Adler's New Book on Relativity: Misprint on Page 16?

[mpresic3]

TL;DR Summary

Misprint in Adler's new book on general relativity; relativity

I bought a copy of Adler's new book on relativity. Is there a misprint on page 16 regarding the Lorentz metric = diag (-1,-1,-1,-1) or am I missing something? The text itself after the equation suggests it is the same metric as on the earlier page so that index placement, two lower indices vs two upper indices is irrelevant to the form of the matrix?

It seems that rather than including an "errata" that includes solution to the exercises, someone could include an errata regarding misprints.

 

[malawi_glenn]

Is this the book you are referring to?
https://link.springer.com/book/10.1007/978-3-030-61574-1

And it is this chapter you are referring to as "errata"?

 

[Ibix]

Difficult to tell without the text. Reproducing a small portion for criticism or comment is regarded as "fair use" in copyright law everywhere, as far as I know, so posting a photo of the offending half page should be fine.

Did you mean the Minkowski metric, usually written $\eta_{ab}$, which is either $\mathrm{diag}(+1,-1,-1,-1)$ or $\mathrm{diag}(-1,+1,+1,+1)$? Then what you've written is misprint, unless he's got into raising and lowering indices and is noting that $\eta^a{}_b=\mathrm{diag}(1,1,1,1)$.

 

[malawi_glenn]

Here is the page from Google Books

and here is the "earlier" page

 

[mpresic3]

Thanks, Malawi_Glenn. It certainly looks like a misprint.

 

[Ibix]

Then yes, it's a misprint (my point about $\eta^a{}_b$ is 2.13, although he uses $g$).

I'd not heard the Minkowski metric referred to as the Lorentz metric before.

 

[malawi_glenn]

Thanks, Malawi_Glenn. It certainly looks like a misprint.

You can always e-mail the publisher and ask them to supply an errata online.

I'd not heard the Minkowski metric referred to as the Lorentz metric before.

https://en.wikipedia.org/wiki/Minkowski_space
More terminology (but not more structure): The Minkowski metric is a pseudo-Riemannian metric, more specifically, a Lorentzian metric, even more specifically, the Lorentz metric, reserved for 4-dimensional flat spacetime with the remaining ambiguity only being the signature convention.

https://en.wikipedia.org/wiki/Pseudo-Riemannian_manifold#Lorentzian_manifold
A Lorentzian manifold is an important special case of a pseudo-Riemannian manifold in which the signature of the metric is (1, n−1) (equivalently, (n−1, 1); see Sign convention). Such metrics are called Lorentzian metrics.

 

[Ibix]

You can always e-mail the publisher and ask them to supply an errata online.

https://en.wikipedia.org/wiki/Minkowski_space
More terminology (but not more structure): The Minkowski metric is a pseudo-Riemannian metric, more specifically, a Lorentzian metric, even more specifically, the Lorentz metric, reserved for 4-dimensional flat spacetime with the remaining ambiguity only being the signature convention.

https://en.wikipedia.org/wiki/Pseudo-Riemannian_manifold#Lorentzian_manifold
A Lorentzian manifold is an important special case of a pseudo-Riemannian manifold in which the signature of the metric is (1, n−1) (equivalently, (n−1, 1); see Sign convention). Such metrics are called Lorentzian metrics.

I knew every word of that except that the Minkowski metric gets called the Lorentz metric. It makes sense - its Lorentzian signature is manifest - but I don't recall coming across it before.

 

[mpresic3]

Adler, Bazin and Schiffers wrote an earlier book on general relativity in 1965, that seems to define diag(1,-1,-1,-1) as the Lorentz metric. He appears to break with this convention these days. The newer book discusses the "east coast" vs "west coast" convention regarding the overall sign of the metric. How interesting?

 

[Ibix]

I think one is more convenient than the other depending on what you are doing - you have to have fewer modulus signs. I typically prefer +--- because I like my four velocities to have positive modulus-squared and positive energies, but I don't think it matters much. You do have to watch very carefully for things where the sign matters and make sure you know what convention is in use.

 

[vanhees71]

It's an obvious typo as becomes clear from the rest of the conventions used in the book. I'd also call this the Minkowski metric. But usually one calls the general-relativistic spacetime pseudo-Riemannian manifold also a Lorentzian manifold, i.e., a differentiable manifold with a fundamental form with signature (1,3) (as in this book or equivalently of signature) and the unique metric-compatible torsion free affine connection (Levi-Civita connection) a Lorentzian manifold.

 

[mpresic3]

I came across what I believe to be yet another misprint, concerning equation 4-16 on page 39. Equation 4-14 applies to contravariant components, as stated. But the entire point of equation 4-16, seems to be that this equation applies to covariant components, not contravariant components as stated. I hate to see so many misprints in a textbook. I think it is a good thing I am not learning this for the first time. On the other hand, maybe students will attend professors's office hours to hash these details out.

 

[malawi_glenn]

On this page you can find the e-mail to the author https://link.springer.com/chapter/10.1007/978-3-030-61574-1_20

 

[mpresic3]

The link you provided is valuable in that it has solutions to the exercises. Thank you for providing the link.

