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From: Thomas Heger <ttt_heg@web.de>
Newsgroups: sci.physics.relativity
Subject: Re: Division by zero
Date: Mon, 3 Feb 2025 08:56:53 +0100
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Am Sonntag000002, 02.02.2025 um 10:30 schrieb Mikko:

>>>> Hi NG
>>>>
>>>> I'm actually not really certain, but found an error in Einstein's 
>>>> 'On the electrodynamics of moving bodies' which is quite serious.
>>>>
>>>>
>>>> See page six, roughly in the middle:
>>>>
>>>> There we find an equation, which says this:
>>>>
>>>> ∂τ/∂y= 0
>>>
>>> Do you mean on page 899 (9th page of the article) in §3?
>>> The operation is not division but a partial derivative.
> 
> You should answer this question. It is not useful to talk without telling
> what you are talking about.
> 
I'm referring to the English translation, which can be found here

https://www.fourmilab.ch/etexts/einstein/specrel/www/

The English pdf version has other page numbers than the original article.

But in a way, these original page numbers are also possible as reference.

But unfortunately I have here only the English version (the German I 
have on a different computer).

So I have to tell you the page from the English version or make the 
meant part available to you by other means.

So, § 3 was meant and roughly the middle, which can be found on page 6 
of the English pdf version.

And you are absolutely right, that a partial derivative was meant.

The problem was: of which function was a partial derivative meant?


I have found already, what Einstein had actually meant:

Einstein didn't define the used variables and simply assumed, the reader 
would know anyhow, what he had in mind.

But that wasn't particularly easy, because Einstein used the symbol τ 
for three different types of objects.

a) the time values of clocks in system k were named τ

b) a function τ was derived, which should serve as coordinate 
transformation between system K and system k

c) this function take (kind of) four-vectors of K as input and spits out 
four-vectors in k as output, while these output vectors were also called τ.


This was rather nasty, because it could lead to several errors, if you 
try to interpret Einstein's intentions.

And I have actually fallen in one of these traps, because I had regarded 
τ as time-value, while actually the function τ of case b) was meant.


TH