Gravity in a Nutshell is too chatty, would like something else

[pat65]

Hello All,

I recently purchased a book on relativity called "Gravity in a Nutshell" by Zee. While it is interesting I find his conversational style to be too chatty. I prefer a little more of a "get to the point" conversational style.

I'm going to be modeling the evolution of the gravitational field of an object with mass as the velocity difference between two frames of reference approaches infinity. The initial conditions will vary, so maybe a point mass without charge and then getting more complicated from there. I will be starting from Einstein's field equations.

So, I need a book that is advanced enough to allow me to do this. I do prefer books that have explicit examples of working through the math involved. I have an undergraduate degree in physics and am quite comfortable with fairly advanced levels of calculus, linear algebra, and differential equations. However, with that said, I have no doubt I will be learning quite a bit of math and physics with this project.

I was warned by some that Zee's style was quite chatty but many people recommended the book so I went with it, but now I see why I was warned. I mean, a little chatty is OK because I don't like really dry conversational styles either, but Zee is too much.

Anyway, any helpful suggestions for an appropriate book would be greatly appreciated.

Thanks,
Pat

 

[Daverz]

I would suggest doing in search in the book section as GR books have been covered extensively here.

Hartle's Gravity is my usual recommendation for a first pass, but his approach deemphasizes Riemannian geometry at first, so I'm not sure it will help you with your project.

Perhaps Sean Carroll's Spacetime And Geometry, then, as he's reasonably succinct.

There are cheap paperback editions of both books, but I don't know anything about the quality of the paper or print of those.

Hopefully you can give Zee another try when you can appreciate his digressions a bit more.

 

[pat65]

Hopefully you can give Zee another try when you can appreciate his digressions a bit more.

No, no, please don't get me wrong. I understand, his "digressions" are interesting and I do appreciate them. But, I have always been somewhat "flat" or "to the point". My brain just seems to work that way. When I read texts that deviate too much from the subject, I tend to get "lost" and find it difficult to keep things straight in my head. It's not matter of "not appreciating" things, it's a matter of delving into a very complex subject and needing to keep things straight in my head. When an author deviates too much or too often, I find this difficult.

For this reason I like textbooks to be for the most part, on point. If I want to read a colorful expose on something then I will do that, but when I am learning, I dislike that. I find the exact same thing when I read news articles. Some news articles are like reading a story book. They go into all this unnecessary stuff and what they say in five long paragraphs could be reduced to one fairly short paragraph. I can't stand news articles like that and I won't read them. I am similar, although not as extreme, when it comes to textbooks.

Yes, now I remember, Hartle and Sean Carroll. I remember them now. Thanks for the suggestions. Also, I wanted specific suggestions given my task which is why I posted.

...But I would also add, if you have ever tutored, then you must know that different people learn and take in new information in different ways. When I tutored I always tried to understand how the pupil thinks and then mold my approach to them. I was quite successful at this and had a high success rate with my pupils. I certainly would never put them down or make them feel inferior because they had a certain way of taking in new information. Anyway, if you have tutored (or taught), I am sure you know this already.

Thanks again!

 

[robphy]

http://www.minkowskiinstitute.org/mip/books/geroch-gr.html

https://www.amazon.com/dp/0987987178/?tag=pfamazon01-20

 

[Demystifier]

I'm going to be modeling the evolution of the gravitational field of an object with mass as the velocity difference between two frames of reference approaches infinity.

How can relative velocity between two frames be larger than $c$?

 

[Demystifier]

I prefer a little more of a "get to the point" conversational style.

Perhaps the most get-to-the-point book on GR is P.A.M. Dirac, General Theory of Relativity. Almost all one needs to know about GR is explained in a book which is only 70 pages long.

 

[pat65]

How can relative velocity between two frames be larger than cc?

WHOOPS! You are correct! LOL, I was doing some meteoroid impact energy calculations yesterday. KE was swimming around in my head. I meant, as the velocity difference approaches c.

Perhaps the most get-to-the-point book on GR is P.A.M. Dirac, General Theory of Relativity. Almost all one needs to know about GR is explained in a book which is only 70 pages long.

70 pages?! Wow, now that is getting to the point. Thanks for the suggestion.

http://www.minkowskiinstitute.org/mip/books/geroch-gr.html

https://www.amazon.com/dp/0987987178/?tag=pfamazon01-20

These look quite good, thank you.

