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Schwarzschild's paper and the uniqueness of the solution

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  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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#377405

On Sunday, February 28, 2016 at 4:13:08 AM UTC-7, Thomas 'PointedEars' Lahn wrote:
>          (c²  0   0   0) 
>   g_µν = (0  −1   0   0) 
>          (0   0  −1   0) 
>          (0   0   0  −1) 

If you're going to be pedantic about Jan's semantics than I will be about your definitions. It is utterly ridiculous to define your terms in such a way that a tensor has different units carried by different elements. Just get a brain and define x0 by ct rather than t so that it has all elements with the same units. 

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#377821

On 2/28/16 2/28/16   9:34 AM, David Waite wrote:
> On Sunday, February 28, 2016 at 4:13:08 AM UTC-7, Thomas 'PointedEars' Lahn wrote:
>>           (c²  0   0   0)
>>    g_µν = (0  −1   0   0)
>>           (0   0  −1   0)
>>           (0   0   0  −1)
>
> If you're going to be pedantic about Jan's semantics than I will be about
> yourdefinitions. It is utterly ridiculous to define your terms in such a way
> that a tensor has different units carried by different elements.

You have made this claim several times here.

This is CLEARLY merely a point of style, and does not contain any physics or 
math. For instance, in SR and GR, many/most physicists use units in which c=1, 
so this does not violate your stylistic choice. Moreover, your dictum seems to 
rule out the use of spherical coordinates, for which different metric components 
necessarily carry different units.


Tom Roberts

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#377853

On Thursday, March 3, 2016 at 2:15:59 PM UTC-7, tjrob137 wrote:
> On 2/28/16 2/28/16   9:34 AM, David Waite wrote:
> > On Sunday, February 28, 2016 at 4:13:08 AM UTC-7, Thomas 'PointedEars' Lahn wrote:
> >>           (c²  0   0   0)
> >>    g_µν = (0  −1   0   0)
> >>           (0   0  −1   0)
> >>           (0   0   0  −1)
> >
> > If you're going to be pedantic about Jan's semantics than I will be about
> > yourdefinitions. It is utterly ridiculous to define your terms in such a way
> > that a tensor has different units carried by different elements.
> 
> You have made this claim several times here.
> 
> This is CLEARLY merely a point of style, and does not contain any physics or 
> math. For instance, in SR and GR, many/most physicists use units in which c=1, 
> so this does not violate your stylistic choice. Moreover, your dictum seems to 
> rule out the use of spherical coordinates, for which different metric components 
> necessarily carry different units.
> 
> 
> Tom Roberts

Sure quote mine my by leaving out the part where I specifically mention that. The full quote reads, If you're going to be pedantic about Jan's semantics than I will be about your definitions. It is utterly ridiculous to define your terms in such a way that a tensor has different units carried by different elements when its not necessary to do so. Just define x0 by ct rather than t so that it has all elements with the same units. Granted use of spherical coordinates for example would necessitate different units for different elements, but for the rectilinear case your posing there and therefor as a standard for simplicity you should just use x0=ct so your example should be 

          (1  0   0   0) 
   g_µν = (0  −1   0   0) 
          (0   0  −1   0) 
          (0   0   0  −1)
Quote mining is lying, and that was you just trolling.

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#377413

>On Sunday, February 28, 2016 at 4:13:08 AM UTC-7, Thomas 'PointedEars' Lahn wrote: 
>          (c²  0   0   0) 
>   g_µν = (0  −1   0   0) 
>          (0   0  −1   0) 
>          (0   0   0  −1) 

If you're going to be pedantic about Jan's semantics than I will be about your definitions. It is utterly ridiculous to define your terms in such a way that a tensor has different units carried by different elements when its not necessary to do so. Just define x0 by ct rather than t so that it has all elements with the same units. Granted use of spherical coordinates for example would necessitate different units for different elements, but for the rectilinear case your posing there and therefor as a standard for simplicity you should just use x0=ct so your example should be

          (1  0   0   0) 
   g_µν = (0  −1   0   0) 
          (0   0  −1   0) 
          (0   0   0  −1)

