. A Department of Mathematics seminar on September 19, 2005 by Dr. Robert Gardner entitled "E=mc² Turns 100.'' Part of the presentation are available online in PDF and PostScript formats.
6. A Department of Physics, Astronomy, and Geology seminar on October 11, 2005 by Dr. Martin Hendry entitled "Gravitational Microlensing as a Probe of Stellar Astrophysics." An announcement of the seminar is available here.
7. A special free public lecture "Black Holes, White Rabbits" given on November 2, 2005 by Scottish astronomer Dr. John Brown. The presentation will be at 7:00 p.m. in the D.P. Culp University Center's Martha Street Culp Auditorium.
8. Probing the Distant Universe with Gravitational Waves. This two-day workshop is organized by East Tennessee State University and the University of Glasgow, UK – with generous support from the Wayne G. Basler Chair of Excellence, College of Arts and Sciences, ETSU. The theme of the workshop is the interface between gravitational wave astronomy and cosmology, with particular focus on the opportunities that will arise from the LISA mission.
9. "The Birth of the Bomb" given by Martin Hendry on Friday, November 18, 2005 in the D.P. Culp Center's Forum Room. In this lecture, Dr. Hendry will explore the dangers of mixing politics and science, as well as share the wonders of quantum physics. He will also participate in readings from Michael Frayn's play, "Copenhagen," with actor Pat Cronin, the 1999 Basler chairholder who is now Permanent Artist in Residence in the Department of Communication's Division of Theatre and director of the Fine and Performing Arts Scholars program in the ETSU Honors College.

OTHER EVENTS AND WEBSITES: Some other events and websites outside of ETSU in commemoration of "Einstein Year," along with relevant websites include:

1. The webpage of Annalen der Physik: http://www3.interscience.wiley.com/cgi-bin/jhome/5006612. Reprints (PDF versions, in German) of Einstein's original 1905 papers (along with some of his later work): http://www.physik.uni-augsburg.de/annalen/history/Einstein-in-AdP.htm.
2. Einstein Year webpage: http://www.einsteinyear.org/.
3. World Year of Physics webpage: http://www.einsteinyear.org/. Also check out some additional details: http://www.physics2005.org/.
4. Albert Einstein online (includes many links to information about Einstein): http://www.westegg.com/einstein/.
5. American Institute of Physics Einstein website: http://www.aip.org/history/einstein/.
6. Einstein's Big Idea website of the Public Broadcasting System (a supplement to a Nova episode to be broadcast October 11, 2005): http://www.pbs.org/wgbh/nova/einstein/. Other interesting PBS sites are Time Travel (http://www.pbs.org/wgbh/nova/time/) and Einstein's Wife (http://www.pbs.org/opb/einsteinswife/).
7. www.fourmilab.ch provides English translations of much of Einstein's 1905 work. In particular: Does the Inertia of a Body Depend on Its Energy Content?"

IMPORTANT DATES:
Monday, September 5 = Labor Day Holiday - University closed.
Monday, September 12 = Last day for 75% refund.
Thursday, September 15 = Public presentation of Einstein planetarium show (7:00 p.m.).
Monday, September 26 = Last day to drop without a grade of "W."
Tuesday, September 27 = 100 year anniversary of submission of Einstein's "Does the Inertia of a Body Depend on Its Energy Content?" ("E=mc²")
Tuesday, October 11, 2005 = Broadcast of NOVA episode Einstein's Big Idea on PBS.
Monday and Tuesday, October 17-18 = Fall Break (no classes).
Monday, October 24 = Last day to drop without dean's permission.
Thursday and Friday, November 24 and 25 = Thanksgiving Holiday (no classes).
Wednesday, December 7 = Last day to withdraw from the university.
Thursday, December 8 = Last day of class.

Return to Bob Gardner's webpage.