Groups > sci.physics.relativity > #582432

Re: Annotated version of SRT

From	Thomas Heger <ttt_heg@web.de>
Newsgroups	sci.physics.relativity
Subject	Re: Annotated version of SRT
Date	2022-04-10 08:49 +0200
Message-ID	<jbfd0cFgk3oU1@mid.individual.net> (permalink)
References	(18 earlier) <t2i00b$e25$1@gioia.aioe.org> <jb4ptjFffd0U1@mid.individual.net> <03a03595-b620-438c-939a-b1efadaa0d79n@googlegroups.com> <jba3mtFg7iqU1@mid.individual.net> <t2rukg$1qn8$1@gioia.aioe.org>

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Am 09.04.2022 um 14:36 schrieb Python:
> Thomas Heger wrote:
> ...
>> E.g. Y was used as x-component in the electric field strength vector
>> at point (x, y, z). That 'Y' is therefore a unitless number, because
>> the n-tuple (X, Y, Z) 'inherits' its units from the coordinate system
>> it belongs to.
>
> *facepalm*
>
> Well, Thomas let's apply this silly idea of yours that vector
> components are unitless. If they are unitless their values
> won't change if you switch from one unit system to another
> one, right?
>
> There is a glass of water in front of me on the table. Taking
> the room walls to define orthogonal axis I can represent the
> position of the glass as a three dimension vector (distance
> from left well, front wall and floor, right?
>
> Using SI (meters) I got (1, 1.50, .50)
>
> Using inches I got (38.37, 59.05, 19.68)
>
> It is weird for "unitless" numbers to behave that way,
> isn't it?

A vector is meant as coordinates within a coordinate system. (without a 
corresponding coordinate system a vector would not make any sense at all.)

Therefore your vector (1, 1.50, .50) 'inherits' the SI units from the 
corresponding coordinate system, which is defined in term of SI units.

In such a coordinate system 1 unit of length in the x-direction, for 
instance, is 1 m long.

Because the coordinate system is already 'normed', the n-tuple (1, 1.50, 
.50) does not need additional units anymore.

Not to norm a coordinate system would not make sense, because 
coordinates are multiples of the unit length used.

And because the coordinate system already 'knows' the units, the vectors 
themselves do not need to know, how long one unit of length is, hence 
carry only numerical values.

If you alter the norm of the coordinate system, you obviously need to 
alter the numerical values, too, while the meant length would not change.

(If vectors carry also units, the system gets 'doubble normed', what is 
not such a good idea.)

Now we could attatch a different coordinate system to a point, which 
carry other units, like V/m for instance.

The field strength vector is then meant as as 'coordinates' in that 
abstract coordinate system.

In this case we also do not need to assing units to the vector entries, 
because that coordinate system already knows the units.

>> But the x-component of the electric field is not a number.
>
> What is it then? A giraffe?
>

'Field' denotes something, what distributes in space.

In case of the electric field, the influence of a charge on the 
surrounding space was meant.

This influence is meant with 'electric field'.

The strength of this influence is then called 'electric field strength'.

As this has a strength and a direction at all of the influenced points, 
we can use vectors starting from these points.

Now we get two possibilities for what we mean by 'vector':

one is the n-tuple, which belongs to the mathematical description

one is the physical field strength, which has a certain strength and 
direction at any point in space.

The physical field strength seems to be decomposable into orthogonal 
fractions, which behave like vector themselves.

These can be represented in mathematical form as a vector, too.

Therefore the y-component of the field vector (X, Y, Z) can be written 
as (0, Y, 0). That is a vector, while Y is a number.

Now I would like to know, which of these interpretations it was, that 
Einstein had in mind.

