Question on Spacetime dilation.
in [Relativity]
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From: Ken S. Tucker on 16 Dec 2008 14:57 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
From: Eric Gisse on 16 Dec 2008 15:17 On Dec 16, 10:57 am, "Ken S. Tucker" <dynam...(a)vianet.on.ca> 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}, No, Ken. It is not "generalized" to be that. > > and then by association equatable to > > = dx_u dx^u , > > = dx_0 dx^0 + dx_i dx^i , {i=1,2,3} , Eq.(1). No, Ken. That is only true for diagonal metrics. > > I expect I should then obtain, > > dt' = ds = (0.6) dt, Eq.(2). No, Ken. Distinguish between coordinate time [t] and proper time [\tau]. > > What differential coefficients should be subbed > into Eq.(1) to yield Eq.(2)? You are asking how to obtain time dilation directly from the metric. That is sad, considering how much on GR you have tried to write about. > > TIA > Regards > Ken S. Tucker
From: Ken S. Tucker on 16 Dec 2008 15:34 LOL, Gisse once again proves his stupidity! As usual PLONKed again :-). Regards Ken S. Tucker On Dec 16, 12:17 pm, Eric Gisse <jowr...(a)gmail.com> wrote: > On Dec 16, 10:57 am, "Ken S. Tucker" <dynam...(a)vianet.on.ca> 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}, SNIP
From: harry on 16 Dec 2008 15:52 Just a little comment on the title! "Spacetime" doesn't dilate (except perhaps in cosmology - but I doubt that that is what you meant). At increased speed, clock frequency decreases ("time dilation") and lengths of objects (but NOT widths) shrink. And of course, all such measurements are "relative". Regards, Harald
From: Androcles on 16 Dec 2008 16:03
"harry" <harald.vanlintelButNotThis(a)epfl.ch> wrote in message news:494814e4_3(a)news.bluewin.ch... > Just a little comment on the title! > "Spacetime" doesn't dilate (except perhaps in cosmology - but I doubt that > that is what you meant). > At increased speed, clock frequency decreases ("time dilation") and > lengths of objects (but NOT widths) shrink. And of course, all such > measurements are "relative". > Regards, > Harald Just a little comment on lying bullshit: "harald.vanlintel" Disregards, Androcles. |