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Re: Time in accelerated reference frames

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Am 02.06.2022 um 14:11 schrieb Tom Roberts:
> On 6/2/22 6:54 AM, Python wrote:
>> In an accelerated frame (think about a rotating frame for instance),
>> it is impossible to materialize, for instance, space axis by rigid
>> bodies. Got it?
>
> For accelerated coordinates, it is often possible to construct three
> mutually-orthogonal spatial axes. But since the coordinates are
> accelerated, the time axis cannot be orthogonal to all of the spatial
> axes. For instance, in cylindrical coordinates {r,phi,z,t} rotating
> around the z axis, the (phi,t) component of the metric is nonzero; the
> spatial components are diagonal (i.e. the three spatial axes are
> mutually orthogonal).



It is actually difficult to get the axis of time orthogonal to the 
spatial axes in eucidean space, if space has only three dimensions.

It is hard to get a visual representation anyhow, if we would not use 
complex numbers and ascribe imaginary units to the spatial axes and real 
to the axis of time (or vice versa).

But with complex numbers, it is easy to see, that the entire system is 
not accelerated, but an observer on a curved worldline, who carries the 
coordinate system in question with him.


TH

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Time in accelerated reference frames Julio Di Egidio <julio@diegidio.name> - 2022-06-02 03:54 -0700
  Re: Time in accelerated reference frames Python <python@python.invalid> - 2022-06-02 13:54 +0200
    Re: Time in accelerated reference frames Tom Roberts <tjroberts137@sbcglobal.net> - 2022-06-02 07:11 -0500
      Re: Time in accelerated reference frames "mitchr...@gmail.com" <mitchrae3323@gmail.com> - 2022-06-02 13:54 -0700
      Re: Time in accelerated reference frames Thomas Heger <ttt_heg@web.de> - 2022-06-09 09:36 +0200
    Re: Time in accelerated reference frames Richard Hachel <r.hachel@tiscali.fr> - 2022-06-02 13:43 +0000
      Re: Time in accelerated reference frames Python <python@python.invalid> - 2022-06-02 17:14 +0200
        Re: Time in accelerated reference frames Maciej Wozniak <maluwozniak@gmail.com> - 2022-06-02 08:50 -0700
          Re: Time in accelerated reference frames Richard Hachel <r.hachel@tiscali.fr> - 2022-06-02 15:57 +0000
        Re: Time in accelerated reference frames Richard Hachel <r.hachel@tiscali.fr> - 2022-06-02 15:51 +0000
          Re: Time in accelerated reference frames Python <python@python.invalid> - 2022-06-03 01:59 +0200
            Re: Time in accelerated reference frames Maciej Wozniak <maluwozniak@gmail.com> - 2022-06-02 22:41 -0700
            Re: Time in accelerated reference frames Richard Hachel <r.hachel@tiscali.fr> - 2022-06-03 13:15 +0000
              Re: Time in accelerated reference frames Python <python@python.invalid> - 2022-06-03 15:25 +0200
                Re: Time in accelerated reference frames Richard Hachel <r.hachel@tiscali.fr> - 2022-06-03 17:16 +0000
                Re: Time in accelerated reference frames Thomas Heger <ttt_heg@web.de> - 2022-06-05 10:12 +0200
  Re: Time in accelerated reference frames nospam@de-ster.demon.nl (J. J. Lodder) - 2022-06-02 13:54 +0200
    Re: Time in accelerated reference frames Julio Di Egidio <julio@diegidio.name> - 2022-06-04 03:40 -0700
  Re: Time in accelerated reference frames "mitchr...@gmail.com" <mitchrae3323@gmail.com> - 2022-06-05 10:40 -0700

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