In the past few days, I have traveled to Phoenix on a business trip. While
my nuts are slowly roasting by the unusual late desert heat, my mind seems
to be working very well. I was able to carry through more on the subject of
time dilation which would satisfy even the most skeptics. Here you go.
Please shoot as many holes in this as you are able to.

- - -

GENERALIZED LORENTZ TRANSFORMATIONS AND PRINCIPLE OF CLOCK INVARIANCE

Again, as Maxwell has pointed out c^2 = 1 / (Uo Eo) in which both the
permeability and the permittivity are the properties of the Aether. Here
on earth, c is what it is today because of the certain value of Uo and Eo.
Therefore, let's generalize into a universe where c is only constant to a
local observer.

Consider two frame of references --- one in frame (c' t', x', y', z' ) with
local speed of light c' and time t', and the other one in (c t, x, y, z)
with c and t. Frame c' sees the speed of light as c' every where even while
observing frame c. Similarly, frame c also sees the speed of light as c
every where even while observing frame c'. Then,

Frame c' will notice it takes

dt' = DL / c', for a photon to travel a distance of DL in frame c

On the other hand, frame c will observe

dt = DL / c, for the same photon to travel a distance of DL in frame c
itself. So,

DL = c' dt' = c dt, or

The observer in frame c' will observe frame c with a time dilation of

dt'/dt = c / c'

Now, frame c' is moving away from frame c with a distance of X between each
other. Then, the speed of frame c' is observed by frame c to be, dX/dt. On
the other hand, the speed of frame c is observed by frame c' to be

dX/dt' = (dX/dt) (dt/dt' ) = (dX/dt) (c' / c), or

(dX/dt' ) / c' = (dX/dt) / c = B

With these basic concepts identified, we can now go on to study the
classical Morley-Michelson experiment. Feynman Lectures give a very good
study of this experiment. The only thing difference applied with
non-identical speed of light is the triangle that derives the time dilation.
That is

(c' dt' )^2 = (B c' dt' )^2 + (c dt)^2, or

dt' = (c / c' ) sqrt(1 - B^2)

Thus, we can follow the footsteps of Larmor, FitzGerald, and Lorentz to
rewrite the Lorentz Transformations in a more generalized form which are

c' dt' = (c dt + B dx) / sqrt(1 - B^2)
dx' = (dx + B c dt) / sqrt(1 - B^2)
dy' = dy
dz' = dz, and

c dt = (c' dt' - B dx' ) / sqrt(1 - B^2)
dx = (dx' - B c' dt' ) / sqrt(1 - B^2)
dy = dy'
dz = dz'

The generalized Lorentz Transformations still based on observations are also
invariant.

The time dilation observed by frame c' on frame c is when dx = 0. So,

c' dt' = (c dt + B dx) / sqrt(1 - B^2) = c dt / sqrt(1 - B^2), or

dt'/dt = (c / c' ) / sqrt(1 - B^2), just as derived from Morley-Michelson
experiment.

Similarly, the length contraction observed by frame c' on frame c is when
dt' = 0. So,

0 = (c dt + B dx) / sqrt(1 - B^2), or dt = - B dx / c, thus

dx' = (dx + B c dt) / sqrt(1 - B^2) = (dx - B c (B dx / c)) / sqrt(1 - B^2)
= dx (1 - B^2) / sqrt(1 - B^2), or

dx' = sqrt(1 - B^2) dx, same as the result of Morley-Michelson experiment.

