Reddit mentions: The best physics of gravity books

Einstein himself wrote a book for the non-scientist to explain both special and general relativity. Here is the preface, which explains the level of the book:

> The present book is intended, as far as possible, to give an exact insight into the theory of Relativity to those readers who, from a general scientific and philosophical point of view, are interested in the theory, but who are not conversant with the mathematical apparatus of theoretical physics. The work presumes a standard of education corresponding to that of a university matriculation examination , and, despite the shortness of the book, a fair amount of patience and force of will on the part of the reader. The author has spared himself no pains in his endeavour to present the main ideas in the simplest and most intelligible form, and on the whole, in the sequence and connection in which they actually originated. In the interest of clearness, it appeared to me inevitable that I should repeat myself frequently, without paying the slightest attention to the elegance of the presentation. I adhered scrupulously to the precept of that brilliant theoretical physicist L. Boltzmann, according to whom matters of elegance ought to be left to the tailor and to the cobbler. I make no pretence of having withheld from the reader difficulties which are inherent to the subject. On the other hand, I have purposely treated the empirical physical foundations of the theory in a "step-motherly" fashion, so that readers unfamiliar with physics may not feel like the wanderer who was unable to see the forest for the trees. May the book bring some one a few happy hours of suggestive thought!

The book is called "Relativity: The Special and the General Theory", and is available for free on Project Gutenberg.

I'd suggest considering getting that and trying to read it. With the math you already know you should be able to get quite a bit out of it. And if you do get stuck on the math somewhere, well, that will give you an idea of what math to study next to get unstuck.

Here is a Project Gutenberg copy of the 3rd edition in PDF and TeX made via OCR of the physical book. =>LINK<=.

Here is a copy that is available in HTML, MS Word, and TeX. I'm not sure what edition this is. =>LINK<=.

There's a Kindle version of the 3rd edition of this on Amazon for $0.99 that is good. Books with math are often terrible on Kindle due to publishers sometimes doing the equations as small image files that are hard to read and ugly if you zoom them. This one, though, is specifically touted as being "with readable equations", and they are right.

Unless you actually want to read on a Kindle there is no advantage that I can see that it has over either of the Gutenberg copies I listed earlier. If you do want to read on a Kindle and are willing to cough up $0.99, here is the link: =>LINK<=.

Another free resource that might be worth taking a look at is the special relativity material in the Feynman Lectures. They use a little more calculus than the Einstein book (I think), and may use more trigonometry than you have at this point, but as with the Einstein book I think you might get quite a bit out of it even if you decide at some point you need more math to go on.

The special relativity material starts at chapter 15 in Volume 1. Volume 1 can be read online =>HERE<=.

Finally, you might take a look at these video lectures: =>LINK<=

They are from a series of courses called "The Theoretical Minimum". Here's their description:

> The Theoretical Minimum is a series of Stanford Continuing Studies courses taught by world renowned physicist Leonard Susskind. These courses collectively teach everything required to gain a basic understanding of each area of modern physics including all of the fundamental mathematics.

The first three lecture series, (1) classical mechanics, (2) quantum mechanics, and (3) special relativity and classical field theory have been released in book form, and just today I was thumbing through the book for the special relativity series at Barnes & Noble and almost bought it, but I didn't and don't remember enough from my bookstore browsing to tell you what that math level was. (I did not buy it because it was $30 in store, compared to around $21 if ordered from B&N online, or $19 from Amazon...I'll pay a little over the online price to support brick & mortar bookstores, but not 40+% over!).

Have you had a look at Carroll's general relativity notes? Chapters 2 and 3 are predominantly about developing the mathematics behind GR, and are very good introductions to this. I have a copy of Carroll's book and I can promise you that those chapters are almost unchanged in the book as compared to the lecture notes. This is my main suggestion really, as the notes are freely available, written by an absolute expert and a joy to read. I can't recommend them (and the book really) enough.

