Re: Jackson Question

Sue... wrote:
Edward Green wrote:
Sue... wrote:

<...>

To be critical about how formalism represents phenomena,
you need several several points of view. Not just rote
manipulation of symbols.

Fine mom and apple pie sentiment. Now, the question involved some
aspects of tensorial definition and manipulation in reference to
multipoles, if I understand it correctly.

You understand only a piece of it then.

No doubt... since I have not worked through the problem, and have so
far been spared the aching general insights that await those who have.
At issue is not my understanding, but yours: you implicitly allege
profound understanding, which you drop tantalizing hints of, but I have
my doubts there is anything behind the curtain.

<...>

If you don't like my references then try Timo's:
M.E. Rose, Elementary theory of angular momentum, Dover, gives a
reasonably thorough coverage of irreducible tensors and their point.

I have no doubt it too will still say:

<<A Lorentz transformation or any other coordinate
transformation will convert electric or magnetic
fields into mixtures of electric and magnetic fields,
but no transformation mixes them with the
gravitational field. >>
http://www.aip.org/pt/vol-58/iss-11/p31.html

Let's put that in context (I'll steal your quoting convention):

<<Even before Klein's work, Einstein had started on a different
approach, based on a simple bit of counting. If you give up the
condition that the 4 × 4 metric tensor should be symmetric, then it
will have 16 rather than 10 independent components, and the extra 6
components will have the right properties to be identified with the
electric and magnetic fields. Equivalently, one can assume that the
metric is complex, but Hermitian. The trouble with this idea, as
Einstein became painfully aware, is that there really is nothing in it
that ties the 6 components of the electric and magnetic fields to the
10 components of the ordinary metric tensor that describes gravitation,
other than that one is using the same letter of the alphabet for all
these fields. **A Lorentz transformation or any other coordinate
transformation will convert electric or magnetic fields into mixtures
of electric and magnetic fields, but no transformation mixes them with
the gravitational field.** This purely formal approach, unlike the
Kaluza-Klein idea, has left no significant trace in current research.
The faith in mathematics as a source of physical inspiration, which had
served Einstein so well in his development of general relativity, was
now betraying him.>>

<emphasis added>

Actually... I was wrong. This quote is not about ideas for extending
GR via extra dimensions; it's about extending GR by dropping a
constraint on the existing metric tensor. This attempt suffers from
a defect, Weinberg says, that the electromagnetic and gravitational
components don't talk to each other -- this is the quote. I've found
you out: I've actually looked at your quote in context. You can't
explain how this is relevant to the question, though you will no doubt
drops continued hints of a profound connection.

The quoted passage however _is_ fascinating -- it's one of those "too
profound a conincidence to be altogether a coincidence, even if we
don't altogether understand what it means" things. Like the
relativisitically correct behavior of deBroglie waves. You drop a
constraint from GR, and you get EM riding along for free, as an
inevitable consequence? Wow.

You are well read in web-science, and have excellent taste in quotes.
But instead of suggesting you are answering questions, why not just
call them "Sue's web picks"? Or just present your choices as topics
for discussion -- they are all good.

.

Relevant Pages

  • Re: Jackson Question
    ... <<A Lorentz transformation or any other coordinate ... fields into mixtures of electric and magnetic fields, ... 10 components of the ordinary metric tensor that describes gravitation, ... components don't talk to each other -- this is the quote. ...
    (sci.physics)
  • Re: Jackson Question
    ... transformation will convert electric or magnetic ... fields into mixtures of electric and magnetic fields, ... but no transformation mixes them with the ... gravitational field. ...
    (sci.physics)
  • Re: GR1916, available online.
    ... is just pure nonsense. ... One from Electromagnetics which is well founded and ... <<A Lorentz transformation or any other coordinate ... electric and magnetic fields to the 10 components of the ordinary ...
    (sci.physics.relativity)
  • Re: SR theory is simplistic
    ... It DOES postulate that all the laws of physics are identical in every ... transformation will convert electric or magnetic ... fields into mixtures of electric and magnetic fields, ... If Maxwell's time dependent equations are among the laws of physics ...
    (sci.physics.relativity)