From: wsovad3322@gmail.com   
      
   On Saturday, September 2, 2023 at 1:32:10=E2=80=AFAM UTC-7, Pat Dolan wrote=   
   :   
   > Consider a distant observer traveling at .867 c ( =F0=9D=9B=BE=3D2 ) rela=   
   tive to the solar system...   
   > In his inertial frame of reference the earth's orbital velocity is only h=   
   alf the velocity   
   > necessary to keep the earth in stable orbit...   
      
   Not true, the earth follows a helical geodesic trajectory through spacetime=   
   , and=20   
   this helical geodesic is not intrinsically altered by being described in te=   
   rms of a=20   
   different system of coordinates (such as the asymptotically flat inertial c=   
   oordinates   
   in which the distant observer is at rest).  By the way, the *extrinsic* cur=   
   vature of the=20   
   earth's trajectory is the same for those two coordinate systems, which may =   
   be=20   
   surprising to you if you aren't taking the time component of the trajectory=   
    into=20   
   account.  (Misner, Thorne, Wheeler illustrates this with a bullet and baseb=   
   all.)   
      
   > Invariant spacetime curvature...   
      
   Be careful... as noted above, the *extrinsic* curvature of the trajectory i=   
   s invariant=20   
   under Lorentz transformation (which is essentially what you're applying by =   
   switching   
   to the asymptotically flat background inertial coordinates in which the dis=   
   tant high=20   
   speed object is at rest, superimposed on the mildly curved spacetime surrou=   
   nding the=20   
   sun), but the components of the *intrinsic* curvature of spacetime are not =   
   invariant   
   under coordinate transformations, they change along with the components of =   
   the=20   
   metric as expressed in terms of the different coordinate systems.  These th=   
   ings   
   are all coordinated so that the invariant intervals are, well, invariant.   
      
   > Will the earth spiral into the sun?   
      
   No, describing the phenomena in terms of a different coordinate system does=   
   n't change   
   the intrinsic phenomena.  For example, if you draw two chalk grids on a put=   
   ting green,=20   
   and describe the trajectory of a putt going into the hole in terms of one c=   
   oordinate=20   
   system, it will also go into the hole when described in terms of the other =   
   coordinate=20   
   system. Yes, the ball has different coordinates at the end, but the cup als=   
   o has different=20   
   coordinates, so the ball still goes into the cup.=20   
      
   The idea that changing the coordinate system used to describe the phenomena=   
    can=20   
   somehow change the phenomena is wrong. And no, this does not imply that loc=   
   al=20   
   Lorentz invariance has no physical dynamical effects. The dynamical equatio=   
   ns of=20   
   physics are locally Lorentz invariant, which is the physical content of spe=   
   cial relativity.   
      
   > Ridiculous!  See Einstein's First vs. Kepler's Third, ibid.   
      
   I'll assume that by "Einstein's First" you are referring to the principle o=   
   f special   
   relativity, i.e., that the equations of physics take the same simple homoge=   
   neous=20   
   and isotropic form in terms of every standard system of inertial coordinate=   
   s, and=20   
   that by "Kepler's Third" you are referring to Kepler's proposition that the=   
    squares of=20   
   the orbital periods of the planets are directly proportional to the cubes o=   
   f the=20   
   semi-major axes of their orbits. =20   
      
   There's no conflict here, and nothing that makes the above explanation=20   
   "ridiculous".  The principle of relativity is contained in local Lorentz in=   
   variance,=20   
   which is clearly satisfied in this situation.  It also happens that Kepler'=   
   s=20   
   proposition remains satisfied (to the same approximation that it ever was),=   
   =20   
   since the angular periods of the helical paths of the planets remain in the=   
   =20   
   same proportion to each other in terms of the asymptotic inertial coordinat=   
   es   
   in which your distant observer is at rest.   
      
   You may be getting confused by trying to apply the Newtonian concepts of=20   
   instantaneous gravity and Galilean invariance of physical laws, etc., (even   
   though you we not invoking Newtonian concepts), leading to the quantitative=   
   =20   
   Newtonian extrapolation of Kelper's law, relating Newtonian mass to force=   
   =20   
   and orbital periods, etc., and pointing out that if all those things were t=   
   rue, then=20   
   special relativity would be false.  That is correct, but it essentially amo=   
   unts to=20   
   saying if special relativity was false then special relativity would be fal=   
   se.  It's=20   
   a true statement, but it has no meaningful cognitive content.   
      
   --- SoupGate-Win32 v1.05   
    * Origin: you cannot sedate... all the things you hate (1:229/2)