I just finished reading The Special Theory of Relativity by David Bohm, based on Bohm's undergraduate lectures at Birkbeck College. Bohm approaches relativity in a somewhat unusual way: he focuses on exposing the implicit assumptions that underlie our common-sense notions of spacetime; it is these assumptions that make relativity seem paradoxical for many people. For that reason I consider it worth reading, even if you've studied relativity before. In addition to the material on relativity itself, Bohm also has some insightful comments about the nature of scientific inquiry as well as about the development of human perception and how we acquire our common-sense notions of spacetime.
Some take-home points:
- Lorentz and proponents of the ether theory actually had predicted many of the well-known relativistic effects (e.g. length contraction and time dilation for moving objects). One of Einstein's major contributions was to focus solely on relationships between objects, which are in principle observable, rather than on substances like the ether, which are not.
- Relativity of simultaneity (i.e. the fact that observers can disagree on whether events occur at the same time or not) is very counterintuitive and can be thought of as the source of a lot of the apparent paradoxes in relativity. For example, when you measure the length of an object you record where its ends are at the same time, but the notion of "at the same time" is relative. Length contraction occurs because different observers disagree on what it is that should be measured.
- It is kind of cute to characterize relativity as saying that "everything is relative" but it is really the things that the theory says are not relative that are of interest (e.g. the speed of light, the spacetime interval, and proper time and mass). It is through invariants that we can understand the aspects of a situation that are really fundamental to it and separate them from those that are contingent, or relative to our viewpoint. The idea is like being able to perceive that a table is circular even if it appears to look like ellipses of various shapes and sizes as we walk around the room. Bohm argues that the same process of inferring invariants is at the heart of both scientific inquiry and human perception.