h.jones
Posts:
32
From:
uk
Registered:
2/21/08
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Einstein's factor of 2 in starlight deflection
Posted:
Aug 20, 2011 1:45 PM
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Einstein's original formula for deflection of light skimming the Sun's
surface breaks down to 2GM/Rc^2. This is merely the Schwarzschild
radius divided by current radius of the Sun. If all things are
considered to be happening at the rate of c and at the Schwarzschild
limit the reckoning gets easier. Then R/R=1, that is one radian, in
terms of angle and one radius in terms of length or distance. You
could say it is an equivalence of distance measured in terms of
radius. All that considered look at it this way:
If we consider that at the Schwarzschild limit, whatever the star's
mass or radius, then in that particular frame the star's mass becomes
the local timescale mass and its diameter becomes the local time
frame. Take the case of the Sun at ,say, 2x10^30kg, radius at
2.9690906x10^3m and thus its local c at 2r, 5.9381812x10^3m. The time
unit here,then, will be 1/5.0485569x10^4 of a second. Looking at this
numerical principle, consider the following.
The formula for free fall, distance travelled, is (gt^2)/2, where g is
gravitational acceleration and t is time in local time units. If g=c
then we could look at the formula as (ct^2)/2. The formula for g is
GM/r^2, so we could look at it like this: {(GM/r^2)t^2}/2. If we
consider time to be one single unit there is no need to include it. So
our formula becomes (GM/r^2)/2. But we need to put everything in
terms of c and radius is equivalent to c/2. So our formula can be
adjusted again to: (4GM/c^2)/2 which breaks back down to 2GM/c^2.
Therefore, the formula 2GM/c^2 means the same thing as (gt^2)/2 where
g=c and refers to length or distance not angle.
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