Learning General Relativity: What Do I Need to Know?

[FantasyQueen]

Hello! I am a grade 8 student and I'm very interested in General Relativity. However, I don't believe that I have the background information to fully understand. What do I need to know in order to learn General Relativity? I'm certain that I need to know certain mathematical concepts, but I don't know exactly WHAT those mathematical concepts are.
Also, are there any books that you would recommend for me to learn General Relativity from?

 

[Kevin_Axion]

Well, this is far above your capabilities right now (I'm assuming), but you'll firstly need a basis of calculus, special relativity, differential geometry, linear algebra, tensor calculus, Newtonian mechanics. A majority of the subjects you'll take in the first 3 years of an undergraduate degree are necessary. But I'm sure you can grasp the basic idea without the mathematics. This is essentially the math: http://en.wikipedia.org/wiki/Mathematics_of_general_relativity.

 

[eri]

You can learn about GR by reading some popular books on the subject; Hawking, Greene, and Carroll have a few. But you can't learn GR itself just yet; that's a graduate level physics subject. You need a strong background in college math (calculus, linear algebra, differential geometry) to take a shot at it.

 

[Nabeshin]

There are really three tiers at which you can really learn anything substantive about general relativity.

Tier I: Primarily algebra based with light calculus. This is suitable for a first or second year university student. Prior knowledge of physics should include the basic rudiments of mechanics from the F=ma point of view. The hallmark textbook is: https://www.amazon.com/dp/020138423X/?tag=pfamazon01-20

Tier II: Calculus based with light differential geometry. This is suitable for a third or fourth year university student. Prior knowledge of physics should include an upper level E&M course and exposure to lagrangians and hamiltonians. The hallmark textbook is: https://www.amazon.com/dp/0805386629/?tag=pfamazon01-20

Tier III: Full general relativity with differential geometry. This is usually relegated to graduate classes, but can be tackled by advanced undergraduates. Prior physics knowledge is basically an entire undergraduate physics/astrophysics education. Some representative textbooks are:
https://www.amazon.com/dp/0226870332/?tag=pfamazon01-20
https://www.amazon.com/dp/0716703440/?tag=pfamazon01-20

 

[Pollywoggy]

I found this book and bought it a few years ago but one of the authors gave me a link to where it can now be downloaded for free:

http://www.adinfinitum.no/einsteins_theory_en.html

The book is in PDF format and is intended for non-mathematicians but it explains the math needed for a basic understanding.

 

[Kevin_Axion]

I think it's very obvious that you won't understand the mathematical foundations of General Relativity but a qualitative description will be more suitable for now.

 

[bobc2]

Hello! I am a grade 8 student and I'm very interested in General Relativity. However, I don't believe that I have the background information to fully understand. What do I need to know in order to learn General Relativity? I'm certain that I need to know certain mathematical concepts, but I don't know exactly WHAT those mathematical concepts are.
Also, are there any books that you would recommend for me to learn General Relativity from?

Hi FantasyQueen,

Don't believe all of that baloney about your inability to learn about General Relativity. If you really have a passion to know about it, do not let all of this talk about those graduate level math and physics courses you must have discourage you from pursuing the subject of General Relativity. At your age and early stage of pursuing the mysteries of Einstein's theories, I think it is most fruitful to pursue the subject with zest.

One thing I would suggest is to start with Special Relativity. The main tough concept you will need from math (which you should be able to dig into) is the Pythagorean Theorem. Couple that with imagining a 4th dimension, and you can get going. There are some good books about Special Relativity that you can find in your high school library, your local city or county library, or a book store. Run down your high school physics teacher. If he's a good one, he will be so pleased to find an 8th grader so interested in physics that he will enjoy talking to you about the subject and pointing you to some good books.

My first exciting exposure to the world of physics was reading "One-Two-Three-Infinity" by George Gamow. I then read a book that began with a comment, "Only a dozen people in the world understand Relativity, and I don't intend to make that a baker's dozen..." After that it was "The Strange Story of the Quantum." My pursuit of physics was sustained reading books of this type and having interesting discussions with a very understanding high school Chemistry teacher. It was years later before I was enrolled in my first College physics course. Developing the Christoffel Symbols equations was insightful, but I would not trade for the wonderment of the high school years either.

Good Luck!

 

[Fredrik]

As others have said, it's not possible to really understand general relativity without differential geometry. Differential geometry is an impossible subject for someone who doesn't know at least the basics of multiple-variable calculus and linear algebra. (It would also help to know some topology, but if you can live with not understanding a few words in the definition of "manifold", you actually won't need it much). You should also study special relativity before you study general relativity.

