[Phys-l] general relativity (was: starlight deflection)

[John Denker <jsd@av8n.com>]

On 10/12/2007 06:22 PM, David Ward wrote:

> In any event, this boils down to "if the sun exerts a force (momentum
> alteration) on a photon does the photon do the same to the sun?"

In general relativity, the structure of Einstein's field 
equation guarantees that the [energy, momentum] 4-vector
is conserved.

==============

Twice now I've mentioned the Einstein field equations.  That
does not mean that starting there is good pedagogy.

One might caricature one possible way of summarizing GR as 
 1) Starting with the source term for the gravitational field,
  i.e. the stress-energy tensor, 
 2) Plugging that into the field equations.
 3) Thereby connecting it to the Einstein curvature tensor.
 4) Which is related to the Ricci curvature tensor.
 5) Which is related to the Riemann curvature tensor.
 6) Which is related to the geodesic deviation equation.
 7) Which is related to physical notions of parallel transport.

My pedagogical point is that AFAICT that sequence is more-or-less 
exactly backwards.  Perhaps that sequence is useful as a mnemonic
once you understand everything (1 reminds you of 2 which reminds
you of 3....) but a good mnemonic for experts isn't necessarily
a good developmental sequence for students.

To express the same idea another way:  Sometimes students say they 
want to "see the Einstein field equation" and then they want to 
"figure out the Einstein field equation" ... but that is unlikely 
to be a good strategy.  What they say they want isn't what they 
ought to want.

Constructive suggestion:  There is a nice survey of general relativity
at
  http://www.math.ucr.edu/home/baez/gr/

It is called a "tutorial" but IMHO it would be better called a survey
or an overview.  I suspect ordinary mortals would have a hard time 
learning GR from documents with this level of non-detail.  Still, I 
strongly recommend reading it;  there's a lot of good sense there.

More generally, as I've said before, there is a ton of good physics
on the John Baez site:
  http://www.math.ucr.edu/home/baez/

============

Also:  It should be obvious that before going anywhere near general 
relativity, students need a solid understanding of special relativity.

Note:  Any "understanding" that depends on FitzGerald-Lorentz contraction 
and time dilation doesn't count.  You can't explain the curvature of
spacetime to students who don't understand spacetime.

 -- FitzGerald-Lorentz contraction is not necessarily wrong physics, 
  but it is bad pedagogy
 -- ditto for time dilation
 -- four-vectors are good
 -- spacetime is good

Next year (2008) is the 100th anniversary of spacetime.  Let's get with
the program.
  http://www.av8n.com/physics/odometer.pdf