Roadmap to Understanding the Theory of Relativity

[JiT]

I just started reading the book The Perfect Theory by Ferreira and it has rekindled an old desire of mine to pursue a study of physics ultimately culminating in being able to fully comprehend (and play with) Einstein's field equations. My problem is I don't exactly know where to begin. I'm hoping some of you can provide some suggestions in that regard.

I'm a masters student in aerospace engineering studying nonlinear guidance and control theory so I'm not a complete novice, but my mathematical background doesn't go beyond the engineering realm (calc I-III, diffEqs, linear systems, Eng. Analysis, etc.). The same goes for physics. I'm very familiar with advanced solid and fluid dynamics, but nothing in the realm of relativity and very little in E&M.

Can anyone recommend an ordered list of math/physics/ topics and/or texts that can serve as a place to get started on my road to fully understanding Eisenstein's ToR?

 

[bcrowell]

You say your goal is to learn the Einstein field equations. The Einstein field equations are the wave equation that governs gravitational fields, just as Maxwell's equations are the wave equations for electromagnetic waves. The E&M case is *much* easier than the gravitational case. If your background includes "very little" E&M, then that means you haven't learned the easy version yet, and that's going to make it a lot harder to learn the hard version. Since your math background is strong, I would suggest that you read Purcell, Electricity and Magnetism, which is the best E&M book ever written. However, it assumes you know a little basic special relativity. So my suggested reading list would be something like the following:

(1) Takeuchi, An Illustrated Guide to Relativity. This is basically a "relativity for poets" book, but it has a good modern approach. Only read the chapters on kinematics, and then stop. The chapters on dynamics are useless.

(2) Read just enough from another SR book to learn the relevant topics in dynamics (the energy-momentum vector, and that's about it). Possibilities that don't use a 1950s approach would be (a) ch. 12 of Morin, Introduction to Classical Mechanics; (b) ch. 4 of my own free SR book http://www.lightandmatter.com/sr/ ; (c) ch. 7 of Spacetime Physics, by Taylor and Wheeler.

(2) Read Purcell (skipping the stuff that's not directly relevant, e.g., circuits). Work as many of the problems as you have time to do.

(3) Go back and read a complete SR book such as the ones I mentioned above.

(4) Learn GR from a book such as Carroll, which is modern and has a free version available online.

 

[DrSirius]

[...]

(2) Read just enough from another SR book to learn the relevant topics in dynamics (the energy-momentum vector, and that's about it). Possibilities that don't use a 1950s approach would be [... (enphasys aded ]

What is the problem with 1950 approach? Relativistic mass? 3+1 dimensions vs 4D? Or more profound? Just curious.

 

[bcrowell]

What is the problem with 1950 approach? Relativistic mass? 3+1 dimensions vs 4D? Or more profound? Just curious.

Yes, the most common yech factor is relativistic mass. Sometimes you still see ict. I don't think it makes sense to use Einstein's original postulates anymore, but that's more a matter of taste. Another problem with many introductory treatments, although this isn't necessarily an old-vs-modern issue, is an overemphasis on length contraction and time dilation, and not enough on the Lorentz contraction.

 

[robphy]

Here's a set of books by the same author that one could work through...
http://pages.pomona.edu/~tmoore/

http://www.physics.pomona.edu/sixideas/ ( http://www.physics.pomona.edu/sixideas/sipref.html )
Units C,N,R,E
then
http://pages.pomona.edu/~tmoore/grw/ ( http://www.uscibooks.com/moore.htm )
(excerpt http://pages.pomona.edu/~tmoore/grw/Resources/GRWBook.pdf )

Tom's article on his approach
http://scitation.aip.org/content/aip/magazine/physicstoday/article/65/6/10.1063/PT.3.1605

 

[bcrowell]

If I add up the price tag for the four units of Moore's freshman course that robphy suggested, plus the GR workbook, I get $231.48. That's excessive. It's also very difficult to evaluate whether the freshman books are any good, because there doesn't seem to be any way to preview them online; Amazon's "look inside" feature is disabled.

 

[robphy]

If I add up the price tag for the four units of Moore's freshman course that robphy suggested, plus the GR workbook, I get $231.48. That's excessive. It's also very difficult to evaluate whether the freshman books are any good, because there doesn't seem to be any way to preview them online; Amazon's "look inside" feature is disabled.

Um... excessive?
How much are Purcell and Morin? Can you just get the chapters you want? Or do you have to buy the books?

If you are comfortable with freshman-level physics, you can probably skip Units C and N... although they offer quite a unique viewpoint about mechanics and conservation laws.
I don't think Moore's sequence C,N,E is that much more than a typical Serway/Young&Freedman-type text.
Sure, there are probably some cheaper books out there.
(Units R, Q, and T are more advanced than a typical post-intro "Modern Physics" text... but just below junior-level courses.)

Focus on Unit R (I am awaiting the 3rd edition, 2016) and the GRWorkbook.
Together, there is the benefit of a more cohesive stream of thought [and notation] from intro to advanced [which could be supplemented with other texts].
These texts were developed at Pomona College (a small liberal arts college in California).
The pre-cursor to all of these texts is Tom Moore's (1995) Traveler's Guide to Spacetime.

(If cost is that prohibitive, ... in a typical college or university, you can get books by interlibrary loan [possibly with help from worldcat ].)
You can probably find chapters from Spacetime Physics (1st ed, 1966) from Edwin Taylor's website.