So I suggest that you start with special relativity. It's a lot less mathematical than general relativity. The essential features of the theory can be understood by drawing a few straight lines on a piece of paper. The book by Taylor & Wheeler gets the most recommendations here. Search the book forum if you want to find more. You can also read a non-mathematical account of general relativity. The book "Black holes and time warps: Einstein's outrageous legacy" by Kip Thorne is excellent.

 

[Kevin_Axion]

Hi FantasyQueen,

Don't believe all of that baloney about your inability to learn about General Relativity. If you really have a passion to know about it, do not let all of this talk about those graduate level math and physics courses you must have discourage you from pursuing the subject of General Relativity. At your age and early stage of pursuing the mysteries of Einstein's theories, I think it is most fruitful to pursue the subject with zest.

One thing I would suggest is to start with Special Relativity. The main tough concept you will need from math (which you should be able to dig into) is the Pythagorean Theorem. Couple that with imagining a 4th dimension, and you can get going. There are some good books about Special Relativity that you can find in your high school library, your local city or county library, or a book store. Run down your high school physics teacher. If he's a good one, he will be so pleased to find an 8th grader so interested in physics that he will enjoy talking to you about the subject and pointing you to some good books.

My first exciting exposure to the world of physics was reading "One-Two-Three-Infinity" by George Gamow. I then read a book that began with a comment, "Only a dozen people in the world understand Relativity, and I don't intend to make that a baker's dozen..." After that it was "The Strange Story of the Quantum." My pursuit of physics was sustained reading books of this type and having interesting discussions with a very understanding high school Chemistry teacher. It was years later before I was enrolled in my first College physics course. Developing the Christoffel Symbols equations was insightful, but I would not trade for the wonderment of the high school years either.

Good Luck!

We're not discouraging him/her, we're just being realistic. Do you expect someone who hasn't even touched the basics of algebra to understand General Relativity? Does that even sound plausible? Graduate students find the subject to be difficult. As I've said, a qualitative description would suffice. Just defining a metric to him/her wouldn't even make sense, as he/she doesn't even know what a differential is. I agree that he/she can read books about it but diving into the mathematics with hope of understanding is not the right approach, in time he/she will understand it if he/she wishes, but grade 8 is too early of a time to be understanding the fundamentals of General Relativity. Special Relativity is even pushing it since a grade 8 hasn't even grasped the concept of what algebra is, I'm assuming they haven't even taken Newtonian Mechanics. This is all speculative, we have to wait for he/she to reply but you must admit, it is a little precarious to tell a 8th grader that they may have the ability to understand an intriguing yet complex field of physics that is the product of tentative work by a genius.

 

[bobc2]

I like Feynman's comment about understanding Quantum Mechanics when addressing a nontechnical audience: "...You will discover that in order to make any reasonable predictions with this new scheme of quantum electrodynamics, you would have to make an awful lot of little arrows on a piece of paper. It takes seven years--four undergraduate and three graduate--to train our physics students to do that in a tricky, efficient way. That's where we are going to skip seven years of education in physics: By explaining quantum electrodynamics to you in terms of what we are really doing. I hope you will be able to understand it better than do some of the students!"

From "QED: The Strange Theory of Light and Matter"

 

[bcrowell]

It is possible to understand a huge amount of general relativity without any math beyond algebra. I would suggest the following approach:
- Learn Newton's laws well enough to get beyond the Aristotelian preconceptions that most people have subconsciously built up.
- Build a really solid background in special relativity. The best book I know of for this purpose is Spacetime Physics by Taylor and Wheeler.
- Read Relativity Simply Explained, by Gardner.
If you really devote some skull-sweat to those three steps, you will know quite a bit about general relativity. After that, we could talk some more. E.g., Nabeshin's suggestion of the book Exploring Black Holes is a good one, but you'd have to learn calculus first.
-Ben

 

[romsofia]

Obviously from this thread, it'd be good if you would've said what math you know already. A lot of people will assume that you "barely know algebra", but what I think most of them are missing is the possibility that you've already conquered calculus.
Sorry, but it just made me mad that they assumed you didn't even know algebra!

I can't really comment on the subject as I haven't even taken a course close to general relativity! What I would suggest for next year (since you'll be a freshman in high school) is to look at local universities and see if they offer an undergrad general relativity course and ask the professor if he'd mind if you sat in on the course (Hopefully he wont) and then that way you can be exposed to the subject!

