Re: Newton: Photon falling from h meters increase its energy.

On Tue, 14 Jan 2025 1:41:44 +0000, rhertz wrote:

On Tue, 14 Jan 2025 0:36:33 +0000, LaurenceClarkCrossen wrote:
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"This is exactly double the value given in 1911, and this doubling
of values has given rise to many speculations, and to many and
varied explanations, on the part of the relativists.
An inspection of the formulas, which Einstein used, shows
exactly what he did and how he derived this result. The essential
factor in the formula is that for the rate of change of velocity
along the wave-front 6c, 6x ; and this is the only factor in which
any change can be made. All the other terms and factors of the
formula are always identically the same." - Poor = "THE RELATIVITY
DEFLECTION OF LIGHT!"

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Years ago, I posted that when Einstein published his 1915 paper on
Mercury, he included a couple of paragraphs announcing that he doubled
his 1911 value due to his work with GR.
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It's all on his 1915 paper, in a single line: Equation 7c.
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Einstein had it easy. He modified Newton's potential Φ = - GM/r for
Φ = - GM/r (1 + B^2/r^2), in his equation (7c). This was in geometrical
units.
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In physical units, Eq 7c is  Φ(r) = - GMm/r [1 + B^2/(mcr)^2]
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Long story short: In the same paper, and using this change, he managed
to obtain Gerber's formula and 43" and, as a bonus, DOUBLED the
gravitational potential on the formula for deflection of starlight, used
in 1911.
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ψ(1911) = 1/c2 2GM/RS = 0.85 arcsec
ψ(1915) = 2 x ψ(1911) = 1/c2 4GM/RS = 1.75 arcsec
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The key for this "magic prediction" is simple. The extra (1 + B^2/r^2)
factor in Φ(r), in physical units, is [1 + B^2/(mcr)^2]
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B = mr2ω  is the constant angular momentum, under Newton's Law of
Gravitation,
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so
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Φ(r) = - GMm/r (1 + r^2ω^2/c^2)
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He made Rs.ω = c at the perigee of the trajectory, at which the test
particle has maximum speed.
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But it implies a variable speed of light, besides that "photons" have
mass and suffer gravitational attraction.
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This is the Newtonian equation that Einstein seek, using 80% of the
paper, before changing for a new Φ:
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m [r^2 (dɸ/dt)^2 + (dr/dt)^2]  - GMm/r = 2E  (E < 0, the total energy of
the system, is CONSTANT).
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The above equations describe any elliptic, parabolic or hyperbolic
orbit, and was used by Einstein TWICE:
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1) To get the final expression of the advance of Mercury's perihelion in
an orbit with e = 0.2025 and E < 0.
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2) For the deflection of light, at the perigee of an hyperbolic
trajectory of a photon, with r = Rs, e >> 1, E > 0.
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Einstein REFUSED to show his calculations for 2) and only presented the
new value for deflection of light plus a lot of gobbledygook using GR.
Astronomers and physicists from ALL OVER the world asked Einstein to
present his calculations. Einstein NEVER delivered them.
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Why did Einstein refused to show his derivation? Because he had to
explain:
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1) The use of light as "quanta of energy" (A.K.A. photons) having mass m
= hf/c^2.
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2) The change of the bounded elliptic orbit of Mercury, with e = 0.2025
into a highly eccentric hyperbolic orbit (e > 200,000), which passed by
the Sun at its perigee (r = RS).
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3) The angular momentum at the perigee, B(RS) = m.RS.c. In this way, the
quotient between brackets of ψ(RS) became equal to 1, DOUBLING the
gravitational potential.
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4) Making the angular velocity of the photon at the orbit's perigee: c =
RS. ωMAX, implied a VARIABLE SPEED OF LIGHT in the trajectory of the
photon:
c' = rω (only reaching c at r = RS).
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He had  a LOT OF THINGS to explain. And because of the above points, his
ETERNAL SILENCE.
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So, his announcement in 1915 came to the fact that in the modified
gravitational potential
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Φ(r) = - GMm/r (1 + r^2ω^2/c^2)
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he made r.ω = c, for which Φ(r_sun) = - GMm/r_sun (1 + 1).
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Doubling the potential when starlight graze the Sun's surface DOUBLED
the 1911 Newtonian value, AT THE COST OF A VARIABLE SPEED OF LIGHT IN
THAT POINT.
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He NEVER, EVER showed his calculations. That's why, in 1930, Poor was
calling him (LITERALLY) a fraudulent crock.

Since Einstein employed Huygens' principle using Huygens' formula for
refraction, he would have had to use a refractive index that doubled
Newtonian. That is just pure invention.