Re: Theory of Relativity


"Ken S. Tucker" <dynamics@xxxxxxxxxxxx> wrote in message
news:1114717067.202370.203430@xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
>
> The fundamental assumption of relativity is
> *absolute _spatial_ motion does not exist*,

I think this issue is blown way over board. Who cares if the absolute rest
frame exists or not. The laws of physics should apply to all inertial
frames which every frame should be inertial.

> The absolute spatial motion I'll define by
>
> dx_i dx^i = Absolute spatial motion.
>
> Absolute spatial motion cannot exist, IOW's
> it vanishes, hence,
>
> dx_i dx^i =0.

If (i) also includes the time dimension, your equation only applies to
photons. If (i) does not include time, then it is very ludicrous to say any
volume of space is zero.

> [...]
>
> U_i = dx_i/ds =0.

(dx_i/ds) is a by-product of applying the principle of least action. It
works for non-photons becuase

ds = time +/- space

In reality, space has nothing to do if the action of an event is minimized
or not. It is the passage of time only that represents the minimal action
of an event.

How do you deal with photons with the equation above where a photon has (ds
= 0). Are you going to be as creative as Ciufolini on his derivation of a
gravitationally deflected photon?

> ds^2 = g_00 dx^0 dx^0 - g_ij dx^i dx^j
>
> == dt^2 - dx^2 - dy^2 - dz^2.
>
> The succinct U_i=0 provides Minkowski spacetime,
> which embodies the Lorentz transformation, but
> done Generally Covariantly.

You have pointed out Noether's Theorem which indicates there are 4 conserved
quantities in Minkowski spacetime. They are

** Energy
** speed along x-axis
** speed along y-axis
** speed along z-axis

Which are all observed parameters.

> Moving to General Relativity, the following absolute
> derivative vanishes (because U_i=0),
>
> DU_i = U_i;w dx^w =0 .
>
> Using association,
>
> U_i = g_iu U^u =0
>
> therefore,
>
> DU_i = g_iu DU^u =0
>
> and thus,
>
> DU^u =0, aka the geodesic equation.

Geodesic equations are the representatives of the principle of least action
where not all equations vanish. In polar coordinate, at best two equations
vanish. For example, using the Schwarzschild metric, the vanished equations
give us the following conserved events:

** energy
** angular momentum

Which are all observed parameters.


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