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Re: Inescapable (symmetric) twins paradox

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JanPB wrote on 10.08.2015 02:59:

> On Sunday, August 9, 2015 at 1:28:36 PM UTC-7, Thomas 'PointedEars' Lahn wrote:
>> wobbly wrote:
>>> JanPB wrote:
>>>> On Saturday, August 1, 2015 at 11:48:00 AM UTC-7, wobbly wrote:
>>>>> JanPB wrote:
>>>>>> This is very basic, it simply follows from the general formula for
>>>>>> arc length which is sqrt(g_ij qdot^i qdot^j) dt when the coordinates
>>>>>> ARE standard inertial, i.e. g = -c^2 dt^2 + dx^2 + dy^2 + dz^2
>>>>>
>>>>> Is this the same as
>>>>>
>>>>>     g = [-(cdt)², (dx)², (dy)², (dz)²]
>>>>
>>>> I don't know what you wrote on the right-hand side. It's not correct
>>>> mathematics, so if it's some private notation that you use, explain it
>>>> first.
>>>
>>> Are you serious, not familiar with vector notation of the same?
>>> https://en.wikipedia.org/wiki/Vector_notation
>>
>> In your own reference, the notation that uses commas (ordered set notation) 
>> uses (round) parentheses or *angular* brackets (like the bra-ket notation in 
>> QM), and the notation that does not (matrix notation) uses rectangular or 
>> round brackets.
>>
>> Your notation uses rectangular brackets *and* commas.
> 
> It's not only that, he writes a 4-tuple of symmetric tensor squares of covectors
> and equates it to g. This simply has no meaning unless he defines what this
> notation is supposed to mean exactly.

I do not think that

  [-(cdt)², (dx)², (dy)², (dz)²]

is “a 4-tuple of symmetric tensor squares of covectors”.  I do not think 
your composition of mathematical terms even has a sensible mathematical 
meaning.

See also:

<http://mathworld.wolfram.com/Tensor.html>
<http://mathworld.wolfram.com/SymmetricTensor.html>
<https://en.wikipedia.org/wiki/Tensor_product#Tensor_powers_and_braiding>
<http://www.wolframalpha.com/input/?i=covector>
<http://mathworld.wolfram.com/n-Tuple.html>


PointedEars
-- 
“Science is empirical: knowing the answer means nothing;
 testing your knowledge means everything.”
   —Dr. Lawrence M. Krauss, theoretical physicist,
    in “A Universe from Nothing” (2009)

