Groups > sci.physics.relativity > #377822

Re: Schwarzschild's paper and the uniqueness of the solution

From	Helénē Swanhild <helenes@gardenclosure.org>
Newsgroups	sci.physics.relativity
Subject	Re: Schwarzschild's paper and the uniqueness of the solution
Date	2016-03-03 21:40 +0000
Organization	Odo Wilfried Institute
Message-ID	<nbab0c$cee$1@gioia.aioe.org> (permalink)
References	(10 earlier) <a7af4ef7-30df-4e09-ab58-60843b519a10@googlegroups.com> <4409213.V5unO0Rk2x@PointedEars.de> <715d4bf4-c699-4a14-a16b-492416282f58@googlegroups.com> <7287934.XPeLYpz2IV@PointedEars.de> <tfKdndZl7qz9PkXLnZ2dnUU7_8zNnZ2d@giganews.com>

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Tom Roberts wrote:

> On 2/28/16 2/28/16   5:13 AM, Thomas 'PointedEars' Lahn wrote:
>> JanPB wrote:
>>> It is. Maybe we simply differ in our tolerance to using loose
>>> terminology.
> 
> Yes, you two do differ on that. As do I.
> 
>>> The fact is that ds^2 is a tensor, not a number.
> 
> Yes. For the simple reason that JanPB wrote the equations and described
> his notation so that ds^2 is a tensor.
> 
> But that is not the only interpretation of that notation, nor even the
> most common meaning.
> 
> In general, one writes
> 
> 	ds^2 = g_ij dx^i dx^j
> 
> This can be interpreted TWO COMPLETELY DIFFERENT WAYS:
>   A) the old/original meaning is that this is a line element,
>   representing
>      an infinitesimal distance along the line defined by {dx^i} (which
>      are elementary differentials). So each of the {dx^i} is a
>      (infinitesimal) real number, as are ds and ds^2 (= (ds)^2); the
>      {g_ij} are a set of real numbers which are the components of the
>      metric tensor (implicitly a function of position on the manifold).
>      One must of course integrate along the line to obtain the square of
>      the distance between any given pair of points on the line.
>   B) the modern interpretation as JanPB described: ds^2 is a rank-2
>   tensor,
>      d is the exterior derivative, the {x^i} are the usual coordinate
>      functions on the manifold, the tensor product on the RHS is
>      implicit, the {g_ij} are a set of real numbers which are the
>      components of the metric tensor (implicitly a function of position
>      on the manifold), and "ds^2" is purely a funny name for a tensor to
>      make it LOOK like the old meaning, with no relationship to either
>      squaring or derivative. This is a rank-2 tensor, and does not
>      represent distance at all (but it can be used to determine distance
>      along a specified line).
> 
> 	[In neither case does g_ij represent the metric tensor; it is
> 	 the COMPONENTS of the metric tensor.]

You said it was different. Where, they both have the same RHS. They are 
not so different, are they, LOL. Same RHS, remember.