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#377418

10:48 AMDavid Waite
>On Sunday, February 28, 2016 at 4:13:08 AM UTC-7, Thomas 'PointedEars' Lahn wrote: 
>          (c²  0   0   0) 
>   g_µν = (0  −1   0   0) 
>          (0   0  −1   0) 
>          (0   0   0  −1) 

If you're going to be pedantic about Jan's semantics than I will be about your definitions. It is utterly ridiculous to define your terms in such a way that a tensor has different units carried by different elements when its not necessary to do so. Just define x0 by ct rather than t so that it has all elements with the same units. Granted use of spherical coordinates for example would necessitate different units for different elements, but for the rectilinear case your posing there and therefor as a standard for simplicity you should just use x0=ct so your example should be 

          (1  0   0   0) 
   g_µν = (0  −1   0   0) 
          (0   0  −1   0) 
          (0   0   0  −1)

Just admit it, we are inside a black hole
Space is (gravitational time dilation)


http://i65.tinypic.com/5ofksg.jpg



That is why your matrix is filled with zeros and (negative one)

(5.60697995045 / (4 * pi * (10^(-7)))) / (376.730313^2) = 31.4382241648	 = 10pi

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#377430

On Sunday, February 28, 2016 at 10:13:27 AM UTC-7, David Fuller wrote:
> Space is (gravitational time dilation)

You might as well say the color of the sky is flavorful, lunatic.

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#378060

On Sunday, February 28, 2016 at 12:09:31 PM UTC-6, David Waite wrote:
> On Sunday, February 28, 2016 at 10:13:27 AM UTC-7, David Fuller wrote:
> > Space is (gravitational time dilation)
> 
> You might as well say the color of the sky is flavorful, lunatic.

https://groups.google.com/forum/#!topic/sci.physics.relativity/RZ6lEr31LB0

Gravitational Time Dilation: Nonexistent Ingredient of Gravitational Waves 

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#377420

David Waite wrote:

>>On Sunday, February 28, 2016 at 4:13:08 AM UTC-7, Thomas 'PointedEars'
> has all elements with the same units.

Not a requirement for a metric (tensor).

> Granted use of spherical coordinates for example would necessitate
> different units for different elements, but for the rectilinear case
> your posing there and therefor as a standard for simplicity you should 
> just use x0=ct so your example should be
> 
>           (1  0   0   0)
>    g_µν = (0  −1   0   0)
>           (0   0  −1   0)
>           (0   0   0  −1)

That is the signature of Minkowski space(time), not its metric.  If  you 
think otherwise, please write down the equation for ds² for Minkowski space 
for me in Einstein summation convention using the metric you suggested.


PointedEars
-- 
Two neutrinos go through a bar ...

(from: WolframAlpha)

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#377421

On Sunday, February 28, 2016 at 10:19:12 AM UTC-7, Thomas 'PointedEars' Lahn wrote:
> David Waite wrote:
> > Granted use of spherical coordinates for example would necessitate
> > different units for different elements, but for the rectilinear case
> > your posing there and therefor as a standard for simplicity you should 
> > just use x0=ct so your example should be
> > 
> >           (1  0   0   0)
> >    g_µν = (0  −1   0   0)
> >           (0   0  −1   0)
> >           (0   0   0  −1)
> 
> That is the signature of Minkowski space(time), not its metric.  

No, its the full expression for the Minkowski metric tensor, crank. Since you don’t understand general relativity, you really shouldn’t be making assertions about it. In fact I am convinced by that statement and by your defining the Minkowski metric tensor with different units with for elements, that you don’t know any more about it than koobee, but since he still hasn’t responded to his challenge I’ll prove you don’t with one for you. This is the Thomas 'PointedEars' Lahn challenge just for you. 
Here is an exact solution to Einstein's field equations(one of mine): 
ds^2={dct^2/[(1-(A*|z|/c^2))^2]}-[(1-(A*|z|/c^2))^(2n)]dx^2-[(1-(A*|z|/c^2))^(2n/(n-1))]dy^2-[(1-(A*|z|/c^2))^((2*(n^2-2n+2))/(n-1))]dz^2
which is vacuum for |z| greater than 0. Find the stress-energy tensor for the sheet at z=0.

