Re: Division by zero

Am Sonntag000002, 02.02.2025 um 10:30 schrieb Mikko:

Hi NG
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I'm actually not really certain, but found an error in Einstein's 'On the electrodynamics of moving bodies' which is quite serious.
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See page six, roughly in the middle:
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There we find an equation, which says this:
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∂τ/∂y= 0

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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