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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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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Thomas Heger <ttt_heg@web.de> wrote:

I'm actually not really certain, but found an error in Einstein's 'On
the electrodynamics of moving bodies' which is quite serious.

Instead of finding imagined errors in Einstein you'd do better
learning some of the elementary ideas about infinitessimals,

Jan

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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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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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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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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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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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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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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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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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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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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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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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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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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, 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?

He obviously means the function needed to determine τ. It does not matter whether he means the function from x, y, z, t or x', y, z, t as ∂/∂y is
the same in both cases.

Einstein didn't define the used variables and simply assumed, the
reader would know anyhow, what he had in mind.

Variables are clearly defined. For example, x, y, z, and t are defined as
the coordinates of the system K.

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

Although modern mathematicians don't consider that correct, it is common
to use the same symbol for a quantity and for a function that computes
that quantity. It is obvious from the context which is meant: function
name is used with arguments, the quantity name without.

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.

Nowhere in the article is any vector called τ.

This was rather nasty, because it could lead to several errors, if you
try to interpret Einstein's intentions.

A careless reader may get a wrong idea but the target audience could
understand it.

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.

That function is a time-valued function.

You are not in the target audience of the article. Nobody still alive is. Therefore your comprehension problems are not an indication of a defect
in the article.

The article is incomplete. It only presents some core ideas. In later
articles Einstein filled gaps in the reasoning and extended to other
problems.

--
Mikko

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W dniu 03.02.2025 o 16:51, Mikko pisze:

The article is incomplete. It only presents some core ideas. In later articles Einstein filled gaps in the reasoning and extended to other problems.

Of courrse, the mumble of the idiot was not
even consistent, but why would other mysticians
care.

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Am Montag000003, 03.02.2025 um 16:51 schrieb Mikko:

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, 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?

He obviously means the function needed to determine τ. It does not matter whether he means the function from x, y, z, t or x', y, z, t as ∂/∂y is the same in both cases.

There ain't no thing as 'obviously'.

If an author doesn't write, what he has in mind, the reader is requirred
to guess. And the result of such a process is by no means 'obvious'.

Einstein used τ for three different types of mathematical objects:
a value τ (meaning: time in k)
a function τ (a coordinate transformation between K and k)
as function value τ of that function τ.

Therefor it would requirre some brains to find out, which one was
actually meant.

Correct would have been to make the type explicit, e.g. by different fonts.

But REALLY bad would be 'switching' between different uses of the same
symbol τ.

This is so, because it is absolutely NOT obvious, which meaning τ has,
if three different meanings are used.

Einstein didn't define the used variables and simply assumed, the
reader would know anyhow, what he had in mind.

Variables are clearly defined. For example, x, y, z, and t are defined as
the coordinates of the system K.

Possibly we disagree about the meaning of the term 'definition'.

For instance t is not really a coordinate in K, because K is an
Euclidean coordinate system, hence 'timeless'.

The construct actually meant is called 'frame of reference' today, which
could be understood as a coordinate system plus time measure.

Those FoRs have coordinates, too, but are not Euclidean spaces (which
Einstein wanted to use).

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

Although modern mathematicians don't consider that correct, it is common
to use the same symbol for a quantity and for a function that computes
that quantity. It is obvious from the context which is meant: function
name is used with arguments, the quantity name without.

It is really bad, to use the same symbol for different types of objects
and do not tell, which meaning was meant.

A funtion f(x), for instance, has an argument x and produces some output f(x)=y.

But 'f' is a name and belongs to the 'machinery' of the function and not
to the output, hence f != f(x).

...


TH

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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

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On 2025-02-04 07:36:34 +0000, Thomas Heger said:

Am Montag000003, 03.02.2025 um 16:51 schrieb Mikko:

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, 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?

He obviously means the function needed to determine τ. It does not matter >> whether he means the function from x, y, z, t or x', y, z, t as ∂/∂y is >> the same in both cases.

There ain't no thing as 'obviously'.

Of course there is.

If an author doesn't write, what he has in mind, the reader is
requirred to guess. And the result of such a process is by no means 'obvious'.

What the author has in mind is not relevant. Relevant is what physicists
at the time understood the text to say.

Einstein used τ for three different types of mathematical objects:
a value τ (meaning: time in k)
a function τ (a coordinate transformation between K and k)
as function value τ of that function τ.

meaning: time in k

Therefor it would requirre some brains to find out, which one was
actually meant.

It is reasonable to assume that the intended readers had brains.

Correct would have been to make the type explicit, e.g. by different fonts.

It is sufficient that the target audence can understand the emaning of the text.

Anyway, non of that is relevant to my first comment that there is
no division (and therefore no division by zero) in ∂τ/∂y.