Thread

Schwarzschild's paper and the uniqueness of the solution JanPB <filmart@gmail.com> - 2016-02-23 17:05 -0800
  Re: Schwarzschild's paper and the uniqueness of the solution Koobee Wublee <koobee.wublee@gmail.com> - 2016-02-23 22:28 -0800
    Re: Schwarzschild's paper and the uniqueness of the solution JanPB <filmart@gmail.com> - 2016-02-23 22:47 -0800
      Re: Schwarzschild's paper and the uniqueness of the solution Koobee Wublee <koobee.wublee@gmail.com> - 2016-02-23 23:01 -0800
        Re: Schwarzschild's paper and the uniqueness of the solution JanPB <filmart@gmail.com> - 2016-02-23 23:04 -0800
          Re: Schwarzschild's paper and the uniqueness of the solution Koobee Wublee <koobee.wublee@gmail.com> - 2016-02-23 23:27 -0800
            Re: Schwarzschild's paper and the uniqueness of the solution JanPB <filmart@gmail.com> - 2016-02-23 23:28 -0800
              Re: Schwarzschild's paper and the uniqueness of the solution Koobee Wublee <koobee.wublee@gmail.com> - 2016-02-23 23:40 -0800
                Re: Schwarzschild's paper and the uniqueness of the solution JanPB <filmart@gmail.com> - 2016-02-24 00:21 -0800
                Re: Schwarzschild's paper and the uniqueness of the solution Maciej Woźniak <mlwozniak@wp.pl> - 2016-02-24 10:39 +0100
                Re: Schwarzschild's paper and the uniqueness of the solution Koobee Wublee <koobee.wublee@gmail.com> - 2016-02-24 12:59 -0800
                Re: Schwarzschild's paper and the uniqueness of the solution David Waite <waitedavid1618@yahoo.com> - 2016-02-24 13:12 -0800
                Re: Schwarzschild's paper and the uniqueness of the solution Odd Bodkin <bodkinodd@gmail.com> - 2016-02-24 08:46 -0600
                Re: Schwarzschild's paper and the uniqueness of the solution "Paul B. Andersen" <relativity@paulba.no> - 2016-02-24 19:54 +0100
            Re: Schwarzschild's paper and the uniqueness of the solution David Waite <waitedavid1618@yahoo.com> - 2016-02-24 01:20 -0800
              Re: Schwarzschild's paper and the uniqueness of the solution David Waite <waitedavid1618@yahoo.com> - 2016-02-24 01:39 -0800
                Re: Schwarzschild's paper and the uniqueness of the solution Maciej Woźniak <mlwozniak@wp.pl> - 2016-02-24 11:12 +0100
            Re: Schwarzschild's paper and the uniqueness of the solution Odd Bodkin <bodkinodd@gmail.com> - 2016-02-24 08:37 -0600
  Re: Schwarzschild's paper and the uniqueness of the solution "Dono," <sa_ge@comcast.net> - 2016-02-24 07:16 -0800
    Re: Schwarzschild's paper and the uniqueness of the solution Koobee Wublee <koobee.wublee@gmail.com> - 2016-02-24 22:31 -0800
      Re: Schwarzschild's paper and the uniqueness of the solution "Dono," <sa_ge@comcast.net> - 2016-02-25 06:30 -0800
      Re: Schwarzschild's paper and the uniqueness of the solution JanPB <filmart@gmail.com> - 2016-02-25 09:11 -0800
        Re: Schwarzschild's paper and the uniqueness of the solution Koobee Wublee <koobee.wublee@gmail.com> - 2016-02-25 16:13 -0800
      Re: Schwarzschild's paper and the uniqueness of the solution David Waite <waitedavid1618@yahoo.com> - 2016-02-25 09:38 -0800
        Re: Schwarzschild's paper and the uniqueness of the solution PC <pc468@hotmail.com> - 2016-02-25 17:44 +0000
          Re: Schwarzschild's paper and the uniqueness of the solution David Waite <waitedavid1618@yahoo.com> - 2016-02-25 09:50 -0800
            Re: Schwarzschild's paper and the uniqueness of the solution Odd Bodkin <bodkinodd@gmail.com> - 2016-02-25 11:51 -0600
              Re: Schwarzschild's paper and the uniqueness of the solution David Waite <waitedavid1618@yahoo.com> - 2016-02-25 09:57 -0800
