Re: My disagreement with Weinberg's approach

From: Ken S. Tucker (dynamics_at_vianet.on.ca)
Date: 01/29/05 

Date: 29 Jan 2005 03:49:56 -0800

Tom Roberts wrote:
> Ken S. Tucker wrote:
> > Tom Roberts wrote:
> >>Weinberg "defines" vectors and tensors as collections of numbers[#]
> >> that transform in specific ways.

*No he doesn't. Show us the quote.

> > That's my problem, where is that?
>
> p35 for vector, last paragraph of p36 for tensors.

*

> > you also suggest he's confused about
> > tensors.
>
> I do not think Weinberg is confused about tensors, but his book sure
is.

Egads, I've had Mathematics Professors recommend
this book. Your spewing, please support with a
specific example, just one will do. Incidentally
those little numbers in the brackets on the
right side of the page are called equation numbers.

> > I want to know what you think.
> > In the chapter "Spaces with Maximally Symmetric Subspaces",
> > he says on pg. 404, "The beautiful new...with no use of
> > the Einstein Field Equations".
>
> That it is rather remarkable that the mere requirement that a
spacetime
> have maximally-symmetic spatial subspaces is sufficient to

Where did he specify "spatial"?

determine the
> metric, without use of the Einstein field equation. After all, that
_IS_
> what he said.

I keep asking for specifics, and you keep tossing ghosts!
Where does he say that?

> >>Weinberg also does not even mention the main property of the
metric:
> >> it defines dot products of 4-vectors.
> >
> > The metric does that but not generally,
>
> Yes, it does so, completely generally -- that's what a metric IS: a
> measure on each tangent space of the manifold. Equivalently it is an
> isomorphism between each tangent space and the corresponding
cotangent
> space of the manifold. That is the essential feature of Riemannian
geometry.

No it is not always, (although I would like to agree
it's best if defined that way), see pg 240, the Kerr
metric component g_0i, and explain how that can be
expressed as a dot product.
Personally I have issues with that metric, partly
for that reason, but that's not the point.

> > His
> > disclaimer appears sharply in "The Geometric Analogy",
> > pg.147.
>
> Weinberg's book is a prisoner of its time. On p147 he says "At one
time
> it was even hoped that the rest of physics could be brought into a
> geometric formulation, but this hope has met with disappointment
[...]".

> In fact, with the advent of the standard model, the "rest of physics"

> _HAS_ been described geometrically, as a gauge theory on a fiber
bundle
> over spacetime.

I think you misunderstand the word "analogy"
as Weinberg used it.

> >>To me, compared to MTW, Wald, and other modern textbooks, Weinberg
> >> seems quaint, outdated, and completely outclassed.
> >
> > Tom, open MTW, note the copyright date, IIRC 1972?
>
> Yes. It's remarkable that Weinberg's book was so completely
outclassed
> by a contemporary book.

That's pure BS, MTW is more comprehensive in that
it has a load of fluff to help beginners, Weinberg
is aimed at more sophisticated readers.

> > Tom, I think you're attitude toward Weinberg is
> > arrogant,
>
> I am not criticising the man, I am criticising the BOOK. And with
good
> reason. Numerous other books share this fault.

I think you are disparaging the man, if you
understood GR you wouldn't make up garbage.
It's one thing to hold an opinion, but quite
another to pronouce dismissively his work as
less than top class, even going so far as to
claim it's mathemtically incorrect without a
single example specific example or quote.

What fault, that's it's not a comic book full
of pretty little diagrams, be specific.

> Tom Roberts tjroberts@lucent.com

If Tom would support his statements with a shred
of integrity, I'd agree with him at that point.

I've crossed checked Weinberg's views with another
good text, P.G. Bergmann's "Intro ...Relativity"
1976 edition. The 1st edition has a recommendation
by Einstein. Bergmann is more advanced (IMO) than
Weinberg's but there are very few contradictions
between the two.

If anyone agrees with Tom Robert's on his accessment
of Weinberg's "Grav and Cosmo", or would like to
comment on Bergmann's text please do so.

These works are starting to become dated, but classical
GR hasn't changed alot. Would anyone please recommend
a good modern text book, that I should study, and
please not fluffy.

TIA
Ken S. Tucker

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