Post by Paul B. AndersenPost by Thomas HegerPost by Thomas HegerPost by Paul B. AndersenCan you quote the sentence in question?
page 22, roughly in the middle
"We will now determine the kinetic energy of the electron. If an
electron moves from rest at the origin of co-ordinates of the system K
along the axis of X under the action of an electrostatic force X, ..."
Is this your translation? Is "the axis of X" what is normally called the
x-axis in English? Maybe you could quote it in German so that someone
who knows more German than I do can comment. Anyway, I agree that
calling the abscissa axis the x-axis is not ideal, but it's very
commonly done. In that case X is not a variable.
I'm actually critizising a certain text, not the work of Einstein per se.
So, my topic is this particular English translation.
"But Einstein gave this another kick and used the same symbol
twice with different meanings within a single sentence."
Einstein didn't use X as the name of the X-axis in ยง10,
he called it the X-Axis.
In the translation is the phrase "the axis of X" is used so
the axis was NOT called X.
The names of the axes in k were defined in ยง 3 page 8 in the footnote
with the dagger.
quote:
"Editorโs note: In Einsteinโs original paper, the symbols (ฮ, H, Z)
for the co-ordinates of the moving system k were introduced without
explicitly de๏ฌning them. In the 1923 English translation, (X, Y, Z) were
used, creating an ambiguity between X co-ordinates in the ๏ฌxed system K
and the parallel axis in moving system k. Here and in subsequent
references we use ฮ when referring to the axis of system k along which
the system is translating with respect to K. "
As I am writing about this translation, I use this footnote as defintion.
This means:
the axes have names, which consist of single large letters (Latin in
case of system K and Greek in case of system k)
the coordinates have also names, but with small letters.
Now:
'x-axis' is correct
'X' is also a valid name of the same x-axis.
But "Let the axes of X of the two systems coincide, ..." is wrong.
(from ยง 3, first paragraph)
This is so, because his definitions require Greek letters for the x-axis
of system k.
But Einstein didn't use his own definitions and ocasionally called the
x-axis of k 'X', while it had to be 'Xsi'.
This is no big deal, of course, but still wrong.
It was also very annoying for the reader (me in this case), because I
had to marter my brain, if I wanted to find out, to which system a
certain variable should actually belong.
It is therefore a serious error, if the relation to the meant system is
not properly defined, because the main point of relativity is the
relation between systems moving in respect to each other.
This would require a proper assignement of any used variable to one of
these systems.
And that in turn would not allow any wrong variable names.
TH
Post by Paul B. Andersen"If an electron moves from rest at the origin of
co-ordinates of the system K along X under the action of
an electrostatic force X .."
The sentence wouldn't even have made sense if X had been used
as name of the X-Axis.
X is explicitly defined to be an "electrostatic force"
Since you have thoroughly scrutinized the text and failed to find
an example of "use of the same symbol twice with different meanings
within a single sentence", we can conclude that no such example exists.
Well done, and don't try to flee from the fact.
Post by Thomas HegerI also didn't want to discuss relativity per se or the validity of the
pyhsical content of this paper.
It's pointless, anyhow, because a paper with 400+ errors in it could
hardly be used for anything of practical value.
It's rather 400+ cases of your failure to understand the text.
Let's review some of the alleged errors.
"Einstein's variable names were EXTREMELY annoying!
"He had eight different uses of the letter 'A'."
#1: as name of a point in space
#2: as name of the local time at point A as 'A-time'
#3: for one end of a flying rod
#4: as index of the time value t_A
#5: as area
#6: in 'electric power of deflection' A_e
#7: in 'magnetic power of deflection' A_m
#8: as (only!) internal reference 'A'
This is actually too stupid to comment, but since
you are too ignorant to understand how stupid it is,
#1: Right.
In ยง1 the symbol 'A' is explicitly defined: "the point A of space",
and this is the only meaning of 'A' in ยง1 to and including ยง5.
#2: "Einstein uses the symbol 'A' to mean 'A-time'" doesn't make sense.
#3: A is the name of the spatial point where one end of the rod
is positioned.
#4: "Einstein uses the symbol 'A' to mean 't_A'" :-D
Doesn't make sense.
#5: 'A' is never used as area in this paper.
#6: "Einstein uses the symbol 'A' to mean 'A_e'" :-D
#7: "Einstein uses the symbol 'A' to mean 'A_m'" :-D
However,
"we call the amplitude of the electric or magnetic force A"
and this is the only meaning of 'A' in ยง7 to and including ยง10.
#8: "Einstein uses the symbol 'A' to mean (A) " :-D
The symbol for numbering of equations '(A)' is not
equal to the symbol 'A', like the symbol '(1)' is not
equal to the symbol '1'.
So there are only two different meanings of 'A' in the paper.
In ยง1 to and including ยง5 'A' is a point in space.
In ยง7 to and including ยง10 'A' is the amplitude of
the electric or magnetic force.