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From: Mikko <mikko.levanto@iki.fi>
Newsgroups: sci.physics.relativity
Subject: Re: Division by zero
Date: Mon, 3 Feb 2025 17:51:05 +0200
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On 2025-02-03 07:56:53 +0000, Thomas Heger said:

> 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?

He obviously means the function needed to determine τ. It does not matter
whether he means the function from x, y, z, t or x', y, z, t as ∂/∂y is
the same in both cases.

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

Variables are clearly defined. For example, x, y, z, and t are defined as
the coordinates of the system K.

> 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

Although modern mathematicians don't consider that correct, it is common
to use the same symbol for a quantity and for a function that computes
that quantity. It is obvious from the context which is meant: function
name is used with arguments, the quantity name without.

> 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.

Nowhere in the article is any vector called τ.

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

A careless reader may get a wrong idea but the target audience could
understand it.

> 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.

That function is a time-valued function.

You are not in the target audience of the article. Nobody still alive is.
Therefore your comprehension problems are not an indication of a defect
in the article.

The article is incomplete. It only presents some core ideas. In later
articles Einstein filled gaps in the reasoning and extended to other
problems.

-- 
Mikko