On Wednesday, April 17, 2019 at 1:02:09 PM UTC-6, Brent wrote: > > > > On 4/17/2019 7:37 AM, [email protected] <javascript:> 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 >>>> >>> >>> *Sorry; I was thinking about QM, where the state of the system is a >>> linear combination of component states of the vector space representing it. >>> In GR, since there is an infinite uncountable set of tangent spaces, how >>> can we be sure that our test particle is in one of those subspaces, called >>> tangent states? That would be the case, I surmise, if the tangent spaces >>> spanned the manifold. I think they do so since there's a tangent space at >>> every point in the manifold. AG * >>> >> >> *The presumed test particle has a history, and each tangent space is a >> proper subset of the manifold. So is there a guarantee that an arbitrary >> test particle will have a history contained in a particular tangent space? >> AG* >> >> >> No. It's guaranteed that at every point on the particles world line >> there is a tangent space. >> >> Brent >> > > *On a different issue, if you agree with Stenger that time is what is read > on a clock, how do you justify labeling all spacetime points with a t > component, which is called "time", and overwhelmingly will never be read on > any clock? AG* > > > Justify? Just like everything in a scientific theory is justified...as > von Neumann says, because it works. The "t" and for that matter the "x y > and z" never show up in any measurement, they are just labels for points > that are smooth and continuous. > > Brent >
*I don't object to the label, t, but once you call it "time" you run into the inconsistency that time in relativity is what observers read (on a clock). So, from my POV, it's better to regard it as a placeholder for a test particle that has that event in its history. AG * -- 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.