 

[bobc2]

Here are two or three books to consider:

"Flatland" by Edwin Abbott (Dover Publications, Inc., N.Y., 1952, but I'm sure there is a more recent publication). I think you could get the knack for imagining the 4th dimension reading this one.

"General Relativity From A to B" by Robert Geroch (The University of Chicago Press, Chicago, IL, 1978). This book would probably be quite readable for you, and it is loaded with nice sketeches.

"Why Does E = mc^2 ?" A fairly recent book for those who don't have much of a background in math or physics but want to know about Relativity. It would give you a background in Special Relativity but also has a final chapter on General Relativity. It's probably in the physics books section of any Border's Book Store.

If you are in a difficult position for accessing any of the books that have been suggested in these posts (SpaceTime Physics was a really good suggestion), send me an e-mail with the address of your high school, and I'll mail a copy of "Why Does E = mc^2 ?" to the physics teacher there with a note suggesting he loan you the book, then put it in the school library. (Don't give your name--I'll tell the teacher you will identify yourself as a Physics Forum student.)

Good Luck!

 

[dkotschessaa]

Why don't we ask Einstein?

The present book [Relativity: The Special and General Theory] 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!

Cool, huh?

Downloadable from http://www.gutenberg.org/ebooks/5001".

The math contained therein is mostly algebra, with a little calculus. I'd say read it now, think about it, study math, read it again, repeat as necessary. Other books may be useful as well.

Note that a few of these formats do not include the equations, which you'll probably want to see even if you don't fully grasp them.

-DaveKA

 

[Vanadium 50]

The work presumes a standard of education corresponding to that of a university matriculation examination

And remember, we are talking about an 8th grader here - years away from that.

 

[dkotschessaa]

Of course, I didn't mean to make it sound easy.

 

[Anonymous217]

I too would suggest learning special relativity first. It doesn't require as much background knowledge. Any first-year student in Physics can learn special relativity and often do.

 

[Kevin_Axion]

I still don't understand how people think he can just learn Special Relativity, he's in grade 8. I'm not trying to be discouraging, but seriously? There is a little absurdity in that statement. I think we can conclude that he hasn't taken an algebra class as it's rare for a grade 8 to have mastered high school mathematics before entering it. The books are good suggestions, but I will have to say the Albert Einstein one introduces metric tensors and the like, clearly the OP won't be able to understand these books. The point is, suggest books that the person will understand so that it will spark an interest. Don't indulge them in the luxury of mathematics because it just spoils the fun, especially when they most likely haven't even factored a polynomial before.

 

[Fredrik]

I still don't understand how people think he can just learn Special Relativity, he's in grade 8. I'm not trying to be discouraging, but seriously? There is a little absurdity in that statement.

"He" is probably a she, since the name ends with "queen".

What kind of math does an 8th grader know? Do they know how to evaluate 8*(5+(-3))? Do they know how to solve t'²=v²t'²+t² for t'?

I haven't read the "easy" introductory texts myself, so I don't know how much math you need to understand them, but I do know that the essential features of the theory can be explained almost completely without math. All you really need to be able to do is to draw straight lines on a piece of paper. So I'm pretty sure that if I had an interested 8th grader here right now, I would be able to explain it to her. But I don't know if the books are as awesome as I am.

 

[Kevin_Axion]

I understand, which is why I said a qualitative description would be better. Some of the books people are suggesting discuss things like metric tensors with matrices and other mathematics that a 8th grader wouldn't know. It's very easy to explain, but as the OP stated, "what mathematics would be necessary?" It's obvious that they won't understand it but we have to wait until they reply. And yes, I was certain it was a she, whenever I write something quickly I don't usually pay attention to those details, he/she would have been better. Have you been watching the World Juniors?

 

[bobc2]

... but I do know that the essential features of the theory can be explained almost completely without math. All you really need to be able to do is to draw straight lines on a piece of paper. So I'm pretty sure that if I had an interested 8th grader here right now, I would be able to explain it to her. But I don't know if the books are as awesome as I am.

I think you've summed it up pretty well, Fredrik, and I'll bet you could do the job pretty well with your straight lines.

And I think most of the books suggested here do not contain any significant amount of math -- the little math there is not enough to be a show stopper (Einstein's book is really too much for the average 8th grader -- but, of course we really don't know if we've got a prodigy on our hands. Hopefully we'll hear back from the Queen).

 

[dkotschessaa]

Perhaps we need to delve into the word "learn" a little bit more here.

https://www.physicsforums.com/showpost.php?p=3064662&postcount=4" defines 3 tiers of learning from a mathematical standpoint. That's a great framework.