I tried another link and got a pop-up box to add an account to outlook, or something of that nature. I do not have outlook on my computer. The pop-up box had an old address that I have not used in 10 years. Does Adler have an E-mail address as the corresponding author rather than a link, so I can use google email?

Can an expert or fellow student weigh in on whether I have misunderstood the notes to equation 4-16 and contravariant is the correct term or whether Adler, clearly meant covariant? This is a question that if I were a student, I would go to a professor during office hours to ask him or her about it. As it is, I am no longer a graduate student, and my colleagues are not relativists or are reading Adler.

I am not trying to be difficult, but reading the textbook is distracting and unclear with these misprints.

 

[vanhees71]

These are covariant vector components. The definition is that covariant components transform like the basis vectors and contravariant components like the corresponding dual-basis vectors.

For holonomous coordinates it's easy to remember: The contravariant components transform like the differentials of the coordinates,
$$\mathrm{d} x^{\prime j}=\frac{\partial x^{\prime j}}{\partial x^k} \mathrm{d} x^k.$$
The covariant components transform like the derivatives
$$\partial_j'=\frac{\partial}{\partial x^{\prime j}} =\frac{\partial x^k}{\partial x^{\prime j}} \frac{\partial}{\partial x^k}= \frac{\partial x^k}{\partial x^{\prime j}} \partial_k.$$

 

[Ibix]

Does Adler have an E-mail address as the corresponding author rather than a link, so I can use google email?

Yes - the page linked by @malawi_glenn in #13 has Adler's name with an envelope icon to the right. Click that and a popup appears including the link "Contact Ronald J Adler". That is a mailto: link, which your browser may be trying to open in an email client. However, if you right-click on it you should be able to copy the link (or copy address, or something like that) and paste it into a text editor, or the To line in your email client. Remove the mailto: at the beginning and the rest is his email address.

Can an expert or fellow student weigh in on whether I have misunderstood the notes to equation 4-16 and contravariant is the correct term or whether Adler, clearly meant covariant?

I'm afraid I don't have the book and those pages appear to be missing from the Google books version.

 

[mpresic3]

I think you are agreeing with me then. The word "contravariant" after equation 4.16 on page 39 in Adler, General Relativity and Cosmology" should be "covariant.

 

[vanhees71]

Yes, lower indices indicate covariant vector/tensor components.

 

[mpresic3]

I found a later explanation after equation 4-24 on page 41, that states (specifically):

The Vi correspond to the covariant component vector in 4-16.

Clearly "contravariant" in equation 4-16, should be "covariant".

 

[dextercioby]

[Issue of misprints makes me think: Prof. Adler in his 80's may not be so sharp in details, but won't the publisher check the material precisely because of that?] Is the original with Bazin and Schiffer from >50 years ago also with typos?

 

[mpresic3]

Reading ahead, I found many ( at least 2 over the next 10 pages, and I stopped counting ) more typos, where Adler cites earlier equations by number as a reference later equations, and turning back to the earlier equation, I find the equation number given is incorrect, but there is an earier equation that can be correctly cited. This seems to be carelessness. Was there a hurry to get the book published? Did anyone look carefully at the drafts?

I read about half of the earlier book and I did not note any mistakes, although there may have been be a few present. I do suspect that the earlier book with three authors had (I presume) at least six eyes proofreading.

I'm going to keep reading, as I think Adler holds to development of general relativity proper, and I think Hartle skips around a lot with applications to GPS, and other diversions, but I do think I would recommend this book more highly, if it had fewer misprints, and more care was taken on the citations to earlier equations.

 

[malawi_glenn]

@Ibix thank you for explaning how to extract e-mail adresses from mail-links.

One can always ask the publishing editor for Graduate texts in physics why there are so many misprints and typos in this particular book. I have not heard anything like this from another book in this series https://www.springer.com/series/8431/editors (right-click on the envelope and select "copy e-mail adress")

 

[vanhees71]

I found a later explanation after equation 4-24 on page 41, that states (specifically):

The Vi correspond to the covariant component vector in 4-16.

Clearly "contravariant" in equation 4-16, should be "covariant".

Yes, that's what we all told you all the time. Of course, it's unfortunate to have such a misprint in a textbook, that leads to confusion particularly of beginners, but unfortunately it's hard to avoid such typos. I wish I had a recipy to produce typo-free texts! That's why you always have to read textbooks and scientific papers with a very critical mind, whether there are mistakes!

 

[malawi_glenn]

I gave my textbook draft to my students and said that they will get a small piece of candy for each mistake they found
I think the count is approx 80 at this point!

 

[mpresic3]

The reason I tend to look critically at the likely misprints is not that I doubt advise given in physics forums. When I came across the misprint in the Lorentz metric with all the -1's, my first thought was to read the section over again. Perhaps, I am taking the discussion out of context.
I have found misprints in textbooks before. My first find was in freshman calculus and I verified the misprint with my professor.
I found a textbook where the author refers to the planet "Earth" by the planet "earth" but I am overlooking English (or is it, english) grammatical and capitalization errors.
I am unhappy to be finding so many misprints in Adler, in the first 50 pages. I am somewhat suprised that in the draft Malawi_glenn gave to his students that contains 80 misprints. Perhaps several students finding the same set of misprints.