 

[vanhees71]

Well, maybe also

Weinberg, Gravitation and Cosmology (1971) (the cosmology is largely outdated, but the GR part is among the best expositions ever written)

Landau and Lifshitz vol. 2 (Classical Field Theory) (among the best treatment of microscopic classical electrodynamics in a modern (i.e., relativistic from the start) way and GR without much ado about nothing)

 

[romsofia]

Honestly, I think you're better off going straight to numerical relativity for your project. You don't need to know EVERYTHING about GR to set up a model, and see how it evolves. You just need to know how to set it up. Unless you're trying to do this by hand, well, then you'll need to know the nitty and gritty of GR and I'd go with Wald because it is probably the best book on the subject of GR if you're wanting to know the nitty and gritty of it. But, my gut says this is a numerical project.

Actually, I'd be surprised on how you'd do this analytically, so if you do end up doing, be sure to share your work here!

If you have the basics of GR down, go for Numerical Relativity by Shapiro (https://www.amazon.com/dp/052151407X/?tag=pfamazon01-20)

And even if you *don't* have the basics down, like I said, this sounds like a numerical project, and I'd get this book, start on the project, and fill in the GR on the way.

 

[phyzguy]

Do you have just one mass and you want to know the curvature in a frame moving at constant velocity with respect to that mass? Then all you need to do is solve for the curvature in the rest frame of the mass, then transform to the moving frame. Or are you considering something more complicated?

 

[pat65]

Well, maybe also

Lol. If you are referring to what I have said then ya, I agree. It depends on how familiar I am with the subject. If I have some familiarity then I can enjoy digressions. If I am not too familiar and it is a subject that takes some serious thinking then I prefer books to be on point. Since I have never had a course specifically on GR or really have never studied GR specifically at all, I want something on point. I will achieve my ends better that way. Thanks the suggestions. Is Weinberg, Gravitation and Cosmology the "Bible" on GR that I have heard about? Someone said (jokingly) that it could be used as a boat anchor as it is so large and heavy but (not jokingly) that it is also an indispensable reference for GR.

Actually, I'd be surprised on how you'd do this analytically, so if you do end up doing, be sure to share your work here!

I would not mind doing that. I do these projects to learn physics and keep me "sharp" concerning physics and math. I am not in school and not employed as a physicist but I do R&D engineering (although proof of concept so lots of physics involved) and I find that it just keeps me sharp and thinking well. So... for this reason this is not just a numerical project. I want to learn GR and get into the mathematical machinery. It will be hard but fun! But ya, if I create something worth showing I will look into posting some of the results here.

Do you have just one mass and you want to know the curvature in a frame moving at constant velocity with respect to that mass? Then all you need to do is solve for the curvature in the rest frame of the mass, then transform to the moving frame. Or are you considering something more complicated?

It will be a simulation program that allows the user to input certain parameters and then shows the gravitational evolution of a mass as the velocity difference between two frames approaches c. The user will be in one frame and the mass will be in the other. So examples of the user adjustable parameters are whether it is a point mass or not and does it have charge or not. These kinds of things. I will start simple with just a point mass, no charge. To be honest I do not know if this will show anything interesting or not. I just wanted to see and visualize for myself what is happening to space as I find it hugely interesting that adding energy to something modifies space (and time). Not exactly headline news, I know, since it has been over 100 years since Einstein introduced his theories on Relativity but still very interesting nonetheless. I have no doubt that my understanding of all this will increase greatly. Thanks for the heads up on what may need to be done (solving then transforming). You'll see me around asking questions once I get into things.Thanks for all the help Everyone, I do appreciate it!

 

[vanhees71]

Lol. If you are referring to what I have said then ya, I agree. It depends on how familiar I am with the subject. If I have some familiarity then I can enjoy digressions. If I am not too familiar and it is a subject that takes some serious thinking then I prefer books to be on point. Since I have never had a course specifically on GR or really have never studied GR specifically at all, I want something on point. I will achieve my ends better that way. Thanks the suggestions. Is Weinberg, Gravitation and Cosmology the "Bible" on GR that I have heard about? Someone said (jokingly) that it could be used as a boat anchor as it is so large and heavy but (not jokingly) that it is also an indispensable reference for GR.