                Re: Schwarzschild's paper and the uniqueness of the solution Odd Bodkin <bodkinodd@gmail.com> - 2016-02-25 12:05 -0600
                Re: Schwarzschild's paper and the uniqueness of the solution David Waite <waitedavid1618@yahoo.com> - 2016-02-25 10:19 -0800
                Re: Schwarzschild's paper and the uniqueness of the solution PC <pc468@hotmail.com> - 2016-02-25 18:13 +0000
                Re: Schwarzschild's paper and the uniqueness of the solution David Waite <waitedavid1618@yahoo.com> - 2016-02-25 10:21 -0800
              Re: Schwarzschild's paper and the uniqueness of the solution PC <pc468@hotmail.com> - 2016-02-25 18:05 +0000
      Re: Schwarzschild's paper and the uniqueness of the solution David Waite <waitedavid1618@yahoo.com> - 2016-02-25 09:48 -0800
      Re: Schwarzschild's paper and the uniqueness of the solution Jackpol11@hotmail.com - 2016-02-25 14:06 -0500
        Re: Schwarzschild's paper and the uniqueness of the solution JanPB <filmart@gmail.com> - 2016-02-25 12:35 -0800
          Re: Schwarzschild's paper and the uniqueness of the solution PC <pc468@hotmail.com> - 2016-02-25 21:44 +0000
          Re: Schwarzschild's paper and the uniqueness of the solution Jackpol11@hotmail.com - 2016-02-25 17:37 -0500
            Re: Schwarzschild's paper and the uniqueness of the solution JanPB <filmart@gmail.com> - 2016-02-25 15:11 -0800
              Re: Schwarzschild's paper and the uniqueness of the solution PC <pc468@hotmail.com> - 2016-02-26 12:44 +0000
                Re: Schwarzschild's paper and the uniqueness of the solution David Waite <waitedavid1618@yahoo.com> - 2016-02-26 06:57 -0800
                Re: Schwarzschild's paper and the uniqueness of the solution PC <pc468@hotmail.com> - 2016-02-26 14:59 +0000
                Re: Schwarzschild's paper and the uniqueness of the solution Gary Harnagel <hitlong@yahoo.com> - 2016-02-26 07:36 -0800
                Re: Schwarzschild's paper and the uniqueness of the solution PC <pc468@hotmail.com> - 2016-02-26 18:45 +0000
                Re: Schwarzschild's paper and the uniqueness of the solution David Waite <waitedavid1618@yahoo.com> - 2016-02-26 07:37 -0800
                Re: Schwarzschild's paper and the uniqueness of the solution PC <pc468@hotmail.com> - 2016-02-26 19:36 +0000
                Re: Schwarzschild's paper and the uniqueness of the solution David Waite <waitedavid1618@yahoo.com> - 2016-02-26 07:50 -0800
                Re: Schwarzschild's paper and the uniqueness of the solution PC <pc468@hotmail.com> - 2016-02-26 18:47 +0000
                Re: Schwarzschild's paper and the uniqueness of the solution JanPB <filmart@gmail.com> - 2016-02-26 11:44 -0800
          Re: Schwarzschild's paper and the uniqueness of the solution Koobee Wublee <koobee.wublee@gmail.com> - 2016-02-25 15:47 -0800
            Re: Schwarzschild's paper and the uniqueness of the solution JanPB <filmart@gmail.com> - 2016-02-25 16:00 -0800
              Re: Schwarzschild's paper and the uniqueness of the solution Koobee Wublee <koobee.wublee@gmail.com> - 2016-02-25 16:09 -0800
                Re: Schwarzschild's paper and the uniqueness of the solution Odd Bodkin <bodkinodd@gmail.com> - 2016-02-25 18:29 -0600
                Re: Schwarzschild's paper and the uniqueness of the solution Koobee Wublee <koobee.wublee@gmail.com> - 2016-02-25 18:43 -0800
                Re: Schwarzschild's paper and the uniqueness of the solution Thomas 'PointedEars' Lahn <PointedEars@web.de> - 2016-02-26 23:04 +0100
                Re: Schwarzschild's paper and the uniqueness of the solution JanPB <filmart@gmail.com> - 2016-02-26 14:59 -0800
