Thanks for the follow-up XinhangShen. My understanding (maybe incorrect) is that the GPS **satellites**' clocks are synchronized. I don't think they are synchronized with the ground clocks. I'll see if I can get someone better versed in this subject to weigh in.

Thanks, Dr. Joe. I think that all the clocks including the ground clocks should be synchronized so that they all have the same time that can be used to determine the position. Some people argue that the clock on a satellite and the clock on the ground are synchronized only relative to the ground reference frame and not synchronized relative to the satellite reference frame. If it was true, then the difference between the clocks observed from the satellite would monotonically grow but can't be corrected because the clocks are still synchronized observed from the ground frame, which is obviously not the case on the clocks of the GPS.

I think, Lorentz Transformation is a redefinition of space and time (called relativistic time in the following) which is no longer the clock time, but a fake time without physical meaning.

In fact, Lorentz Transformation is mathematically equivalent to the following definitions:

t' = (1/γ)T' - (γv/c^2)X'

x' = γX'

y' = Y'

z' = Z'

where γ = 1/sqrt(1 - v^2/c^2), (X', Y', Z', T') is the Galilean spacetime of the inertial reference frame moving at speed v in the X-direction relative to aether, (x', y', z', t') is the relativistic spacetime of the same inertial reference frame. When v = 0, relativistic spacetime (x, y, z, t) becomes the same as Galilean spacetime (X, Y, Z, T).

Galilean spacetime follows Galilean Transformation:

T' = T

X' = X - vT

Y' = Y

Z' = Z

We can verify that the speed of light defined by Galilean spacetime follows Newton's velocity addition law, while the speed of light defined by relativistic spacetime is constant relative to all inertial reference frames:

C = X/T

C' = X'/T' = (X - vT)/T = X/T - v = C - v

c = x/t = X/T = C

c' = x'/t'

= (γX')/[(1/γ)T' - (γv/c^2)X']

= (X'/T')/[(1/γ^2) - (v/c^2)(X'/T')]

= C'/[(1 - v^2/c^2) - (v/c^2)C']

= (C - v)/[1 - v^2/c^2 - (v/c^2)C + v^2/c^2]

= (c - v)/(1 - v/c)

= c

That means, all what Lorentz Transformation does is to redefine spacetime.

Since the clock time Tc is defined by the number N of cycles of a physical periodical process:

Tc = N/k

where k is a calibration constant and equals 9,192,631,770 for a cesium atomic clock.

The clock times Tc and Tc' of two clocks attached to the inertial reference frames defined by Galilean spacetime (X, Y, Z, T) and (X', Y', Z', T') are

Tc' = N'/k = (T'/

*Τ'* )/k = (T/

*Τ*)/k = N/k = Tc

where the Galilean periods

*Τ and **Τ'* of the two clocks are the same because Galilean time is absolute.

This equation tells us that clock time is also absolute same as Galilean time.

In special relativity, the clock times Tc and Tc' of two clocks attached to the inertial reference frames defined by relativistic spacetime (x, y, z, t) and (x', y', z', t') can be calculated by:

N' = t'/𝜏'

N = t/𝜏

t' = t/γ

𝜏' = 𝜏/γ

Tc' = N'/k = (t'/𝜏')/k = (t/𝜏)/k = N/k = Tc

where N', t' and 𝜏' are the number of cycles, elapsed relativistic time and the relativistic period of the moving clock, respectively, N, t and 𝜏 are the number of cycles, elapsed relativistic time and the relativistic period of the stationary clock respectively.

This equation tells us that clock time is Lorentz invariant and thus is still absolute and independent of the reference frame, which confirms that the property of the clock time (i.e. the absoluteness of the clock time) won't change with the change of the definition of time. Thus, the relativistic time is no longer the clock time but a meaningless mathematical variable.

Therefore, based on such a fake time, special relativity is wrong and so are all relativistic spacetime based theories including the Big Bang theory.