Weinberg's book vs undergraduate course

[davidge]

I found the Weinberg's book on General Relativity the most complete book on the fundamentals of the theory.

I would like to know (apart from laboratory clases and having a professor to guide you) what is the difference of self-learning General Relativity from that book, compared to a 4-5 years that it takes (in my country) to complete a undergraduate course on physics at uni? I mean how many knowledge one woud have at the end comparing the two cases?

I hope you understand my question as English isn't my native language.

 

[davidge]

Maybe it would be better to put my question in another way: what topics a undergraduate course covers that Weinberg's book does not cover?

 

[dextercioby]

Maybe it would be better to put my question in another way: what topics a undergraduate course covers that Weinberg's book does not cover?

Weinberg is/was no specialist in GR, nor did he ever show that he knows the true mathematical modelation of General Relativity, hence specialists in GR would rather point you to the book by Robert Wald if GR is really what you want to learn. I think a more recent book by Hartle or Carroll would better and more appropriate for a lower degree of mathematical involvement.

 

[davidge]

Thanks, dextercioby.

 

[Demystifier]

Weinberg is/was no specialist in GR, nor did he ever show that he knows the true mathematical modelation of General Relativity, hence specialists in GR would rather point you to the book by Robert Wald if GR is really what you want to learn. I think a more recent book by Hartle or Carroll would better and more appropriate for a lower degree of mathematical involvement.

Well, Weinberg's book is a very good work for a "non-specialist".

 

[vanhees71]

Hm, if Weinberg is not a specialist in GR, I don't know, whom you'd consider to be a specialist?

On the other hand, it might explain, why his book (and Landau&Lifshitz vol. II) appears to me (definitely not a specialist in GR, because I didn't research in this field) to be more readable than many other GR textbooks. It's emphasizing the physics rather than the differential geometry aspects.

 

[Demystifier]

Hm, if Weinberg is not a specialist in GR, I don't know, whom you'd consider to be a specialist?

On the other hand, it might explain, why his book (and Landau&Lifshitz vol. II) appears to me (definitely not a specialist in GR, because I didn't research in this field) to be more readable than many other GR textbooks. It's emphasizing the physics rather than the differential geometry aspects.

Perhaps Weinberg is not even a QFT expert, because his books do not exploit full mathematical rigor of functional analysis and differential geometry of gauge theories.

If that is criterion, then in some branches of theoretical physics (e.g. condensed matter QFT) experts do not exist at all.

 

[Demystifier]

Zee, in his book "Einstein Gravity in a Nutshell", is particularly sarcastic about sophisticated mathematics in general relativity. Here are some quotes from the book:

It might seem that the first approach is much more direct. One writes down (2) and that
is that. The second approach appears more roundabout and involves some “fancy math.”
It might even provoke an adherent of the first “more macho” approach to wisecrack, “Why,
with a bit of higher education, sine and cosine are not good enough for you any more? You
have to go around doing fancy math!” The point is that the second approach generalizes
to higher dimensional spaces (and to other situations) much more readily than the first
approach does, as we will see presently. Dear reader, in going through life, you would be
well advised to always separate fancy but useful math from fancy but useless math.

The set of D-by-D matrices R that satisfy these two conditions forms the simple orthogonal group SO(D),
which is just a fancy way of saying the rotation group in D-dimensional space.

Fancy people call the upper index contravariant and the lower index covariant—I can never
remember which is which. If you like big words, go for it.

I feel that it would be good for those readers seeing Riemannian geometry for the first time
to work through some “classical” differential geometry dealing with curves and surfaces,
“real” stuff that you could actually see and “hold in your hands.” Throughout this chapter,
we will be living in good old 3-dimensional Euclidean space. I am going to tell you how the
greats like Frenet and Gauss thought about curves and surfaces. None of the fancy tangent
bundle talk for us; we will just do it. Action, not talk!

