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Division by zero

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  Division by zero Thomas Heger <ttt_heg@web.de> - 2025-02-01 09:14 +0100
    Re: Division by zero Mikko <mikko.levanto@iki.fi> - 2025-02-01 11:36 +0200
      Re: Division by zero Ross Finlayson <ross.a.finlayson@gmail.com> - 2025-02-01 18:19 -0800
        Re: Division by zero Thomas Heger <ttt_heg@web.de> - 2025-02-02 07:58 +0100
          Re: Division by zero Mikko <mikko.levanto@iki.fi> - 2025-02-02 11:40 +0200
            Re: Division by zero "Paul.B.Andersen" <relativity@paulba.no> - 2025-02-03 12:27 +0100
          Re: Division by zero (0, 1, infinity) Ross Finlayson <ross.a.finlayson@gmail.com> - 2025-02-02 07:45 -0800
      Re: Division by zero Thomas Heger <ttt_heg@web.de> - 2025-02-02 07:52 +0100
        Re: Division by zero Thomas Heger <ttt_heg@web.de> - 2025-02-02 09:26 +0100
          Re: Division by zero Mikko <mikko.levanto@iki.fi> - 2025-02-02 11:38 +0200
            Re: Division by zero Thomas Heger <ttt_heg@web.de> - 2025-02-03 09:14 +0100
              Re: Division by zero Mikko <mikko.levanto@iki.fi> - 2025-02-03 17:20 +0200
                Re: Division by zero Thomas Heger <ttt_heg@web.de> - 2025-02-04 08:16 +0100
                  Re: Division by zero Mikko <mikko.levanto@iki.fi> - 2025-02-05 09:48 +0200
                    Re: Division by zero Thomas Heger <ttt_heg@web.de> - 2025-02-05 10:09 +0100
        Re: Division by zero Mikko <mikko.levanto@iki.fi> - 2025-02-02 11:30 +0200
          Re: Division by zero Thomas Heger <ttt_heg@web.de> - 2025-02-03 08:56 +0100
            Re: Division by zero Athel Cornish-Bowden <me@yahoo.com> - 2025-02-03 10:02 +0100
              Re: Division by zero Thomas Heger <ttt_heg@web.de> - 2025-02-03 11:17 +0100
              Re: Division by zero Thomas Heger <ttt_heg@web.de> - 2025-02-03 11:17 +0100
            Re: Division by zero Mikko <mikko.levanto@iki.fi> - 2025-02-03 17:51 +0200
              Re: Division by zero Maciej Wozniak <mlwozniak@wp.pl> - 2025-02-03 17:33 +0100
              Re: Division by zero Thomas Heger <ttt_heg@web.de> - 2025-02-04 08:36 +0100
                Re: Division by zero Mikko <mikko.levanto@iki.fi> - 2025-02-04 11:13 +0200
                  Re: Division by zero Maciej Wozniak <mlwozniak@wp.pl> - 2025-02-04 11:58 +0100
                  Re: Division by zero Thomas Heger <ttt_heg@web.de> - 2025-02-05 09:32 +0100
    Re: Division by zero nospam@de-ster.demon.nl (J. J. Lodder) - 2025-02-01 23:28 +0100
      Re: Division by zero Ross Finlayson <ross.a.finlayson@gmail.com> - 2025-02-01 20:26 -0800
    Re: Division by zero film.art@gmail.com (JanPB) - 2025-02-20 21:45 +0000
      Re: Division by zero The Starmaker <starmaker@ix.netcom.com> - 2025-02-20 21:18 -0800

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#660930 — Division by zero

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

Now, 'tau' is a time belonging to the moving system k.

This system k moves along the x-axis of system K with velocity v, while 
x- and xsi-axis coincide and etha- and y axis remain parallel.

In other words v_y is permanently zero, or: ∂y=0.

So we have a 'divide by zero' case.

∂τ/∂y is a time value divided by a space value, hence has the form of 1/v.

Because it contains ∂y, the velocity along the y-axis was meant.

But for a straight lateral movement along the x-axis (only) there should 
be no movement along the y axis, hence ∂y remains zero, because the 
y-coordinate remains permanently zero, which is, of course, a constant 
value.


∂τ/∂y could approach a value, however, but if v_y goes to zero, the 
quotient ∂τ/∂y would go to infinity and NOT to zero (as the equation says).

Iow: this equation '∂τ/∂y= 0' is wrong!