Most undergraduate books on general relativity start with a "physics first" type approach, where the underlying material about manifolds and curvature is developed as it is needed. The only problem with this is that it makes seeing the underlying picture for how the material works more difficult. I wouldn't neccessarily say avoid these sort of books (my favourite two of this kind would be Cheng's book and Hartle's.) but be aware that they are probably not what you are looking for if you want a consistent description of the mathematics.

I would also say avoid the harder end of the scale (Wald) till you've at least done your course. Wald is a tough book, and certainly not aimed at people seeing the material for the first time.

Another useful idea would be looking for lecture notes from other universities. As an example, there are some useful notes here from cambridge university. Generally I find doing searches like "general relativity site:.ac.uk filetype:pdf" in google is a good way to get started searching for decent lecture notes from other universities.

If you're willing to dive in a bit more to the mathematics, the riemannian geometry book by DoCarmo is supposed to be excellent, although I've only seen his differential geometry book (which was very good). As a word of warning, this book might assume knowledge of differential geometry from his earlier book. The book you linked by Bishop also looks fine, and there is also the book by Schutz which is supposed to be great and this book by Sternberg which looks pretty good, although quite tough.

Finally, if you would like I have a dropbox folder of collected together material for GR which I could share with you. It's not much, but I've got some decent stuff collected together which could be very helpful. As a qualifier, I had to teach myself GR for my undergrad project, so I know how it feels being on your own with it. Good luck!

Griffiths is the go-to for advanced undergraduate level texts, so you might consider his Introduction to Quantum Mechanics and Introduction to Particle Physics. I used Townsend's A Modern Approach to Quantum Mechanics to teach myself and I thought that was a pretty good book.

I'm not sure if you mean special or general relativity. For special, /u/Ragall's suggestion of Taylor is good but is aimed an more of an intermediate undergraduate; still worth checking out I think. I've heard Taylor (different Taylor) and Wheeler's Spacetime Physics is good but I don't know much more about it. For general relativity, I think Hartle's Gravity: An Introduction to Einstein's General Relativity and Carroll's Spacetime and Geometry: An Introduction to General Relativity are what you want to look for. Hartle is slightly lower level but both are close. Carroll is probably better if you want one book and want a bit more of the math.

Online resources are improving, and you might find luck in opencourseware type websites. I'm not too knowledgeable in these, and I think books, while expensive, are a great investment if you are planning to spend a long time in the field.

One note: teaching yourself is great, but a grad program will be concerned if it doesn't show up on a transcript. This being said, the big four in US institutions are Classical Mechanics, E&M, Thermodynamics/Stat Mech, and QM. You should have all four but you can sometimes get away with three. Expectations of other courses vary by school, which is why programs don't always expect things like GR, fluid mechanics, etc.

I hope that helps!

I'm going to be a little over-focused on textbooks, but I think the best treatments of these topics begin to move out of the "popular science" book territory.

For regular gravity, if you have decent linear algebra (matrix math), vector calculus skills (divergence, gradient, curl and the like), and preferably some familiarity with Lagrangian mechanics then I'd recommend Hartle's Gravity. I think that's pretty much the minimum set of prerequisites to be able to do General Relativity and see gravity come from that.

It doesn't hurt that the same math is pretty much what you need for basic quantum mechanics; but you need a much longer sequence to get to quantum field theory, the point where you can start doing the necessary particle physics of the problem.

A summary?

Gravity is what we call the fact that massive objects (and energy, by extension) tend to follow geodesics in curved spacetime.

From a GR perspective, it's not a "thing" in the same way as electromagnitism, or the strong force, or the weak force. It's simply the tendency for massive objects to move in a straight line.

This is an analogy. It's designed to give intuition, but it's not at all rigorous. Again, if you want the rock solid explanation, you have to deal with differential geometry and tensor calculus and those field equations linked above.

It's not a perfect analogy. You would (rightfully) ask: "what about things that aren't already moving? why would something like gravity 'pulling' on them cause them to move, that's not them continuing to move in a straight line.", and you'd be right. But that's because the best I can do with out getting absurdly mathy is give you a mediocre analogy. If you want to know the real deal, you have to crack a book.