There are likely some levels before (and after) these which will give one a very general idea, and my hope is that someone on this level would be inspired to take it further by studying the mathematics involved. This is a great motivation to study math.

-DaveKA

 

[twofish-quant]

I still don't understand how people think he can just learn Special Relativity, he's in grade 8.

Grade 8 is plenty old enough to learn special relativity. If they can do the pythagorean theorem and basic algebra, then that's enough to do special relativity. If they don't know algebra, then they can understand the basic *physics* of special relativity.

The books are good suggestions, but I will have to say the Albert Einstein one introduces metric tensors and the like, clearly the OP won't be able to understand these books.

And most people if given a book on the Peano's axioms and arithmetic set theory will find it totally over their heads. However, that doesn't keep five year olds from being able to count.

Don't indulge them in the luxury of mathematics because it just spoils the fun, especially when they most likely haven't even factored a polynomial before.

It depends on how the math is taught.

 

[FantasyQueen]

It seems that my age is making a controversy here about whether I will be able to understand or not...
Also, I am a FEMALE student. I am sure you can infer that from my username-FantasyQUEEN.
Nevertheless, I appreciate the time and effort you put into answering my question.
I also apologise for asking this question I have recently received a personal message stating that by posting this, I have violated the rules of this forum. I am terribly sorry for this...I am very new to forums.

 

[Kevin_Axion]

So, what are your mathematical abilities/knowledge?

 

[Fredrik]

I also apologise for asking this question I have recently received a personal message stating that by posting this, I have violated the rules of this forum. I am terribly sorry for this...I am very new to forums.

It's definitely OK to ask the kind of question you asked in post #1 in this thread, so if you got reprimanded for that, it must be some sort of joke (a bad one), or just a weird mistake. Perhaps the PM was about something you wrote in another thread. (Something that got deleted perhaps, because I can't see anything wrong with any of your posts).

 

[evanallmighty]

Hi FantasyQueen,

Don't believe all of that baloney about your inability to learn about General Relativity. If you really have a passion to know about it, do not let all of this talk about those graduate level math and physics courses you must have discourage you from pursuing the subject of General Relativity. At your age and early stage of pursuing the mysteries of Einstein's theories, I think it is most fruitful to pursue the subject with zest.

One thing I would suggest is to start with Special Relativity. The main tough concept you will need from math (which you should be able to dig into) is the Pythagorean Theorem. Couple that with imagining a 4th dimension, and you can get going. There are some good books about Special Relativity that you can find in your high school library, your local city or county library, or a book store. Run down your high school physics teacher. If he's a good one, he will be so pleased to find an 8th grader so interested in physics that he will enjoy talking to you about the subject and pointing you to some good books.

My first exciting exposure to the world of physics was reading "One-Two-Three-Infinity" by George Gamow. I then read a book that began with a comment, "Only a dozen people in the world understand Relativity, and I don't intend to make that a baker's dozen..." After that it was "The Strange Story of the Quantum." My pursuit of physics was sustained reading books of this type and having interesting discussions with a very understanding high school Chemistry teacher. It was years later before I was enrolled in my first College physics course. Developing the Christoffel Symbols equations was insightful, but I would not trade for the wonderment of the high school years either.

Good Luck!

Thanks this is really helpful and very encouraging! I'm pretty much in his same position and this makes me feel really good!

 

[qspeechc]

Relativity for the Layman by James A. Coleman. Einstein said of this book:

"Gives a really clear idea of the problem, especially the development of our knowledge concerning the propogation of light and the difficulties which arose from the apparently inevitable introduction of the ether. The relativity of motion judged from the cinematic point of view is vividly demonstrated and also the principle of equivalence."

There's almost no math in the book, very little at least. In fact, the book was written so it could be understood by children. I particularly like the historical build up to the discovery of relativity.

 

[bobc2]

Relativity for the Layman by James A. Coleman. Einstein said of this book:

"Gives a really clear idea of the problem, especially the development of our knowledge concerning the propogation of light and the difficulties which arose from the apparently inevitable introduction of the ether. The relativity of motion judged from the cinematic point of view is vividly demonstrated and also the principle of equivalence."

There's almost no math in the book, very little at least. In fact, the book was written so it could be understood by children. I particularly like the historical build up to the discovery of relativity.

Good job, qspeechc! Great reference.

 

[CJSGrailKnigh]

Okay I'm going to make an assumption here. The original poster is probably a student who is rather bored with the status quo. As such I'm going to make the assumption that the OP is willing to learn something so I'm going to throw out something.

