Re: Bending of light not well authenticated

On Sun, 22 May 2005 "Koobee Wublee" wrote:
>By minimizing integral of dt, the equations of motion ... are
> (r dH/dt)^2 / c^2 = (1 - 2 U)^2 b^2 / r^2
> (dr/dt)^2 / c^2 = (1 - 2 U)^2 (1 - (1 - 2 U) b^2 / r^2)

Yes, we've established that. These equations defines the light-like
paths in the vicinity of a spherically symmetrical gravitational
field. All we need to do now is check to see how much deflection
there is for a path that grazes the edge of the sun. The perihelion of
the light path is a distance R from the center of the field, where R
is the radius of the sun. It follows (from the second equation at the
perihelion, where dr/dt = 0) that the constant of integration is b =
R/sqrt(1-2U). Then integrate dH/dr to give the total angular travel as
the ray of light goes from r = infinity down to r = R, and then back
to r = infinity. The result is pi + 4GM/(Rc^2), so the deflection is
4GM/(Rc^2).

>However, these only represent half of the equations of motion...

No, the equations of motion are the equations of motion. They
identify, for any coordinate time t, the radial position r and the
angular position H of the path. This completely defines the path in
terms of these coordinates, which uniquely identify each time and
place.

The rest of what you have typed is gibberish. Most of your sentences
don't even parse, let alone make any kind of mathematical or physical
sense.

>Now, we are ready to address the heart of this problem. So, after arriving
>at (dH/dr), the angle of deflection can be calculated by its integral. By
>integrating from infinity to (R - dR), if you don't know the value of dR,
>how can you arrive at the correct answer? In your language which you say
>R is the perihelion, if you don't know what R is, how can you arrive at a
>definite answer?

The parameter R is the minimum distance from the path of light to the
center of the gravitational field. When we examine the deflection of
starlight grazing the surface of the Sun during an eclipse (for
example), the value of R is simply the radius of the Sun. Do you
understand this? The value of R is known; the unknown we are
trying to find is the integral of dH for any given R. The result is
pi +4GM/(Rc^2).

You seem to be looking at the problem backwards, as if you are
starting with a straight ray of light in flat spacetime, and then
inserting the Sun and trying to calculate how far the ray of light is
deflected. In other words, is seems that you are thinking of the
parameter R as the distance from the ray of light to the origin of
flat spacetime, and then you are imagining placing the Sun at the
origin and seeing the amount dR that the light ray deflects, almost
like a clothes line being held at the ends, with the Sun pulling on it
in the middle. If this is indeed what you are thinking, then you are
completely misguided. Rays of light are not clothes lines. You need to
go back to grade school science class and understand how rays of light
propagate. It's futile for you to be trying to understand general
relativity, lacking the equivalent of a grade-school understanding of
basic physics.
.

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