Best (or at least good) GR and SR textbook for a 15-year-old highschool student

  • #1
AdvaitDhingra
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Hi,

I'm a 15-year-old highschool student and I was wondering what textbook you guys recommend for Special- and General Relativity. I'm familiar with the concept of the Metric Tensor and Christoffel Symbols, but I wanted a good textbook where I can really learn derive it all and gain a deeper understanding of the subject. I'm familiar with differentiation, vectors etc.

What do you recommend?
 

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  • #2
andresB
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I'm sure somebody will recommend newer books, so I'll point out old but good books. I like "special relativity" by A.P French for a first intro in SR and "gravitation and cosmology" by Weinberg for GR.
 
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  • #3
martinbn
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Hawking and Ellis.
 
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  • #4
George Jones
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I'm familiar with differentiation, vectors etc.
I am not sure what this means. Can you do most of the problems in a typical multivariable calculus text? Can you most of the problems in a typical introductory linear algebra text?
 
  • #5
PeroK
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Special Relativity is something you may be able to learn without advanced mathematics. General Relativity is essentially a graduate subject and, in any case, requires advanced mathematics.

For SR there is Morin, the first chapter of which is here:

https://scholar.harvard.edu/files/david-morin/files/relativity_chap_1.pdf

I like Helliwell (which is a good undergraduate-level introduction)

https://www.goodreads.com/book/show/6453378-special-relativity

For GR, I like Sean Carroll's book, which also has some online lecture notes:

https://www.preposterousuniverse.com/grnotes/

https://www.cambridge.org/core/books/spacetime-and-geometry/38EDABF9E2BADCE6FBCF2B22DC12BFFE

That said, if you are learning GR at 15 then you are either a genius or delusional!

Personally, I'd steer clear of older books like A.P. French. We get homework questions from time to time from that book and it is "horribly out of date". There was one today:

https://www.physicsforums.com/threa...finition-of-a-metre-a-p-frenchs-book.1002093/
 
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  • #6
AdvaitDhingra
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I am not sure what this means. Can you do most of the problems in a typical multivariable calculus text? Can you most of the problems in a typical introductory linear algebra text?
My apologies. What I meant by that is that I have a basic understanding of them.
 
  • #7
AdvaitDhingra
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Special Relativity is something you may be able to learn without advanced mathematics. General Relativity is essentially a graduate subject and, in any case, requires advanced mathematics.

For SR there is Morin, the first chapter of which is here:

https://scholar.harvard.edu/files/david-morin/files/relativity_chap_1.pdf

I like Helliwell (which is a good undergraduate-level introduction)

https://www.goodreads.com/book/show/6453378-special-relativity

For GR, I like Sean Carroll's book, which also has some online lecture notes:

https://www.preposterousuniverse.com/grnotes/

https://www.cambridge.org/core/books/spacetime-and-geometry/38EDABF9E2BADCE6FBCF2B22DC12BFFE

That said, if you are learning GR at 15 then you are either a genius or delusional!

Personally, I'd steer clear of older books like A.P. French. We get homework questions from time to time from that book and it is "horribly out of date". There was one today:

https://www.physicsforums.com/threa...finition-of-a-metre-a-p-frenchs-book.1002093/
Thank you
 
  • #8
Ibix
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I like Spacetime Physics by Taylor and Wheeler. It's now free to download from Taylor's website, so I'd recommend getting it even if you don't end up using it.
 
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  • #9
Frabjous
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Personally, I'd steer clear of older books like A.P. French. We get homework questions from time to time from that book and it is "horribly out of date". There was one today:

I am not sure what this means in practice. I can think of books by authors like Dirac, Landau and Feynman that are even older and are worth a gander. I personally have fond memories of French.
 
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  • #10
George Jones
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I am not sure what this means in practice. I can think of books by authors like Dirac, Landau and Feynman that are even older and are worth a gander.
We should not exclude older books, but nor should we consider them exclusively. I am 60; many, many outstanding books have been written since I was a student, including many of my favourites.