If you want a basic understanding of general relativity (something I don't claim to myself since I'm an engineer and the usefulness of relativity ended at special rel) learn special relativity a good and relatively cheap book is "Physics for Scientists and Engineers Volume 5". It explains a general sense of modern physics and it is mainly algebraic math. The next best thing after that is to read one of the non math based general relativity books. I only suggest this because after special relativity the math does become quite in depth and it will take an understanding of math that an eighth grader would not have. If that doesn't satisfy you ask your math teachers if you can borrow an old calculus textbook because if you really want to you can teach yourself a lot more math than high school gives you credit for.

Good Luck with your endeavor

 

[Sankaku]

There are really three tiers at which you can really learn anything substantive about general relativity.

This is a good general description.

"General Relativity From A to B" by Robert Geroch

This is a great book for tier 1. Here is an amazon link:
https://www.amazon.com/dp/0226288641/?tag=pfamazon01-20

It is possible to understand a huge amount of general relativity without any math beyond algebra.

Dr. Crowell knows what he is talking about. He has a free Relativity e-book here:
http://www.lightandmatter.com/genrel/
Although it lies on tier 2 of Nabeshin's post.

There is one more book that is somewhat unusual. Once you have some calculus under your belt, try this:
https://www.amazon.com/dp/1589880447/?tag=pfamazon01-20

In general, don't let the discussion of all the requirements put you off. One of the great things about GR is how it draws together many of the most interesting parts of Math and Physics. Hopefully, you can see that as good motivation to learn all these other topics!

 

[Cbray]

I don't think I've ever face palm'd myself as hard before I read this post.
You're obviously thinking GR is something you can do after learning basic mechanics off reading for a couple of weeks or months, at your level it would take you about a few years to learn multi-variable calculus, linear algebra (and other mathematical tools), and learn probably at the least a first year undergraduates physics course to just dip your toes in GR if you work about 4 hours a day.

OR you can just read a basic book on it to give you a description of it, or Brian Greene documentaries that make me livid.
By all means, just learn single-variable calculus then learn basic Newtonian mechanics up to conservation of angular momentum, and then read about special relativity.

 

[Matterwave]

I don't think I've ever face palm'd myself as hard before I read this post.
You're obviously thinking GR is something you can do after learning basic mechanics off reading for a couple of weeks or months, at your level it would take you about a few years to learn multi-variable calculus, linear algebra (and other mathematical tools), and learn probably at the least a first year undergraduates physics course to just dip your toes in GR.

OR you can just read a basic book on it to give you a description of it, or Brian Greene documentaries that make me livid.
By all means, just learn single-variable calculus then learn basic Newtonian mechanics up to conservation of angular momentum, and then read about special relativity.

Why would you facepalm over an interested student? Are we not supposed to be encouraging of the younger generation rather than trying to be elitist? I see no benefit to the argument "oh, you're too young, this is too complicated, forget about it".

For the low-level GR, I always recommend Lilian R Lieber's "Einstein's Relativity" https://www.amazon.com/dp/1406765236/?tag=pfamazon01-20.

You do need to know some algebra to understand that book, but that'd be about it.

It's pretty outdated since it was written in the 50's I believe, and so its concepts of "vector" and "tensor" are explained from a "transformational properties" perspective. But, for the quickest and easiest introduction, I think this book is best.

 

[Cbray]

Why would you facepalm over an interested student? Are we not supposed to be encouraging of the younger generation rather than trying to be elitist? I see no benefit to the argument "oh, you're too young, this is too complicated, forget about it".

For the low-level GR, I always recommend Lilian R Lieber's "Einstein's Relativity" https://www.amazon.com/dp/1406765236/?tag=pfamazon01-20.

You do need to know some algebra to understand that book, but that'd be about it.

It's pretty outdated since it was written in the 50's I believe, and so its concepts of "vector" and "tensor" are explained from a "transformational properties" perspective. But, for the quickest and easiest introduction, I think this book is best.

I'm happy for her to be interested, we no doubt need more people interested in physics. I'm still only a two years older than her and she is probably as keen to learn, I just face palm'd since it sounded funny and it was me thinking how naive the question was.

 

[dkotschessaa]

I'm happy for her to be interested, we no doubt need more people interested in physics. I'm still only a two years older than her and she is probably as keen to learn, I just face palm'd since it sounded funny and it was me thinking how naive the question was.

It was unnecessarily elitist, since the amount of math you described is not even necessary to get through Einstein's own Relativity: The Special and General Theory.

"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!"

- Albert Einstein - from the introduction