On Tuesday, April 23, 2019 at 4:00:26 AM UTC-6, Bruno Marchal wrote: > > > On 20 Apr 2019, at 23:14, agrays...@gmail.com <javascript:> wrote: > > > > On Friday, April 19, 2019 at 2:53:00 AM UTC-6, Bruno Marchal wrote: >> >> >> On 19 Apr 2019, at 04:08, agrays...@gmail.com wrote: >> >> >> >> On Thursday, April 18, 2019 at 6:53:33 PM UTC-6, Brent wrote: >>> >>> Sorry, I don't remember what, if anything, I intended to text. >>> >>> I'm not expert on how Einstein arrived at his famous field equations. I >>> know that he insisted on them being tensor equations so that they would >>> have the same form in all coordinate systems. That may sound like a >>> mathematical technicality, but it is really to ensure that the things in >>> the equation, the tensors, could have a physical interpretation. He also >>> limited himself to second order differentials, probably as a matter of >>> simplicity. And he excluded torsion, but I don't know why. And of course >>> he knew it had to reproduce Newtonian gravity in the weak/slow limit. >>> >>> Brent >>> >> >> Here's a link which might help; >> >> https://arxiv.org/pdf/1608.05752.pdf >> >> >> >> Yes. That is helpful. >> >> The following (long!) video can also help (well, it did help me) >> >> https://www.youtube.com/watch?v=foRPKAKZWx8 >> >> >> Bruno >> > > *I've been viewing this video. I don't see how he established that the > metric tensor is a correction for curved spacetime. AG * > > > ds^2 = dx^2 + dy^2 is Pythagorus theorem, in the plane. The “g_mu,nu” are > the coefficients needed to ensure un non-planner (curved) metric, and they > can be use to define the curvature. > > Bruno >
*Thanks for your time, but I don't think you have a clue what the issues are here. And, as a alleged expert in logic, it puts your other claims in jeopardy. Firstly, in the video you offered, the presenter has a Kronecker delta as the leading multiplicative factor in his definition of the Metric Tensor, which implies all off diagonal terms are zero. And even if that term were omitted, your reference to Pythagorus leaves much to be desired. In SR we're dealing with a 4 dim space with the Lorentz metric, not a Euclidean space where the Pythagorean theorem applies. How does a diagonal signature of -1,1,1,1 imply flat space? Why would non-zero off diagonal elements have anything to do with a departure from flat space under Lorentz's metric? AG * > > > > > > >> >> >> >> AG >> >>> >>> On 4/18/2019 7:59 AM, agrays...@gmail.com wrote: >>> >>> >>> >>> On Wednesday, April 17, 2019 at 7:16:45 PM UTC-6, agrays...@gmail.com >>> wrote: >>>> >>>> *I see no new text in this message. AG* >>>> >>> >>> Brent; if you have time, please reproduce the text you intended. >>> >>> I recall reading that before Einstein published his GR paper, he used a >>> trial and error method to determine the final field equations (as he raced >>> for the correct ones in competition with Hilbert, who may have arrived at >>> them first). So it's hard to imagine a mathematical methodology which >>> produces them. If you have any articles that attempt to explain how the >>> field equations are derived, I'd really like to explore this aspect of GR >>> and get some "satisfaction". I can see how he arrived at some principles, >>> such as geodesic motion, by applying the Least Action Principle, or how he >>> might have intuited that matter/energy effects the geometry of spacetime, >>> but from these principles it's baffling how he arrived at the field >>> equations. >>> >>> AG >>> >>>> >>>> >>>> On Wednesday, April 17, 2019 at 7:00:55 PM UTC-6, Brent wrote: >>>>> >>>>> >>>>> >>>>> On 4/17/2019 5:20 PM, agrays...