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#377423

David Waite wrote:

> On Sunday, February 28, 2016 at 10:19:12 AM UTC-7, Thomas 'PointedEars'
> Lahn wrote:
>> David Waite wrote:
>> > Granted use of spherical coordinates for example would necessitate
>> > different units for different elements, but for the rectilinear case
>> > your posing there and therefor as a standard for simplicity you should
>> > just use x0=ct so your example should be
>> > 
>> >           (1  0   0   0)
>> >    g_µν = (0  −1   0   0)
>> >           (0   0  −1   0)
>> >           (0   0   0  −1)
>> 
>> That is the signature of Minkowski space(time), not its metric.
> 
> No, its the full expression for the Minkowski metric tensor, crank.

No, I do not think so.

> Since you don’t understand general relativity, you really shouldn’t be
> making assertions about it.

I am not discussing general relativity.  What I posted is (supposed to be) 
the metric for Minkowski space(time), so I am obviously discussing special 
relativity.

I wonder who’s the crank here.

> In fact I am convinced by that statement and by your
> defining the Minkowski metric tensor with different units

AISB, it is not required for all components of a metric to have the same 
unit.

However, in natural units where c = 1, my metric is identical to your metric 
as then c² = 1.  So I am at a loss to understand the fuss you are making 
about this.


PointedEars
-- 
Q: What happens when electrons lose their energy?  
A: They get Bohr'ed.

(from: WolframAlpha)

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#377426

On Sunday, February 28, 2016 at 10:34:03 AM UTC-7, Thomas 'PointedEars' Lahn wrote:
> David Waite wrote:
> 
> > On Sunday, February 28, 2016 at 10:19:12 AM UTC-7, Thomas 'PointedEars'
> > Lahn wrote:
> >> David Waite wrote:
> >> > Granted use of spherical coordinates for example would necessitate
> >> > different units for different elements, but for the rectilinear case
> >> > your posing there and therefor as a standard for simplicity you should
> >> > just use x0=ct so your example should be
> >> > 
> >> >           (1  0   0   0)
> >> >    g_µν = (0  −1   0   0)
> >> >           (0   0  −1   0)
> >> >           (0   0   0  −1)
> >> 
> >> That is the signature of Minkowski space(time), not its metric.
> > 
> > No, its the full expression for the Minkowski metric tensor, crank.
> 
> No, I do not think so.

Yeah, but you're a crank that apparently doesn't know what a rank2 covariant metric tensor is, but calls the Minkowski metric tensor a signature. So it doesn't matter what you think. Anyway the signature is (+,-,-,-).

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#377431

David Waite wrote:

> On Sunday, February 28, 2016 at 10:34:03 AM UTC-7, Thomas 'PointedEars'
> Lahn wrote:
>> David Waite wrote:
>> > On Sunday, February 28, 2016 at 10:19:12 AM UTC-7, Thomas 'PointedEars'
>> > Lahn wrote:
>> >> David Waite wrote:
>> >> > Granted use of spherical coordinates for example would necessitate
>> >> > different units for different elements, but for the rectilinear case
>> >> > your posing there and therefor as a standard for simplicity you
>> >> > should just use x0=ct so your example should be
>> >> > 
>> >> >           (1  0   0   0)
>> >> >    g_µν = (0  −1   0   0)
>> >> >           (0   0  −1   0)
>> >> >           (0   0   0  −1)
>> >> 
>> >> That is the signature of Minkowski space(time), not its metric.
>> > 
>> > No, its the full expression for the Minkowski metric tensor, crank.
>> No, I do not think so.
> 
> Yeah, but you're a crank that apparently doesn't know what a rank2
> covariant metric tensor is,

How did you get that idea?

> but calls the Minkowski metric tensor a signature.

What you have posted is _not_ “the full expression for the Minkowski metric 
tensor”, period.

> Anyway the signature is (+,-,-,-).

Or (−,+,+,+), which is another way of saying that

  η_µν = diag(+1,−1,−1,−1)

or

  η_µν = diag(−1,+1,+1,+1).

