Once Again: Relativity for Thought Experiments

On Feb 25, 7:57 am, Daryl McCullough wrote:

There exists a coordinate system such that, as measured
using that coordinate system,

1. Light travels as constant velocity, with magnitude c, in any
direction.

This was first proposed by Voigt in 1887. shrug

2. A standard clock will show an elapsed time T that satisfies
dT/dt = square-root(1-(v/c)^2).

Let’s not confuse Doppler effect with time dilation. shrug

3. A standard measuring rod, with equilibrium length L when
at rest, will have equilibrium length L square-root(1-(v/c)^2)
when traveling at speed v in a direction parallel to its length.

4. A standard measuring rod, with equilibrium length L when
at rest, will also have equilibrium length L when traveling
at speed v in a direction perpendicular to its length.

FitzGerald-Lorentz speculation. shrug

5. An object in freefall (no external forces acting on it)
will travel with constant velocity

That is called the conservation of momentum. shrug

with magnitude less than c.

Speed limit to c is a consequence of all the infinite transforms that
satisfy the null results of the MMX but not satisfy the principle of
relativity including Larmor’s transform that gives rise to the Lorentz
transform from a mathematical mistake made by Poincare. shrug

Theorem: If (x,y,z,t) is a coordinate system satisfying 1-5,
and (x',y',z',t') is a second coordinate system related to the
first through some combination of
rotations, translations, or Lorentz transformations,
then the second coordinate system will also satisfy 1-5.

Yes, and this is exactly where the paradox manifests itself. shrug

For those who believe that relativity is paradoxical
or inconsistent, could you please show how claims 1-5
lead to a contradiction?

You are still shrouded in mysticism. Concentrate on the symmetry in
which the paradox lies within. shrug