On Sunday, April 21, 2019 at 5:23:33 AM UTC-5, [email protected] 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, [email protected] >> 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 >>>> >>>> >>>> >>>> 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 [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.
