Re: Division by zero

Am Montag000003, 03.02.2025 um 16:20 schrieb Mikko:

On 2025-02-03 08:14:10 +0000, Thomas Heger said:
 

Am Sonntag000002, 02.02.2025 um 10:38 schrieb Mikko:
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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.

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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.
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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.
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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.
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So we had a function of time tau, which is 'vertical' upon the value zero of y.
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In my view, such a function would VERY steep, hence ∂τ/∂y= infinity (and not zero!)

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

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

...
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This is actually not true, because Einstein wrote this:
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" We first define τ as a function of x', y, z, and t. ..."

 No need to revise my comment. The problem was to determine τ from x, y, z,
and t. The variable x' is just an intermediate step in that process.
 

The meaning of x' was also not defined properly and I'm still chewing on the problem to estimate, which interpretation is actually correct.

 The definition x' was x' = x - vt, leaving no room for interpretations.

If a variable x' as 'intermediate step' without a meaning would be introduced, then the equation is no longer a representation of the real world.
But Einstein treated x' as if it would be real.
That was actually, what I thought he meant with x'.
If x' had no real meaning, he could not possibly place a mirror there, as he wrote here:
"From the origin of system k let a ray be emitted at the time τ_0 along the X-axis to x'...".
So, I cannot agree with our interpretation, because a mirror would require a real place to be placed.
As that should be x', that x' had to be a fixed coordinate upon the x-axis of K.
The interpretation of x' is a very important point, because x' was used in the subsequent derivation.
I thought: ok, there is a mirror at x', hence x' has a fixed value in respect to system K.
Other interpretations are certainly possible, but I was unable to find any interpretation, which would not violate other statements or restrictions.

 

As far as I can tell, Einstein had this setting in mind:
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 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.

 The title of §3 indicates otherwise. In particular, there is no light
and no mirror in the discussion around the formula ∂τ/∂y = 0.
 

?????
What?
I'm discussing the text on page 6, which is part of §3.
But the text is important, of course, and not only the headline.
TH