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Re: New version of my annotations to SRT

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Am 15.02.2024 um 11:32 schrieb Paul B. Andersen:
> Den 15.02.2024 07:10, skrev Thomas Heger:
>>> Den 14.02.2024 08:34, skrev Thomas Heger:
>>>>
>>>> Einstein's variable names were EXTREMELY annoying!
>>>>
>>>> For instance:
>>>> he had eight different uses of the letter 'A'.
>
>
> In §1 the symbol 'A' is explicitly defined: "the point A of space",
> and this is the only meaning of 'A' in §1 to and including §5.
>
> In §6 the symbol 'A' is not used.
>
> In §7 the symbol 'A' is explicitly defined:
>   "we call the amplitude of the electric or magnetic force A"
> and this is the only meaning of 'A' in §7 to and including §10.
>
> The numbering of an equation (A) is not another use of the symbol 'A'.
>
> This is two well defined uses of the letter 'A' used to identify
> a physical or mathematical entity.
>
> Can you name the other six?

'A' is an ASCII character and actually a very short text.

To use it as a symbol, for instance as name of a variable, you need to 
connect text and variable by a definition.

For instance you could write, that 'A' shall contain the value of a 
certain area.

But Einstein didn't do that.

Instead he seemingly assumed, that the reader could also read his mind.


His uses of 'A' were:


as name of a point in space

as name of the local time at point A as 'A-time'

for one end of a flying rod

as index of the time value t_A

as area

in 'electric power of deflection' A_e

in 'magnetic power of deflection' A_m

as (only!) internal reference 'A'


But why didn't he use other letters, like e.g. F or Q ???

>
>> But both uses within a single text are wrong, because it is not
>> possible to know, which particular meaning a symbol in an equation
>> has, if both meanings use the same symbol.
>>
>> But Einstein gave this another kick and used the same symbol twice with
>> different meanings within a single sentence.
>
> Can you quote the sentence in question?

sure:
page 22, roughly in the middle

"We will now determine the kinetic energy of the electron. If an 
electron moves from rest at the origin of co-ordinates of the system K 
along the axis of X under the action of an electrostatic force X, ..."

I disliked already the used of 'force' for electrical field strength.

But anyhow...

'X' is here the x-component of the electric field-strength vector and 
called 'X'

'X' is also the name of the x-axis of system K.

Therefore we have twice the symbol 'X' in the same sentence (actually 
also in the same line), but with two different meanings.

It is not really wrong, but VERY bad writing style.

At least Einstein could have made different types of symbols 
distinguishable by attributes like italic or bold fonts.


TH

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Re: New version of my annotations to SRT Thomas Heger <ttt_heg@web.de> - 2024-02-16 07:20 +0100
  Re: New version of my annotations to SRT "Paul B. Andersen" <relativity@paulba.no> - 2024-02-16 09:43 +0100
  Re: New version of my annotations to SRT Athel Cornish-Bowden <me@yahoo.com> - 2024-02-16 09:46 +0100
  Re: New version of my annotations to SRT Mikko <mikko.levanto@iki.fi> - 2024-02-16 11:53 +0200
  Re: New version of my annotations to SRT "Paul B. Andersen" <relativity@paulba.no> - 2024-02-16 13:59 +0100

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