Re: Bending of light not well authenticated

"Koobee Wublee" <kublai@xxxxxxx> wrote in message
news:hiehe.32316$fI.18194@xxxxxxxxxxxxx
> Since the curvature is in spacetime and not just in space, why do
> you expect the photon to be deflected permanently with an angle
> of displacement in space?

I'd say that's missing the point I was making slightly. The curvature is
in spacetime, and the curvature factor effects both space and time, and
both have a deflection effect on the path of a photon. Or put another
way the curvature factor (1-2M/r) appears in the Schwarzschild equation
both in the time component and in the radial distant component.

>Since you model the curvature of spacetime as a prism, why do you
> not expect the light to follow what a prism would bend the light that
> is unbending or correcting the deflection as the photon leaves the
> sun which ends up with no deflection at all?

In every analogy, there is a part that is analogous and the part that is
not at all analogous. The difference is when something is like something
vs. actually is something. The prism was an analogy. The analogous part
was Fermat's principle applies to both. The light passing the sun would
be deflected toward the sun from passing through a denser optical
medium, just as light arriving at an angle to a slower medium would be
bent toward a smaller angle. That's the analogous part. The unanalogous
part would be the shap of the prism and the shape of space near the
gravitating body. Now we could probably further define this shape with
effort, but it's not worth bothering.

> GR math actually shows gravitational lens behaves very much like a
> true lens where the index of refraction is a gradient highest at the
> center. However, whoever first derrived this after 1915 incorrectly
> simplifed the integration limit of the integral.

Well, I'm reasonably certain the first to derive the deflection after
1915 was Einstein himself. So I don't really understand the references
that follow.

> That depends on dr which is related to an integration constant
> associated with the conservation of angular momentum.

The derivation indeed is based on the ratio of angular momentum and
energy, which turns out in the no mass limit to be simply b, the impact
parameter.

Far away from the gravitating body, where r is large the path of the ray
will have a parallel ray which can go straight along a single radial to
infall to the gravitating body. The distance between these two parallel
rays in flat space is called the impact parameter.

So the geodesic motion of a massless particle depends on only two
things, its effective potential defined by the Schwarzschild metric, and
it's inital displacement from a straight in radial, the impact
parameter.
(MTW 673)

--
Randy M. Dumse

Caution: Objects in mirror are more confused than they appear.



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