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Re: Annotated version of SRT

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Am 15.05.2022 um 10:26 schrieb Mikko:
> On 2022-05-12 19:05:22 +0000, Thomas Heger said:
>
>> Am 12.05.2022 um 09:31 schrieb Mikko:
>>> On 2022-05-12 05:39:45 +0000, Thomas Heger said:
>>>
>>>> You need to distinguish numbers, vectors and points.
>>>
>>> In Einstein's text that is simple: all symbols represent scalars
>>> unless otherwise specified.
>>
>> Well, no, I do not agree.
>>
>> Einstein made no distinction between different types of mathematical
>> objects, but did not only use scalars.
>>
>> So, any Latin letter can represent several types of objects and
>> Einstein gave no hints, which would allow to identify the intended
>> meaning.
>
> At the time it was commonly thought that all formulas, or at least the
> useful ones, were always about numbers and only numbers, as most formulas
> indeed were. Therefore it wast not necessary to point out that a symbol
> in a formula represents a scalar but very important to clearly say if
> it represents something else.


Vectors and vector equations were already known in the 19th century. 
Especially in connection to electromagnetism vector equations were state 
of the art since Maxwell's times.

>> To assume, that only scalars were meant was plain wrong, because also
>> functions and vectors had similar symbols, which the reader was
>> requested to identify.
>
> Functions can be identified as fucntions because function symbols are
> only used before a left parenthesis (except for a small number of well
> known symbols). Unless otherwise specified, function values are scalar.

Parenthesises can have different meanings. To distinguish a function a 
of argument x in a(x)=0 from a multiplication of a scalar a with the 
vector (x) in a(x)=0, we need certain signs, which distinguish different 
uses of the used symbols.

>> I have complained several times about this, but JanPB meant, that the
>> intended audience could decipher Einstein's intentions with ease.
>>
>> I do not quite agree, but would accept, that professionals certainly
>> know, what Einstein wanted.
>
> And that is sufficient.

Sure, but not all professional physicists can read Einstein's mind.

To enable common mortals to understand something, it is useful, if an 
arbitrary reader is able to identify, what an author tries to express.

It can eventualy be difficult. But finally the reader should be able to 
find out, what was actually meant.


>> But still you cannot claim, that all symbols mean scalars. Which
>> interpretations was intended, that is a riddle, which the reader was
>> requested to solve.
>
> Not all, only those that are not specified to mean something else.
???

An author of a scientific paper is obliged to be specific. There should 
be no space for interpretations and questions about the intended meaning 
of a certain symbol.

If an author fails to distinguish between possible interpretations, the 
reader may chose, what would fit to the possible interpretations to his 
own liking, what in most cases is not, what the author wanted.

Therefore a reader can disprove a paper, simply by finding a possible 
interpretation of the text, which leads to nonsense.

In this case the text flies into the waste bin.

Even if this sounds a little tough, you should bear in mind, that 
scientific papers are not toys.

>> And that riddle is not as easy as you apparently think.
>
> Easy enough.
>
>>> You should be clear with your symbols. When discussing Einstein's text,
>>> you should use the same conventions. Einstein's x and xi are scalars,
>>> so for points you should use different symbols.
>>
>> Points had large Latin letters, like 'A' or 'B' (I guess there was
>> also a 'C', but as far as I can recall, there was no 'D').
>
> Yes, that is the common style in geometry. However, upper case letters
> were also used for other purposes. Where A and B are introduced in the
> article they are clearly identified as points.


There were eight different uses of the capital 'A' in Einstein's text.

This alone would be sufficiant to dismiss the entire paper.

>>> Coordinates are scalars. The xi-coordinate of "zero spot of k" is
>>> zero because "zero spot of k" means the poit where xi = 0, eta = 0,
>>> and zeta = 0.
>>
>> Not really. A component of a vector is a scalar, but 'coordinate'
>> could be interpreted as a vector, too. That would be a scaled version
>> of the unit vector in that direction.
>
> Yes really. Nobody wanted to think about any other possibility without
> a very good reason.

You should meantion, which of the possibilities above is that obvious.

Is a coordinate a scalar or a vector?

>> But also 'numerical value of the entry of the position vector of a
>> point' would fit to the description, what is a scalar.
>>
>> Usually the author should tell, how he liked his variables to be
>> interpreted. But Einstein left that more or less to the reader.
>
> Not just should but did. But not what the readers would consider
> self-evident. Unless otherwise told, every symbol is scalar by
> default.
>
>>>> The xsi-component of the position vector of the zero spot is called
>>>> xsi_0, which has the numerical value zero.
>>>
>>> You don't need any position vectors because you already have
>>> coordinates.
>>
>> A point has a location, which is represented by a position vector.
>
> Not in Einstein's article, where coordinates are used instead.