This sounds more like Misner, Thorne and Wheeler (aka "The Phone Book"), which makes gravity intuitive by its sheer weight ;-)). It's one of the most brillant books on the subject, not only concerning the physics but also didactically, but it's the opposite of what you want. It's comprehensive and comes in "two tracks", and it's easy to get lost. That's why I recommended Weinberg (which I like, because it's not overemphasizing the geometric interpretation of gravity but the physics of gravitation as a field) and Landau+Lifshitz vol. 2 (which I like because it's minimally sufficient, i.e., it contains the necessary math and emphasizes the physics arguments without any digressions whatsoever).

 

[martinbn]

Weinberg, Gravitation and Cosmology (1971) (the cosmology is largely outdated, but the GR part is among the best expositions ever written)

That opinion is not shared by everyone.

 

[vanhees71]

Why not? Is there anything wrong with Weinberg's exposition of the theory or is it just the didactics and his sometimes unusual notation?

 

[Daverz]

If it didn't have the name Weinberg on it, would anyone still recommend it?

 

[Demystifier]

That opinion is not shared by everyone.

No opinion, about anything, is shared by everyone. But you probably wanted to say that he should add an "in my opinion" clause because being "one of the best expositions" is a very subjective property.

That being said, I would add that I also like Weinberg's Gravitation and Cosmology very much. And it's not only because it's written by Weinberg, because, for instance, I don't like that much his QFT books.

 

[Demystifier]

If it didn't have the name Weinberg on it, would anyone still recommend it?

I would.

 

[Demystifier]

Why not? Is there anything wrong with Weinberg's exposition of the theory or is it just the didactics and his sometimes unusual notation?

Martinbn is a mathematician, so he prefers Wald over Weinberg.

 

[martinbn]

No opinion, about anything, is shared by everyone. But you probably wanted to say that he should add an "in my opinion" clause because being "one of the best expositions" is a very subjective property.

Yes.

That being said, I would add that I also like Weinberg's Gravitation and Cosmology very much. And it's not only because it's written by Weinberg, because, for instance, I don't like that much his QFT books.

It seems that many physicists like it, in particular particle physicists. But are there any relativists that think it is the best ever written or even just liking it.

 

[Demystifier]

It seems that many physicists like it, in particular particle physicists. But are there any relativists that think it is the best ever written or even just liking it.

Good point! Relativists probably don't like Weinberg's book that much.

I think that both perspectives (particle physics and relativity/geometry), as two complementary perspectives, need to be understood for a complete physical picture. For instance, when one looks at things only from a particle-physics perspective one may arrive at wrong conclusions, as I noted recently in https://arxiv.org/abs/1802.04025 . (In fact, I think that also a third perspective - the condensed-matter perspective - is needed, but that's another, more controversial, story.)

 

[vanhees71]

If it didn't have the name Weinberg on it, would anyone still recommend it?

Yes, I would. I think it's a pretty good treatment of the fundamentals of GR. More than 40 years old and given the great progress in the field, it's naturally outdated concerning cosmology.

 

[vanhees71]

Martinbn is a mathematician, so he prefers Wald over Weinberg.

Well, I like mathematics too, but mathematicians tend to overemphasize (differential) geometry over physics. I like to think in terms of fields rather than curved 4D spaces, but that's also only a matter of taste. I don't know Wald well enough to compare it to Weinberg's book. So I can't say, whether I like the one or the other more.

 

[robphy]

I think the various texts each have their strengths, depending on what you want to get out of it.

Unlike typical relativity texts that (say) treat the classical tests of GR and aspects of cosmology as field equations (nonlinear coupled partial differential equations) to be solved,
relativity texts by relativists also treat aspects of causal structure, measurement (what can be measured and how to measure it), and geometry (...not just spacetime geometry, but geometry of fields, geometry of the space of solutions, foundational issues [which might suggest how to approach quantum gravity], etc...).

 

[Demystifier]

relativity texts by relativists also treat ... measurement (what can be measured and how to measure it), ...

Are you suggesting that non-relativists don't discuss so much what can be measured? Or perhaps you wanted to say that relativists study how to mathematically define diffeomorphism-invariant observables?

If you meant the former, then I strongly disagree. If you meant the latter, then I would agree but add that it has more to do with mathematical nit-picking than with actual measurements.

 

[vanhees71]

What are non-relativists? Are there any of such dinosaurs left in the physics community? Hard to believe...

 

[martinbn]

What are non-relativists? Are there any of such dinosaurs left in the physics community? Hard to believe...

