On Friday, April 19, 2019 at 2:53:00 AM UTC-6, Bruno Marchal wrote: > > > On 19 Apr 2019, at 04:08, [email protected] <javascript:> 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 * > > > > > AG > >> >> On 4/18/2019 7:59 AM, [email protected] wrote: >> >> >> >> On Wednesday, April 17, 2019 at 7:16:45 PM UTC-6, [email protected] >> 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, [email protected] wrote: >>>> >>>> >>>> >>>> On Wednesday, April 17, 2019 at 5:11:55 PM UTC-6, Brent wrote: >>>>> >>>>> >>>>> >>>>> On 4/17/2019 12:36 PM, [email protected] wrote: >>>>> >>>>> >>>>> >>>>> On Wednesday, April 17, 2019 at 1:02:09 PM UTC-6, Brent wrote: >>>>>> >>>>>> >>>>>> >>>>>> On 4/17/2019 7:37 AM, [email protected] wrote: >>>>>> >>>>>> >>>>>> >>>>>> On Tuesday, April 16, 2019 at 9:15:40 PM UTC-6, Brent wrote: >>>>>>> >>>>>>> >>>>>>> >>>>>>> On 4/16/2019 6:14 PM, [email protected] wrote: >>>>>>> >>>>>>> >>>>>>> >>>>>>> On Tuesday, April 16, 2019 at 6:39:11 PM UTC-6, [email protected] >>>>>>> wrote: >>>>>>>> >>>>>>>> >>>>>>>> >>>>>>>> On Tuesday, April 16, 2019 at 6:10:16 PM UTC-6, Brent wrote: >>>>>>>>> >>>>>>>>> >>>>>>>>> >>>>>>>>> On 4/16/2019 11:41 AM, [email protected] wrote: >>>>>>>>> >>>>>>>>> >>>>>>>>> >>>>>>>>> On Monday, April 15, 2019 at 9:26:59 PM UTC-6, Brent wrote: >>>>>>>>>> >>>>>>>>>> >>>>>>>>>> >>>>>>>>>> On 4/15/2019 7:14 PM, [email protected] wrote: >>>>>>>>>> >>>>>>>>>> >>>>>>>>>> >>>>>>>>>> On Friday, April 12, 2019 at 5:48:23 AM UTC-6, >>>>>>>>>> [email protected] wrote: >>>>>>>>>>> >>>>>>>>>>> >>>>>>>>>>> >>>>>>>>>>> On Thursday, April 11, 2019 at 10:56:08 PM UTC-6, Brent wrote: >>>>>>>>>>>> >>>>>>>>>>>> >>>>>>>>>>>> >>>>>>>>>>>> On 4/11/2019 9:33 PM, [email protected] wrote: >>>>>>>>>>>> >>>>>>>>>>>> >>>>>>>>>>>> >>>>>>>>>>>> On Thursday, April 11, 2019 at 7:12:17 PM UTC-6, Brent wrote: >>>>>>>>>>>>> >>>>>>>>>>>>> >>>>>>>>>>>>> >>>>>>>>>>>>> On 4/11/2019 4:53 PM, [email protected] wrote: >>>>>>>>>>>>> >>>>>>>>>>>>> >>>>>>>>>>>>> >>>>>>>>>>>>> On Thursday, April 11, 2019 at 4:37:39 PM UTC-6, Brent wrote: >>>>>>>>>>>>>> >>>>>>>>>>>>>> >>>>>>>>>>>>>> >>>>>>>>>>>>>> On 4/11/2019 1:58 PM, [email protected] 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 inconsistency of the gravitational force >>>>>>>>>> with the >>>>>>>>>> other forces. Maybe gravity is just different. AG >>>>>>>>>> >>>>>>>>>> >>>>>>>>>> That's one possibility, e.g entropic gravity. >>>>>>>>>> >>>>>>>>>> <br class="webkit > > -- You received this message because you are subscribed to the Google Groups "Everything List" group. To unsubscribe from this group and stop receiving emails from it, send an email to [email protected]. To post to this group, send email to [email protected]. Visit this group at https://groups.google.com/group/everything-list. For more options, visit https://groups.google.com/d/optout.
