*I see no new text in this message. AG* On Wednesday, April 17, 2019 at 7:00:55 PM UTC-6, Brent wrote: > > > > On 4/17/2019 5:20 PM, [email protected] <javascript:> 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. >>>>>>> >>>>>>> >>>>>>>> >>>>>>>> >>>>>>>>> What is gets you is it enforces and explains the equivalence >>>>>>>>> principle. And of course Einstein's theory also correctly predicted >>>>>>>>> the >>>>>>>>> bending of light, gravitational waves, time dilation and the >>>>>>>>> precession of >>>>>>>>> the perhelion of Mercury. >>>>>>>>> >>>>>>>> >>>>>>>> I was referring earlier just to the transformation to the tangent >>>>>>>> space; what specifically does it buy us; why would we want to execute >>>>>>>> this >>>>>>>> particular transformation? AG >>>>>>>> >>>>>>> >>>>>>> For one thing, you know the acceleration due to non-gravitational >>>>>>> forces in this frame. >>>>>>> >>>>>> >>>>>> *IIUC, the tangent space is a vector space which has elements with >>>>>> constant t. So its elements are linear combinations of t, x, y, and z. >>>>>> How >>>>>> do you get accelerations from such sums (even if t is not constant)? AG* >>>>>> >>>>>> So you can transform to it, put in the accelerations, and transform >>>>>>> back. >>>>>>> >>>>>> >>>>>> *I see no way to put the accelerations into the tangent space at any >>>>>> point in spacetime. AG* >>>>>> >>>>>> >>>>>> The tangent space is just a patch of Minkowski space. d/t(dx/dt) = >>>>>> acceleration. >>>>>> >>>>>> Brent >>>>>> >>>>> >>>>>
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