--
Mikko

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W dniu 04.02.2025 o 10:13, Mikko pisze:

On 2025-02-04 07:36:34 +0000, Thomas Heger said:

Am Montag000003, 03.02.2025 um 16:51 schrieb Mikko:

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, 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?

He obviously means the function needed to determine τ. It does not
matter
whether he means the function from x, y, z, t or x', y, z, t as ∂/∂y is >>> the same in both cases.

There ain't no thing as 'obviously'.

Of course there is.

If an author doesn't write, what he has in mind, the reader is
requirred to guess. And the result of such a process is by no means
'obvious'.

What the author has in mind is not relevant. Relevant is what physicists
at the time understood the text to say.

Einstein used τ for three different types of mathematical objects:
a value τ (meaning: time in k)
a function τ (a coordinate transformation between K and k)
as function value τ of that function τ.

meaning: time in k

Therefor it would requirre some brains to find out, which one was
actually meant.

It is reasonable to assume that the intended readers had brains.

Correct would have been to make the type explicit, e.g. by different
fonts.

It is sufficient that the target audence can understand the emaning of the text.

Stop fucking, trash. If the audience was able to
comprehend what the idiot mumbled they would ROTFL.
It was not even consistent.

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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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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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Am Dienstag000004, 04.02.2025 um 10:13 schrieb Mikko:

On 2025-02-04 07:36:34 +0000, Thomas Heger said:

Am Montag000003, 03.02.2025 um 16:51 schrieb Mikko:

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, 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?

He obviously means the function needed to determine τ. It does not
matter
whether he means the function from x, y, z, t or x', y, z, t as ∂/∂y is >>> the same in both cases.

There ain't no thing as 'obviously'.

Of course there is.

If an author doesn't write, what he has in mind, the reader is
requirred to guess. And the result of such a process is by no means
'obvious'.

What the author has in mind is not relevant. Relevant is what physicists
at the time understood the text to say.

Well, no....

As I see it, an author tells his story and that story is his.

Therefore the author needs to say, what he wants to say and make it
clear, how he wanted to be understood.

The 'background' of current state of science isn't part of the story,
but more or less the stage, upon which the author places his piece.

It has something to say, but scientific statements are meant to be
absolute and cannot refer to 'common believes' (whatever that might be).

IOW: I cannot grant errors to former scientists, while don't do that
with current science.

Wrong is wrong and it doesn't matter, when this occurred.

Einstein used τ for three different types of mathematical objects:
a value τ (meaning: time in k)
a function τ (a coordinate transformation between K and k)
as function value τ of that function τ.

meaning: time in k

No, in this case of

∂τ/∂y= 0

the function τ was meant.

Time of system k was also called τ, but that interpretation would make ∂τ/∂y= 0 wrong.

That 'time in k' was the trap I had fallen into, hence I know how this
worked.

It made me a little angry, because I would expect from a scientific
paper, that different types of mathematical objects are distinguishable
from each other (e.g. by different fonts).


But not so in Einstein's text, where none of the variables are defined
properly and where he also switched back and forth between different types.

E.g. vectors and scalars were often used interchangeable, while that is actually an error.

For instance he wrote, that velocity of light is constant, while he
actually meant speed.

Also the same symbols were 'reused' or the same quantity was symbolized
by different variables.

Therefor it would requirre some brains to find out, which one was
actually meant.

It is reasonable to assume that the intended readers had brains.

Sure, but how much brains would you need to read Einstein's mind?

Correct would have been to make the type explicit, e.g. by different
fonts.

It is sufficient that the target audence can understand the emaning of the text.

Well, that's why it was said, that only three people in the world could understand Einstein's text.

BUT: if the author tells a story, he had to write for the reader and
allow them to estimate, at least after some thinking, what was
eventually meant.

This would require, for instance, naming conventions, which common
mortals are able to decipher.

Much better would be, if the author writes a little table, where the
names and symbols are explained.

But Einstein made understanding even more difficult than it should be by declaring certain conventions for names, but actually used other ones.

In a way the text is more or less a riddle, similar to soduko, where the
reader is supposed to fill in the gaps.

...

TH

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JanPB wrote:

On Sat, 1 Feb 2025 8:14:08 +0000, Thomas Heger wrote:

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.

Oh dear, what is it this time.

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.

Good grief. People with ZERO understanding of mathematics try to
critique Einstein's paper. Brilliant.

One HUGE difference between a genuine expert and an ignoramus is that
the expert always *knows EXACTLY the boundaries of his knowledge*.
An ignoramus OTOH always assumes he knows everything and everyone else
is stupid.

--
Jan

--

piano is mathematics, but you'll never play the piano again...


--
The Starmaker -- To question the unquestionable, ask the unaskable,
to think the unthinkable, mention the unmentionable, say the unsayable,
and challenge the unchallengeable.

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