TH

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#660931

On 2025-02-01 08:14:08 +0000, Thomas Heger said:

> 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.

> Now, 'tau' is a time belonging to the moving system k.

Yes, but it is also a number that is computed from coordinates of K.

> This system k moves along the x-axis of system K with velocity v, while 
> x- and xsi-axis coincide and etha- and y axis remain parallel.
> 
> In other words v_y is permanently zero,

Yes,

>  or: ∂y=0.

No. ∂y is not a number but a part of an operator. There are points with
different values of y and ∂/∂y refers to a line where t, x, and z (but not
y) have the same value at every point.

See https://en.wikipedia.org/wiki/Partial_derivative

-- 
Mikko

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#660936

On 02/01/2025 01:36 AM, Mikko wrote:
> On 2025-02-01 08:14:08 +0000, Thomas Heger said:
>
>> 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.
>
>> Now, 'tau' is a time belonging to the moving system k.
>
> Yes, but it is also a number that is computed from coordinates of K.
>
>> This system k moves along the x-axis of system K with velocity v,
>> while x- and xsi-axis coincide and etha- and y axis remain parallel.
>>
>> In other words v_y is permanently zero,
>
> Yes,
>
>>  or: ∂y=0.
>
> No. ∂y is not a number but a part of an operator. There are points with
> different values of y and ∂/∂y refers to a line where t, x, and z (but not
> y) have the same value at every point.
>
> See https://en.wikipedia.org/wiki/Partial_derivative
>

Zero meters/second is infinity seconds/meter.

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#660939

Am Sonntag000002, 02.02.2025 um 03:19 schrieb Ross Finlayson:
> On 02/01/2025 01:36 AM, Mikko wrote:
>> On 2025-02-01 08:14:08 +0000, Thomas Heger said:
>>
>>> 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.
>>
>>> Now, 'tau' is a time belonging to the moving system k.
>>
>> Yes, but it is also a number that is computed from coordinates of K.
>>
>>> This system k moves along the x-axis of system K with velocity v,
>>> while x- and xsi-axis coincide and etha- and y axis remain parallel.
>>>
>>> In other words v_y is permanently zero,
>>
>> Yes,
>>
>>>  or: ∂y=0.
>>
>> No. ∂y is not a number but a part of an operator. There are points with
>> different values of y and ∂/∂y refers to a line where t, x, and z (but 
>> not
>> y) have the same value at every point.
>>
>> See https://en.wikipedia.org/wiki/Partial_derivative
>>
> 
> Zero meters/second is infinity seconds/meter.
> 
yes, but that was my complain!

If there is not movement along the y-axis, then time tau would pass, but 
y would remain zero.

This would mean, that ∂τ/∂y= infinity  (and NOT zero).

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#660944

On 2025-02-02 06:58:32 +0000, Thomas Heger said:

> Am Sonntag000002, 02.02.2025 um 03:19 schrieb Ross Finlayson:
>> On 02/01/2025 01:36 AM, Mikko wrote:
>>> On 2025-02-01 08:14:08 +0000, Thomas Heger said:
>>> 
>>>> 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.
>>> 
>>>> Now, 'tau' is a time belonging to the moving system k.
>>> 
>>> Yes, but it is also a number that is computed from coordinates of K.
>>> 
>>>> This system k moves along the x-axis of system K with velocity v,
>>>> while x- and xsi-axis coincide and etha- and y axis remain parallel.
>>>> 
>>>> In other words v_y is permanently zero,
>>> 
>>> Yes,
>>> 
>>>>  or: ∂y=0.
>>> 
>>> No. ∂y is not a number but a part of an operator. There are points with
>>> different values of y and ∂/∂y refers to a line where t, x, and z (but not
>>> y) have the same value at every point.
>>> 
>>> See https://en.wikipedia.org/wiki/Partial_derivative

Did you read https://en.wikipedia.org/wiki/Partial_derivative ?

