curvature of spacetime
in [Relativity]
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From: Bill Hobba on 10 Mar 2006 19:24 "kolt" <sabbath450(a)yahoo.com> wrote in message news:1141980808.068520.167440(a)u72g2000cwu.googlegroups.com... > Around the proton and the electron is a force. There is a field - not a force. >Can we not suppose that > there is an outward and an inward curvature to account for the positive > and negative electric forces? Curvature of what? >However, the opposing curvatures within > the atom would cancel each other out resulting in a net curvature of > zero. Such a view totally disregards the roll the electric forces may > have in the force of gravity since positive plus an equal amount of > negative is zero. There is no role - electricial forces a described by a 4 vector - gravity by a 4x4 tensor (1) >What I mean is that I think Positive plus negative > might equal gravity. It can't because of (1). Bill >
From: Tom Roberts on 11 Mar 2006 11:29 Ken S. Tucker wrote: > Tom, your post has serious issues. Please see Dover's "...Relativity" pg 156 , Eq,(66) > aka AE's GR1916 Not really. It's just that your understanding of Einstein's paper seems to have "serious issues". Here's a test of your understanding of that paper: Today we commonly write the Einstein Field Equation (using component notation and units comparable to Einstein's): G^uv = 8 pi G T^uv The name "Einstein Field Equation" comes from the fact that Einstein first derived and presented it in this paper -- in which equation of the paper is it presented? If you cannot answer this question, you don't understand that paper. Or almost certainly, GR itself. > Please see Dover's "...Relativity" pg 156 , Eq,(66) > aka AE's GR1916 Eq.(66) and see how the > energy density is defined entirely by the EM > field tensor, where the "energy density" > determines the curvature and so on to the metrics. Actually, his eq. 66 only applies to the EM field -- there can be other contributions to the energy-momentum tensor; it's just that in this section he is discussing only the contribution due to the EM field. > That in my mind, compells a metric related to > the EM field tensor Yes, of course -- that's what the Einstein Field Equation does. But of course the metric is related to other contributions to the energy-momentum tensor as well, not just the EM field contribution. > and permits the assumption > that "mass" itself is appropriately defined to have > an electromagnetic origin, Not true. Mass can be intrinsic, and in the context of Einstein's paper, and in today's general context of GR, that is non-electrodynamic. In particular, _neutral_ objects can have nonzero mass, as we observe every day (e.g. this rock, your body, etc.). > eliminating the > necessity of adding an ambiguous generic quantity > "m" by hand into the metric. But one _never_ does that. The Einstein field equation relates the metric tensor to the energy-momentum tensor. For the case of point masses the "generic quantity m" appears "by hand" in the energy-momentum tensor, not the metric. Tom Roberts tjroberts(a)lucent.com
From: Ken S. Tucker on 11 Mar 2006 13:34 Tom Roberts wrote: > Ken S. Tucker wrote: > > Tom, your post has serious issues. Please see Dover's "...Relativity" pg 156 , Eq,(66) > > aka AE's GR1916 > > Not really. It's just that your understanding of Einstein's paper seems > to have "serious issues". You can take the phrase "serious issues" in the positive tone I alleged or the negative tone you cast on my fully referenced post. > Here's a test of your understanding of that paper: Today > we commonly write the Einstein Field Equation (using > component notation and units comparable to Einstein's): > G^uv = 8 pi G T^uv > The name "Einstein Field Equation" comes from the fact > that Einstein first derived and presented it in this paper > -- in which equation of the paper is it presented? Shall we add pedantry... > If you cannot answer this question, you don't understand > that paper. Or almost certainly, GR itself. LOL, Tom, you're a piece of work... > > Please see Dover's "...Relativity" pg 156 , Eq,(66) > > aka AE's GR1916 Eq.(66) and see how the > > energy density is defined entirely by the EM > > field tensor, where the "energy density" > > determines the curvature and so on to the metrics. > > Actually, his eq. 66 only applies to the EM field -- there can be other > contributions to the energy-momentum tensor; Define one by scientific results apart from EM. > > That in my mind, compells a metric related to > > the EM field tensor > > Yes, of course -- that's what the Einstein Field Equation does. But of > course the metric is related to other contributions to the > energy-momentum tensor as well, not just the EM field contribution. Apart from the generic "m" what is your definition. > > and permits the assumption > > that "mass" itself is appropriately defined to have > > an electromagnetic origin, > Not true. Mass can be intrinsic, Ok, define intrinsic. > and in the context of Einstein's paper, > and in today's general context of GR, that is non-electrodynamic. Agreed >In > particular, _neutral_ objects can have nonzero mass, as we observe every > day (e.g. this rock, your body, etc.). True, but a neutral "H" atom is composed of electrical charges. > > eliminating the > > necessity of adding an ambiguous generic quantity > > "m" by hand into the metric. > > But one _never_ does that. The Einstein field equation relates the > metric tensor to the energy-momentum tensor. For the case of point > masses the "generic quantity m" appears "by hand" in the energy-momentum > tensor, not the metric. Careful, where GR is concerned we're talking about "generic density" T_uv. If you mean the 4 vector p^u, that is a controversial bridge, since p^u can occupy a finite volume, so how do you apply a metric defined at a point to a vector p^u that requires a finite volume. I happen to agree but you're on thin ice, that's where HUP meets GR. > Tom Roberts tjroberts(a)lucent.com Regards Ken S. Tucker
