> On 23 Apr 2019, at 13:39, [email protected] wrote: > > > > On Tuesday, April 23, 2019 at 4:00:26 AM UTC-6, Bruno Marchal wrote: > >> On 20 Apr 2019, at 23:14, [email protected] <javascript:> wrote: >> >> >> >> On Friday, April 19, 2019 at 2:53:00 AM UTC-6, Bruno Marchal wrote: >> >>> On 19 Apr 2019, at 04:08, [email protected] <> 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 <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 >> <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
Oops sorry. Since long I do relativity only in its euclidian form, through the transformation t' := it. (I being the square root of -1). This makes Minkowski euclidean again. I should have mentioned this. Bruno > > > > > >> >> >> >>> >>> 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 > > > -- > 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] > <mailto:[email protected]>. > To post to this group, send email to [email protected] > <mailto:[email protected]>. > Visit this group at https://groups.google.com/group/everything-list > <https://groups.google.com/group/everything-list>. > For more options, visit https://groups.google.com/d/optout > <https://groups.google.com/d/optout>. -- 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.