Also: I "referenced" that book because it's one of a few introductory General Relativity books that people who are in grad school for physics use. That means most professors who are actively involved in research use it. So your claim that "no one of any authority" would use it is absurd.

Here it is incase you're being sincere, something tells me you're not though:

https://www.amazon.com/Gravity-Introduction-Einsteins-General-Relativity/dp/0805386629/ref=pd_lpo_sbs_14_t_1?_encoding=UTF8&psc=1&refRID=VCK5YK7ZV42TXM7CTYPZ&dpID=41ACB2FKGBL&preST=_SX218_BO1,204,203,200_QL40_&dpSrc=detail

Some general searches through the Phil Sci archives might turn up papers related to your interests here. In particular, there might be something under the general topics of cosmology, quantum gravity, or relativity theory.

Within that archive, some that stand out to me in relation to your question are: this paper on anthropic reasoning about many worlds, this paper summarizing unification arguments for string theory, this paper on the ethical implications of many worlds, this paper on general trends in philosophy of physics (one of which is the cosmological many worlds), this paper on whether or not string theory posits mereological simples that are extended, and this paper on what is involved in deriving GR from some string theories.

Some theoretical physicists who work on string theory or quantum gravity in general and who come to my mind as conscious of history & philosophy of science as well as metaphysics are: Lee Smolin, especially his books The Trouble with Physics and Three Roads to Quantum Gravity; Sean Carroll, perhaps even his lectures on time and his book The Big Picture; and Carlo Rovelli, especially his books Reality is Not What it Seems and Quantum Gravity. Again, I don't mention them to point to philosophical work on those topics but only to mention some physicists who work on those topics and who have a more philosophical bent.

I know Alexander Blum has looked into the history of quantum gravity but I don't know what he's written on the philosophy of quantum gravity or specifically on string theory. Tim Maudlin and Craig Callender do quite a lot of work on philosophy of space-time but I don't know that they have specifically discussed string theory. In general, you might find some interesting papers in the philpapers browser for the philosophy of string theory or of cosmology.

Also, Jeffrey Barrett has done quite a lot of work on quantum interpretations and Everettian many-worlds, which is not to be confused with the string-theoretic landscape of many worlds but you might find some of his work interesting.

Hope that helps!

Hartle: http://www.amazon.com/Gravity-Introduction-Einsteins-General-Relativity/dp/0805386629/ref=sr_1_7?ie=UTF8&qid=1420630637&sr=8-7&keywords=general+relativity

Pretty introductory, not a ton of math but enough to satisfy most undergrads. Includes a section on introductory Tensor Calculus.

Carroll: http://www.amazon.com/Spacetime-Geometry-Introduction-General-Relativity/dp/0805387323/ref=sr_1_3?ie=UTF8&qid=1420630637&sr=8-3&keywords=general+relativity

Probably the best intermediate book, does GR at an intermediate level. Includes several chapters on the math needed.

Wald: http://www.amazon.com/General-Relativity-Robert-M-Wald/dp/0226870332/ref=sr_1_2?ie=UTF8&qid=1420630637&sr=8-2&keywords=general+relativity

Covers GR at a fairly advanced level. More rigorous books exist, but are not appropriate for a first course.

To learn about the cosmology, black holes and the fate of the universe, I recommend two superb books:

Kip Thorne: Black Holes and Time Warps (http://www.amazon.com/Black-Holes-Time-Warps-Commonwealth/dp/0393312763/ref=sr_1_1?ie=UTF8&s=books&qid=1254000781&sr=8-1)

Tony Zee: An Old Man's Toy (http://www.amazon.com/Old-Mans-Toy-Einsteins-Universe/dp/002040915X/ref=sr_1_1?ie=UTF8&s=books&qid=1254000896&sr=1-1)

Enjoy!

Here's a great book that might interest you: Solving The UFO Enigma: How Modern Physics is Revealing the Technology of UFOs


And a decent interview with the writer, Robert Schroeder - Solving the UFO Enigma (The Moore Show), for an insight into what the book is about without delving into details.

