Question on Spacetime dilation.
in [Relativity]
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From: Eric Gisse on 20 Dec 2008 00:48 On Dec 19, 4:21 pm, "Ken S. Tucker" <dynam...(a)vianet.on.ca> wrote: [snip] > In GR it's fairly common to approximate > g^00 = 1/g_00 , g^11 = 1/g_11 > that works 99.9% of the time in weak fields, > and is where Alen's suggested notation will > lead to. No, Ken. It is neither "fairly common" nor does it "work 99.9% of the time in weak fields". A trivial counterexample is weak field Kerr, weak field anything in rotating coordinates, etc. You are also unable to substantiate your claim that it is "fairly common", but you will be able to - as expected - insult me rather than argue against what I ever say. It is really simple, Ken: g_uv g^uv = 1 if u = v, 0 otherwise. That's the definition of the inverse metric. What you write is only ever true for diagonal metrics, which is then only ever true in specific cases which do not hold in general. Koobs here makes the same kind of idiotic mistake, and carries it into the general case without knowing why it is true in a specific case. Just like you. In fact, I'd argue both you and kooby have roughly commensurate educations in general relativity. Both of you are arrogant idiots who happen to know a few of the correct words and in some cases some of the correct equations. But neither of you can actually work the tools the both of you claim to be experts in using. > > Unlike you Tom, I'm NOT a goose-stepping idiot who > automatically assumes an unfamiliar suggestion is > verboten, on the contrary, I respected my fellow > poster's (Alen) suggestion, and after consideration, > and wide experience with variations of notation, > find it reasonable, that's my expert opinion. Why do you respect the opinions of the entirely uneducated and dismiss those of a learned professional? Why do you believe ignorance is a way of knowing things, Ken? You and your ilk seem to value lack of knowledge to the same degree that rational people value knowledge. [snip]
From: Ken S. Tucker on 20 Dec 2008 12:13 On Dec 19, 11:37 pm, Koobee Wublee <koobee.wub...(a)gmail.com> wrote: > On Dec 19, 6:08 pm, "Ken S. Tucker" wrote: > > On Dec 19, 5:55 pm, Koobee Wublee < wrote: Hi .... bye Ken
From: Alen on 20 Dec 2008 21:14 On Dec 20, 12:21 pm, "Ken S. Tucker" <dynam...(a)vianet.on.ca> wrote: [...] > > Maybe Alen is a math genious, and knows more > than Tom does, but that's easy to do anyway. > Regards > Ken S. Tucker I don't think I have to be a genius, and don't see what the fuss is about, although I know that Tom always likes to insist on 'absolute' precision in notation. Even so, suppose we represent a vector x + iy as A^i and define A^iA_i = 1, then we will have A_i = (1/|A^i|^2)(x - iy) If you multiply them you will get 1. Therefore we should be able to meaningfully say A_i = 1/A^i since we can say A_iX = X/A^i and, if X = A^i, A_iA^i = A^i/A^i = 1 There is therefore some kind of meaningful 'inverse' relationship between A^i and A_i, in this case, and to realise this is helpful to complete an understanding of the nature of their relationship Similarly, if we have x^ix_j = d^i_j, with d for delta, we will have x^ix_i = 1 and this therefore 'must' always confer 'some' kind of valid meaning on x_i = 1/x^i 'whatever' kind of an object x might refer to. 'Some' kind of inverse is always a conceptual counterpart of the simple fact that x^ix_i = 1. Is that not so?? Alen
From: Eric Gisse on 20 Dec 2008 23:13 On Dec 20, 5:14 pm, Alen <al...(a)westserv.net.au> wrote: > On Dec 20, 12:21 pm, "Ken S. Tucker" <dynam...(a)vianet.on.ca> wrote: > [...] > > > > > Maybe Alen is a math genious, and knows more > > than Tom does, but that's easy to do anyway. > > Regards > > Ken S. Tucker > > I don't think I have to be a genius, and don't see > what the fuss is about, although I know that Tom > always likes to insist on 'absolute' precision in > notation. Even so, suppose we represent a vector > x + iy as A^i and define Vectors have components, a complex number is a scalar. Notation isn't just there to frustrate idiots. [snip rest]
From: Alen on 21 Dec 2008 07:58
On Dec 21, 3:13 pm, Eric Gisse <jowr...(a)gmail.com> wrote: > On Dec 20, 5:14 pm, Alen <al...(a)westserv.net.au> wrote: > > > On Dec 20, 12:21 pm, "Ken S. Tucker" <dynam...(a)vianet.on.ca> wrote: > > [...] > > > > Maybe Alen is a math genious, and knows more > > > than Tom does, but that's easy to do anyway. > > > Regards > > > Ken S. Tucker > > > I don't think I have to be a genius, and don't see > > what the fuss is about, although I know that Tom > > always likes to insist on 'absolute' precision in > > notation. Even so, suppose we represent a vector > > x + iy as A^i and define > > Vectors have components, a complex number is a scalar. > > Notation isn't just there to frustrate idiots. > > [snip rest] Call it a complex number, then, if you want to. You have to be inflexible, don't you? You surely know that a complex number also has components, and can be represented by a vector!? Alen |