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 > > 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 > > > >> 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 > >> >> Brent >> > -- 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.