The best explanation, even at the level of a high school graduate, is to have the mathematical description of relativity explained to you.

Anything less than that will leave possible ambiguity for you to potentially mislead yourself.

Anybody know of any relevant YouTube series? I was lucky enough to do a math major before I got interested so I just read books.

Never read it, but heard good things about https://www.amazon.com/gp/aw/reviews/B004M8S53U/ref=cm_cr_dp_mb_btm?ie=UTF8

Griffith's Electrodynamics has a decent introduction to special relativity. Otherwise, Hartle's book is geared towards the advanced undergrad. Also, Schultz is good too.

My thoughts as well. Trains are the traditional thought device ("gedanken experiment") used to explain relativity. It's the go-to explanation.

I get the idea. I agree with the idea. I just think a landslide would have been a better metaphor.

I was actually referring to Frankel's short book Gravitational Curvature where he goes from SR -> GR -> Schwarzschild solution in about 50 pages. There's only a couple pages "introducing" math, mostly to fix notation and define extrinsic curvature. He gets there quickly with good conceptual ideas, but like I said, a firm grasp of differential geometry is needed to follow it.

Weber's book is General Relativity and Gravitational Waves. Einstein equation appears on page 50. Taught myself GR from this book as an undergrad.

I suppose I never thought of Wald as an introductory book as I've only ever read the later sections. It also requires a comfortability with more formal presentations of mathematics.

> And if i then stop accelerating his time will again go slower?

Yeah, I think that would be the case.

I could recommend a textbook on special relativity if that's what you want. Here's a list with a few options that should be good. Also some textbooks on general relativity include introductions to special relativity in the beginning; I'm a fan of Hartle's book but Schutz (in the list linked previously) is also a classic. Though I don't know offhand which books (if any) discuss this particular detail of the twin paradox.

If you're not interested in a textbook, there are definitely "popularized" relativity books out there, but I don't know much about them. I couldn't tell you which books, if any, might include this specific information, and it's even possible for things to be "lost in translation" when authors try to explain relativity without using math. Ultimately the source is learning how to do the calculations yourself.

I'm pretty sure you have to use Tensors... and I can't do that. :)

http://www.amazon.com/Gravity-Introduction-Einsteins-General-Relativity/dp/0805386629

Carlo Rovelli is a physicist who does a lot to put philosophy in dialogue with physics, and physics in dialogue with philosophy. There is a lot of his stuff that you could read, but perhaps "Reality is not What it Seems" would be a good place to start. In that book he even shows how Newton and Einstein were benefiting from their knowledge of philosophy.

On a more technical note, his particular thing is quantum gravity and particularly relational quantum mechanics. He is coauthor on an article on the topic for the Stanford Encyclopedia of Philosophy.

Don't bother, just pick up a GR textbook like Hartle or Schutz. Those books teach the math as they go.

Would you be interested in this for the Douglas Adams?

Einstein himself wrote a layman's guide to his theories if you want to learn more. He wrote it specifically for people that aren't mathematically inclined. It's literally $1 on the kindle, too:
https://www.amazon.com/Relativity-Special-General-Readable-Equations-ebook/dp/B004M8S53U/ref=tmm_kin_swatch_0?_encoding=UTF8&qid=1502032803&sr=8-5

Actually we can calculate the bending of photon using newtonian mechanics assuming it has a mass given by

m = E/c^2 = h \nu/c^2

The answer we get is exactly half of what GR predicts. You can find the this problem done in this book

http://www.amazon.com/Gravity-Introduction-Einsteins-General-Relativity/dp/0805386629

New one, called Something Deeply Hidden , it's goal is to explain quantum mechanics to everyone.

There have been many developments since, but it makes sense to start with the original source material.

The Quantum Universe is a good, rigorous, but well-explained book that might be along the lines you're looking for. Possibly also Reality is Not What it Seems, but I've barely started that one so I can't say for sure.