None Occurring Time Dilation in Gravity
Actually, this can all be generalized.
* * *
Consider the world famous Minkowski Space-Time Diagram,
(c dt)^2 = (c' dt')^2 - (dr')^2 = (c' dt')^2 - (dr'/dt')^2 (dt')^2, where
c = local. speed of light under gravity
c' = speed of light very far away
t = local time observed under gravity
t' = time observed very far way
r = local length observed under gravity
r' = length observed very far away
c^2 = c'^2 (dt'/dt)^2 - (dr'/dt')^2 (dt'/dt)^2
Since all time dilation of gravity all came down on the speed issues, I am
not convinced that gravity does cause time nor length dilations. Time and
length dilations are manifestation of Relativity (based on speed alone). If
an object is not observed to move at any speed, it is not under time
dilation even with gravity applied to it. Therefore,
dt = dt', dr = dr', or
c^2 = c'^2 - (dr/dt)^2
Differentiate both sides,
2 c (dc/dr) (dr/dt) = - 2 (dr/dt) (d^2r/dt^2) = - 2 (dr/dt) (dU/dr), where
U = gravitational potential, where
U = G M / r if r 2 G M / c'^2, where
G = gravitational constant
M = mass caused this gravitation in which
r = 0 is the center of M, therefore
2 c dc = - 2 (dU/dr) dr = - 2 dU
Solve this very, very simple differential equation,
c^2 = K - 2 U, where
K = integration constant
At r = oo, U = 0, c = c', therefore K = c'^2
c^2 = c'^2 - 2 U, or
c(r) = c' sqrt(1 - 2 U(r) / c'^2), or
m c'^2 = m c^2 + 2 m U, where
m = mass
What does it all mean? Matter that has mass causes distortion in this
Aether which 100 years the whole scientific community following the cult of
Einstein turned their backs on. The distortion is in the increase in the
permittivity of free space around it. That caused the speed of light to
decrease (c = 1 / sqrt(permittivity * permeability)). GRAVITY IS CAUSED BY
THE STRESS IN THE AETHER (GRADIENT in the PERMITTIVITY) and not by the
curved space mumbo jumbo proposed by the General Theory of Relativity in
which it even fails to explain why matter falls into this curved space in
the first place.
We can then come up with a U that fits observation, such as
** Star refraction under solar eclipse
** Precesion of perihelion of Mercury
Because the manefistation of this stress in the Aether is perceived as
gravity.
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