Lights All Askew in the Heavens or How to Learn Relativity

| June 25, 2012 | 0 Comments

“Einstein theory thriumphs!” announced the New York Times headline back in November 10 1919. It was celebrating the famous confirmation of Einstein’s general theory of relativity, which was confirmed by observing the bending of light by the sun during the solar eclipse. Einstein became a celebrity all over the world instantly.


As the headline says no more than 12 men could understand Einsteins revolutionary work back in those days and even that number was probably a little optimistic. These days, even though GR is still a hard-to-learn theory , a lot has changed. Perhaps the greatest work by Albert Einstein is not as essoteric as it used to be. Actually, even undergraduate students could start learning the basics of the theory.

The problem with learning general relativity is that it uses advance mathematics, for instance tensor calculus, which in most cases is too advanced for undergraduate students. This, according to a remarkable article at, can be mitigated by using 4 different approaches. These approaches include:

  • The adjusted math-first approach.
  • The calculus-only approach.
  • The physics-first approach.
  • The intertwined + active-learning approach.

As you might guess, these techniques use various amounts of unknown math when teaching undergraduates.  For instance, the “physics-first” approach focuses of the physical implications of GR and uses minimum amount of math, whereas the “calculus-only” approach uses only single-variable calculus.  This is highly useful for someone learning the theory individually, as the article gives various teaching and studying strategies.

To be honest, this article is amazing. I’m learning general relativity on my own right now and I can personally tell you it’s really hard to find good learning material. When it comes to lectures the best thing I’ve seen by far are lectures by Leonard Susskind. However, when it comes to books it’s harder to choose as always.  Usually people will recommend you the good old “A First Course in General Relativity” by Bernard Schutz, which a good book, but a little too hairy for absolute beginners. The mentioned article also gives some good introductory level books. Some of them have more math than Schutz’s book, some have less, but overall all the books are really handy. Most of the books are hard to find on the internet so I added the amazon links. Here’s the book list:

  1.  S. Weinberg, Gravitation and Cosmology: Principles and Applications of the General Theory of Relativity Wiley, New York (1972).
  2. C. W. Misner, K. S. Thorne, J. A. Wheeler, Gravitation, W. H. Freeman, San Francisco (1973).
  3. R. M. Wald, General Relativity, U. Chicago Press, Chicago (1984).
  4. B. F. Schutz, A First Course in General Relativity, Cambridge U. Press, New York (1985; 2nd ed. 2009).
  5. H. C. Ohanian, R. Ruffini, Gravitation and Spacetime, 2nd ed. Norton, New York (1994). The first edition was written by Ohanian alone in 1976.
  6. E. F. Taylor, J. A. Wheeler, Exploring Black Holes: Introduction to General Relativity, Addison Wesley Longman, San Francisco (2000).
  7. J. B. Hartle, Gravity: An Introduction to Einstein’s General Relativity, Addison-Wesley, San Francisco (2003).
  8. B. F. Schutz, Gravity from the Ground Up, Cambridge U. Press, New York (2003).
  9. S. Carroll, Spacetime and Geometry: An Introduction to General Relativity, Addison-Wesley, San Francisco (2004).
  10. T.-P. Cheng, Relativity, Gravitation and Cosmology: A Basic Introduction, Oxford U. Press, New York (2005, 2nd ed. 2010).
  11.  L. Ryder, Introduction to General Relativity, Cambridge U. Press, New York (2009).
  12. R. J. A. Lambourne, Relativity, Gravitation and Cosmology, Cambridge U. Press, New York (2010).
  13. R. N. Henriksen, Practical Relativity: From First Principles to the Theory of Gravity, Wiley, Chichester, UK (2011).
  14. T. A. Moore, A General Relativity Workbook, University Science Books, Sausalito, CA (in press)




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