General Relativity at SUNY GeneseoSavi Iyer

AAPT/LIGO Topical Conference/Workshop: Teaching General RelativitySyracuse University, July 20-21, 2006

Spring 2006 January 17, 2006 Dr. S. Iyer

Course Syllabus PHYS 388: (Expr) GRAVITY

(TR 9:55am – 11:10a m, Greene 234)

INSTRUCTOR: Dr. S. Iyer Office: Greene 136E Tel.: 245-5540 Email: iyer@geneseo.edu

Web: http://www.geneseo.edu/~iyer OFFICE HOURS: posted on the course web page

TEXTBOOK: “GRAVITY: An Introduction to Einstein’s General Relativity ,”

by James Hartle (Addison -Wesley). GENERAL INSTRUCTIONS : This course will cover Newtonian gravity, special and general theories of relati vity and cosmology. Some of the topics include Newton's law of gravitation, Keplerian orbits, special relativity with spacetime diagrams and metrics, generalization to accelerated frames, the Equivalence Principle, curvature of spacetime, classical tests of GR, stationary and spinning black holes, large scale structure of the universe, big bang theory and the cosmological model. Emphasis will be made on approaching the above topics using geometrical methods .

Homework problems will be assigned every week. Weekly homework assignments will be due every Thursday, 3:00pm. No late home work accepted . Note that mathematical software packages like MathCad are to be used ONLY as a way to check your work. Do not turn in MathCad printouts as homework assignments unless specifically stated as required. Please show all your work clearly. You are allowed to consult with me (and your classmates) before you turn in your work . However, the material you submit must be your own work. GRADING: There will be t hree tests and a final exam. The grade distribution is as follows:

HW 25% Test 1 25% Test 2 25% Final 25%

TEST SCHEDULE:

Test 1 Thursday, February 23, in class Test 2 Thursday, March 30, in class Final Tuesday, May 9, 12:00 -3:00pm, Greene 234

Spring 2006 January 17, 2006 Dr. S. Iyer CLASS SCHEDULE:

LEC # DAY DATE TOPICS (final version ) HW DUE 1 Tues Jan 17 Intro, Newtonian gravity 2 Thurs Jan 19 3 Tues Jan 24 Ch 2: Geometry as Physics 4 Thurs Jan 26 HW 1 due 5 Tues Jan 31 Ch 3: Space, Time and Gravity in NP 6 Thurs Feb 02 HW 2 due 7 Tues Feb 07 Ch 4: Principles of Special Relativity 8 Thurs Feb 09 HW 3 due 9 Tues Feb 14 Ch 5: Special Relativistic Mechanics

10 Thurs Feb 16 HW 4 due 11 Tues Feb 21 12 Thurs Feb 23 Ch 6: Gravity as Geometry HW 5 due 13 Tues Feb 28 Test 1 (Chapers 1 -5) 14 Thurs Mar 02 HW 5 due 15 Tues Mar 07 Ch 7: The Description of Curved Spacetime 16 Thurs Mar 09 HW 6 due

Tues Mar 14 SPRING BREAK Thurs Mar 16 No classes

17 Tues Mar 21 18 Thurs Mar 23 HW 7 due 19 Tues Mar 28 Ch 8: Geodesics 20 Thurs Mar 30 HW 8 due 21 Tues Apr 04 Test 2 (Chapters 6 -8) 22 Thurs Apr 06 Ch 9: The Geometry Outside a Spherical Star 23 Tues Apr 11 24 Thurs Apr 13 25 Tues Apr 18 Ch 10: Solar System Tests of GR 26 Thurs Apr 20 HW 9 due 27 Tues Apr 25 Ch 17: The Universe Observed 28 Thurs Apr 27 Ch 18: Cosmological Models HW 10 due

Tues May 09 Final Exam, 12:00 -3:00pm

Spring 2006 January 17, 2006 Dr. S. Iyer

CLASS SCHEDULE:

