Re: Division by zero

Am Sonntag000002, 02.02.2025 um 10:38 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.

>
τ was the name of the time coordinate in k and also the name of a function, which was meant as coordinate transformation between K and k.
>
The time coordinate of an event in K has also a value in respect to k, hence time t of K should belong to the parameters of this function τ.
>
But y should not, because the velocity along the y-axis was assumed to be zero and the axes of y and eta are assumed to remain parallel.
>
So we had a function of time tau, which is 'vertical' upon the value zero of y.
>
In my view, such a function would VERY steep, hence ∂τ/∂y= infinity (and not zero!)

 

For me seemingly ∂y/∂τ= 0 was meant, but ∂τ/∂y= 0 was written.

 That "seemingly" is only possible if you don't understand the text
you are attempting to discuss.
 The topic at the point is to discuss how τ is determined from x, y, z, and t.

...
This is actually not true, because Einstein wrote this:
" We first define τ as a function of x', y, z, and t. ..."
(the difference is the primed x).
The meaning of x' was also not defined properly and I'm still chewing on the problem to estimate, which interpretation is actually correct.
As far as I can tell, Einstein had this setting in mind:
 From the origin of the moving system k a light beam is emitted and moves along the x/xsi axis towards a mirror at position x', which is stationary in K, and gets reflected back from there to its origin at the center of k.
Now x' has some position in K, which is fixed but otherwise unknown.
But tau is also the time of system k and that is certainly not a function of the position of a mirror in K.
So: I still scratch my head and cannot find a solution to the problem, how to associate the used symbols with the two coordinate systems K and k.
As naive person as I am, I would expect from an author, that the author would simply tell me, how his symbols are meant.
But instead of defining the used symbols, Einstein wrote nothing at all in this direction and seemingly assumed, that I could read his mind.

 You should find out what the symbols in the formulas mean and how the
formulas relate to the surrounding prose before you continue this discussion.

I can almost sing this particular text, but still can't decipher relatively simple things.
For instance: what was actually the meaning of x' ???
I had guesses, sure, but how was the actual meaning intended by Einstein?
TH