                Re: Schwarzschild's paper and the uniqueness of the solution Koobee Wublee <koobee.wublee@gmail.com> - 2016-02-26 16:19 -0800
                Re: Schwarzschild's paper and the uniqueness of the solution Thomas 'PointedEars' Lahn <PointedEars@web.de> - 2016-02-27 10:27 +0100
                Re: Schwarzschild's paper and the uniqueness of the solution JanPB <filmart@gmail.com> - 2016-02-27 17:55 -0800
                Re: Schwarzschild's paper and the uniqueness of the solution Thomas 'PointedEars' Lahn <PointedEars@web.de> - 2016-02-28 12:13 +0100
                Re: Schwarzschild's paper and the uniqueness of the solution Emigdio Sophronius <emigg@augustvisitors.org> - 2016-02-28 11:37 +0000
                Re: Schwarzschild's paper and the uniqueness of the solution Thomas 'PointedEars' Lahn <PointedEars@web.de> - 2016-02-28 12:56 +0100
                Re: Schwarzschild's paper and the uniqueness of the solution David Waite <waitedavid1618@yahoo.com> - 2016-02-28 08:03 -0800
                Re: Schwarzschild's paper and the uniqueness of the solution Thomas 'PointedEars' Lahn <PointedEars@web.de> - 2016-02-28 18:13 +0100
                Re: Schwarzschild's paper and the uniqueness of the solution Thomas 'PointedEars' Lahn <PointedEars@web.de> - 2016-02-28 18:26 +0100
                Re: Schwarzschild's paper and the uniqueness of the solution David Waite <waitedavid1618@yahoo.com> - 2016-02-28 09:36 -0800
                Re: Schwarzschild's paper and the uniqueness of the solution Thomas 'PointedEars' Lahn <PointedEars@web.de> - 2016-02-28 18:50 +0100
                Re: Schwarzschild's paper and the uniqueness of the solution David Waite <waitedavid1618@yahoo.com> - 2016-02-28 09:54 -0800
                Re: Schwarzschild's paper and the uniqueness of the solution Thomas 'PointedEars' Lahn <PointedEars@web.de> - 2016-02-28 20:40 +0100
                Re: Schwarzschild's paper and the uniqueness of the solution Emigdio Sophronius <emigg@augustvisitors.org> - 2016-02-28 19:44 +0000
                Re: Schwarzschild's paper and the uniqueness of the solution David Waite <waitedavid1618@yahoo.com> - 2016-02-28 12:20 -0800
                Re: Schwarzschild's paper and the uniqueness of the solution Emigdio Sophronius <emigg@augustvisitors.org> - 2016-02-28 20:58 +0000
                Re: Schwarzschild's paper and the uniqueness of the solution David Waite <waitedavid1618@yahoo.com> - 2016-02-28 13:02 -0800
                Re: Schwarzschild's paper and the uniqueness of the solution David Waite <waitedavid1618@yahoo.com> - 2016-02-28 12:31 -0800
                Re: Schwarzschild's paper and the uniqueness of the solution David Waite <waitedavid1618@yahoo.com> - 2016-02-29 22:40 -0800
                Re: Schwarzschild's paper and the uniqueness of the solution David Waite <waitedavid1618@yahoo.com> - 2016-02-28 10:54 -0800
                Re: Schwarzschild's paper and the uniqueness of the solution David Waite <waitedavid1618@yahoo.com> - 2016-02-28 07:30 -0800
                Re: Schwarzschild's paper and the uniqueness of the solution Thomas 'PointedEars' Lahn <PointedEars@web.de> - 2016-02-28 17:46 +0100
                Re: Schwarzschild's paper and the uniqueness of the solution David Waite <waitedavid1618@yahoo.com> - 2016-02-28 08:51 -0800
                Re: Schwarzschild's paper and the uniqueness of the solution Emigdio Sophronius <emigg@augustvisitors.org> - 2016-02-28 17:01 +0000
                Re: Schwarzschild's paper and the uniqueness of the solution David Waite <waitedavid1618@yahoo.com> - 2016-02-28 07:34 -0800
