On Sunday, April 21, 2019 at 5:23:33 AM UTC-5, agrays...@gmail.com wrote: > > > > On Sunday, April 21, 2019 at 12:07:07 AM UTC-6, Philip Thrift wrote: >> >> >> >> On Saturday, April 20, 2019 at 4:14:27 PM UTC-5, agrays...@gmail.com >> wrote: >>> >>> >>> >>> On Friday, April 19, 2019 at 2:53:00 AM UTC-6, Bruno Marchal wrote: >>>> >>>> >>>> On 19 Apr 2019, at 04:08, agrays...@gmail.com 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 >>>> >>>> >>>> >>>> Yes. That is helpful. >>>> >>>> The following (long!) video can also help (well, it did help me) >>>> >>>> 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 * >>> >>>> >>>> >> >> >> The physicists' vocabulary can be baffling (at least it is to me). >> >> I think the basic thing though is that the Einstein Field Equations (EFE) >> is not - in a sense - absolute. EFE is relative. >> >> Once one has established a coordinate system/metric (c-sys1) for "the >> world" independently, then EFE(c-sys1) provides a recipe for making >> predictions within c-sys1. Change c-sys1 to c-sys2, and EFE(c-sys2) >> calculates predictions in c-sys2. >> >> There is no absolute c-sys for "the world". >> >> - pt >> > > I don't follow your argument. GR satisfies the Principle of General > Covariance since it's written in tensor form, and tensors transform > covariantly. Whether the video shows what is alleged as the metric tensor > is truly a representation of departure from flatness is an entirely > different matter, as I explained to Brent. AG >
I think that the first thing is that there is no such thing as an a priori "flat" geometry. We take certain phenomenon - like the path a light beam takes when there is no mass around - and then define that is what a "straight line" is. There is no a priori thing that is a "straight line". From that a "flat" coordinate system is defined. And then EFE takes it from there. It provides a recipe for how light beam paths change when matter is nearby. - pt -- 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 everything-list+unsubscr...@googlegroups.com. To post to this group, send email to everything-list@googlegroups.com. Visit this group at https://groups.google.com/group/everything-list. For more options, visit https://groups.google.com/d/optout.