Guess what diag(…) expands to…

<http://mathworld.wolfram.com/MetricTensor.html> (once again)


PointedEars
-- 
Q: Where are offenders sentenced for light crimes?  
A: To a prism.

(from: WolframAlpha)

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#377432

On Sunday, February 28, 2016 at 11:12:32 AM UTC-7, Thomas 'PointedEars' Lahn wrote:
> David Waite wrote:
> 
> > On Sunday, February 28, 2016 at 10:34:03 AM UTC-7, Thomas 'PointedEars'
> > Lahn wrote:
> >> David Waite wrote:
> >> > On Sunday, February 28, 2016 at 10:19:12 AM UTC-7, Thomas 'PointedEars'
> >> > Lahn wrote:
> >> >> David Waite wrote:
> >> >> > Granted use of spherical coordinates for example would necessitate
> >> >> > different units for different elements, but for the rectilinear case
> >> >> > your posing there and therefor as a standard for simplicity you
> >> >> > should just use x0=ct so your example should be
> >> >> > 
> >> >> >           (1  0   0   0)
> >> >> >    g_µν = (0  −1   0   0)
> >> >> >           (0   0  −1   0)
> >> >> >           (0   0   0  −1)
> >> >> 
> >> >> That is the signature of Minkowski space(time), not its metric.
> >> > 
> >> > No, its the full expression for the Minkowski metric tensor, crank.
> >> No, I do not think so.
> > 
> > Yeah, but you're a crank that apparently doesn't know what a rank2
> > covariant metric tensor is,
> 
> How did you get that idea?
> 
> > but calls the Minkowski metric tensor a signature.
> 
> What you have posted is _not_ “the full expression for the Minkowski metric 
> tensor”, period.

Being childish isn't a logical response Mr.Spock. Its the rank 2 covariant Minkowski metric tensor, and no matter how much you act childish and scream nah ah and stamp your feet, you're not going to change that fact. You were wrong. Get over it.

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#377436

On Sunday, February 28, 2016 at 11:12:32 AM UTC-7, Thomas 'PointedEars' Lahn wrote:
>..

Just to spell it out as pedantically as you were being to Jan, the line element ds then is given by
ds²=dct²-dx²-dy²-dz²
or
ds²=(dx⁰)²-(dx¹)²-(dx²)²-(dx³)²
and often in a synonymous way this is referred to as just the metric because all of the elements of the rank 2 covariant expression for the metric tensor can be directly read off of this expression for the line element as its elements are the coefficients of its differential squared terms.

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#377644

On Sunday, February 28, 2016 at 3:13:08 AM UTC-8, Thomas 'PointedEars' Lahn wrote:
> JanPB wrote:
> 
> > On Saturday, February 27, 2016 at 1:27:22 AM UTC-8, Thomas 'PointedEars'
> > Lahn wrote:
> >> JanPB wrote:
> >> > On Friday, February 26, 2016 at 2:05:01 PM UTC-8, Thomas 'PointedEars'
> >> > Lahn wrote:
> >> >> According even to Einstein himself, ds *is* "a scalar that represents
> >> >> the (spacetime) geometry" indeed; that is not at all "a meaningless
> >> >> string of words".
> >> > 
> >> > This is because professionals don't need to be pedantic and the
> >> > difference between ds^2 as a tensor (which is what it really is) and
> >> > its value on the relevant curve's tangent vector (which is a number),
> >> > as well as the square root of this number (the "ds") is presumed
> >> > understood and obvious and not worth elaborating. Everyone knows what's
> >> > what.
> >> 
> >> You have been at least ambiguous about the correctness of the use of
> >> “scalar”.  You have claimed that using “scalar” instead of “tensor” would
> >> not be correct, and that something “represents the [spacetime] geometry”
> >> would be nonsense, by saying to this “incorrect” and calling it “a
> >> meaningless string of words”.  Neither is true.
> > 
> > It is. Maybe we simply differ in our tolerance to using loose terminology.
> > The fact is that ds^2 is a tensor, not a number.
>                                      ^^^^^^^^^^^^
> How did you get that idea?