                Re: Schwarzschild's paper and the uniqueness of the solution Tom Roberts <tjroberts137@sbcglobal.net> - 2016-03-03 15:15 -0600
                Re: Schwarzschild's paper and the uniqueness of the solution David Waite <waitedavid1618@yahoo.com> - 2016-03-03 19:54 -0800
                Re: Schwarzschild's paper and the uniqueness of the solution David Waite <waitedavid1618@yahoo.com> - 2016-02-28 08:48 -0800
                Re: Schwarzschild's paper and the uniqueness of the solution David Fuller <fuller.david@hotmail.com> - 2016-02-28 09:13 -0800
                Re: Schwarzschild's paper and the uniqueness of the solution David Waite <waitedavid1618@yahoo.com> - 2016-02-28 10:09 -0800
                Re: Schwarzschild's paper and the uniqueness of the solution David Fuller <fuller.david@hotmail.com> - 2016-03-06 10:56 -0800
                Re: Schwarzschild's paper and the uniqueness of the solution Thomas 'PointedEars' Lahn <PointedEars@web.de> - 2016-02-28 18:19 +0100
                Re: Schwarzschild's paper and the uniqueness of the solution David Waite <waitedavid1618@yahoo.com> - 2016-02-28 09:24 -0800
                Re: Schwarzschild's paper and the uniqueness of the solution Thomas 'PointedEars' Lahn <PointedEars@web.de> - 2016-02-28 18:34 +0100
                Re: Schwarzschild's paper and the uniqueness of the solution David Waite <waitedavid1618@yahoo.com> - 2016-02-28 09:44 -0800
                Re: Schwarzschild's paper and the uniqueness of the solution Thomas 'PointedEars' Lahn <PointedEars@web.de> - 2016-02-28 19:12 +0100
                Re: Schwarzschild's paper and the uniqueness of the solution David Waite <waitedavid1618@yahoo.com> - 2016-02-28 10:19 -0800
                Re: Schwarzschild's paper and the uniqueness of the solution David Waite <waitedavid1618@yahoo.com> - 2016-02-28 11:17 -0800
                Re: Schwarzschild's paper and the uniqueness of the solution JanPB <filmart@gmail.com> - 2016-03-01 17:06 -0800
                Re: Schwarzschild's paper and the uniqueness of the solution Koobee Wublee <koobee.wublee@gmail.com> - 2016-03-01 17:54 -0800
                Re: Schwarzschild's paper and the uniqueness of the solution JanPB <filmart@gmail.com> - 2016-03-01 19:41 -0800
                Re: Schwarzschild's paper and the uniqueness of the solution Thomas 'PointedEars' Lahn <PointedEars@web.de> - 2016-03-04 01:17 +0100
                Re: Schwarzschild's paper and the uniqueness of the solution JanPB <filmart@gmail.com> - 2016-03-03 17:12 -0800
                Re: Schwarzschild's paper and the uniqueness of the solution Koobee Wublee <koobee.wublee@gmail.com> - 2016-03-03 17:53 -0800
                Re: Schwarzschild's paper and the uniqueness of the solution Tom Roberts <tjroberts137@sbcglobal.net> - 2016-03-03 22:19 -0600
                Re: Schwarzschild's paper and the uniqueness of the solution JanPB <filmart@gmail.com> - 2016-03-03 21:36 -0800
                Re: Schwarzschild's paper and the uniqueness of the solution Tom Roberts <tjroberts137@sbcglobal.net> - 2016-03-10 11:14 -0600
                Re: Schwarzschild's paper and the uniqueness of the solution Maciej Woźniak <mlwozniak@wp.pl> - 2016-03-10 18:32 +0100
                Re: Schwarzschild's paper and the uniqueness of the solution Luigi Durante <luigdu@jaccappo.org> - 2016-03-10 20:22 +0000
                Re: Schwarzschild's paper and the uniqueness of the solution JanPB <filmart@gmail.com> - 2016-03-10 13:02 -0800
                Re: Schwarzschild's paper and the uniqueness of the solution Luigi Durante <luigdu@jaccappo.org> - 2016-03-10 21:08 +0000