From: George Hammond on 15 Mar 2006 18:58 "Tom Roberts" <tjroberts(a)lucent.com> wrote in message news:CVCQf.51646$H71.7983(a)newssvr13.news.prodigy.com... > > Ken S. Tucker wrote: >> Tom, your post has serious issues. Please see Dover's "...Relativity" pg >> 156 , Eq,(66) >> aka AE's GR1916 > > [Roberts] > Not really. It's just that your understanding of Einstein's paper seems to > have "serious issues". > > Here's a test of your understanding of that paper: Today > we commonly write the Einstein Field Equation (using > component notation and units comparable to Einstein's): > G^uv = 8 pi G T^uv > The name "Einstein Field Equation" comes from the fact > that Einstein first derived and presented it in this paper > -- in which equation of the paper is it presented? > > If you cannot answer this question, you don't understand > that paper. Or almost certainly, GR itself. > [Hammond] I notice Tucker never gave a direct answer to your question Tom,... but I will. I say the answer to your (Tom Roberts') specific question (above) is: "Equation 53, page 149" of Einstein's famous 1916 paper (ibid: Dover's "...Relativity") ... and the reason why, is because G_uv (the Einstein tensor reduces to R_uv (the Ricci tensor) for sqrt(-g) =1 which is the case in eqn 53.....hence eqn 53 is actually the first appearance of "Einstein's EFE" in his famous 1916 paper! > >> [Tucker] >> Please see Dover's "...Relativity" pg 156 , Eq,(66) >> aka AE's GR1916 Eq.(66) and see how the >> energy density is defined entirely by the EM >> field tensor, where the "energy density" >> determines the curvature and so on to the metrics. > > [Roberts] > Actually, his eq. 66 only applies to the EM field -- there can be other > contributions to the energy-momentum tensor; it's just that in this > section he is discussing only the contribution due to the EM field. > > [Hammond] Correct, Tom. >> [Tucker] >> That in my mind, compells a metric related to >> the EM field tensor > > [Roberts] > Yes, of course -- that's what the Einstein Field Equation does. But of > course the metric is related to other contributions to the energy-momentum > tensor as well, not just the EM field contribution. > > [Hammond] Yes, of course.... the principle contribution to the source term in the EFE is not the EM part at all.... in fact it is the "rest mass" energy of the mass distribution density, rho, as any one knows. Fact is, the "rest mass energy" is generally the largest component in the source term.... dwarfing the EM component as a general rule! >> [Tucker] >> and permits the assumption >> that "mass" itself is appropriately defined to have >> an electromagnetic origin, > [Hammond] Na, na, na.... you're way out in left field Tucker. > > > [Roberts] > Not true. Mass can be intrinsic, and in the context of Einstein's paper, > and in today's general context of GR, that is non-electrodynamic. In > particular, _neutral_ objects can have nonzero mass, as we observe every > day (e.g. this rock, your body, etc.). > [Hammond] Correct. > >> eliminating the >> necessity of adding an ambiguous generic quantity >> "m" by hand into the metric. > > But one _never_ does that. The Einstein field equation relates the metric > tensor to the energy-momentum tensor. For the case of point masses the > "generic quantity m" appears "by hand" in the energy-momentum tensor, not > the metric. > [Hammond] Correct, ..... of course. > > Tom Roberts tjroberts(a)lucent.com -- ======================================== SCIENTIFIC PROOF OF GOD WEBSITE http://geocities.com/scientific_proof_of_god mirror site: http://proof-of-god.freewebsitehosting.com ========================================
From: Tom Roberts on 16 Mar 2006 11:34
George Hammond wrote: > "Tom Roberts" <tjroberts(a)lucent.com> wrote in message > news:CVCQf.51646$H71.7983(a)newssvr13.news.prodigy.com... >> Here's a test of your understanding of that paper: Today >> we commonly write the Einstein Field Equation (using >> component notation and units comparable to Einstein's): >> G^uv = 8 pi G T^uv >> The name "Einstein Field Equation" comes from the fact >> that Einstein first derived and presented it in this paper >> -- in which equation of the paper is it presented? >> >> If you cannot answer this question, you don't understand >> that paper. Or almost certainly, GR itself. >> > [Hammond] > I notice Tucker never gave a direct answer to your > question Tom,... but I will. I say the answer to your > (Tom Roberts') specific question (above) is: > "Equation 53, page 149" > of Einstein's famous 1916 paper > (ibid: Dover's "...Relativity") Yes. > ... and the reason why, is > because G_uv (the Einstein > tensor reduces to R_uv > (the Ricci tensor) for > sqrt(-g) =1 which is > the case in eqn 53..... No. There is no situation in which G_uv "reduces" to R_uv -- G_uv is defined: G_uv = R_uv - 0.5 g_uv R and your claim would imply either g_uv=0 or R=0, neither of which makes any sense at all (R=0 applies in certain manifolds with unphysical symmetries, but not in general). In fact, Einstein's Eq. 53 uses the alternate form of the Einstein field equation: R_uv = 8 pi G (T_uv - 0.5 g_uv T) Exercise for the reader: show the relationship between the LHS of Einstein's eq. 53 and R_uv. > hence > eqn 53 is actually the first > appearance of "Einstein's EFE" > in his famous 1916 paper! Yes. Tom Roberts tjroberts(a)lucent.com |