LEC # DAY DATE TOPICS (tentative only ) HW DUE 1 Tues Jan 17 Intro, Newtonian gravity 2 Thurs Jan 19 3 Tues Jan 24 Ch 2: Geometry as Physics 4 Thurs Jan 26 HW 1 due 5 Tues Jan 31 Ch 3: Space, Time and Gravity in NP 6 Thurs Feb 02 HW 2 due 7 Tues Feb 07 Ch 4: Principles of Special Relativity 8 Thurs Feb 09 HW 3 due 9 Tues Feb 14 Ch 5: Special Relativistic Mechanics

10 Thurs Feb 16 HW 4 due 11 Tues Feb 21 Ch 6: Gravity as Geometry 12 Thurs Feb 23 Test 1 13 Tues Feb 28 14 Thurs Mar 02 Ch 7: The Description of Curved Spacetime HW 5 due 15 Tues Mar 07 16 Thurs Mar 09 Ch 8: Geodesics HW 6 due

Tues Mar 14 SPRING BREAK Thurs Mar 16 No classes

17 Tues Mar 21 18 Thurs Mar23 Ch 9: The Geometry Outside a Spher ical Star HW 7 due 19 Tues Mar 28 20 Thurs Mar 30 Test 2 21 Tues Apr 04 Ch 10: Solar System Tests of GR 22 Thurs Apr 06 Ch 11: Relativistic Gravity in Action HW 8 due 23 Tues Apr 11 24 Thurs Apr 13 Ch 13: Astrophysical Black Holes HW 9 due 25 Tues Apr 18 Ch 14: A Little Rotation 26 Thurs Apr 20 HW 10 due 27 Tues Apr 25 Ch 17: The Universe Observed 28 Thurs Apr 27 Ch 18: Cosmological Models HW 11 due

Tues May 09 Final Exam, 12:00 -3:00pm

1. GravitationalPhysics

2. Geometryas Physics

3. Space, Timeand Gravity inNewtonianPhysics

4. Principlesof SpecialRelativity

5. SpecialRelativisticMechanics

6. Gravity asGeometry

7. The Descriptionof CurvedSpacetime

8. Geodesics

9. The GeometryOutside aSpherical Star

16. GravitationalWaves

17. The UniverseObserved

10. Solar SystemTests of GeneralRelativity

12. GravitationalCollapse andBlack Holes

14. A LittleRotation

18. CosmologicalModels

11. RelativisticGravity inAction

13. AstrophysicalBlack Holes

15. RotatingBlackHoles

19. WhichUniverseandWhy?

20. A Little MoreMath

21. Curvatureand theEinsteinEquation

22. The Sourceof Curvature

24. RelativisticStars

23. GravitationalWave Emission

Material covered

Ran out of time

Not included in syllabus

End-of-semester Course Survey

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1 2 3 4 5Strongly Disagree Strongly Agree

Num

ber o

f Stu

dent

Res

pons

es

(out

of 1

5 to

tal)

as advertisedmet my expectations

course at right levelright math/phys balance

good elective choicetopics relevant

I learned a lot

Student ResponsesThis course turned out “as advertised”.

• Very math based, I was expecting idea based.• It was about gravity.• I expected more GR from the start.• Wasn’t exactly sure what to expect.• I came to learn about General Relativity and Idid.• I didn’t know there would be so muchastronomy.

Student ResponsesThis course met my expectations.

• It was more mathematical than it wasconceptual, not that I am complaining.• Very cool stuff taught; it constantly keptmy attention.

Student ResponsesThe course was taught at the right level.

• Definitely upperclass material.• A difficult course.• Most of it was very new.• Some assumed prerequisite knowledge.• Definitely. I feel like I have a leg up on theother kids in grad school.• Make some pre-requisites; this course should befor juniors and seniors only.• It was at the right level but sometimes I wantedmore details, and other times the informationwas a little overwhelming.

Student ResponsesThe mathematical to physical content

balance was at the right level.• The amount of mathematics was not thatdifficult but at the same time it allowed me tolearn a lot.• Not enough math.• Too much math. Needed too much math toshow a small physical item. You must knowwhat something is before you can “showthat”, but this course assumes you know whatit is already.• At many points I didn’t understand themath behind the equations.• Some of the concepts may have been dilutedby the mathematics.• Seemed like too much emphasis on puremath.• Most of the first half of GR was verymathematical and I didn’t understandphysically what it meant.

