Re: Question on Spacetime dilation.
- From: "Ken S. Tucker" <dynamics@xxxxxxxxxxxx>
- Date: Wed, 17 Dec 2008 04:07:01 -0800 (PST)
Hi Alen, et al.
On Dec 16, 7:23 pm, Alen <al...@xxxxxxxxxxxxxxx> wrote:
On Dec 17, 6:57 am, "Ken S. Tucker" <dynam...@xxxxxxxxxxxx> wrote:
A clock (in K) moving at 0.8c (relative to K') is
dilated 0.6 by t' = t*sqrt(1 - v^2/c^2), so that
t'=(0.6)*t.
In GR that is generalized to be,
ds^2 =g_uv dx^u dx^v , {u,v=0,1,2,3},
and then by association equatable to
= dx_u dx^u ,
= dx_0 dx^0 + dx_i dx^i , {i=1,2,3} , Eq.(1).
I expect I should then obtain,
dt' = ds = (0.6) dt, Eq.(2).
What differential coefficients should be subbed
into Eq.(1) to yield Eq.(2)?
TIA
Regards
Ken S. Tucker
c^2dt'^2 = c^2dt^2 -dx^2 -dy^2 -dz^2
= c^2dt^2 -ds^2
= c^2dt^2(1 - v^2/c^2)
so
dt' = (1/g)dt, where g = 1/sqrt(1 - v^2/c^2)
Yes that looks right to me.
I say, of course, that these are time dilation
equations only, and that the first equation has
been misinterpreted as a metric equation for
100 years now! You can write it in the form
using g_uv, and it works mathematically, with
g_uvs being 1 and -1, but all this doesn't really
mean anything of any significance physically.
Alen
"significance physically"
It seems 4D spacetime is becoming deeply
ingrained into our equations, possibly
underestimating there complexity.
Ken S. Tucker
.
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