From special to general relativity: why?

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Discussion Overview

The discussion centers on the motivations for transitioning from special relativity (SR) to general relativity (GR), focusing on the physical and mathematical considerations involved in this generalization. Participants seek references and resources that explain these concepts clearly.

Discussion Character

  • Exploratory, Technical explanation, Conceptual clarification

Main Points Raised

  • One participant notes that special relativity addresses spacetime without gravity, where trajectories appear straight in a Euclidean sense, while general relativity incorporates gravity, allowing for curved trajectories that are still considered straight in a different sense.
  • It is mentioned that the line element in special relativity must be modified to account for varying metric coefficients in general relativity, which can change with location and time.
  • The Riemann tensor is introduced as a way to encapsulate the effects of gravity on the worldlines of interacting masses.
  • Several participants suggest various resources for understanding the transition from SR to GR, including Einstein's original paper, Martin Gardner's book, and Taylor and Wheeler's work on black holes.
  • One participant expresses frustration that the motivations for the transition are often assumed to be obvious and not well covered in available literature.
  • A suggestion is made to look into "Nordström theory of gravity" as a potential resource.

Areas of Agreement / Disagreement

Participants express a range of viewpoints regarding the clarity and availability of resources on the motivations for general relativity. There is no consensus on a single best reference or explanation, indicating multiple competing views on how well these concepts are covered in existing literature.

Contextual Notes

Some participants note that the motivations for transitioning from SR to GR may depend on specific interpretations of gravity and spacetime, and that existing resources may not adequately address these motivations.

Who May Find This Useful

This discussion may be useful for individuals interested in the foundational aspects of relativity, particularly those seeking to understand the transition from special to general relativity and looking for appropriate references.

Goldbeetle
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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
 
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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 [itex]ds^2 = \sum g_{ab}dx^adx^b[/itex] where the metric coefficients gab 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.
 
Thanks, any good reference?
 
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.
 
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.
 
Try Googling "nordstrom theory of gravity".
 

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