Classical Rational Reasoning

(1) The year 1900.
(2) Plank made the crucial discovery, the fundamental law of existence:
(3) [itex]\Delta E = h \cdot \nu [/itex]
(4) In the same year, Henry Poincare derived the equation
(5) [itex]E = m \cdot c^2 [/itex] (http colon slash slash arxiv.org/ftp/physics/papers/0608/0608289.pdf) (page 2)
(6) Newton's law of gravitation was known for a long time already.
(7) That what either of them (Plank, Poincare, or anybody after them)
(8) could then had tried to do is the following:
(9) The intensity of the Earth's gravitational force is
(10) [itex]\displaystyle F = \frac{G \cdot m}{r^2} \cdot m_p = a(r) \cdot m_p [/itex]
(11) where [itex]m[/itex] is the Earth's mass, and [itex]m_p[/itex] is the mass of an entity
(12) within the Earth's gravitational field.
(13) The amount of work which has to be done in order to move the mass [itex]m_p[/itex]
(14) infinitesimally radially away from Earth [itex]dr[/itex] is
(15) [itex]dA = a(r)\cdot m_p \cdot dr[/itex]
(16) In the case of a photon which moves away from Earth, and according to the energy
(17) conservation principle, and according to the [itex]m = E/c^2[/itex]
(18) we would have:
(19) [itex]d \Delta E = -dA = -\frac{G \cdot m}{r^2} \cdot \frac{\Delta E}{c^2} \cdot dr \Rightarrow [/itex]
(20) [itex]\frac{d \Delta E}{\Delta E} = -\frac{G \cdot m}{c^2r^2} \cdot dr[/itex]