Serious mistakes in Jackson's "Classical Electrodynamics"
Eric Baird
re: Jackson's "Classical Electrodynamics"
Someone recently referred me to this book for something.
I actually quite liked the section on SR, but some of the math is a
bit dodgy.
-
The book's section on SR refers throughout to the formula
f'/f = (c-v)/c
(v being recession velocity) as being "the customary Doppler shift".
-
Not under SR it isn't. That's the shift equation normally used by
"variable-lightspeed" theories.
For SR to work properly, it needs to use the alternative
"fixed-observer" Doppler formula of
f'/f = c/(c+v)
, instead.
-
This choice of Doppler formula comes inevitably from SR's decision to
treat light-propagation as if it occurred within a stationary rigid
ether for each observer, i.e. when you treat lightspeed as being
constant for the observer, this is the Doppler formula you get for
directly-observed colinear shifts.
The full SR equation (with a Lorentz redshift) should therefore be
f'/f = root(1 - v²/c²) * c/(c + [recession velocity component])
-
This is where Jackson does a very silly thing. The book tries to
express the formula as if the stationary-emitter Doppler version were
appropriate, and instead gives the full SR equation as:
f'/f = (c - [recession velocity])/c / root(1 - v²/c²)
, in other words, it makes a "political" decision to use the wrong
Doppler formula, and achieves this by turning the whole rhs of the
equation upside down (and quietly reversing the velocity sign).
-
As an unfortunate side-effect of this boo-boo, this supposed "SR"
equation predicts that light coming from a moving object has a
transverse ***blueshift***!
<oh dear>
-
HOW IT HAPPENED?
==================
The first edition of the book quotes the formula in full, and seems to
have copied it as-is from a similarly faulty formula in Einstein's
original 1905 "electrodynamics" paper, which contains a number of
mistakes and mis-derivations. When Einstein later wrote material that
was about a "special theory" or "special principle", he was usually a
lot more careful (contrary to general belief, the 1905 paper doesn't
use the terms "special theory" &c. anywhere).
-
The second edition of the Jackson book is slightly less explicit about
the formula, and rewrites the equation in a shortened form with
stand-in greek characters, which makes the mistake less obvious.
However, it's still in there, and the section still describes the f'/f
= (c-v)/c component as "the customary Doppler shift, modified ..." [by
the Lorentz term], and still gives a transverse blueshift equation as
being "SR".
My guess is that nobody told Jackson about the errors in Einstein's
1905 paper, or referred him to Einstein's later, explicitly-SR
"corrected" stuff, and that he simply took the formula on trust
without looking at it too closely.
Einstein might be forgiven for making this sort of boo-boo in what was
his first proper paper on the subject, but there's no way that this
sort of mistake should still be cropping up in a well-known textbook
that was last revised in (the 1970's?).
-
Maybe this is the reason why I've had so many disagreements with
particle physicists about non-SR Doppler issues - perhaps some of them
are assuming that the 1905 equations and the treatment of Doppler
shifts given in Jackson are correct (they aren't).
-
=Erk=
___________________________________________________
email: 10013...@compuserve.com
web: http://ourworld.compuserve.com/homepages/eric_baird/
___________________________________________________
rsansbury
are implied later after reading your post more carefully. I recently read
about your April post on Kelly's article on the relative size of error
and data in the Hafele Keating experiment. Is that an IEE paper or do you
have the specific numbers discussed and are there other similar
experiments with space pobes? Please email
Ralph Sansbury r...@concentric.net
mburns
: Einstein might be forgiven for making this sort of boo-boo in what was
: his first proper paper on the subject, but there's no way that this
: sort of mistake should still be cropping up in a well-known textbook
: that was last revised in (the 1970's?).
: -
: =Erk=
: ___________________________________________________
: email: 10013...@compuserve.com
: web: http://ourworld.compuserve.com/homepages/eric_baird/
: ___________________________________________________
I checked your formulas for fun. So this is why Jackson is cited as an
authority for the classical consistency of magnetic monopoles.
--
Michael J. Burns http://www.indirect.com/www/mburns/
"We are such stuff "Oh brave new world,
As dreams are made on, and our little life That has such people in't!"
Is rounded with a sleep."
Jim Carr
Note that this article did not appear in the one group where it belongs,
sci.physics.relativity, because Eric put sci.relativity by mistake.
I have corrected that, and set followups to sci.physics.relativity.
-----------------------------------
10013...@compuserve.com (Eric Baird) writes:
>
>re: Jackson's "Classical Electrodynamics"
>Someone recently referred me to this book for something.
It is the definitive reference for graduate-level E+M. In what follows,
I will be refering to equations in the bilious green edition, where SR
is presented in chapter 11.
>I actually quite liked the section on SR, but some of the math is a
>bit dodgy.
Sophisticated. Jackson assumes you know a lot of mathematics and that
you can fill in the blanks. For some of the things discussed here, it
could be that the additional detail presented in "Mechanics", vol. 1 of
the Berkeley physics series, by Kittel et al could be helpful. I also
note that the key results are also given by Halliday and Resnick.
>-
>The book's section on SR refers throughout to the formula
> f'/f = (c-v)/c
>(v being recession velocity) as being "the customary Doppler shift".
I am puzzled. I could not find this anywhere in Ch. 11, let alone
"throughout" the section. There is one statement describing the first
line in eq. (11.37) with that term. Since the description of the
problem is where f' is measured by an observer in K' moving relative
to the source in K, we have a moving observer and the "customary"
non-relativistic formula is exactly that, (1 - v_o/v), in eq. (20-9b)
in Ye Olde Blue Bible (Halliday and Resnick) for recessional motion.
>-
>Not under SR it isn't. That's the shift equation normally used by
>"variable-lightspeed" theories.