With these more sophisticated concepts understood, the next step is to
re-derive the Minkowski Space-Time Equation based on the generalized Lorentz
Transformations. We have

(c' dt')^2 - dx'^2 - dy'^2 - dz'^2 = ((c dt + B dx)^2 - (dx + B c dt)^2) /
(1 - B^2) - dy^2 - dz^2, or

(c' dt')^2 - dx'^2 - dy'^2 - dz'^2 = (c dt)^2 - dx^2 - dy^2 - dz^2

This Minkowski Space-Time Equation under the concept of Aether clearly
points out that time dilation is totally delusional. It is the change in
the local speed of light due to speed and/or gravity that causes this
delusion of time dilation. It is the clocks which depends directly or
indirectly on the speed of light that this delusion results. Applying the
actual time, the delusion goes away. The different speed of light presents
itself. As an observed particle moves, it distorts the Aether. Thus, its
local speed of light reduces according to the Minkowski Space-Time Equation
under the concept of Aether satisfying

c^2 = c'^2 (1 - B^2), where

c = local speed of light
c' = speed of light of observing frame
B = speed of frame c moving as observed from frame c'

If one allows his mind to be tricked by different local speed of light, he
will see a time dilation and curved space if ever more enlightened. If one
does not, he will see clearly different local speed of light and no time
dilation and perfectly flat Euclidean space in accordance with common sense.

For example, frame c' observes an atomic clock in frame c. To read off
time, an atomic clock depends on atomic resonance of individual atoms due to
electromagnetism. So,

fr oc 1 / sqrt(Lr Cr) oc 1 / sqrt(Uo Eo) oc c, where

fr = the resonant frequency
Lr = corresponding equivalence of inductance in this resonance
Cr = corresponding equivalence of capacitance in this resonance
Uo = permeability of free space
Eo = permittivity of free space

Again, any clock that depends on the speed of any mechanism or phenomenon
will be affected by its local speed of light, that also includes the
mechanical movements of the arms of a clock (B = v / c = invariant). All
clocks built in frame c' would read the same answer if suddenly replaced in
frame c. Or frame c' will always measure the same speed of light as frame c
because the basic unit of time measurement depends on the speed of light
itself. This is the Principle of Clock Invariance. However, frame c' can
observe ?o and ?o of frame c and intelligently deduce the speed of light in
frame c is accordingly c not c', and vice versa.

LOCAL SPEED OF LIGHT IN VACUUM UNDER GRAVITY

With the concept of the Principle of Clock Invariance well understood, we
can now explore the what causes gravity, and Newton can rest in pace. Let's
start with one of the most powerful equations ever discovered, the Minkowski
Space-Time Equation under the concept of Aether. Observing an object in
free fall,

(c dt)^2 = (c' dt')^2 - (dr')^2, where

c', r', t' are all observed parameters under U = 0, thus

c2 (dt/dt')^2 = c'^2 - (dr'/dt')^2

As we understand the whole situation, dt/dt' = 1. So,

c^2 = c'^2 - (dr'/dt')2, then

2 c (dc/dr') (dr'/dt') = - 2 (dr'/dt') (d^2r'/dt'^2) = - 2 (dr'/dt')
(dU/dr'), or

2 c (dc/dr') = - 2 (dU/dr'), or

2 c dc = - 2 dU, therefore

c^2 = K - 2 U, where K = integration constant

At U = 0, c^2 = c'^2, therefore K = c'^2, thus

c^2 = c'^2 - 2 U, or

c'^2 = c^2 + 2 U, the Aether Stress Equation.

This equation shows how a central object with rest mass, M, is able to
stress the space around it by reducing the speed of light. This stress
inflicted on the space around M is Maxwell's Aether. The Aether then allows
a photon to travel at a well defined speed. This Aether is what makes all
forces possible. It resides in the interstellar space and in the
intergalactic space. The speed of light is the property of this Aether, and
gravity is the manifestation of the Aether. The equation explaining this is

dU/dr' = - (dc^2/dr') / 2, or

gradient(U) = - gradient(c^2 / 2)

The speed of light is stamped across every laws and theories in physics, and
as explained earlier all time measurement depends on its local speed of
light. Thus, this is how gravity through the speed of light would unite
with all other forces. All forces would become weaker as the gravitational
potential increases. At some point, gravity will become stronger than
electrostatic force for example. Also under very low speed of light, matter
and anti-matter can coexist comfortably.