                Re: Schwarzschild's paper and the uniqueness of the solution JanPB <filmart@gmail.com> - 2016-03-10 13:19 -0800
                Re: Schwarzschild's paper and the uniqueness of the solution Luigi Durante <luigdu@jaccappo.org> - 2016-03-10 21:27 +0000
                Re: Schwarzschild's paper and the uniqueness of the solution JanPB <filmart@gmail.com> - 2016-03-10 14:04 -0800
                Re: Schwarzschild's paper and the uniqueness of the solution "Paul B. Andersen" <relativity@paulba.no> - 2016-03-11 13:33 +0100
                Re: Schwarzschild's paper and the uniqueness of the solution Maciej Woźniak <mlwozniak@wp.pl> - 2016-03-10 22:49 +0100
                Re: Schwarzschild's paper and the uniqueness of the solution JanPB <filmart@gmail.com> - 2016-03-10 14:20 -0800
                Re: Schwarzschild's paper and the uniqueness of the solution Thomas 'PointedEars' Lahn <PointedEars@web.de> - 2016-03-05 05:24 +0100
                Re: Schwarzschild's paper and the uniqueness of the solution JanPB <filmart@gmail.com> - 2016-03-04 21:36 -0800
                Re: Schwarzschild's paper and the uniqueness of the solution Koobee Wublee <koobee.wublee@gmail.com> - 2016-03-04 22:50 -0800
                Re: Schwarzschild's paper and the uniqueness of the solution Thomas 'PointedEars' Lahn <PointedEars@web.de> - 2016-03-05 11:24 +0100
                Re: Schwarzschild's paper and the uniqueness of the solution JanPB <filmart@gmail.com> - 2016-03-05 20:07 -0800
                Re: Schwarzschild's paper and the uniqueness of the solution Tom Roberts <tjroberts137@sbcglobal.net> - 2016-03-03 14:49 -0600
                Re: Schwarzschild's paper and the uniqueness of the solution Helénē Swanhild <helenes@gardenclosure.org> - 2016-03-03 21:40 +0000
                Re: Schwarzschild's paper and the uniqueness of the solution Tom Roberts <tjroberts137@sbcglobal.net> - 2016-03-03 18:58 -0600
                Re: Schwarzschild's paper and the uniqueness of the solution JanPB <filmart@gmail.com> - 2016-03-03 14:04 -0800
                Re: Schwarzschild's paper and the uniqueness of the solution Koobee Wublee <koobee.wublee@gmail.com> - 2016-03-03 17:46 -0800
                Re: Schwarzschild's paper and the uniqueness of the solution Tom Roberts <tjroberts137@sbcglobal.net> - 2016-03-03 22:21 -0600
                Re: Schwarzschild's paper and the uniqueness of the solution JanPB <filmart@gmail.com> - 2016-02-25 16:42 -0800
                Re: Schwarzschild's paper and the uniqueness of the solution "Paul B. Andersen" <relativity@paulba.no> - 2016-02-26 20:00 +0100
                Re: Schwarzschild's paper and the uniqueness of the solution PC <pc468@hotmail.com> - 2016-02-26 19:03 +0000
  Re: Schwarzschild's paper and the uniqueness of the solution John Gogo <jfgogo22@yahoo.com> - 2016-02-25 19:36 -0800
  Re: Schwarzschild's paper and the uniqueness of the solution alsor@interia.pl - 2016-02-26 09:36 -0800
    Re: Schwarzschild's paper and the uniqueness of the solution JanPB <filmart@gmail.com> - 2016-02-26 11:33 -0800
      Re: Schwarzschild's paper and the uniqueness of the solution alsor@interia.pl - 2016-02-26 12:05 -0800
        Re: Schwarzschild's paper and the uniqueness of the solution JanPB <filmart@gmail.com> - 2016-02-26 12:47 -0800
          Re: Schwarzschild's paper and the uniqueness of the solution alsor@interia.pl - 2016-02-26 14:16 -0800
            Re: Schwarzschild's paper and the uniqueness of the solution JanPB <filmart@gmail.com> - 2016-02-26 15:02 -0800

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