Question on Spacetime dilation.
in [Relativity]
|
From: Ken S. Tucker on 16 Dec 2008 17:17 Hi Harald. On Dec 16, 12:52 pm, "harry" <harald.vanlintelButNotT...(a)epfl.ch> wrote: > Just a little comment on the title! > "Spacetime" doesn't dilate (except perhaps in cosmology - but I doubt that > that is what you meant). The quantity "ds" is often called the "spacetime interval". I'm hoping to see how others (you too) would solve the problem I posted. What I want to do is draw the 4 differentials (dx^0, dx_0, dx_1, dx^1) on a 0,1 diagram with ds as well. > At increased speed, clock frequency decreases ("time dilation") and lengths > of objects (but NOT widths) shrink. And of course, all such measurements are > "relative". Can that be diagrammed? > Regards, > Harald Regards Ken
From: xxein on 16 Dec 2008 19:44 On Dec 16, 5:17 pm, "Ken S. Tucker" <dynam...(a)vianet.on.ca> wrote: > Hi Harald. > > On Dec 16, 12:52 pm, "harry" <harald.vanlintelButNotT...(a)epfl.ch> > wrote: > > > Just a little comment on the title! > > "Spacetime" doesn't dilate (except perhaps in cosmology - but I doubt that > > that is what you meant). > > The quantity "ds" is often called the "spacetime > interval". I'm hoping to see how others (you too) > would solve the problem I posted. > > What I want to do is draw the 4 differentials > (dx^0, dx_0, dx_1, dx^1) on a 0,1 diagram with > ds as well. > > > At increased speed, clock frequency decreases ("time dilation") and lengths > > of objects (but NOT widths) shrink. And of course, all such measurements are > > "relative". > > Can that be diagrammed? > > > Regards, > > Harald > > Regards > Ken xxein: Before I address you I must give kudos to Harry. Ken. Why do you screw around with math instead of physical logic? The math can't produce the physic, but understanding the physic, bit by bit, will change the math formulation so that it can fit. As Harry says, all such measurements are relative. But they are all subjectively made measurements. Wouldn't you like to have a god-like objective view to make your math upon? We don't live in Oz or Hogsworth where a clearly subjective viewpoint can survive and have only a singular physics. We live in a universe (maybe among other universes) and a cosmology gives us a pretty good idea of what an objective viewpoint would look like, but we still measure things under the local and subjective conditions of what we CAN measure. What of those we can't? Without an a priori knowledge, no math can filter down or up to bridge the gap between cosmos and quantum. That's why we make guesses and don't set up a homestead in Oz. But many apparently do. Using an Oz math, only, to hopefully find home is not realistic. Math is an infinite set. We need another form of guidance. A logic doesn't seem much better (look at these posts). But if a logic is allowed to flow without being subject to a belief plateau or a made-math to fortify it, we would fare much better. I did. Ken. Math is fun for you. Have a good time exploring it. But when you get hungry, just eat the hamburger and don't worry if it fits into your math or not. Think of other bigger things also. I try to remain your friend.
From: Alen on 16 Dec 2008 22:23 On Dec 17, 6:57 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}, > > 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) 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
From: Eric Gisse on 16 Dec 2008 22:43 On Dec 16, 6:23 pm, Alen <al...(a)westserv.net.au> wrote: > On Dec 17, 6:57 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}, > > > 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) > > 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! Except it is a metric equation, regardless of your ability to understand. >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. The metric signature does not matter, as you would be able to see through direct calculation of measurable quantities. > > Alen
From: Tom Roberts on 17 Dec 2008 00:13
harry wrote: > At increased speed, clock frequency decreases ("time dilation") and > lengths of objects (but NOT widths) shrink. That is a VERY poor statement. So poor it is tantamount to being wrong. When you say "clock frequency decreases" or "lengths of objects shrink", one naturally interprets those phrases as pertaining to the objects themselves, which is just plain wrong. It is one's MEASUREMENTS of such properties that change with relative motion, not the objects themselves. While you alluded to this in your next sentence, that is insufficient to prevent the reader from interpreting your words incorrectly. Insufficient precision is the underlying cause of much of the confusion around here. As it indicates insufficient precision in thought, it behooves you to think and write more accurately. Tom Roberts |