@gmail.com wrote: >>>>> >>>>> >>>>> >>>>> On Wednesday, April 17, 2019 at 5:11:55 PM UTC-6, Brent wrote: >>>>>> >>>>>> >>>>>> >>>>>> On 4/17/2019 12:36 PM, agrays...@gmail.com wrote: >>>>>> >>>>>> >>>>>> >>>>>> On Wednesday, April 17, 2019 at 1:02:09 PM UTC-6, Brent wrote: >>>>>>> >>>>>>> >>>>>>> >>>>>>> On 4/17/2019 7:37 AM, agrays...@gmail.com wrote: >>>>>>> >>>>>>> >>>>>>> >>>>>>> On Tuesday, April 16, 2019 at 9:15:40 PM UTC-6, Brent wrote: >>>>>>>> >>>>>>>> >>>>>>>> >>>>>>>> On 4/16/2019 6:14 PM, agrays...@gmail.com wrote: >>>>>>>> >>>>>>>> >>>>>>>> >>>>>>>> On Tuesday, April 16, 2019 at 6:39:11 PM UTC-6, agrays...@gmail.com >>>>>>>> wrote: >>>>>>>>> >>>>>>>>> >>>>>>>>> >>>>>>>>> On Tuesday, April 16, 2019 at 6:10:16 PM UTC-6, Brent wrote: >>>>>>>>>> >>>>>>>>>> >>>>>>>>>> >>>>>>>>>> On 4/16/2019 11:41 AM, agrays...@gmail.com wrote: >>>>>>>>>> >>>>>>>>>> >>>>>>>>>> >>>>>>>>>> On Monday, April 15, 2019 at 9:26:59 PM UTC-6, Brent wrote: >>>>>>>>>>> >>>>>>>>>>> >>>>>>>>>>> >>>>>>>>>>> On 4/15/2019 7:14 PM, agrays...@gmail.com wrote: >>>>>>>>>>> >>>>>>>>>>> >>>>>>>>>>> >>>>>>>>>>> On Friday, April 12, 2019 at 5:48:23 AM UTC-6, >>>>>>>>>>> agrays...@gmail.com wrote: >>>>>>>>>>>> >>>>>>>>>>>> >>>>>>>>>>>> >>>>>>>>>>>> On Thursday, April 11, 2019 at 10:56:08 PM UTC-6, Brent wrote: >>>>>>>>>>>>> >>>>>>>>>>>>> >>>>>>>>>>>>> >>>>>>>>>>>>> On 4/11/2019 9:33 PM, agrays...@gmail.com wrote: >>>>>>>>>>>>> >>>>>>>>>>>>> >>>>>>>>>>>>> >>>>>>>>>>>>> On Thursday, April 11, 2019 at 7:12:17 PM UTC-6, Brent wrote: >>>>>>>>>>>>>> >>>>>>>>>>>>>> >>>>>>>>>>>>>> >>>>>>>>>>>>>> On 4/11/2019 4:53 PM, agrays...@gmail.com wrote: >>>>>>>>>>>>>> >>>>>>>>>>>>>> >>>>>>>>>>>>>> >>>>>>>>>>>>>> On Thursday, April 11, 2019 at 4:37:39 PM UTC-6, Brent wrote: >>>>>>>>>>>>>>> >>>>>>>>>>>>>>> >>>>>>>>>>>>>>> >>>>>>>>>>>>>>> On 4/11/2019 1:58 PM, agrays...@gmail.com wrote: >>>>>>>>>>>>>>> >>>>>>>>>>>>>>> >>>>>>>>>>>>>>>>> >>>>>>>>>>>>>>>> He might have been referring to a transformation to a >>>>>>>>>>>>>>>> tangent space where the metric tensor is diagonalized and its >>>>>>>>>>>>>>>> derivative at >>>>>>>>>>>>>>>> that point in spacetime is zero. Does this make any sense? >>>>>>>>>>>>>>>> >>>>>>>>>>>>>>>> >>>>>>>>>>>>>>>> Sort of. >>>>>>>>>>>>>>>> >>>>>>>>>>>>>>> >>>>>>>>>>>>>>> >>>>>>>>>>>>>>> Yeah, that's what he's doing. He's assuming a given >>>>>>>>>>>>>>> coordinate system and some arbitrary point in a non-empty >>>>>>>>>>>>>>> spacetime. So >>>>>>>>>>>>>>> spacetime has a non zero curvature and the derivative of the >>>>>>>>>>>>>>> metric tensor >>>>>>>>>>>>>>> is generally non-zero at that arbitrary point, however small we >>>>>>>>>>>>>>> assume the >>>>>>>>>>>>>>> region around that point. But applying the EEP, we can >>>>>>>>>>>>>>> transform to the >>>>>>>>>>>>>>> tangent space at that point to diagonalize the metric tensor >>>>>>>>>>>>>>> and have its >>>>>>>>>>>>>>> derivative as zero at that point. Does THIS make sense? AG >>>>>>>>>>>>>>> >>>>>>>>>>>>>>> >>>>>>>>>>>>>>> Yep. That's pretty