-- 
Mikko

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#660967

Den 02.02.2025 10:40, skrev Mikko:
> On 2025-02-02 06:58:32 +0000, Thomas Heger said:
> 
>> Am Sonntag000002, 02.02.2025 um 03:19 schrieb Ross Finlayson:
>>> On 02/01/2025 01:36 AM, Mikko wrote:
>>>> On 2025-02-01 08:14:08 +0000, Thomas Heger said:
>>>>
>>>>> 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.
>>>>
>>>>> Now, 'tau' is a time belonging to the moving system k.
>>>>
>>>> Yes, but it is also a number that is computed from coordinates of K.
>>>>
>>>>> This system k moves along the x-axis of system K with velocity v,
>>>>> while x- and xsi-axis coincide and etha- and y axis remain parallel.
>>>>>
>>>>> In other words v_y is permanently zero,
>>>>
>>>> Yes,
>>>>
>>>>>  or: ∂y=0.
>>>>
>>>> No. ∂y is not a number but a part of an operator. There are points with
>>>> different values of y and ∂/∂y refers to a line where t, x, and z 
>>>> (but not
>>>> y) have the same value at every point.
>>>>
>>>> See https://en.wikipedia.org/wiki/Partial_derivative
> 
> Did you read https://en.wikipedia.org/wiki/Partial_derivative ?
> 

Thomas Heger wouldn't understand it if he tried to read it.

Back in 2020 I tried to explain this equation:
(from the same page as the above)

  1/2*[ tau(0,0,0,t) + tau(0,0,0,t+ x'/(c-v)+x'/(c+v)) ]
   = tau ( x',0,0,t+x'/(c-v))

Thomas idea was that:  1/2*tau(0,0,0,t) = tau(0,0,0,t/2)

So I defined a simpler function and wrote
a simpler equation:

|Den 23.03.2020 17:41, skrev Thomas Heger:
|> Am 23.03.2020 um 10:10 schrieb Paul B. Andersen:
|>>
|>> Given the linear function f(x',t) = x'+2t
|>>
|>>  0.5*[f(0,1)+f(0,2)] = f(1,1)    (3 = 3)
|>>
|>>  0.5*[f(0,k)+f(0,2k)] = f(k,k)   (3k = 3k)
|>>
|>>  0.5*[2+4] = 3      [1+2] = 3
|>>  0.5*[2k+4k] = 3k   [1k+2k] = 3k
|> no
|>
|> 1/2 * f(0,1) = f(0*x', 1/2*1*t) = f(0,1/2*t)= 1/2*t
|> + 1/2 * f(0,2)= f(0, t)=t
|> ------------------------
|> = 0.5*[f(0,1)+f(0,2)] = f(0, 1.5 *t)=1.5*t
|>
|>
|> TH

Thomas Heger seems incapable to learn, so he probably still don't
know what a function is.

-- 
Paul

https://paulba.no/

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#660951 — Re: Division by zero (0, 1, infinity)

On 02/01/2025 10:58 PM, Thomas Heger wrote:
> Am Sonntag000002, 02.02.2025 um 03:19 schrieb Ross Finlayson:
>> On 02/01/2025 01:36 AM, Mikko wrote:
>>> On 2025-02-01 08:14:08 +0000, Thomas Heger said:
>>>
>>>> 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.
>>>
>>>> Now, 'tau' is a time belonging to the moving system k.
>>>
>>> Yes, but it is also a number that is computed from coordinates of K.
>>>
>>>> This system k moves along the x-axis of system K with velocity v,
>>>> while x- and xsi-axis coincide and etha- and y axis remain parallel.
>>>>
>>>> In other words v_y is permanently zero,
>>>
>>> Yes,
>>>
>>>>  or: ∂y=0.
>>>
>>> No. ∂y is not a number but a part of an operator. There are points with
>>> different values of y and ∂/∂y refers to a line where t, x, and z
>>> (but not
>>> y) have the same value at every point.
>>>
>>> See https://en.wikipedia.org/wiki/Partial_derivative
>>>
>>
>> Zero meters/second is infinity seconds/meter.
>>
> yes, but that was my complain!
>
> If there is not movement along the y-axis, then time tau would pass, but
> y would remain zero.
>
> This would mean, that ∂τ/∂y= infinity  (and NOT zero).

It's usually always more
"sensible, fungible, tractable"
when things go to zero instead
of infinity, so that all things
go to some common zero instead of
each whatever infinity.

Yet, it is so that mathematics is replete,
and so "space inversion" and these kinds
of things are mathematical with regards
to a point, and, the space.

One way to look at geometry is that
it is that there's a continuum that
makes a spiral space-filling curve
from an origin, then thusly the Euclid's
geometry can be _derived_ from that,
instead of what needs be _defined_.


https://www.youtube.com/watch?v=9r-HbQZDkU0&list=PLb7rLSBiE7F4_E-POURNmVLwp-dyzjYr-&index=29

"Logos 2000: natural infinities"


"The regular singular points of the hypergeometric
are zero, one, and infinity."


