From special to general relativity: why?

[Goldbeetle]

Dear all,
where can I find a good discussion (books, online etc) of the physical and mathematical consideration that motivate the generalisation from special to general relativity?

Thanks,
Goldbeetle

 

[Mentz114]

Since no suggestions have been made, consider this.

Special relativity deals with spacetime with no gravity. The trajectories of bodies moving uniformly when plotted on a spacetime diagram are straight in the euclidean sense.
Einstein realized that objects falling freely in a gravitational field also experienced force-free motion even though accelerating, so their trajectories were also in a sense straight lines although in the euclidean sense they would appear curved. This requires that the SR line element ds²= dt² - dx² - dy² - dz² must become $ds^2 = \sum g_{ab}dx^adx^b$ where the metric coefficients g_ab can change from place to place, or even with time. The signature of Minkowski space is preserved.

If two masses are interacting through gravity their worldlines ( geodesics) will approach. The rate of approach turns out to given completely by the Riemann tensor.Thus the effect of gravity can be encapsulated in this tensor.

So, in short the motivation is to include gravity in SR while still maintaining SR in some sense.

 

[Goldbeetle]

Thanks, any good reference?

 

[bcrowell]

The introduction to Einstein's paper "The foundation of the general theory of relativity" is actually very readable. It's public domain, and you can find it online.

Martin Gardner's Relativity Simply Explained is the first book I always point people to if they're interested in relativity. (Some parts of the book are out of date.)

Exploring Black Holes: Introduction to General Relativity, by Taylor and Wheeler, is also in my opinion a great book for people making the transition from SR to GR. They avoid introducing all the techniques of tensors and index gymnastics, concentrating on one specific topic in GR -- black holes. What this allows them to do is to develop lots of good conceptual stuff without getting bogged down in mathematics.

 

[Mentz114]

No, it's not covered well in any of my books. I think it's assumed to be obvious.
[edit] posted at the same time as bcrowell.

 

[Daverz]

Try Googling "nordstrom theory of gravity".