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 AG > > On 4/18/2019 7:59 AM, [email protected] <javascript:> 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. >>>>>>>>> >>>>>>>>> -- 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.
