Instructor

Time and Location

Office Hours

Lecture Notes

Lecture 1, Lecture 2, Lecture 3, Lecture 4, Lecture 5, Lecture 6, Lecture 7, Lecture 8, Lecture 9,
Lecture 10, Lecture 11, Lecture 12, Lecture 13, Lecture 14, Lecture 15, Lecture 16, Lecture 17,
Lecture 18, Lecture 19, Lecture 20, Lecture 21, Lecture 22, Lecture 23, Lecture 24, Lecture 25,
Lecture 26, Lecture 27, Lecture 28 (Last).

Homework

Weekly homework assignments are due every Thursday. In order to learn the subject, it is extremely important that you complete the homework.

1. Due 02/03/10: Exercises 1 (lecture 3) and 2 (lecture 4).
2. Due 02/10/10: Exercises 3 (lecture 5) and 4 (lecture 6).
3. Due 02/16/10: Exercises 5, 6 (lecture 7) and 7, 8 (lecture 8).
4. Due 02/24/10: Exercises 9, 10 (lecture 9) and 11 (lecture 10).
5. Due 03/03/10: Exercises 12, 13 (lecture 11) and 14, 15 (lecture 12).
6. Due 03/10/10: Exercises 15, 16, 17, 18 (lecture 14).
7. Due 03/24/10: Exercises 19, 20, 21 (lecture 15).
8. Due 03/31/10: Exercises 22, 23, 24 (lecture 16). Solution.
9. Due 04/07/10: Exercises 25, 26 (lecture 17). Solution.
10. Due 04/14/10: Exercises 27 (lecture 19) and 28 (lecture 20). Solution.
11. Due 04/21/10: Exercises 29, 30 (lecture 22). Solution.
12. Due 04/28/10: Exercise 31 (lecture 23), 32 (lecture 24). Solution.

Links (Diversions)

1. Graph paper
2. Lecture 18: A test of the equivalence principle
3. Lecture 22: The life of Karl Schwarzschild.
4. Lecture 24: The black hole at the center of our galaxy.
5. Lecture 25: An Atlas of the Universe.
6. Lecture 26: An Geometry of space according to WMAP.
7. Lecture 26: Escher's Angels and Devils (hyperbolic geometry).

Content

Our understanding of nature basically rests on two fundamental pillars: General relativity and Quantum Mechanics. This course is designed to outline and cover one of those pillars: the theory of general relativity, its precursor, special relativity, and its application to the description and understanding of the universe.

We shall describe the developments that led to special relativity, and its implications about the nature of space and time. We shall also study some of the striking phenomena that it predicts, like time dilation and length contraction, and with some of the paradoxes that relativity seems to imply. The marriage of special relativity and quantum mechanics results in quantum field theory, a framework that succesfully accounts for all non-gravitational interactions known to us.

But special relativity has nothing to say about gravitation. This is what led Einstein to extend his special theory of relativity to general relativity, which is a theory of gravity and much more. We will explore the conceptional foundations of general relativity, and some of the mathematical apparatus upon which it rests. We shall also devote some time talking about one of the most dramatic objects in general relativity: black holes and wormholes.

Finally, we shall apply general relativity to the whole universe in our study of cosmology. We shall see that the universe can have different shapes, and how observations determine what the shape of our universe is. Using the equations of general relativity we will be able to study the evolution of the universe, its origins and its future. We shall see that, perhaps to your dismay, we only understand 5% of what the universe is actually made of.

Requirements

Exams

Grading

Literature

• Don Marolf, Notes on Relativity and Cosmology for PHY312, unpublished.
• Edwin F. Taylor and John A. Wheeler, Spacetime Physics, W. H. Freeman.
• Albert Einstein Relativity: The Special and the General Theory, Penguin Classics.

Academic Integrity

The Syracuse University Academic Integrity Policy holds students accountable for the integrity of the work they submit. Students should be familiar with the Policy and know that it is their responsibility to learn about instructor and general academic expectations with regard to proper citation of sources in written work. The policy also governs the integrity of work submitted in exams, in laboratories, and in assignments, as well as the veracity of signatures on attendance sheets and other verifications of participation in class activities. Serious sanctions can result from academic dishonesty of any sort. For more information and the complete policy, see http://academicintegrity.syr.edu.

Disability-Related Accommodations

If you believe that you need accommodations for a disability, please contact the Office of Disability Services(ODS), http://disabilityservices.syr.edu, located in Room 309 of 804 University Avenue, or call (315) 443-4498 for an appointment to discuss your needs and the process for requesting accommodations. ODS is responsible for coordinating disability-related accommodations and will issue students with documented disabilities Accommodation Authorization Letters, as appropriate. Since accommodations may require early planning and generally are not provided retroactively, please contact ODS as soon as possible.