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From: "Paul.B.Andersen" <relativity@paulba.no>
Newsgroups: sci.physics.relativity
Subject: Re: Newton: Photon falling from h meters increase its energy.
Date: Mon, 13 Jan 2025 19:54:29 +0100
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Den 13.01.2025 06:07, skrev LaurenceClarkCrossen:
> "Soldner, Einstein, Gravitational Light Deflection and Factors of Two"
> This paper gives an interesting discussion of Soldner's calculation.
This paper is written by Tilman Sauer in 2021.

In 1801 Johann Georg von Soldner calculated the Newtonian prediction
for the deflection of light grazing the Sun to be 0.84",
which is quite close to the correct value 0.875".

Sauer speculates if there are misprints in Soldner's calculation
so that his result should be a factor of two higher, that is 1.68"
which is quite close to Einstein's 1916 calculation 1.7".
(With somewhat better precision GR predicts 1.75")

If Soldner had calculated 1.68", he would be wrong.
The Newtonian prediction is  0.875".

> 
> And Einstein used a refraction formula to double the deflection=
> "photographic plates? 

How ridiculous! :-D

Einstein calculated the GR prediction 1.7" in 1916,
before any measurements of the deflection was made.

See:
https://paulba.no/paper/Foundation_of_GR.pdf

At the top of page 69:

  "We examine the curvature undergone by a ray of light passing
   by a mass M at the distance Δ."

The calculation is shown on page 69 and the result is given
at the bottom of the page:

  "According to this, a ray of light going past the sun undergoes
   a deflexion of 1.7"."

So in 1916 nobody, including Einstein, knew what the correct
value was, because no measurements were ever made.


> Poor did, and he completely repudiated the
> findings of Eddington. This should have given pause to any ethical
> scientist.

Poor did what? Use a refraction formula to repudiate
Eddington's measurements? If Poor had done so,
wouldn't that have been to explain Eddington's measurements?

But of course Poor did no such thing. See below.

> Here are some quotes from Poor's summary: "The mathematical
> formula, by which Einstein calculated his deflection of 1.75
> seconds for light rays passing the edge of the sun, is a well known
> and simple formula of physical optics"; 

Ah! So that's where you found the "refraction formula"! :-D

In 1930 Poor obviously knew 'The mathematical formula,
by which Einstein calculated his deflection of 1.75".'

This is the equation:  Θ = 4GM/Δ⋅c² 

where:
Δ = the impact parameter, closest approach to Sun
c = speed of light in vacuum
G = gravitational constant
M = solar mass
In this case Δ = R, the radius of the Sun.

This is indeed "a well known and simple formula" and
since it is about physics and optics (light)
Poor called it a "formula of physical optics".

It has nothing to do with refraction, obviously.

Why did you think that Poor claimed it was about refraction? :-D


> "Not a single one of the
> fundamental concepts of varying time, or warped or twisted space,
> of simultaneity, or of the relativity of motion is in any way involved
> in Einstein's prediction of, or formulas for, the deflection of light";

Quite right.
Einstein's formula  Θ = 4GM/Δ⋅c² is a well known and simple formula
of physical optics which contains nothing about time dilation
or relativity of simultaneity.

> "The many and elaborate eclipse expeditions have, therefore,
> been given a fictitious importance. Their results can neither prove
> nor disprove the relativity theory" (emphasis added) (Poor, 1930)." -

This was right(ish) in 1930.

The eclipse measurements are notorious imprecise,
and are now of historical interest only.

Many measurement (of EM-radiation NOT grazing the Sun) are performed:

https://paulba.no/paper/PPN_gamma_Hipparcos.pdf
https://paulba.no/paper/PPN_gamma_Cassini.pdf
https://paulba.no/paper/Shapiro_2004.pdf
https://paulba.no/paper/Fomalont.pdf
https://paulba.no/paper/PPN_gamma_Cassini_2.pdf

GR's prediction for the gravitational deflection of EM-radiation
is so thoroughly experimentally confirmed that you have to be
extremely ignorant not to accept it.


-- 
Paul

https://paulba.no/