TH

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Re: Annotated version of SRT Michael Moroney <moroney@world.std.spaamtrap.com> - 2022-04-05 13:58 -0400
  Re: Annotated version of SRT Thomas Heger <ttt_heg@web.de> - 2022-04-06 08:22 +0200
    Re: Annotated version of SRT Thomas Heger <ttt_heg@web.de> - 2022-04-07 07:45 +0200
      Re: Annotated version of SRT JanPB <filmart@gmail.com> - 2022-04-07 01:20 -0700
        Re: Annotated version of SRT Thomas Heger <ttt_heg@web.de> - 2022-04-08 08:14 +0200
          Re: Annotated version of SRT JanPB <filmart@gmail.com> - 2022-04-07 23:47 -0700
    Re: Annotated version of SRT JanPB <filmart@gmail.com> - 2022-04-07 01:06 -0700
      Re: Annotated version of SRT Thomas Heger <ttt_heg@web.de> - 2022-04-08 08:40 +0200
        Re: Annotated version of SRT JanPB <filmart@gmail.com> - 2022-04-07 23:56 -0700
          Re: Annotated version of SRT Thomas Heger <ttt_heg@web.de> - 2022-04-08 20:50 +0200
            Re: Annotated version of SRT Michael Moroney <moroney@world.std.spaamtrap.com> - 2022-04-08 19:05 -0400
              Re: Annotated version of SRT Thomas Heger <ttt_heg@web.de> - 2022-04-09 08:08 +0200
                Re: Annotated version of SRT JanPB <filmart@gmail.com> - 2022-04-08 23:51 -0700
                Re: Annotated version of SRT Odd Bodkin <bodkinodd@gmail.com> - 2022-04-09 13:02 +0000
                Re: Annotated version of SRT Coke Hishikawa <uhva@blseummh.nm> - 2022-04-09 13:21 +0000
                Re: Annotated version of SRT Michael Moroney <moroney@world.std.spaamtrap.com> - 2022-04-09 12:18 -0400
                Re: Annotated version of SRT Thomas Heger <ttt_heg@web.de> - 2022-04-10 09:14 +0200
                Re: Annotated version of SRT Mikko <mikko.levanto@iki.fi> - 2022-04-10 11:29 +0300
                Re: Annotated version of SRT nospam@de-ster.demon.nl (J. J. Lodder) - 2022-04-10 12:28 +0200
                Re: Annotated version of SRT Mikko <mikko.levanto@iki.fi> - 2022-04-10 16:54 +0300
                Re: Annotated version of SRT Michael Moroney <moroney@world.std.spaamtrap.com> - 2022-04-11 00:50 -0400
                Re: Annotated version of SRT Maciej Wozniak <maluwozniak@gmail.com> - 2022-04-10 21:52 -0700
                Re: Annotated version of SRT Thomas Heger <ttt_heg@web.de> - 2022-04-11 07:42 +0200
                Re: Annotated version of SRT Odd Bodkin <bodkinodd@gmail.com> - 2022-04-11 11:01 +0000
                Re: Annotated version of SRT Paparios <mrios@ing.puc.cl> - 2022-04-11 05:50 -0700
                Re: Annotated version of SRT nospam@de-ster.demon.nl (J. J. Lodder) - 2022-04-11 18:20 +0200
                Re: Annotated version of SRT Maciej Wozniak <maluwozniak@gmail.com> - 2022-04-11 09:48 -0700
                Re: Annotated version of SRT Paparios <mrios@ing.puc.cl> - 2022-04-11 09:54 -0700
                Re: Annotated version of SRT Maciej Wozniak <maluwozniak@gmail.com> - 2022-04-11 12:32 -0700
                Re: Annotated version of SRT Michael Moroney <moroney@world.std.spaamtrap.com> - 2022-04-11 18:39 -0400
                Re: Annotated version of SRT Maciej Wozniak <maluwozniak@gmail.com> - 2022-04-11 21:28 -0700
                Re: Annotated version of SRT Python <python@example.invalid> - 2022-04-12 06:36 +0200
                Re: Annotated version of SRT Maciej Wozniak <maluwozniak@gmail.com> - 2022-04-11 21:38 -0700
                Re: Annotated version of SRT Python <python@example.invalid> - 2022-04-12 06:47 +0200
                Re: Annotated version of SRT Maciej Wozniak <maluwozniak@gmail.com> - 2022-04-11 21:58 -0700
                Re: Annotated version of SRT Richard Hachel <r.hachel@tiscali.fr> - 2022-04-12 11:14 +0000
                Re: Annotated version of SRT Richard Hachel <r.hachel@tiscali.fr> - 2022-04-12 11:10 +0000