A postition vector in three dimensional space has three components, 
called 'coordinates'.

Now is essential to define the meaning of 'coordinate'.

I would use a orthogonal set of three unit vectors as coordinate system 
and unitless vectors, where the entries are sclalars, that multiply with 
the cooresponding unit vectors. These scaled unit vectors are added to 
the position vector of the point.

What Einstein wanted to use, that would be his decision. It would have 
been nice, if he had told the reader, which decisions he made.

...


TH

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Re: Annotated version of SRT Thomas Heger <ttt_heg@web.de> - 2022-05-10 07:12 +0200
  Re: Annotated version of SRT JanPB <filmart@gmail.com> - 2022-05-10 00:19 -0700
    Re: Annotated version of SRT Thomas Heger <ttt_heg@web.de> - 2022-05-11 07:55 +0200
      Re: Annotated version of SRT Mikko <mikko.levanto@iki.fi> - 2022-05-11 11:25 +0300
        Re: Annotated version of SRT Thomas Heger <ttt_heg@web.de> - 2022-05-12 07:39 +0200
          Re: Annotated version of SRT Mikko <mikko.levanto@iki.fi> - 2022-05-12 10:31 +0300
            Re: Annotated version of SRT Thomas Heger <ttt_heg@web.de> - 2022-05-12 21:05 +0200
              Re: Annotated version of SRT Mikko <mikko.levanto@iki.fi> - 2022-05-15 11:26 +0300
                Re: Annotated version of SRT Thomas Heger <ttt_heg@web.de> - 2022-05-18 07:38 +0200
                Re: Annotated version of SRT Mikko <mikko.levanto@iki.fi> - 2022-05-18 16:42 +0300
      Re: Annotated version of SRT JanPB <filmart@gmail.com> - 2022-05-12 11:33 -0700
        Re: Annotated version of SRT Thomas Heger <ttt_heg@web.de> - 2022-05-12 21:28 +0200
          Re: Annotated version of SRT Thomas Heger <ttt_heg@web.de> - 2022-05-13 08:41 +0200
            Re: Annotated version of SRT Thomas Heger <ttt_heg@web.de> - 2022-05-14 06:43 +0200
            Re: Annotated version of SRT JanPB <filmart@gmail.com> - 2022-05-14 19:49 -0700
              Re: Annotated version of SRT Thomas Heger <ttt_heg@web.de> - 2022-05-15 08:34 +0200
                Re: Annotated version of SRT JanPB <filmart@gmail.com> - 2022-05-15 12:53 -0700
                Re: Annotated version of SRT Thomas Heger <ttt_heg@web.de> - 2022-05-18 08:01 +0200
                Re: Annotated version of SRT JanPB <filmart@gmail.com> - 2022-05-18 10:02 -0700
                Re: Annotated version of SRT Thomas Heger <ttt_heg@web.de> - 2022-05-20 09:32 +0200
          Re: Annotated version of SRT JanPB <filmart@gmail.com> - 2022-05-14 19:29 -0700
            Re: Annotated version of SRT Thomas Heger <ttt_heg@web.de> - 2022-05-15 08:50 +0200
            Re: Annotated version of SRT Thomas Heger <ttt_heg@web.de> - 2022-05-19 08:39 +0200
              Re: Annotated version of SRT Python <python@python.invalid> - 2022-05-19 11:03 +0200
                Re: Annotated version of SRT Maciej Wozniak <maluwozniak@gmail.com> - 2022-05-19 06:56 -0700
              Re: Annotated version of SRT JanPB <filmart@gmail.com> - 2022-05-19 02:05 -0700
                Re: Annotated version of SRT Thomas Heger <ttt_heg@web.de> - 2022-05-20 09:17 +0200
                Re: Annotated version of SRT JanPB <filmart@gmail.com> - 2022-05-20 15:10 -0700
                Re: Annotated version of SRT Thomas Heger <ttt_heg@web.de> - 2022-05-21 08:38 +0200
                Re: Annotated version of SRT Python <python@python.invalid> - 2022-05-21 18:41 +0200
                Re: Annotated version of SRT Maciej Wozniak <maluwozniak@gmail.com> - 2022-05-21 11:51 -0700
                Re: Annotated version of SRT Thomas Heger <ttt_heg@web.de> - 2022-05-22 07:29 +0200
                Re: Annotated version of SRT Maciej Wozniak <maluwozniak@gmail.com> - 2022-05-21 23:10 -0700
              Re: Annotated version of SRT "Paul B. Andersen" <paul.b.andersen@paulba.no> - 2022-05-19 20:00 +0200

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