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Re: Inescapable (symmetric) twins paradox Thomas 'PointedEars' Lahn <PointedEars@web.de> - 2015-08-09 22:24 +0200
  Re: Inescapable (symmetric) twins paradox JanPB <filmart@gmail.com> - 2015-08-09 17:59 -0700
    Re: Inescapable (symmetric) twins paradox Felipe Delgado <fd@spreadspectrum.org> - 2015-08-10 18:24 +0000
      Re: Inescapable (symmetric) twins paradox JanPB <filmart@gmail.com> - 2015-08-10 11:33 -0700
        Re: Inescapable (symmetric) twins paradox Thomas 'PointedEars' Lahn <PointedEars@web.de> - 2015-08-19 22:16 +0200
          Re: Inescapable (symmetric) twins paradox Tom Roberts <tjroberts137@sbcglobal.net> - 2015-08-19 18:43 -0500
            Re: Inescapable (symmetric) twins paradox Odd Bodkin <bodkinodd@gmail.com> - 2015-08-24 09:52 -0500
            Re: Inescapable (symmetric) twins paradox Koobee Wublee <koobee.wublee@gmail.com> - 2015-08-25 00:01 -0700
              Re: Inescapable (symmetric) twins paradox JanPB <filmart@gmail.com> - 2015-08-25 00:05 -0700
                Re: Inescapable (symmetric) twins paradox Koobee Wublee <koobee.wublee@gmail.com> - 2015-08-25 00:29 -0700
                Re: Inescapable (symmetric) twins paradox JanPB <filmart@gmail.com> - 2015-08-25 11:16 -0700
                Re: Inescapable (symmetric) twins paradox Koobee Wublee <koobee.wublee@gmail.com> - 2015-08-25 22:36 -0700
                Re: Inescapable (symmetric) twins paradox JanPB <filmart@gmail.com> - 2015-08-25 23:06 -0700
                Re: Inescapable (symmetric) twins paradox Koobee Wublee <koobee.wublee@gmail.com> - 2015-08-26 00:19 -0700
                Re: Inescapable (symmetric) twins paradox JanPB <filmart@gmail.com> - 2015-08-26 10:54 -0700
                Re: Inescapable (symmetric) twins paradox Maciej Woźniak <mlwozniak@wp.pl> - 2015-08-26 20:32 +0200
                Re: Inescapable (symmetric) twins paradox JanPB <filmart@gmail.com> - 2015-08-26 15:58 -0700
              Re: Inescapable (symmetric) twins paradox Tom Roberts <tjroberts137@sbcglobal.net> - 2015-08-27 11:44 -0500
                Re: Inescapable (symmetric) twins paradox alsor@interia.pl - 2015-08-27 15:24 -0700
                Re: Inescapable (symmetric) twins paradox Tom Roberts <tjroberts137@sbcglobal.net> - 2015-08-27 22:15 -0500
                Re: Inescapable (symmetric) twins paradox Koobee Wublee <koobee.wublee@gmail.com> - 2015-08-27 23:49 -0700
                Re: Inescapable (symmetric) twins paradox Odd Bodkin <bodkinodd@gmail.com> - 2015-08-28 07:19 -0500
                Re: Inescapable (symmetric) twins paradox Tom Roberts <tjroberts137@sbcglobal.net> - 2015-08-28 09:55 -0500
                Re: Inescapable (symmetric) twins paradox Koobee Wublee <koobee.wublee@gmail.com> - 2015-08-28 16:52 -0700
                Re: Inescapable (symmetric) twins paradox kefischer <emoneyjoe@iglou.com> - 2015-08-28 20:49 -0400
                Re: Inescapable (symmetric) twins paradox JanPB <filmart@gmail.com> - 2015-08-28 21:45 -0700
                Re: Inescapable (symmetric) twins paradox alsor@interia.pl - 2015-09-07 11:13 -0700
                Re: Inescapable (symmetric) twins paradox JanPB <filmart@gmail.com> - 2015-09-07 12:21 -0700
                Re: Inescapable (symmetric) twins paradox "Lleyton H. Bellucci" <lleyb@stratospheree.org> - 2015-09-07 19:36 +0000
                Re: Inescapable (symmetric) twins paradox alsor@interia.pl - 2015-09-07 12:38 -0700
                Re: Inescapable (symmetric) twins paradox JanPB <filmart@gmail.com> - 2015-09-07 15:49 -0700
                Re: Inescapable (symmetric) twins paradox Koobee Wublee <koobee.wublee@gmail.com> - 2015-09-07 20:45 -0700
                Re: Inescapable (symmetric) twins paradox JanPB <filmart@gmail.com> - 2015-09-08 02:15 -0700
                Re: Inescapable (symmetric) twins paradox Koobee Wublee <koobee.wublee@gmail.com> - 2015-09-08 10:10 -0700
                Re: Inescapable (symmetric) twins paradox JanPB <filmart@gmail.com> - 2015-09-08 11:35 -0700
                Re: Inescapable (symmetric) twins paradox Koobee Wublee <koobee.wublee@gmail.com> - 2015-09-08 12:46 -0700
                Re: Inescapable (symmetric) twins paradox JanPB <filmart@gmail.com> - 2015-09-08 13:15 -0700
                Re: Inescapable (symmetric) twins paradox Maciej Woźniak <mlwozniak@wp.pl> - 2015-09-08 22:47 +0200
                Re: Inescapable (symmetric) twins paradox JanPB <filmart@gmail.com> - 2015-09-08 15:09 -0700
                Re: Inescapable (symmetric) twins paradox JanPB <filmart@gmail.com> - 2015-09-08 15:11 -0700
                Re: Inescapable (symmetric) twins paradox alsor@interia.pl - 2015-09-08 10:17 -0700
                Re: Inescapable (symmetric) twins paradox JanPB <filmart@gmail.com> - 2015-09-08 11:25 -0700
                Re: Inescapable (symmetric) twins paradox alsor@interia.pl - 2015-09-08 13:18 -0700
                Re: Inescapable (symmetric) twins paradox JanPB <filmart@gmail.com> - 2015-09-08 13:30 -0700
                Re: Inescapable (symmetric) twins paradox alsor@interia.pl - 2015-09-08 15:34 -0700
                Re: Inescapable (symmetric) twins paradox JanPB <filmart@gmail.com> - 2015-09-08 18:22 -0700
                Re: Inescapable (symmetric) twins paradox alsor@interia.pl - 2015-09-09 10:25 -0700
                Re: Inescapable (symmetric) twins paradox paparios <paparios@gmail.com> - 2015-09-09 10:54 -0700
                Re: Inescapable (symmetric) twins paradox alsor@interia.pl - 2015-09-09 12:40 -0700
          Re: Inescapable (symmetric) twins paradox JanPB <filmart@gmail.com> - 2015-08-20 22:24 -0700
            Re: Inescapable (symmetric) twins paradox kefischer <emoneyjoe@iglou.com> - 2015-08-21 02:44 -0400
            Re: Inescapable (symmetric) twins paradox Koobee Wublee <koobee.wublee@gmail.com> - 2015-08-20 23:58 -0700
            Re: Inescapable (symmetric) twins paradox alsor@interia.pl - 2015-08-21 08:14 -0700
    Re: Inescapable (symmetric) twins paradox Thomas 'PointedEars' Lahn <PointedEars@web.de> - 2015-08-19 22:10 +0200
  Re: Inescapable (symmetric) twins paradox Felipe Delgado <fd@spreadspectrum.org> - 2015-08-11 18:19 +0000

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