On Apr 26, 10:18 pm, Tom Roberts wrote: > On 4/25/13 4/25/13 12:26 PM, Koobee Wublee wrote:
> > There is still no mathematical proof showing that null Ricci tensor > > with non-vanishing Riemann tensor. > > This is just plain wrong. The Schwarzschild manifold has Ricci=0 everywhere, and > Riemann!=0 everywhere. Indeed EVERY vacuum region of EVERY manifold of GR has > Ricci=0, and most of them have Riemann!=0 (only a handful are flat).
For no apparently good reasons, Levi-Civita decided to create his own curvature tensor by defining the Ricci tensor as follows.
** [R]_ij = Elements of the Ricci tensor ** [R]^n_ijk = Elements of the Riemann tensor
When ([R]_ij = 0), [R]^0_ij0, [R]^1_ij1, [R]^2_ij2, or [R]^3_ij3 may not be zero according to the simple equation above. However, Koobee Wublee is merely asking can you do better than that show mathematically that [R]^0_ij0, [R]^1_ij1, [R]^2_ij2, or [R]^3_ij3 is not necessarily zero when ([R]_ij = 0). That is all to this unimportant claim since the Riemann tensor play no role in to construction of the field equations. Does Tom know that? If so, why do the self-style physicists keep bringing out the Riemann tensor? <shrug>
> It's remarkable how much effort Koobee Wublee expends while trying to pose as > knowledgeable; he actually knows almost nothing about GR and its mathematics. > Essentially everything he says is wrong, with the exceptions being > indistinguishable from occasional lucky guesses.
The Riemann tensor was created by Ricci out of his then newly defined operator known as the covariant derivative. Only the elements [R]^0_ij0, [R]^1_ij1, [R]^2_ij2, and [R]^3_ij3 are considered in manufacturing the Ricci tensor while the other 12 elements within the sub-matrix of [R]^n_ijk are tossed away. So, what is the big deal if the Riemann tensor is not null? Tom, please answer this one, or else it would make you look stupid on raising a fuss over nothing. <shrug>
> That's why I rarely respond to his nonsense. He has repeatedly > proven he is incapable of learning....
After continuous bruising of his knowledge and ego inflicted by Koobee Wublee, if Tom wants to keep his morale up, an insignificant Doolittle Raid is not going to cut it. Tom needs to focus all his energy when dealing with Koobee Wublee. The historic record has shown that Tom has been buried by Koobee Wublee. Only in Tom?s own self-condolence, he is hallucinating that Koobee Wublee is incapable of learning anything. Sorry, Tom. The records in these newsgroups do not support your delusion. For example on the GPS calendar synchronization, has Tom finally understood that it is a myth that the GPS definitely has supported GR. <shrug>