On Tuesday, March 26, 2019 at 5:08:15 PM UTC-6, smitra wrote: > > On 26-03-2019 20:29, [email protected] <javascript:> wrote: > > On Tuesday, March 26, 2019 at 11:29:08 AM UTC-6, John Clark wrote: > > > >> On Tue, Mar 26, 2019 at 1:14 PM <[email protected]> wrote: > >> > >>> _> How do the mathematicians prove it?_ > >> > >> Mathematicians can't prove that a physical theory is correct, all > >> they can do is show that changing the coordinate system (for example > >> by rotating the X and Y axis) does not result in different physical > >> predictions. Only exparament can tell you if the predictions is > >> right, or at least mostly right. > >> > >> John K Clark > > > > I'm not asking if GR is correct; rather, whether it is covariant. > > Moreover, for SR we can prove covariance, since under the LT, the law > > of physics don't change and the SoL is c in any inertial frame. ME are > > also invariant under the LT. AG > > > > There are many ways one can do this, the most elegant way is to start > with a Lagrangian of a field theory and then demand that it be invariant > under general coordinate transforms, which requires factors of the > square root of the determinant of the metric tensor to be inserted to > compensate for the Jacobian of a coordinate transform. This seemingly > rather trivial insertion, will yield the field equations of GR as far as > the coupling with the fields desribed by the field theory are concerned. > > Compare this with the way you can derive the Maxwell equations from > scratch. You start of a scalar field theory, that is invariant under > global gauge transforms phi ---> exp(i alpha) phi. And then you make the > constant alpha an arbitrary function of space-time, which destroys the > invariance due to derivatives generating additional terms. But you can > compensate for these derivatives by including a gauge potential. This > then yields the coupling of the scalar field to a new field that we can > call the electromagnetic field, and this field will have its own gauge > invariant term proportional to the field strength tensor squared. > > So, as Paul Davies puts it, in principle mathematically gifted cave men > who had never done any experiments involving electromagnetism and > gravity could have deduced the Maxwell equations and the Einstein > equations of GR from scratch based only on mathematical elegance. > > Saibal >
*As I just told Brent, I think I should spend more time reading relevant articles, * *than asking questions. With that objective, please post some links describing * *the methods you reference above, and the article with Davies quote. TIA, 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.
