American Association of Physics Teachers

 Rai Weiss's TALK  -- p. 7
About Teaching General Relativity:
           History, motivation, experiment

from the AAPT Topical Workshop:
Teaching General Relativity to Undergraduates
Syracuse University, July 20-21, 2006

Rainer Weiss

The 38 slides from Weiss's talk are here in 9 web pages. In the narrative below you can click on any subject to go to its page. Click here for a full PDF version.

pg. 1 GR is one of several possible covariant theories of gravity. It is only from observation and experiment that we conclude that GR is the valid theory. So, Weiss argues, we should base the teaching of GR on experiment and observation. To make his points, he uses the historically important examples of gravitational red shift, bending of light, advance of perihelion of Mercury, Shapiro test, and Nordstrom's scalar theory of gravity, which, though Lorentz covariant, fails to predict correctly the precession of perihelion of Mercury or the gravitational redshift.

pg. 2  You can motivate the need for curved space by imagining coordinates on a rotating platform. Basic phenomena, such as gravitational redshift, can be inferred from the principle of equivalence. The difficulty comes when you try to measure something: For the redshift there are subtle corrections to be determined and made.

pg. 3  For bending of starlight around the Sun the effect is small and the results are ambiguous.

pg. 4 Data from 9 solar eclipses show how imprecise these measurements were. There are no error bars, but tiny changes in the position or orientation of the plates or small shifts in the telescope from thermal variations occurring as the Sun was eclipsed would have produced large fractional errors in the results. There were other difficulties too.

pg. 5  The modern data are much more precise and convincing. With radio interferometry the Sun's bending of microwaves from three radio stars has been measured to a precision of about 1%.

pg. 6  Weiss contrasts the rate of precession of Mercury's perihelion with that of the apsides of the Hulse Taylor binary pulsar. Where the old measurements were only weak evidence for GR, modern measurements with precisions of ppm are strong evidence that GR is right. These data also yield convincing evidence for gravitational radiation as well as precise masses of the pulsar and its companion. Thirty years of observation continue to improve precision.

pg. 7 Shapiro time delay provides a good context for teaching about coordinate freedom. To test two different theories you must make complete consistent calculations with each. Shapiro had to express the results in coordinate free form (as invariants), and then compare. He found that Einstein's GR predicted what was observed; Newton's theory did not. 

[Cliff Will's book Was Einstein Right? gives a nice account of Shapiro's experiments that first detected this effect. --editor]

pg. 8 Shortly after publishing his GR theory, Einstein showed that there should be gravitational radiation. To remind us that there are important subtleties in this prediction Weiss points out two mistakes that Einstein made in his  first papers on gravity waves: 1) He erroneously predicted gravitational radiation from spherically symmetric motion, which we now understand to be impossible; 2) He made a factor of 2 error when calculated the quadrupolar radiation that is the dominant form of gravitational radiation.

pg. 9 The take-home message: In the effort to detect gravitational radiation there is much other physics than gravity itself. Use it to interest your students. And motivate them with the elegance of the technical prowess and instruments needed to examine the physical consequences of GR.



To make subtle conceptual issues concrete, teach them in terms of real physical observations. For instance, how do you show that there is a global deflection and delay of light passing a star, even though in a succession of local frames the speed of light is invariant? To detect this Shapiro time delay requires both technological sophistication and careful comparison of the results of a fully consistent GR calculation using Einstein's theory with a calculation that uses only the Newtonian and Maxwellian theories. GR results formulated in coordinate-free terms match observation; results from the other calculation do not.





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