It's the definition. You don't believe me? OK, if it's a number, what
is ds^2 equal to for the unit sphere? (Hint: it's not 42 :-) )

> > And I don't approve of statements like "X represents the geometry" - what 
> > does it mean? If X defines the geometry, that's how it should be phrased.
> 
> But “ds” alone does _not_ define the geometry;

Since we differ what the symbol "ds" means, we won't agree here.

> the equation does that (most 
> notably the metric tensor, which was hidden behind the signs in the equation 
> given for Minkowski space(time).  We have been over this:
> 
>    ds² = c²dt² − dx² − dy² − dz²
>        = c²(dx₀)² − (dx₁)² − (dx₂)² − (dx₃)²
>        = g_µν dx^µ dx^ν
> 
> for the metric (tensor)
> 
>          (c²  0   0   0)
>   g_µν = (0  −1   0   0)
>          (0   0  −1   0)
>          (0   0   0  −1)
> 
> (which – surprise! – *is* also a matrix indeed).
> 
> “ds” is the line element of the manifold only; it defines how distances in 
> that manifold, Minkowski spacetime, are measured.  And in that sense, it 
> represents the (spacetime) geometry.  Your claim that it does not is simply, 
> provably and proven wrong.

I simply object to the term "represents" as it's a hazy term. If it defines
the geometry, I prefer "defines".

> >> It would be appropriate if you admitted your mistake instead of making
> >> further spurious claims (with weasel words) about what “everyone knows”.
> > 
> > What mistake?
> 
> ,-<news:ab39b83e-4cf4-4245-a1eb-e46f1f691c85@googlegroups.com>
> | 
> | > No, ds^2 is just a scalar that represents the geometry.
> | 
> | Incorrect (also, the phrase "scalar that represents the geometry" is
> | a meaningless string of words).
> 
> *That* mistake.

No, it's not. The phrase "ds^2 is just a scalar that represents the geometry"
is wrong: it's not a scalar, it's a rank-2 tensor. It's a scalar only in the
sense that when it's operating of a pair of vectors, it produces a number.
This number is still not a "scalar" in the usual physics sense as it
depends on a (fixed) vector field pair.

> >> If one is explaining, one inherently starts from the assumption that
> >> _not_ “everyone knows”.  Being ambiguous and imprecise is the failure
> >> of the person explaining, not of the person something is explained to.
> > 
> > It is me who is trying to be precise.
> 
> Then you are doing a pretty bad job at it.
> 
> >> “Infinitesimal *change*” (which I said) and “infinitesimal” (which I did
> >> not say) are neither “undefined notion” nor “non-standard analysis”.
> > 
> > It is an undefined object in mathematics unless you use non-standard
> > analysis or something similar.
> 
> Already shown by me to be wrong.

Not at all. You have never produced a single infinitesimal (hint: you
cannot do it unless you're operating within non-standard analysis regime).
Infinitesimals in the standard regime are metaphors, nothing else.
Pros know how to operate them but they know what they _really_ stand for.

The rest is just repetition and variation of the above.

--
Jan

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#377647

On March 1, 2016 at 5:06:33 PM, Jan the relativistic moron wrote:

> It's the definition. OK, if it's a number, what is ds^2 equal to
> for the unit sphere? (Hint: it's not 42 :-) )

ds^2 would not make any sense to anyone if not mapped/equated to a man-defined coordinate system with the metric connecting between the coordinate system and ds^2 (the invariant geometry).  <shrug>

**  ds^2 = [g]_ij d[q]^i d[q]^j

Where

**  ds = spacetime
**  [g] = matrix that represents the metric
**  [q] = matrix that represents the coordinate system
**  [g]^i, [g]^j, [q]^i, [q]^j = elements to these matrices

Thus, both the metric and the coordinate system are abstract mathematical models.  <shrug>

> The phrase "ds^2 is just a scalar that represents the geometry"
> is wrong: it's not a scalar, it's a rank-2 tensor.

Absolute nonsense.  Since the quantity ([g]_ij d[q]^i d[q]^j) is a scalar, ds^2 being equated to it must be also a fvcking scalar.