I personally have fond memories of French.
French uses relativistic mass. A student learning relativity today should not have their first serious exposure to special relativity from a book that uses relativistic mass.
 
  • #11
PeroK
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I am not sure what this means in practice. I can think of books by authors like Dirac, Landau and Feynman that are even older and are worth a gander. I personally have fond memories of French.
That's the over-generalisation fallacy. Feynman's lectures have stood the test of time; whereas, it seems to me that French may have been old-fashioned even when it was published (relativistic mass couldn't have been the currency in the 1960's).

I believe that we shouldn't be recommending older books because we have fond memories of them, but because we honestly believe they are suited to the modern student. Do you really believe it is one of the best possible sources for the modern student?
 
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  • #12
Frabjous
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That's the over-generalisation fallacy. Feynman's lectures have stood the test of time; whereas, it seems to me that French may have been old-fashioned even when it was published (relativistic mass couldn't have been the currency in the 1960's).

I believe that we shouldn't be recommending older books because we have fond memories of them, but because we honestly believe they are suited to the modern student. Do you really believe it is one of the best possible sources for the modern student?

I am not sure about your timelines.
https://physicstoday.scitation.org/doi/abs/10.1063/1.881171
https://physicstoday.scitation.org/doi/abs/10.1063/1.2810555

I am not arguing that his Relativity book is the most appropriate, but after looking at
https://www.physicsforums.com/threa...finition-of-a-metre-a-p-frenchs-book.1002093/
I am not sure that I would reject a book on mechanics because it mentions the old definition of the meter. Is it a requirement for books that stand the test of time to be 100% anachronism free?
 
  • #13
martinbn
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Geroch, R. "Relativity from A to B".
 
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  • #14
Falgun
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At this level you can check out the GR textbook by Taylor, Wheeler & Bertschinger which is available for free on Taylor's Homepage:
https://www.eftaylor.com/exploringblackholes/

This book assumes you are familiar with calculus and basic physics.
 
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  • #15
AndreasC
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Hawking and Ellis.
I don't think it's particularly suited for high school students to say the least...
 
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  • #16
PeroK
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I think the issue with older texts is this:

Experienced physicists can appreciate them because they know which parts are out of date and generally see them in their proper context; whereas, the novice has no idea about that and must take everything at face value.

Regarding relativistic mass, in particular, there is an inevitable and potentially bitter battle to persuade the student to forgo the concept in order to move on with their studies. Don Lincoln sums it up in one of his videos when he says, regarding relativistic mass, that the time comes when "we must put away childish things".
 
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  • #17
martinbn
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I don't think it's particularly suited for high school students to say the least...
Of course not. But he said he knew what a metric tensor is and what the Christofell symbols are. Either he is that good, and he can have a go at Hawking-Ellis, or he needs a reality check, and for that he can also have a go at their book.
 
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  • #18
AndreasC
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But he said he knew what a metric tensor is and what the Christofell symbols are
I know what these are too and I can't read Hawking and Ellis lol (well, I can because I also know other stuff but it's gonna be hard and I won't get as much out of it as I would get by reading a book targeted towards people who haven't studied GR yet). It's not hard to learn what the Christoffel symbols and the metric tensor are. It's like someone saying "I am a high school student and I know what the Lorentz force and a vector potential is, can you suggest me a book on EM?" and someone suggesting Jackson instead of, idk Griffiths or something.

OP may very well be capable of understanding a basic GR book like Hartle or at least a basic SR book first or something while being unable to understand a hard book like Hawking and Ellis, or they may not. Regardless, trying to read Hawking and Ellis won't be a good indicator either way. A 15 year old kid with no prior exposure to GR is extremely unlikely to get much out of H&E.
 
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  • #19
AndreasC
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The suggestion to read H&E as a high school student reminds me of when I found Weinberg's QFT books on the internet at a similar age and I thought why not, I will download it and try to read that because I had no idea of the background and the level required, and then I didn't understand anything past the foreword. Actually I didn't really understand the foreword either lol
 
  • #20
atyy
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That's the over-generalisation fallacy. Feynman's lectures have stood the test of time; whereas, it seems to me that French may have been old-fashioned even when it was published (relativistic mass couldn't have been the currency in the 1960's).