                Re: Annotated version of SRT JanPB <filmart@gmail.com> - 2022-04-11 12:38 -0700
                Re: Annotated version of SRT Thomas Heger <ttt_heg@web.de> - 2022-04-12 18:48 +0200
                Re: Annotated version of SRT JanPB <filmart@gmail.com> - 2022-04-12 11:37 -0700
                Re: Annotated version of SRT Michael Moroney <moroney@world.std.spaamtrap.com> - 2022-04-13 02:37 -0400
                Re: Annotated version of SRT Thomas Heger <ttt_heg@web.de> - 2022-04-14 08:36 +0200
                Re: Annotated version of SRT JanPB <filmart@gmail.com> - 2022-04-13 23:44 -0700
                Re: Annotated version of SRT Michael Moroney <moroney@world.std.spaamtrap.com> - 2022-04-14 04:16 -0400
                Re: Annotated version of SRT Maciej Wozniak <maluwozniak@gmail.com> - 2022-04-14 01:34 -0700
                Re: Annotated version of SRT Odd Bodkin <bodkinodd@gmail.com> - 2022-04-14 12:47 +0000
                Re: Annotated version of SRT Python <python@example.invalid> - 2022-04-10 13:06 +0200
            Re: Annotated version of SRT Thomas Heger <ttt_heg@web.de> - 2022-04-09 07:48 +0200
        Re: Annotated version of SRT Python <python@example.invalid> - 2022-04-09 14:36 +0200
          Re: Annotated version of SRT Maciej Wozniak <maluwozniak@gmail.com> - 2022-04-09 06:18 -0700
          Re: Annotated version of SRT Thomas Heger <ttt_heg@web.de> - 2022-04-10 08:49 +0200
            Re: Annotated version of SRT Maciej Wozniak <maluwozniak@gmail.com> - 2022-04-09 23:52 -0700
              Re: Annotated version of SRT Python <python@example.invalid> - 2022-04-10 12:54 +0200
            Re: Annotated version of SRT Python <python@example.invalid> - 2022-04-10 12:51 +0200
              Re: Annotated version of SRT Maciej Wozniak <maluwozniak@gmail.com> - 2022-04-10 05:02 -0700
              Re: Annotated version of SRT Thomas Heger <ttt_heg@web.de> - 2022-04-10 21:04 +0200
                Re: Annotated version of SRT Python <python@example.invalid> - 2022-04-10 22:08 +0200
                Re: Annotated version of SRT Maciej Wozniak <maluwozniak@gmail.com> - 2022-04-10 21:20 -0700
                Re: Annotated version of SRT Thomas Heger <ttt_heg@web.de> - 2022-04-11 07:48 +0200
                Re: Annotated version of SRT Reinhardt Behm <rbehm@hushmail.com> - 2022-04-11 08:43 +0000
                Re: Annotated version of SRT nospam@de-ster.demon.nl (J. J. Lodder) - 2022-04-11 13:55 +0200
                Re: Annotated version of SRT Thomas Heger <ttt_heg@web.de> - 2022-04-11 21:09 +0200
                Re: Annotated version of SRT Reinhardt Behm <rbehm@hushmail.com> - 2022-04-12 02:52 +0000
                Re: Annotated version of SRT Thomas Heger <ttt_heg@web.de> - 2022-04-13 07:49 +0200
                Re: Annotated version of SRT Reinhardt Behm <rbehm@hushmail.com> - 2022-04-13 07:41 +0000
                Re: Annotated version of SRT Thomas Heger <ttt_heg@web.de> - 2022-04-14 08:21 +0200
                Re: Annotated version of SRT Python <python@example.invalid> - 2022-04-14 14:38 +0200
                Re: Annotated version of SRT Maciej Wozniak <maluwozniak@gmail.com> - 2022-04-14 07:47 -0700
                Re: Annotated version of SRT Reinhardt Behm <rbehm@hushmail.com> - 2022-04-14 15:26 +0000
                Re: Annotated version of SRT Odd Bodkin <bodkinodd@gmail.com> - 2022-04-14 15:42 +0000
  Re: Annotated version of SRT Coke Hishikawa <uhva@blseummh.nm> - 2022-04-09 11:33 +0000
    Re: Annotated version of SRT JanPB <filmart@gmail.com> - 2022-04-09 13:08 -0700
      Re: Annotated version of SRT nospam@de-ster.demon.nl (J. J. Lodder) - 2022-04-10 11:54 +0200
        Re: Annotated version of SRT Thomas Heger <ttt_heg@web.de> - 2022-04-10 21:10 +0200
        Re: Annotated version of SRT JanPB <filmart@gmail.com> - 2022-04-11 12:43 -0700

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