Student ResponsesThis course would serve well as one of the

elective choices.• General Relativity should definitely beoffered in this form. Students should beexposed to it.•This course almost needs to be 2 semesterslong.• It was one of the more interesting upper levelclasses that I took.• I think other students would enjoy it.• Only if you are going to grad school for this,otherwise it seems like it should be

Student ResponseTopics covered in this course strike me as “relevant”.• It’s physics… what more relevance do you need?!

Student ResponsesI learned a lot in this course.

• I did enjoy the material of this course.• Some of what I learned I couldn’t reallyconvey.• When it wasn’t a topics course and therewas math I did.• I had seen most of this before, but that’snot your fault.• I wish I had had special relativity beforetaking this class.• I received more of an overall education onthe topic as opposed to learning a lot ofdetails.

Student ResponsesList topics that were covered in the course that you

think may have been left out:• Spent too much time on S.R. for a course on G.R.• None.• Einstein’s equation explanation.• None (all were important)• Everything seemed reasonably relevant.

Student ResponsesList topics that you would have like to have

covered in this course:• More on expanding universe.• More GR, less cosmology• More about the general knowledge topics toreally increase general knowledge of GR.• More on cosmology. I think we rushed alittle.• Anything and everything• Maybe more theory about black holes.

Student ReponsesOther comments: (textbook, prerequisites, etc.)

• What a ride! I wish that there were a Gravity 2course so I could continue delving into the hardestsubject I’ve ever encountered.•Nothing to compare to but the book was prettyeasy to sift through for methods.• Textbook was scarce on example & come toconclusions & formulas without explaining howor why. Book seemed to only explain things ifthey were easy to grasp.• I didn’t like the text. It was hard to read. Ifound that the examples we did in class were thesame as the text. It would have helped to havevariety.• Textbook was a little annoying. It treated thingslike physical constants and vectors tooextraordinarily. The chapters were not at all easyto read.• The text book was hard to use. More exampleproblems would have been nice.• I didn’t understand a lot of the textbook. I wishthere had been more discussions of what the mathmeant. The homework questions in the bookwere not really clear of what they were getting atand they didn’t help my understanding much.• All fine. I didn’t take Advanced [Mechanics] &I had no problem.•Advanced Mechanics! I think more opendiscussion would make the class more interesting.• The course was taught very well to even thosewho did not have any other prerequisites.

Instructor ReflectionsThe “ad” was basically what

you see under GENERALINSTRUCTIONS in the

syllabus (top left)

Instructor ReflectionsThe course was meant to be a

junior/senior level course.However, a couple of

sophomore students weregiven special permission to

take the course.

Instructor ReflectionsThe amount mathematicalcontent in a GR course forundergraduates is a trickyissue. I took the “physicsfirst” approach, but there

was quite a generous amountof math content as well.

Instructor ReflectionsJunior/senior year electivesoffered by the department.

Offered every year:Intermediate E&M I and II

Electric Circuit AnalysisStatistical Thermodynamics

Paired off for two year rotation:Atomic and Nucl. Phys/Adv. QM

Solid State Phys/Fluid Mech.Astrophysics/Gravity (proposed)

Instructor ReflectionsMy intention here wasto get a sense of how

much students felt likethey learned (not

necessarily related totheir performance on

HW and tests)

Instructor ReflectionsMixed reactions here. I felt

like the last third of thesemester was somewhat

rushed as well. If I were toteach the course again, I

would probably cut back onthe time spent on the first five

chapters.

Instructor ReflectionsAs the instructor, I liked

the text very much(except for the typos…) Iespecially liked teachingchapters 6, 7 and 8. The

class erupted into anapplause when I showed-

--the hard way---thatgeodesics in flat space are

y=mx+b straight lines!I would use the same textwhen I teach this course

again.