Some sophisticated types favor a fancy-schmancy index-free notation.
This is analogous to the vector notation v that you are fluent with, instead of the index
notation v_i . But it takes considerable effort to learn the index-free notation, and when push comes to shove, in an
actual calculation, even a sophisticate might have to descend to indices. Besides, you have to learn to walk before
you can fly, and I think that for a first introduction to Einstein gravity, grappling with indices is an essential and
ennobling experience.

Unaccountably, some students are twisted out of shape by this trivial act of notational
sloth. “What?” they say, “There are two kinds of vectors?” Yes, fancy people speak of
contravariant vectors (p^μ for example) and covariant vectors (p_μ for example), but let
me assure the beginners that there is nothing terribly profound going on here. Just a
convenient notation.

Meanwhile, a mathematician friend of yours—could have been James Joseph Sylvester,
a rather astute fellow, since he demanded that his salary from Johns Hopkins University
be paid in gold before accepting its invitation to move from England to a scientifically
impoverished but economically upstart country called the United States—told you about
some fancy-pants math called matrix theory.

Because of general coordinate invariance, we have considerable freedom in choosing
the coordinates. This corresponds to picking a gauge in electromagnetism. At this point,
the rich man with his or her wealth of fancy terms starts talking about Killing vectors, and
possibly even foliation. We will get to all that later. But for the moment, it is pedagogically
more transparent to follow the poor man’s way,∗ using explicit nuts and bolts, wearing no
fancy pants.

You get the idea before I run out of Greek letters! As before, fancy people who like big
words call the upper indices contravariant and the lower indices covariant.

At this point, our friend the rich man could start spouting fancy talk about the covariant
derivative, presumably without writing down a single index and disdaining such “quaint
old-fashioned notions” as transformation, and thus cause our other friend the Jargon Guy
to become flush with joy. Instead, let’s be more modest and, together with our friend the
poor man, try to understand what the covariant derivative really means by working out a
simple example. Again, a tale best told through a fable.

... we see that speaking of Killing vectors is just an extra fancy way of saying
that the static isotropic metric in chapter V.4 does not depend on the coordinates t and φ.

But at the level of this book, it is
a small price to pay to avoid going into fiber bundles and other fancy mathematical topics.

No need to take a fancy course in partial differential equations!
Beginning students often snicker at this sort of getting an answer by “winging it,” compared to solving a
partial differential equation in all its glory, complete with factors of 2π and what not. But in fact, in cutting edge
research, the ability to do the former is often much more prized than the ability to do the latter. On the cutting
edge, the analog of the partial differential equation is typically not known, but the truly great theorists are often
able to grope for what they want in the dark “by the seat of their pants.”

 

[vanhees71]

Perhaps Weinberg is not even a QFT expert, because his books do not exploit full mathematical rigor of functional analysis and differential geometry of gauge theories.

If that is criterion, then in some branches of theoretical physics (e.g. condensed matter QFT) experts do not exist at all.

Well, don't cry. Feynman was proud of being not "an expert", and he had a point!

 

[martinbn]

I also don't like Zee's book.

 

[vanhees71]

Why? I'm prejudiced against Zee since I've seen his QFT book. Is the GR book as bad?

 

[dextercioby]

It's funny how A. Zee wrote that passage in his GR book against "fancy mathematics", however, just at the same time, he was writing a book on group theory for physicists. True, the mathematical level of his group theory book is not like Barut & Raczka, but nonetheless it's funny how he advocates for the proper math methods in physics, but not "fancy ones".

OTOH, Weinberg's QFT book has some advanced group theory results in his chapter 2, but discarding differential geometry in his GR text would still be be a no-no in my book.

 

[martinbn]

Why? I'm prejudiced against Zee since I've seen his QFT book. Is the GR book as bad?

I didn't say it was bad. I said I didn't like it.

 

[Daverz]

Why? I'm prejudiced against Zee since I've seen his QFT book. Is the GR book as bad?

