Re: Theory of Relativity
- From: "Ken S. Tucker" <dynamics@xxxxxxxxxxxx>
- Date: 29 Apr 2005 12:42:47 -0700
To all...
On the basis on the presented OP understanding
of relativity the GP-b experiment should null,
as I'll explain below...
Ken S. Tucker wrote:
> In this post, it's my intention to show the
> extraordinary beauty and simplicity I find
> in the Theory of Relativity.
> It employs the ingenious logic developed
> by mathematicians called tensor analysis.
>
> The fundamental assumption of relativity is
> *absolute _spatial_ motion does not exist*,
> however placing that principle into a succint
> mathematical form seems to be difficult. So
> that's what I'll try to do.
>
> Beginning with the well known
>
> ds^2 = g_uv dx^u dx^v , u,v,w={0,1,2,3}.
>
> We can use association provided the covariant
> derivative,
>
> g_uv;w = 0.
>
> Then by association,
>
> ds^2 = dx_u dx^u.
>
> Expanding to time and space gives,
>
> ds^2 = dx_0 dx^0 + dx_i dx^i , i,j={1,2,3}.
>
> 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.
>
> However, relative spatial motion cannot vanish,
> it is always possible, so I'll select dx^i to
> be relative spatial motion, so that dx^i >0 generally
> and then require
>
> dx_i =0 always,
>
> to insure
>
> dx_i dx^i=0 always,
>
> and is the mathematical description of the
> Principle of Relativity. More formally it's
> expressed using the covariant 3-velocity,
>
> U_i = dx_i/ds =0.
>
> By using tensor algebra we obtain from that,
>
> g_0i = - g_ij dx^j/dx^0,
>
> and generally,
ds^2 = g_00 dx^0 dx^0 - g_ij dx^i dx^j , (always).
Below...
Here the metric under the condition U_i=0
has collapsed so that g_0i terms are excluded.
For ref to the basis of GP-b, please see Weinbergs,
"Grav & Cosmo" pg 239-241, and note the Kerr metric.
The Kerr metric depends upon the use of g_0i, that
can be excluded by the vanishing of *absolute motion*
demo'd by U_i=0.
And further note, the need for Mach's principle.
It can found in AE's book, "The Meaning of Relativity",
on pg. 100, AE writes, *a dependancy on Mach's Principle*
that I find tenuous.
Tucker predicts, on the basis of his posts, the expected
result from GP-b, will not be measured, and shows why.
The GP-b is testing Kerr's metric or Mach's Principle,
depending on interpretation, but neither works if
U_i=0 is true.
I'll get my ask kicked when I'm wrong, but that's
where I come down to a decision.
Regards
Ken S. Tucker
[...good stuff]
.
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- Theory of Relativity
- From: Ken S. Tucker
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