much the defining characteristic of a >>>>>>>>>>>>>>> Riemannian space. >>>>>>>>>>>>>>> >>>>>>>>>>>>>>> Brent >>>>>>>>>>>>>>> >>>>>>>>>>>>>> >>>>>>>>>>>>>> But isn't it weird that changing labels on spacetime points >>>>>>>>>>>>>> by transforming coordinates has the result of putting the test >>>>>>>>>>>>>> particle in >>>>>>>>>>>>>> local free fall, when it wasn't prior to the transformation? AG >>>>>>>>>>>>>> >>>>>>>>>>>>>> It doesn't put it in free-fall. If the particle has EM >>>>>>>>>>>>>> forces on it, it will deviate from the geodesic in the tangent >>>>>>>>>>>>>> space >>>>>>>>>>>>>> coordinates. The transformation is just adapting the >>>>>>>>>>>>>> coordinates to the >>>>>>>>>>>>>> local free-fall which removes gravity as a force...but not other >>>>>>>>>>>>>> forces. >>>>>>>>>>>>>> >>>>>>>>>>>>>> Brent >>>>>>>>>>>>>> >>>>>>>>>>>>> >>>>>>>>>>>>> In both cases, with and without non-gravitational forces >>>>>>>>>>>>> acting on test particle, I assume the trajectory appears >>>>>>>>>>>>> identical to an >>>>>>>>>>>>> external observer, before and after coordinate transformation to >>>>>>>>>>>>> the >>>>>>>>>>>>> tangent plane at some point; all that's changed are the labels of >>>>>>>>>>>>> spacetime >>>>>>>>>>>>> points. If this is true, it's still hard to see why changing >>>>>>>>>>>>> labels can >>>>>>>>>>>>> remove the gravitational forces. And what does this buy us? AG >>>>>>>>>>>>> >>>>>>>>>>>>> >>>>>>>>>>>>> You're looking at it the wrong way around. There never were >>>>>>>>>>>>> any gravitational forces, just your choice of coordinate system >>>>>>>>>>>>> made >>>>>>>>>>>>> fictitious forces appear; just like when you use a merry-go-round >>>>>>>>>>>>> as your >>>>>>>>>>>>> reference frame you get coriolis forces. >>>>>>>>>>>>> >>>>>>>>>>>> >>>>>>>>>>>> If gravity is a fictitious force produced by the choice of >>>>>>>>>>>> coordinate system, in its absence (due to a change in coordinate >>>>>>>>>>>> system) >>>>>>>>>>>> how does GR explain motion? Test particles move on geodesics in >>>>>>>>>>>> the absence >>>>>>>>>>>> of non-gravitational forces, but why do they move at all? AG >>>>>>>>>>>> >>>>>>>>>>> >>>>>>>>>>> Maybe GR assumes motion but doesn't explain it. AG >>>>>>>>>>> >>>>>>>>>>> >>>>>>>>>>> The sciences do not try to explain, they hardly even try to >>>>>>>>>>> interpret, they mainly make models. By a model is meant a >>>>>>>>>>> mathematical >>>>>>>>>>> construct which, with the addition of certain verbal >>>>>>>>>>> interpretations, >>>>>>>>>>> describes observed phenomena. The justification of such a >>>>>>>>>>> mathematical >>>>>>>>>>> construct is solely and precisely that it is expected to work. >>>>>>>>>>> --—John von Neumann >>>>>>>>>>> >>>>>>>>>>> >>>>>>>>>>>> Another problem is the inconsistency of the fictitious >>>>>>>>>>>> gravitational force, and how the other forces function; EM, >>>>>>>>>>>> Strong, and >>>>>>>>>>>> Weak, which apparently can't be removed by changes in coordinates >>>>>>>>>>>> systems. >>>>>>>>>>>> AG >>>>>>>>>>>> >>>>>>>>>>> >>>>>>>>>>> It's said that consistency is the hobgoblin of small minds. I am >>>>>>>>>>> merely pointing out the >>>>>>>>>>> >>>>>>>>>>> -- You received this message because you are subscribed to the Google Groups "Everything List" group. 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