So, indeed, mathematics _owes_ physics
more and better mathematics of infinity,
to explain continuity.  These days there
is something like "quasi-invariant measure
theory" to go along with "the pseudo-differential"
to address problems with "the measure problem"
and about "the real fictitious forces",
about a true sum-of-histories sum-of-potentials
least-action least-gradient theory that's
a continuum mechanics with Poincare completion
in continuous manifolds, replete.


The partial derivatives are merely partial,
and pretty much always involve numerical
methods somewhere thusly always have a
nominally non-zero error term, then that
besides, the theory of potentials is
more than Laplacians (sums of partials).

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#660938

Am Samstag000001, 01.02.2025 um 10:36 schrieb Mikko:
> On 2025-02-01 08:14:08 +0000, Thomas Heger said:
> 
>> 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!)


...


TH

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#660941

Am Sonntag000002, 02.02.2025 um 07:52 schrieb Thomas Heger:
> Am Samstag000001, 01.02.2025 um 10:36 schrieb Mikko:
>> On 2025-02-01 08:14:08 +0000, Thomas Heger said:
>>
>>> 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.

∂y/∂τ= 0 would make sense for me, because that could be interpreted as:

the velocity along the y-axis is zero

(what is obviously correct).

But ∂τ/∂y would be the inverse, hence should be infinity.

TH

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#660943

On 2025-02-02 08:26:00 +0000, Thomas Heger said:

> Am Sonntag000002, 02.02.2025 um 07:52 schrieb Thomas Heger:
>> Am Samstag000001, 01.02.2025 um 10:36 schrieb Mikko:
>>> On 2025-02-01 08:14:08 +0000, Thomas Heger said:
>>> 
>>>> 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.
In that context ∂y/∂τ is irrelevat.

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

-- 
Mikko

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#660961

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

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#660969

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.

> 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.

-- 
Mikko

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#660988

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

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#661005

On 2025-02-04 07:16:57 +0000, Thomas Heger said:

> 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.

Irrelevant as Einstein defined x' when introduced it.

No need to revise my first comment about ∂τ/∂y.

-- 
Mikko

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#661010

Am Mittwoch000005, 05.02.2025 um 08:48 schrieb Mikko:
...
>>>> 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.
> 
> Irrelevant as Einstein defined x' when introduced it.
> 
Almost none of his variables were defined properly.

But Einstein wrote actually:

"If we place x'= x − vt"

'...we place ...' sounds like he meant some sort of position of 
something, which is placed there.

 From the context would fit 'position of a mirror on the x-axis of K', 
because a mirror could be placed there.

So far, so good.

But: if we place a mirror there, the equation does not fit!

This is so, because x is belonging to K, too, because it is a variable 
in Latin letters, which belong to K.

 From the context of x, we are able to assume, that the position of an 
event in K was meant with x, which has a certain x-coordinate, why x has 
a fixed value in K

But if we subtract v*t from that x, the position x' would move, while 
the placed mirror shouldn't.

So: what else was actually meant?


TH

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#660942

On 2025-02-02 06:52:34 +0000, Thomas Heger said:

> Am Samstag000001, 01.02.2025 um 10:36 schrieb Mikko:
>> On 2025-02-01 08:14:08 +0000, Thomas Heger said:
>> 
>>> 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.

-- 
Mikko

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#660960

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?


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

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#660963

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,

Of course you are, as you always do, but why? You can read German. 
Referring to an English translation as "Einstein's 'On the 
electrodynamics of moving bodies'" is little short of a lie.


-- 
Athel -- French and British, living in Marseilles for 37 years; mainly 
in England until 1987.

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#660964

Am Montag000003, 03.02.2025 um 10:02 schrieb Athel Cornish-Bowden:

>>>>>> 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,
> 
> Of course you are, as you always do, but why? You can read German. 
> Referring to an English translation as "Einstein's 'On the 
> electrodynamics of moving bodies'" is little short of a lie.
> 

.

German would be rather useless in this forum.

Sure, I can speak German. But what sense would it make to write German here?

TH

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#660965

Am Montag000003, 03.02.2025 um 10:02 schrieb Athel Cornish-Bowden:

>>>>>> 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,
> 
> Of course you are, as you always do, but why? You can read German. 
> Referring to an English translation as "Einstein's 'On the 
> electrodynamics of moving bodies'" is little short of a lie.
> 

.

German would be rather useless in this forum.

Sure, I can speak German. But what sense would it make to write German here?

TH

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