Not sure if that link to Pound-Rebka experiment and successors is meant to imply it confirms GR over say Yilmaz gravity. Even the last listed result, at ~ 99.99% correspondence with GR prediction, is still quite a few orders of magnitude below a distinction between the two. Only in very strong gravity regime will noticeable differences become apparent. For instance, GPS could just as well use Yilmaz theory with no discernible difference to standard GR.
Further refinements in the so-called SMBH observations via the EHT may allow a clear observational winner, but a comparison has to be explicitly looked for. Similarly for the proposed 3rd generation Einstein Telescope GW detector.
If there's no discernible difference between Yilmaz and GR, why would we prefer the former?
Because of the supposed observational evidence you claim isn't being looked for? Another "prove me wrong" argument.
Sigh. Some don't know when they're beat. Lazy rhetoric distorting/misrepresenting my clear statements wins no awards worth winning.
Showing terrerstrial level redshift experiments are too insensitive to be a decider is easy to do. Plug the relevant data into g_00 expressions and compare.
GR; g_00 = sqrt[1 - 2GM/(Rc^2)] = sqrt(1 - r/R)
Yilmaz; g_00 = exp(-2GM/(Rc^2)) = exp(-r/R)
Where r ~ 8.75mm is the so-called Schwarzschild radius of Earth, and R ~ 6370km = 6.37 x 10^9mm is Earth's actual mean radius. r/R for Earth is ~ 1.37/10^9.
Hence
g_00 (GR) -> 0.99999999931499999976538749983929
g_00 (Yilmaz) -> 0.99999999863000000093844999957144
Proving my claim earlier. Lazy shits find empty disparagement easier.
As for my earlier remarks re SMBH EHT observations, see Appendix 5 A. Central body metric here:
https://www.researchgate.net/publication...a_Redshift (freely downloadable pdf)
, where relevant parameters are compared.
Even in accessible strong gravity situations, there's not much to choose between unless precision measurements are possible AND LOOKED FOR!
You only seem to be verifying that there is no current evidence that would compel anyone to prefer Yilmaz.
And unless you are LOOKING FOR such evidence, your argument is "prove me wrong." The refrain of the wild crackpot.
Errata: In #33 wherever g_00 was used, it should of course have been sqrt(g_00). As expected the nasty minded stalker here wasn't up to noticing such a slipup.
Errata 2: Failed to apply sqrt to expression for Yilmaz g_00 in #33. When done, the corrected result is
0.99999999931500000023461249994643
Which gives the ratio of time dilation factors as
g_00(GR)/g_00(Yilmaz) = (0.99999999931499999976538749983929)/(0.99999999931500000023461249994643) = 0.99999999999999999953077499957144
A fractional difference far below any hope of detecting. At the other extreme (for GR) at 'BH' 'EH', the inverse of that ratio blows out to infinity (time 'stops' for GR, but clocks continue to tick all the way down to a notional r = 0 for Yilmaz).
There is a question? Just go back to ppt slide 8 to get a clear definition of k. It's simply a convenient calculational aid. You may find the more 'traditional' equivalent method given in Appendix A of Robertson's first linked to article on p3 #24 easier to follow. It's certainly more compact overall.
I wouldn't get hung up on the e^arctanh(x) power series expansion as anything significant. And which anyway takes different forms depending on the range of x considered - as indeed the Wolfram Alpha page sets out.
PS - yet again, a minor Erratum. In #36 g_00(GR)/g_00(Yilmaz) should have appeared as sqrt(g_00)(GR)/sqrt(g_00)(Yilmaz). The numerical values there are the correct ones.
Kornee Wrote:go back to ppt slide 8 to get a clear definition of k. It's simply a convenient calculational aid. You may find the more 'traditional' equivalent method given in Appendix A of Robertson's first linked to article on p3 #24 easier to follow. It's certainly more compact overall.
Thanks for that. Roberstson clarified a point I was missing - the elevator could accelerate fast enough for the difference in velocity to be relativistic. Bother! I don't think I can work that out on my own - I'll have to find a 'traditional' analysis to crib and compare.