I believe that we shouldn't be recommending older books because we have fond memories of them, but because we honestly believe they are suited to the modern student. Do you really believe it is one of the best possible sources for the modern student?
Feynman uses relativistic mass.
 
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  • #21
JLowe
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I like Spacetime Physics by Taylor and Wheeler. It's now free to download from Taylor's website, so I'd recommend getting it even if you don't end up using it.

I've read this book and did find it useful. It's approaching the limit of my high school drop out math ability. Do you know of an alternative, at generally same level of mathematics, perhaps presented in a different way?
 
  • #22
PeroK
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I've read this book and did find it useful. It's approaching the limit of my high school drop out math ability. Do you know of an alternative, at generally same level of mathematics, perhaps presented in a different way?
There are two alternative suggestions in post #2.

For SR there is Morin, the first chapter of which is here:

https://scholar.harvard.edu/files/david-morin/files/relativity_chap_1.pdf

I like Helliwell (which is a good undergraduate-level introduction)

https://www.goodreads.com/book/show/6453378-special-relativity
 
  • #23
vanhees71
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I am not sure what this means in practice. I can think of books by authors like Dirac, Landau and Feynman that are even older and are worth a gander. I personally have fond memories of French.
Yes, that's what I said in the mentioned other thread too. You should not abandon a textbook only because it's "old". My personal favorites for general theory textbooks are Sommerfeld - Landau Lifshitz - Feynman lectures (in that order) and they are all pretty old. Of course there are also bad textbooks from the old times, but most of them are simply forgotten. Old textbooks that are not forgotten are always good. It's like Darwin's "survival of the fittest" for textbooks ;-).
 
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  • #24
AdvaitDhingra
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I know what these are too and I can't read Hawking and Ellis lol (well, I can because I also know other stuff but it's gonna be hard and I won't get as much out of it as I would get by reading a book targeted towards people who haven't studied GR yet). It's not hard to learn what the Christoffel symbols and the metric tensor are. It's like someone saying "I am a high school student and I know what the Lorentz force and a vector potential is, can you suggest me a book on EM?" and someone suggesting Jackson instead of, idk Griffiths or something.

OP may very well be capable of understanding a basic GR book like Hartle or at least a basic SR book first or something while being unable to understand a hard book like Hawking and Ellis, or they may not. Regardless, trying to read Hawking and Ellis won't be a good indicator either way. A 15 year old kid with no prior exposure to GR is extremely unlikely to get much out of H&E.
Thank you for your advice. It may well be that I overestimate what I understand.
 
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  • #25
AndreasC
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Thank you for your advice. It may well be that I overestimate what I understand.
I think you should try watching Susskind's lectures on special relativity on youtube. He released a book based on the lectures a couple years ago too. They are pretty easy going and don't assume a lot of background. He also has lectures on general relativity. Hawking and Ellis is an advanced book targeted at specialists and graduate students, not a first exposure, maybe not even a second exposure.
 
  • #26
AdvaitDhingra
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I think you should try watching Susskind's lectures on special relativity on youtube. He released a book based on the lectures a couple years ago too. They are pretty easy going and don't assume a lot of background. He also has lectures on general relativity. Hawking and Ellis is an advanced book targeted at specialists and graduate students, not a first exposure, maybe not even a second exposure.
Ah yes, I've heard of Leonard Susskind. Thanks for the recommendation.
 
  • #27
Mondayman
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I'm not sure of any legit GR resources without mathematics. The book Black Holes and Time Warps by Kip Thorne won't teach you relativity per se, but it is a very good read as far as pop-sci books go.
Abraham Pais wrote a great scientific biography about Albert Einstein called Subtle is the Lord. It is pretty technical, but interesting to read how Einstein came to his insights regarding special and general relativity.