> You have never produced a single infinitesimal [rest of bullshit
> snipped]

Jan the relativistic moron is indeed a moron.  <shrug>

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#377653

On Tuesday, March 1, 2016 at 5:54:33 PM UTC-8, Koobee Wublee wrote:
> On March 1, 2016 at 5:06:33 PM, Jan the relativistic moron wrote:
> 
> > It's the definition. OK, if it's a number, what is ds^2 equal to
> > for the unit sphere? (Hint: it's not 42 :-) )
> 
> ds^2 would not make any sense to anyone if not mapped/equated to a man-defined coordinate system with the metric connecting between the coordinate system and ds^2 (the invariant geometry).  <shrug>

False.

> > The phrase "ds^2 is just a scalar that represents the geometry"
> > is wrong: it's not a scalar, it's a rank-2 tensor.
> 
> Absolute nonsense. 

False.

> Since the quantity ([g]_ij d[q]^i d[q]^j) is a scalar, ds^2 being equated to it must be also a fvcking scalar.

False.

--
Jan

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#377839

JanPB wrote:

> On Sunday, February 28, 2016 at 3:13:08 AM UTC-8, Thomas 'PointedEars'
> Lahn wrote:

Attribution _line_, not attribution novel.

>> JanPB wrote:
>> > […] Thomas 'PointedEars' Lahn wrote:
>> >> You have been at least ambiguous about the correctness of the use of
>> >> “scalar”.  You have claimed that using “scalar” instead of “tensor”
>> >> would not be correct, and that something “represents the [spacetime]
>> >> geometry” would be nonsense, by saying to this “incorrect” and calling
>> >> it “a meaningless string of words”.  Neither is true.
>> > It is. Maybe we simply differ in our tolerance to using loose
>> > terminology. The fact is that ds^2 is a tensor, not a number.
>>                                      ^^^^^^^^^^^^
>> How did you get that idea?
>
> It's the definition.

Proof by assertion.

> You don't believe me?

No, as always, I have to see evidence supporting your opinion.

> OK, if it's a number, what is ds^2 equal to for the unit sphere? (Hint:
> it's not 42 :-) )

False logic.

>> > And I don't approve of statements like "X represents the geometry" -
>> > what does it mean? If X defines the geometry, that's how it should be
>> > phrased.
>> But “ds” alone does _not_ define the geometry;
>
> Since we differ what the symbol "ds" means, we won't agree here.

Non sequitur.

>> “ds” is the line element of the manifold only; it defines how distances
>> in that manifold, Minkowski spacetime, are measured.  And in that sense,
>> it represents the (spacetime) geometry.  Your claim that it does not is
>> simply, provably and proven wrong.
>
> I simply object to the term "represents" as it's a hazy term. If it
> defines the geometry, I prefer "defines".

But *that* it “*defines* the geometry” is only your idea.  So whether your
preference in terminology is justified is an open issue at this point.

>> >> It would be appropriate if you admitted your mistake instead of making
>> >> further spurious claims (with weasel words) about what “everyone
>> >> knows”.
>> >
>> > What mistake?
>>
>> ,-<news:ab39b83e-4cf4-4245-a1eb-e46f1f691c85@googlegroups.com>
>> |
>> | > No, ds^2 is just a scalar that represents the geometry.
>> |
>> | Incorrect (also, the phrase "scalar that represents the geometry" is
>> | a meaningless string of words).
>>
>> *That* mistake.
>
> No, it's not. The phrase "ds^2 is just a scalar that represents the
> geometry" is wrong: it's not a scalar, it's a rank-2 tensor.

As for that, I refer you to Tom Robert’s excellent explanation in the upper
part¹ of <news:tfKdndZl7qz9PkXLnZ2dnUU7_8zNnZ2d@giganews.com> , and rest my
case. (We are both correct in our respective interpretations.)

________
¹  I do not agree with the lower part: contrary to what he claims, “ds” is
   definitely _not_ the metric (tensor) according to Wolfram MathWorld and
   other sources:

   | Roughly speaking, the metric tensor g_{ij} is a function which tells
   | how to compute the distance between any two points in a given space.
   | Its components can be viewed as multiplication factors which must be
   | placed in front of the differential displacements dx_i in a
   | generalized Pythagorean theorem:
   |
   |   ds² = g_{11} dx_1^2 + g_{12} dx_1 dx_2 + g_{22} dx_2^2 + ….

   ds cannot be the metric tensor if the (the components of the) metric
   tensor is/are (the) g_{ij}.

