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From: Thomas Heger <ttt_heg@web.de>
Newsgroups: sci.physics.relativity
Subject: Re: Division by zero
Date: Tue, 4 Feb 2025 08:16:57 +0100
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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:
>>
>>>>>>> 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. ..."
> 
> 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:
>>
>>  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