I would suggest Spacetime Physics by Wheeler-Taylor, followed by Exploring Black Holes by the same authors. It requires basic knowledge of linear algebra and multivariable calculus. It's about as basic an introduction to GR as you can get.

I used to like the A.P. French series. I still think Newtonian Mechanics is okay as a supplement, and Vibrations and Waves is a pretty good book in my opinion. But they are quite old fashioned and I wouldn't use it for anything other than second resource. Despite owning them, I haven't used his special relativity or quantum physics texts. Just much better resources out there now.
 
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  • #28
vanhees71
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I think, Born's famous book Einstein's theory of relativity is the right thing here. It's written for people with a knowledge of highschool math (though the highschool math of the time around 1920 ;-)). So it gives a real glimpse about the theory without being too technical. Though it's written about 100y ago, it's still a very good read!
 
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  • #29
robphy
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Given the background you noted,
others to consider are

some books by Tom Moore:
Unit R of Six Ideas That Shaped Physics http://www.physics.pomona.edu/sixideas/
and A General Relativity Workbook https://pages.pomona.edu/~tmoore/grw/

a text by Andrew Steane
Relativity Made Relatively Easy
https://www.amazon.com/dp/0199662851/?tag=pfamazon01-20

some books by Bob Geroch
General Relativity from A to B (mentioned earlier) https://www.amazon.com/dp/0226288641/?tag=pfamazon01-20
General Relativity: 1972 Lecture Notes
http://www.minkowskiinstitute.org/mip/books/geroch-gr.html
https://www.amazon.com/dp/0987987178/?tag=pfamazon01-20
 
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  • #30
AdvaitDhingra
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Given the background you noted,
others to consider are

some books by Tom Moore:
Unit R of Six Ideas That Shaped Physics http://www.physics.pomona.edu/sixideas/
and A General Relativity Workbook https://pages.pomona.edu/~tmoore/grw/

a text by Andrew Steane
Relativity Made Relatively Easy
https://www.amazon.com/dp/0199662851/?tag=pfamazon01-20

some books by Bob Geroch
General Relativity from A to B (mentioned earlier) https://www.amazon.com/dp/0226288641/?tag=pfamazon01-20
General Relativity: 1972 Lecture Notes
http://www.minkowskiinstitute.org/mip/books/geroch-gr.html
https://www.amazon.com/dp/0987987178/?tag=pfamazon01-20
Thank you
 
  • #31
Kolmo
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I learned General Relativity from Schutz "A First Course in General Relativity" when I was younger and I know several who did similar. The first edition in particular is a nice compact volume that reviews special relativity, gives a nice "physicst's" view of tensors, motivates the field equations and handles the "fun" early parts of general relativity like Mercury's orbit and black holes and it has good exercises.
 
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  • #33
Demystifier
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Hawking and Ellis.
Since he is a beginner who does not know yet all needed mathematics, perhaps you would also recommend to first study N. Bourbaki, Elements of Mathematics, 11 books. And just to be sure that he understands foundations properly, e.g. why 1+1=2, before Bourbaki perhaps you would also recommend to study Principia Mathematica by Whitehead and Russell (3 books). After Principia, then Bourbaki, then Hawking and Ellis, perhaps he will be ready to study the recommendations by others. :oldbiggrin:
 
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  • #34
martinbn
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Since he is a beginner who does not know yet all needed mathematics, perhaps you would also recommend to first study N. Bourbaki, Elements of Mathematics, 11 books. And just to be sure that he understands foundations properly, e.g. why 1+1=2, before Bourbaki perhaps you would also recommend to study Principia Mathematica by Whitehead and Russell (3 books). After Principia, then Bourbaki, then Hawking and Ellis, perhaps he will be ready to study the recommendations by others. :oldbiggrin:
If someone asks about maths books the same way the first post was written, then yes, I will be equally sarcastic and recommend Bourbaki.
 
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  • #35
Frabjous
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If someone asks about maths books the same way the first post was written, then yes, I will be equally sarcastic and recommend Bourbaki.
My concern with that line of thought is that other people will take recommendations from this thread based on its title.
 
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