I think Zee's GR book is much better than his QFT book, which seemed too handwavy to me.

 

[atyy]

Weinberg is/was no specialist in GR, nor did he ever show that he knows the true mathematical modelation of General Relativity, hence specialists in GR would rather point you to the book by Robert Wald if GR is really what you want to learn. I think a more recent book by Hartle or Carroll would better and more appropriate for a lower degree of mathematical involvement.

It's funny how A. Zee wrote that passage in his GR book against "fancy mathematics", however, just at the same time, he was writing a book on group theory for physicists. True, the mathematical level of his group theory book is not like Barut & Raczka, but nonetheless it's funny how he advocates for the proper math methods in physics, but not "fancy ones".

OTOH, Weinberg's QFT book has some advanced group theory results in his chapter 2, but discarding differential geometry in his GR text would still be be a no-no in my book.

Do you like Wald's coordinate-dependent tensors?

 

[dextercioby]

I like all tensors, as soon as one first explains what a manifold is, what a tangent space is, what a cotangent space is, etc. Coordinates or not it won't matter, as soon as the math is right.

 

[Demystifier]

Someone should open a thread "Theoretical Physics vs Mathematical Physics".
Or perhaps "Physics First vs Math First".

 

[Demystifier]

I like all tensors, as soon as one first explains what a manifold is, what a tangent space is, what a cotangent space is, etc. Coordinates or not it won't matter, as soon as the math is right.

Do you like Christoffel symbols? Or would you prefer to avoid them whenever possible?

 

[Demystifier]

I think Zee's GR book is much better than his QFT book, which seemed too handwavy to me.

I like them both, but for different reasons. The styles of writing are very different, as if they were not written by the same person.

 

[vanhees71]

We are talking about

https://www.amazon.com/dp/069114558X/?tag=pfamazon01-20

and

https://www.amazon.com/dp/0691140340/?tag=pfamazon01-20

I always thouth there's only one Anthony Zee around.

 

[Demystifier]

Feynman was proud of being not "an expert", and he had a point!

You mean, because it helped him to look at things from new perspectives? That's why one should often change the research area and try to publish something new in the area before learning everything old.

 

[Demystifier]

I always thouth there's only one Anthony Zee around.

People evolve, they are never the same as they used to be.

 

[martinbn]

Do you like Wald's coordinate-dependent tensors?

There are no coordinate dependent tensors, neither in Wald's book nor anywhere else. Tensors are independent of coordinates. Perhaps you mean something else? That he uses coordinates or that he uses abstract index notation or ...

 

[Demystifier]

There are no coordinate dependent tensors, neither in Wald's book nor anywhere else. Tensors are independent of coordinates. Perhaps you mean something else? That he uses coordinates or that he uses abstract index notation or ...

Wald is quite unique by distinguishing $T^{\mu\nu...}$ from $T^{ab...}$. The former represents tensor components (which is quite a standard notation) while the latter represents the tensor itself (in a rather non-standard notation).

 

[George Jones]

I always thouth there's only one Anthony Zee around.

His operator doesn't commute with the Hamiltonian of his system.

measured value --> time evolution --> different measured value --> ...

 

[martinbn]

That's the abstract index notation. I thought it was standard.

 

[atyy]

There are no coordinate dependent tensors, neither in Wald's book nor anywhere else. Tensors are independent of coordinates. Perhaps you mean something else? That he uses coordinates or that he uses abstract index notation or ...

Wald considers Christoffel symbols to be coordinate-dependent tensors. See his comments between 3.1.15 and 3.1.16 on p34.

 

[martinbn]

Wald considers Christoffel symbols to be coordinate-dependent tensors. See his comments between 3.1.15 and 3.1.16 on p34.

Hahaha!

 

[smodak]

Why? I'm prejudiced against Zee since I've seen his QFT book. Is the GR book as bad?

The GR book is Fantastic.