# Special relativity and steps towards general relativity

Type classification: this resource is a course. |

**Special relativity and steps towards general relativity** is a one-semester Wikiversity course that uses the geometrical approach to understanding special relativity and presents a few elements towards general relativity. The course may be used in a traditional university, within the conditions of the free licensing terms indicated at the bottom of this Wikiversity web page. It may be modified and redistributed according to the same conditions, for example, via the Wikiversity and Wikimedia Commons web sites. For similar Wikiversity courses and learning resources on special and general relativity, see Topic:Special relativity and Topic:General relativity. *(shortcut to this page: SRepsilonGR)*

## Contents

## Lectures[edit]

### PDF presentations[edit]

The images used in the PDFs and the animation playable from the PDF are listed in /image gallery.

### How to use these[edit]

#### Teacher[edit]

- classroom mode

These lectures are designed to be used by a teacher in fullscreen mode (e.g. *xpdf -fullscreen*) using a computer projector (beamer) in a face-to-face, real-life classroom. Internal clickable links at the bottom of the presentations (except for the opening slide) can be used to navigate between key ideas.

#### Student[edit]

- post-classroom desktop mode

After participating in lectures, you may use the pdf files to think through the ideas at your own pace. It is highly recommended that you click on links in the pdf files to read Wikipedia articles that go to more depth and lead in turn to introductory and research-level literature. Using a pdf viewer like xpdf, clicking on a Wikipedia link in the pdf file should open that page in a new panel in a web browser. You may need to view the pdf files in partial screen mode, not fullscreen mode.

- no-classroom desktop mode

Viewing these pdf's without "classroom" help from someone who knows the subject is unlikely to be enough to learn the subject. Possible ways to learn without a face-to-face teacher giving lectures include:

- reactivate the Study Group For Relativity page and wiki-coordinate with a teacher and other students
- ask at the w:Wikipedia:Reference desk/Science
- use the pdf's in parallel to reading the associated Wikipedia articles
- read Schutz and/or Bertschinger (links below) in parallel to looking through the pdf's

## Exercises[edit]

Exercises using the WIMS system are available on WIMS servers, including University of Paris Sud, University of Nice and Leiden University.

As of June 2012, these exercises do not cover the full content of the course, and do not use diagrams or computer algebra, so they are not *sufficient* to give strong confidence that you understand all the material of the pdf files of the course. However, they are *necessary*, in the sense that if you cannot get full marks on a few realisations of the full set of questions, then you probably do not yet understand the material. Students working through these exercises in 2011 and 2012 found them to be of a reasonable level of difficulty.

## Exams[edit]

You can give yourself an examination by using the exercises on one of the above servers.

- Select the full set of exercises (the default is the full set).
- Set the number of exercises per series to 9.
- Set a time limit of 3600 seconds.

You should be able to get a score of nearly 10.

Keeping in mind what Wikiversity is not, the claim that any Wikiversity participant has passed the exam with a given grade on a given date will **not** be certified in any way by the Wikimedia Foundation. The primary aim of having an exam in this Wikiversity course is for the student to judge for him/herself if s/he has attained a satisfactory level of understanding.

## Reading list[edit]

### General[edit]

- Ed Bertschinger GR notes: http://web.mit.edu/edbert/GR/
- Working through the full set of Bertschinger's notes will give you a more thorough introduction than the pdf's and exercises above. The GR part of this Wikiversity course approximately corresponds to most of gr1.pdf and parts of gr2.pdf.
- These notes have the nice characteristic of explicitly writing tilde and arrow symbols on the nabla symbol when the operations increase the number of 1-form-like (covariant) or vector-like (contravariant)
- As of 18:46, 23 June 2011 (UTC), the notes have some minor errors. Exercise: find these errors and correct them.

*A First Course in General Relativity*, Bernard Schutz, Cambridge University Press, 2nd edition, 2009, ISBN 0521887054, ISBN 978-0521887052- This Wikiversity course approximately corresponds (thematically) to a large part of the 1st edition of this book.

### Key ideas[edit]

- SR:
- Understanding SR and judging if the empirical evidence supports it are best done in that order: first the geometrical understanding (where the constancy of the speed of light is true by definition), second the evidence (where it's true experimentally). The geometrical point of view is well-presented in Edwin F. Taylor, John A. Wheeler,
*Spacetime Physics: Introduction to Special Relativity*, W. H. Freeman Press, New York, 1992, ISBN 0716723271, ISBN 978-0716723271 - Minkowski space
- World line

- Understanding SR and judging if the empirical evidence supports it are best done in that order: first the geometrical understanding (where the constancy of the speed of light is true by definition), second the evidence (where it's true experimentally). The geometrical point of view is well-presented in Edwin F. Taylor, John A. Wheeler,
- GR: General relativity
- Riemannian geometry (and pseudo-Riemannian geometry)
- Intermediate treatment of tensors
- coordinate basis, gradient of vector field, Christoffel symbols http://web.mit.edu/edbert/GR/gr1.pdf
- directional derivative, parallel transport, geodesics http://web.mit.edu/edbert/GR/gr2.pdf
- Riemann tensor, curvature, Ricci identity, Ricci tensor, Einstein tensor http://web.mit.edu/edbert/GR/gr2.pdf

- GR
*(mentioned, not explained, in the 2011 version of the course)*- Stress–energy tensor http://web.mit.edu/edbert/GR/gr2b.pdf
- Einstein field equations http://web.mit.edu/edbert/GR/gr5.pdf
- exact solutions:
- Equivalence principle - can be thought of as
*consequence*of the model