"Dan Winters" <dwinters@despam.com> wrote in message 
news:42705e70.535227546@news.gte.net...
> On Mon, 25 Apr 2005 John C. Polasek <jpolasek@cfl.rr.com> wrote:
>>I have not been able to find a really satisfactory derivation of
>>general relativity's  1.75" bending of the sun's rays...does anyone
>>know of a downloadable document that uses actual mathematics
>>to prove the 1.75" deviation.
>
>
> A quick search on google turns up this page, which includes a complete
> derivation of the relativistic deflection of light:
>
> http://www.mathpages.com/rr/s6-03/6-03.htm

At the perihelion, if (r = r0), then there is no deflection.  To have a 
deflection, it should be that (r = r0 - dr) where (dr = deflected amount at 
perihelion).  Granted

    r0 >> dr

However, the angle of deflection is so small that including (r = r0 - dr) 
into the equating, it will null out the deflected angle at r = infinity. 
That means in the inward bound, the photon will be deflected closer to the 
sun, and at its perihelion, the deflected distance is (dr).  However, as the 
photon leaves the sun, it will undo its deflection.  It will end up with no 
deflection at all at (r = infinity).

Since the derivation that leads to the Christoffel symbols is nothing but 
applying the principle of the least action.  A simple Euler-Lagrange method 
with a few substitutions should leads to equations (2).  So far, we are 
looking at how the photon is behaving in the observed spacetime whose 
curvature is influenced by the sun.  The article also mentions (dtau = 0) 
which means we can also write an equation to describe the path of the photon 
in proper space using proper time.  That is

    c^2 dtau^2 = drho^2 - rho^2 dtheta^2

Applying the principle of least action (Euler-Lagange or Christoffel 
symbols), we have no distortion to the photon's travel.  The points of 
interest are when the photon just stars out its journey and when the photon 
ends its journey.  Since in proper spacetime there is no deflection, in 
distorted observed spacetime there must not be any deflection at all at (r = 
infinity).  This agrees with the condition above where the perihelion occurs 
at (r = r0 - dr).

GR does not predict a deflection of a photon near a gravitation mass in the 
end result.  However, in between, the severity of the deflection is not a 
function of the deflected angle but its deflected position.