 

[malawi_glenn]

I am somewhat suprised that in the draft Malawi_glenn gave to his students that contains 80 misprints.

Write your own 220 page book from scratch during the summer months with a newborn baby. Then please get back to me.

90% of the misprints are grammatical and spelling errors, like switching tense in a paragraph, and "Tagnetfart" instead of "Tangentfart", a word that was somehow not caught by the spell checker software.

Perhaps several students finding the same set of misprints

They do but it is first come first service when it comes to receiving that sweet precious candy

And it was partially my intention to read it myself only once before handing it to the students - they love the challenge. Actually, I am thinking about saving a few typos for next years students so that can have chance to receive candy

I am unhappy to be finding so many misprints in Adler, in the first 50 pages.

My suggestion is that you e-mail the author and maybe also the publisher. Instead of just sitting here complaining. Now you know how to extract e-mail adresses on a homepage

 

[mpresic3]

Write your own 220 page book from scratch during the summer months with a newborn baby. Then please get back to me.

90% of the misprints are grammatical and spelling errors, like switching tense in a paragraph, and "Tagnetfart" instead of "Tangentfart", a word that was somehow not caught by the spell checker software.They do but it is first come first service when it comes to receiving that sweet precious candy

And it was partially my intention to read it myself only once before handing it to the students - they love the challenge. Actually, I am thinking about saving a few typos for next years students so that can have chance to receive candy My suggestion is that you e-mail the author and maybe also the publisher. Instead of just sitting here complaining. Now you know how to extract e-mail adresses on a homepage

 

[malawi_glenn]

@mpresic3 I would also ask the publisher for a refund or something. It is free to ask.

 

[mpresic3]

Fair enough, malawi_glenn. My papers,I tend to write to my superiors, (thesis advisor, bosses, and the like), so I tend to limit my misprints to (perhaps) 1 or 2 for each 5 pages. I might expect my students to be more forgiving though.

An engish teacher I had in college, corrected one of my papers with: Don't use contractions.
Apparently she had a sense of humor. You can see in my posts in the forums, I use contractions, and take other liberties, that I would not take if I were trying to publish in a journal.

Also I am not really counting grammar and spelling mistakes ( surprisingly, I haven't found one) in Adler, as a misprint. Your eighty figure is down to only 8, if you discount your 90% grammar and spelling errors.

I would never ask the pubisher for a refund. I have to be honest, and I expect over time to get my money's worth out of the text. I do find the older book, where Adler was one of the co-authors, was more complete, and had fewer mistakes. Maybe because there were, 3 pair of eyes, collectively for the coauthors.

 

[malawi_glenn]

I use contractions, and take other liberties, that I would not take if I were trying to publish in a journal.

You also take the liberty to not incude vital information, like full title of the book (you have two threads on this book, none of them had the correct title displayed) and to include the information needed to answer your questions (I had to do some research my self to figure out what you were asking for).

My PhD thesis had one "true" misprint, I had forgotten to write a factor $1/\sqrt{2}$ in an equation in the introduction.

 

[mpresic3]

Thank you again for your clarification earlier where you copied the relevant sections from Adler, General Relativity and Cosmology, in your first post. in the future, I will be mindful of you, and the other reader's time, and effort and I will include specific titles, and characteristic information.

Cheers.

 

[vanhees71]

@mpresic3 I would also ask the publisher for a refund or something. It is free to ask.

Against this they legally protect themselves:

The use of general descriptive names, registered names, trademarks, service marks, etc. in this
publication does not imply, even in the absence of a specific statement, that such names are exempt from
the relevant protective laws and regulations and therefore free for general use.
The publisher, the authors and the editors are safe to assume that the advice and information in this
book are believed to be true and accurate at the date of publication. Neither the publisher nor the
authors or the editors give a warranty, expressed or implied, with respect to the material contained
herein or for any errors or omissions that may have been made. The publisher remains neutral with regard
to jurisdictional claims in published maps and institutional affiliations.

 

[mpresic3]

Here is a an interesting side note regarding the textbook, Introduction to General Relativity, by Adler, Bazin, and Schiffer. In Chaper 8, on page 235 of the 1965 edition the authors, write:
"It will be convenient in this chapter to use Minkowski coordinates ict, x, y, z, in place of the usual coordinates in special relativity. In this coordinate system, the Lorentz metric has the simple form"

( The matrix shown in equation 8.2 is diag(-1,-1,-1,-1) )

The equation 8.2 that follows give the metric as negative of the Kronecker delta, as the authors themselves state in the next sentence.

This time, of course, there is no misprint. The context of the presentation where they specify the coordinates is important.

The use of coordinate ict seems to be far less popular, nowadays.

I'm not trying to re-open the thread and generate further discussion. I think it has been discussed thoroughly.