Neither. It is the formula such as one uses for sound waves. Jackson
assumes this is obvious to his readers. For SR you must use the full
expression in eq. (11.37), which H+R write the same way, while Kittel
et al prefer the more symmetric sqrt{ (1-v/c) / (1+v/c) } form.
>For SR to work properly, it needs to use the alternative
>"fixed-observer" Doppler formula of
> f'/f = c/(c+v)
>, instead.
In SR, it should be clear that it does not matter if the source or
observer is moving, and you should use eq. (11.37) rather than
something as inappropriate as the non-relativistic formula here.
>-
>This choice of Doppler formula comes inevitably from SR's decision to
>treat light-propagation as if it occurred within a stationary rigid
>ether for each observer, ...
or for each source, but "as if" is not relevant to the derivation,
which is straightforward and only requires algebra, not analogies.
>-
>This is where Jackson does a very silly thing. The book tries to
>express the formula as if the stationary-emitter Doppler version were
>appropriate, and instead gives the full SR equation as:
> f'/f = (c - [recession velocity])/c / root(1 - v²/c²)
>, in other words, it makes a "political" decision to use the wrong
>Doppler formula, and achieves this by turning the whole rhs of the
>equation upside down (and quietly reversing the velocity sign).
No, Jackson does an extremely silly thing called a *derivation*.
Since he assumes a sophisticated audience, he does this by defining
the problem carefully to obtain eq. (11.35) -- and then tells you
what to do to obtain (11.36), from which (11.37) follows easily.
Since "Mechanics" was written for freshmen rather than graduate
students, somewhat more detail is given there.
>-
>As an unfortunate side-effect of this boo-boo, this supposed "SR"
>equation predicts that light coming from a moving object has a
>transverse ***blueshift***!
><oh dear>
Oh dear, indeed. This conclusion can only result from a failure
to read carefully or pay attention to which frame is doing the
observing. A careful reader will notice that eq. (11.38) is
included to make it easy to calculate the transverse doppler
shift with the observer in K', while the text makes reference
to a case where the observer is in K.
Because of the angle transformation (searchlight effect), you must be
careful to use the correct values for the frame you are in. If you
are observing from K' at 90 degrees, then cos(theta) = v/c in (11.37).
>-
>HOW IT HAPPENED?
>==================
>The first edition of the book quotes the formula in full, and seems to
>have copied it as-is
Sir, you slander J. D. Jackson when you do not take his words "we find
that" at face value. Do the derivation yourself if you doubt him. Just
waving your hands over a schematic argument by analogy will not suffice.
Further,
>from a similarly faulty formula in Einstein's
>original 1905 "electrodynamics" paper, which contains a number of
>mistakes and mis-derivations.
there are some errors in that paper, as there are in any paper that
goes through the process of review, revision, and typesetting, but
those have long since been corrected. The formula in eq. (11.37)
is not one of them. The error is in the reader's failure to be
careful when applying the equation.
>When Einstein later wrote material that
>was about a "special theory" or "special principle", he was usually a
>lot more careful (contrary to general belief, the 1905 paper doesn't
>use the terms "special theory" &c. anywhere).
At that time it was the *only* theory of relativity. The adjective
became necessary when another, more general, theory was developed.
>-
>The second edition of the Jackson book is slightly less explicit about
>the formula, and rewrites the equation in a shortened form with
>stand-in greek characters, which makes the mistake less obvious.
The new edition of Jackson uses the conventional modern notation of
beta and gamma, which should not be surprising since it only makes
sense to teach the subject in the form that it is currently used.
IMHO, the more compact notation makes it easier to see what is
going on, and much easier to do the algebra as long you you know
little details like gamma*(1-beta) = sqrt{ (1-beta) / (1+beta) }.
>Einstein might be forgiven for making this sort of boo-boo in what was
>his first proper paper on the subject, but there's no way that this
>sort of mistake should still be cropping up in a well-known textbook
>that was last revised in (the 1970's?).
A student new to the subject can be forgiven the boo-boo of not noticing
the second line in eq. (11.37), which tells you that the angle is
transformed as well as the frequency. This requires care when working
out the transverse doppler shift to be sure that everything is
evaluated in such a way that the photon was at 90 degrees in the frame
of the observer.
--
James A. Carr <j...@scri.fsu.edu> | Raw data, like raw sewage, needs
http://www.scri.fsu.edu/~jac | some processing before it can be
Supercomputer Computations Res. Inst. | spread around. The opposite is
Florida State, Tallahassee FL 32306 | true of theories. -- JAC
Joseph D Warner
In article <52nkhe$1...@juliana.sprynet.com>, 10013...@compuserve.com
says...
>
>re: Jackson's "Classical Electrodynamics"
>Someone recently referred me to this book for something.
>bit dodgy.
>The book's section on SR refers throughout to the formula
> f'/f = (c-v)/c
>(v being recession velocity) as being "the customary Doppler shift".
>Not under SR it isn't. That's the shift equation normally used by
>"variable-lightspeed" theories.
>"fixed-observer" Doppler formula of
> f'/f = c/(c+v)
>, instead.
>This choice of Doppler formula comes inevitably from SR's decision to
>treat light-propagation as if it occurred within a stationary rigid
>constant for the observer, this is the Doppler formula you get for
>directly-observed colinear shifts.
>The full SR equation (with a Lorentz redshift) should therefore be
> f'/f = root(1 - v²/c²) * c/(c + [recession velocity component])
>-
>
Well there are numerous errors in Jackson and numerous times he makes
approximations without explaining that he did. Almost all of the later
chapters of Jackson should be worked through by yourself before using the
formulas. Especially the chapters on plasmas and electromagnet wave
propagation.