Instructor ReflectionsAdvanced Mechanics (an

intermediate levelclassical mechanics

course) was a suggestedprerequisite for thecourse. This wasn’t

enforced strictly for thisfirst time offering of the

course. A classicalmechanics course whereLagrangian dynamics is

covered should be aprerequisite for the GR

course.

Spring 2006 PHYS 388: GRAVITY Course Survey Dr. S. Iyer Extra feedback for the course. Use the space provided under each item for comments. Thank you! strongly

disagree disagree agree strongly

agree 1 2 3 4 5 This course turn ed out “as advertised ”. This course met my expectations . The course was taught at the right level . The mathematical to physical content balance was at the right level . This course would serve well as one of the elective choices. Topics covered in this course strike me as “relevant” . I learned a lot in this course . List topics that were covered in the course that you think may have been left out: List topics that you would have liked to have covered in th is course: Other comments: (textbook, prerequisites, etc.)

PHYS 388: Gravity (3 credits) (Experimentalcourse offering)

The class met twice a week (Tues and Thurs)for 1 hour and 15 minutes each period.

Textbook “GRAVITY: An Introduction toEinstein’s General Relativity,”by James Hartle (Addison-Wesley).

Weekly homework problems were assignedfrom the textbook.

There were 17 students enrolled in the class (2sophomores, 7 juniors and 8 seniors).

15 out of the 17 students returned the end-of-semester course surveys.

The overall response from the students wasextremely positive.

This course will be offered on a two-yearrotation with an Astrophysics elective.

The flowchart below is taken from the text.

SUNY Geneseo department of physics and astronomy has been nationally recognized for excellence in undergraduate physics education.

In 2002, the National Task Force on Undergraduate Physics conducted a one-year study called Strategic Programs for Innovations in Undergraduate Physics (SPIN-UP), where Geneseowas identified as one of twenty "thriving departments" across the nation.

Geneseo physics department is routinely listed among the top ten Bachelor's-granting departments in the nation in terms of number of degrees granted per year (AIP Enrollments andDegrees Report).

The total number of physics majors has increased from 78 in 1999-2000 to 103 in 2003-2004. This is a large number of physics majors for a four-year college of this (or any) size.

Two-thirds of the twenty or so graduates each year go on to graduate school in physics and related areas, while many of the rest go into teaching in local schools.

SUNY Geneseo physics faculty are committed to a vibrant undergraduateresearch environment.

Most undergraduates are involved in research activity during some part oftheir four years at Geneseo.

The department has a 2MV Van de Graaff accelerator, which is beingdismantled to make room for a new 1.7 MV Tandem Pelletron accelerator. Ina typical summer, as many as fifteen students are supported by this project.

Research areas represented besides General Relativity are Astronomy,Nuclear Physics, Solid State Physics, Optics and Engineering-related.

GR-related undergraduate research at SUNY Geneseo:

Spring 2004: Alex Waldauer, The Eikonal Equation in Flat Space

Fall 2003: Alex Waldauer, Gravitational Lensing (contd.)

Spring 2003:Dan Riley and Chris Peters, Vortex Dynamics (contd.); AlexWaldauer, Gravitational Lensing

Fall 2002: Dan Riley and Chris Peters, Vortex Dynamics

Fall 1998: Neil Di Spigna, Evolution of Wavefronts in the SpacetimeManifold (Senior Lab Project); Tom Wakeman, Symmetry and ConservationLaws

Spring 1998: Greg Benson, General Relativity and the GPS (Honorsresearch); Richard Schugart, Knot Theory and Physics

Fall 1997: Greg Benson, Computational Special Relativity (Honorsresearch); Richard Schugart, Introduction to Quantization of Gravity

Summer 1997: Neil Di Spigna and Josh Klyber, Evolution of Wavefronts

Spring 1997: Joshua Klyber, Numerical General Relativity

Fall 1996: Emmanuel Ambroise: Mathematical Techniques in Science andEngineering; Joshua Klyber, Introduction to the Theories of Relativity

Spring 1995: James Giumarra, Introduction to Tensors

Fall 1994: Robert Fuentes, Introduction to General Relativity (Senior LabProject)