   <http://mathworld.wolfram.com/MetricTensor.html>

> It's a scalar only in the sense that when it's operating of a pair of
                                                 ^^^^^^^^^^^^^^^^^^^^^^
> vectors, it […]
  ^^^^^^^

What does that mean?

>> >> “Infinitesimal *change*” (which I said) and “infinitesimal” (which I
>> >> did not say) are neither “undefined notion” nor “non-standard
>> >> analysis”.
>> > It is an undefined object in mathematics unless you use non-standard
>> > analysis or something similar.
>> Already shown by me to be wrong.
>
> Not at all. You have never produced a single infinitesimal

I do not have to.  I had not used the word “infinitesimal” as a *noun* to
refer to “ds”, “dt” aso. in the first place.  In addition, I have showed
that “infinitesimal” both as an *adjective* (which is how I used it, citing
textbooks) and as a noun has a well-defined mathematical meaning,
respectively.  Contrary to your claims.

> (hint: you cannot do it unless you're operating within non-standard
> analysis regime).

Non sequitur.

> Infinitesimals in the standard regime are metaphors, nothing else.

You are still missing the point.

> Pros know how to operate them but they know what they _really_ stand for.

Pros know how to read.  You evidentially do not.

> The rest is just repetition and variation of the above.

Precisely.  You have not presented any new, let alone convincing argument
that your opinion on this has any basis in fact.  You have not managed to
produce a single reference that supports your opinion.  I have produced
several, repeatedly now, and you have managed to ignore all of it and of
them.


PointedEars
-- 
I heard that entropy isn't what it used to be.

(from: WolframAlpha)

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#377846

On Thursday, March 3, 2016 at 4:17:02 PM UTC-8, Thomas 'PointedEars' Lahn wrote:
> JanPB wrote:
> 
> > On Sunday, February 28, 2016 at 3:13:08 AM UTC-8, Thomas 'PointedEars'
> > Lahn wrote:
> 
> Attribution _line_, not attribution novel.
> 
> >> JanPB wrote:
> >> > [...] Thomas 'PointedEars' Lahn wrote:
> >> >> You have been at least ambiguous about the correctness of the use of
> >> >> "scalar".  You have claimed that using "scalar" instead of "tensor"
> >> >> would not be correct, and that something "represents the [spacetime]
> >> >> geometry" would be nonsense, by saying to this "incorrect" and calling
> >> >> it "a meaningless string of words".  Neither is true.
> >> > It is. Maybe we simply differ in our tolerance to using loose
> >> > terminology. The fact is that ds^2 is a tensor, not a number.
> >>                                      ^^^^^^^^^^^^
> >> How did you get that idea?
> >
> > It's the definition.
> 
> Proof by assertion.

Sorry, this just is the definition of ds^2. I cannot change it.

> > You don't believe me?
> 
> No, as always, I have to see evidence supporting your opinion.

Pick any book on differential geometry (not an undergraduate hand-waving
text though), e.g.:

Barrett O'Neill: "Semi-Riemannian Geometry",
Michael Spivak: "Comprehensive Introduction to Differential Geometry",
Robert Wald: "General Relativity",
Abraham & Marsden: "Foundations of Mechanics",
etc. etc.

> > OK, if it's a number, what is ds^2 equal to for the unit sphere? (Hint:
> > it's not 42 :-) )
> 
> False logic.

You said it was a scalar. So it must be a well-defined number at each point
of the sphere. What number is it? What's the formula? Be precise.

> >> > And I don't approve of statements like "X represents the geometry" -
> >> > what does it mean? If X defines the geometry, that's how it should be
> >> > phrased.
> >> But "ds" alone does _not_ define the geometry;
> >
> > Since we differ what the symbol "ds" means, we won't agree here.
> 
> Non sequitur.

So now we DO agree what the symbol "ds" means? I'll take your non-sequitur
and raise it to falsehood then :-) Make up your mind!