By relativists I meant people whose subfield of expertise is relativity. Of course every physicists has studied relativity to a degree (even if it has been from a text that was not good, you know which text I mean ).

 

[robphy]

Are you suggesting that non-relativists don't discuss so much what can be measured? Or perhaps you wanted to say that relativists study how to mathematically define diffeomorphism-invariant observables?

If you meant the former, then I strongly disagree. If you meant the latter, then I would agree but add that it has more to do with mathematical nit-picking than with actual measurements.

I was thinking more about the what could be called the "theory of measurement"...
what would observers in different states of motion (e.g. inertial, uniformly accelerating, rotating, general motion) measure?
What measuring devices (in principle) would an experimental setup require?
(For example, how would I measure the components of the Riemann tensor?
What would a particular component mean to our observer of interest?)
["What actual device with current technology that is needed for a precision measurement" is a different story, but would have presumably been guided by the preceding question.]
As examples, I'm referring to issues like "what is the theory [the principles] behind..."
"how GPS works", "how we measure a gravitational wave", "how we do numerical calculations of black hole collisions", "what actually happens at the event horizon", etc...
"...and how do we know that we aren't possibly being fooled by (say) choice-of-coordinate effects"

I'm saying that these issues (among the others I listed earlier) are more likely treated/mentioned/discussed in relativity texts written by relativists.

 

[Demystifier]

By relativists I meant people whose subfield of expertise is relativity. Of course every physicists has studied relativity to a degree (even if it has been from a text that was not good, you know which text I mean ).

What would you think about the corresponding analogy between the major branches of physics and math?
classical mechanics - analysis
relativity - geometry and topology
quantum physics - algebra
interpretations of QM - logic and set theory
statistical physics - probability and statistics
XXX - number theory

Any idea for the XXX?

 

[vanhees71]

I've no clue what XXX might be, but I object against relativity - geometry and topology. It's also mostly multivariable analysis (classical part) and functional analysis (quantum part). I'd say all of physics has a strong relation to geometry and topology, particularly in the sense of Klein's Erlangen program, i.e., in terms of its relation to group theory. In some sense most of the physical essence of modern physics since Einstein and Noether is applied (Lie-)group theory (symmetries).

 

[martinbn]

What would you think about the corresponding analogy between the major branches of physics and math?
classical mechanics - analysis
relativity - geometry and topology
quantum physics - algebra
interpretations of QM - logic and set theory
statistical physics - probability and statistics
XXX - number theory

Any idea for the XXX?

But there is geometry in classical mechanics, and analysis/PDE in relativity and functional analysis in QM. So i am not convinced about this correspondence to begin with. On the other hand there "shouldn't" be any XXX. Number theory is pure and without any analogy in physics.

 

[vanhees71]

I took the table rather as what math is applied in which subarea of (theoretical) physics. I've also no idea, where number-theoretical methods are used in physics, but one should never think one doesn't need a specific mathematical subject ever in physics. Usually it's according to Murphy's Law: Whenever you hit a problem in theoretical physics you exactly need math you don't know about ;-)). That's why it is so important to have a good education in mathematical methods to be able to learn the math you may need in some problem but you don't know yet.

 

[Demystifier]

But there is geometry in classical mechanics, and analysis/PDE in relativity and functional analysis in QM.

Just as there is analysis in differential geometry/topology, or algebra in algebraic geometry/topology, or relativity in QM, or ... Nobody said that there is no overlap between different branches. The analogies should correspond to the typical styles of thinking within certain branches. For instance, I matched interpretations of QM with logic and set theory because those are the most philosophical branches of physics/mathematics.

Personally, I find it most difficult to think like a number theorist, which may be related to the fact that it is hard to associate it with anything in physics.

 

[vanhees71]

I'd match "interpretations of QM" with esoterics and non-scientific approaches to realtity. SCNR.

 

[Daverz]

I lost my copy of Weinberg in a move. Were there more insights and better exposition that in any texts written in the 45 years since? Wondering if I should look for a new copy.

 

[Demystifier]

I'd match "interpretations of QM" with esoterics and non-scientific approaches to realtity. SCNR.

Well, perhaps some mathematicians have similar feelings about set theory. If you have ever been reading about the theory of infinite ordinal numbers, you will probably know what I am talking about.
Indeed, the famous mathematician Poincare considered such mathematical constructs totally meaningless.