> >> "ds" is the line element of the manifold only; it defines how distances
> >> in that manifold, Minkowski spacetime, are measured.  And in that sense,
> >> it represents the (spacetime) geometry.  Your claim that it does not is
> >> simply, provably and proven wrong.
> >
> > I simply object to the term "represents" as it's a hazy term. If it
> > defines the geometry, I prefer "defines".
> 
> But *that* it "*defines* the geometry" is only your idea.  So whether your
> preference in terminology is justified is an open issue at this point.

It's not open to debate. Geometry in this context(*) is defined as an 
equivalence class of isometric tensors of certain type (covariant rank-2 
symmetric).

(*)i.e. in the context of _differential geometry_. There exist different
concepts of "geometry", some of them not related to calculus on manifolds
at all. They are not relevant to GR.

> >> >> It would be appropriate if you admitted your mistake instead of making
> >> >> further spurious claims (with weasel words) about what "everyone
> >> >> knows".
> >> >
> >> > What mistake?
> >>
> >> ,-<news:ab39b83e-4cf4-4245-a1eb-e46f1f691c85@googlegroups.com>
> >> |
> >> | > No, ds^2 is just a scalar that represents the geometry.
> >> |
> >> | Incorrect (also, the phrase "scalar that represents the geometry" is
> >> | a meaningless string of words).
> >>
> >> *That* mistake.
> >
> > No, it's not. The phrase "ds^2 is just a scalar that represents the
> > geometry" is wrong: it's not a scalar, it's a rank-2 tensor.
> 
> As for that, I refer you to Tom Robert's excellent explanation in the upper
> part¹ of <news:tfKdndZl7qz9PkXLnZ2dnUU7_8zNnZ2d@giganews.com> , and rest my
> case. (We are both correct in our respective interpretations.)

I disagree because you still haven't shown me any viable alternative except
metaphors like "infinitesimal distance" and the like.

Trust me, I really know this stuff cold, I also know this "metaphoric"
language very well. But these metaphors are not the real deal, they are
shortcuts, they are useful for communicating ideas and intuition, but they
don't refer to actual, legal, mathematical objects (unless you do Robinson's
non-standard analysis). I only object to that aspect of them.

> ¹  I do not agree with the lower part: contrary to what he claims, "ds" is
>    definitely _not_ the metric (tensor) according to Wolfram MathWorld and
>    other sources:
> 
>    | Roughly speaking, the metric tensor g_{ij} is a function which tells
>    | how to compute the distance between any two points in a given space.
>    | Its components can be viewed as multiplication factors which must be
>    | placed in front of the differential displacements dx_i in a
>    | generalized Pythagorean theorem:
>    |
>    |   ds² = g_{11} dx_1^2 + g_{12} dx_1 dx_2 + g_{22} dx_2^2 + ....
> 
>    ds cannot be the metric tensor if the (the components of the) metric
>    tensor is/are (the) g_{ij}.
> 
>    <http://mathworld.wolfram.com/MetricTensor.html>
> 
> > It's a scalar only in the sense that when it's operating of a pair of
>                                                  ^^^^^^^^^^^^^^^^^^^^^^
> > vectors, it [...]
>   ^^^^^^^
> 
> What does that mean?

Good grief. OK, I'll stop here.

--
Jan

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#377850

On March 3, 2016, Jan the relativistic moron wrote:
> > Tom Roberts wrote:

> Sorry, this just is the definition of ds^2. I cannot change it.

ds^2 can never be defined but can only be mapped/observed into an abstract number by an observer using the coordinate system and the metric which are both abstract parameters.  <shrug>

> You said it was a scalar. So it must be a well-defined number at
> each point of the sphere. What number is it? What's the formula?
> Be precise.

Idiot!  How many times has Jan the relativistic moron seen the following equation?  <shrug>

> > ds^2 = g_ij dx^i dx^j

Notice the RHS is a scalar.  So, this scalar is whatever it turns out to be.  Please demonstrate something more intelligent so that Koobee Wublee does not have to call Jan the relativistic moron a relativistic moron.  <shrug>

> [rest of garbage snipped]

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