I want to understand the universe

Looh

Hello!

As I'm new on the forum, I might aswell start off with an introduction as that may be helpful given the purpose of the thread. I'm 19 years old and I'm currently in high school; my scientific knowledge is quite limited, I do have a basic knowledge of maths reaching up to and around calculus, I've taken courses in physics due to a genuine interest but I failed them because I've been such a lazy fool. I have a basic understanding of forces, but I lack knowledge in most other necessary fields within physics. Besdies that, I have a very limited understanding of basic chemistry and I'd say I'm quite well versed in biology and genetic engineering at basic levels.

Now, to the true purpose of the thread. As the topic says, I want to understand the universe. My current goal is a complete understanding of both the special and general theories of relativity; and as I want to truly understand it, I assume knowing the maths behind it is essential. I'm also very interested in uncertainty and quantum mechanics, but I know close to nothing about those subjects. Nor do I know about string theory, but it does indeed look interesting as it, as far as I understand, could very well turn out to be a complete theory of everything.
So I'm basically asking for help here; where do I start? Are there any good e-books or online courses that you can recommend? Am I in need of an education at a university, or could I find enough material on the internet or in the library? I won't be able to attend courses that costs money, but I'll check the library for books that could help me reach my goal.

Thank you for reading, I hope that I'll be able to evolve intellectually during my time here on this forum.

genericusrnme

Mary Boas - Mathematical Methods in the Physica Sciences
That book will get you started on the basic maths you need to know
Landau & Lifshitz - Mechanics - Vol 1 of A Course of Theoretical Physics
That book will get you started on the basics of physics (aka lagranges equations)

You'll also want lots of linear algebra
Gilbert Strang - Introduction to Linear Algebra
Kunze & Hoffman - Linear Algebra (I'm pretty sure I spelled the first guys name wrong)
Steven Roman - Advanced Linear Algebra

Maybe some mathy algebra too;
Poalo Aluufi - Algebra: Chapter 0
Bourbaki - Theory of Sets and Algebra Vol 1 &2 (although these are a little out dated)

For quantum mechanics
Landau and Lifshitz - Non Relatavistic Quantum Mechanics (a little out dated but it gives you a better feel for it than the more elegent modern books do imo)
JJ Sakurai - Modern Quantum Mechanics

You'll also want to know a little analysis;
Tom Apostol - Mathematical Analysis

Once you've got thatunder your belt, I recently found a nice little textbook you may enjoy
Mikio Nakahara - Geometry Topology and Physics

But really, once you've got the first two books read you'll know the general jist of what it is you're looking for..

In my opinion you can learn whatever you want and at a pace more suited to you without going to university (provided you have some will power and discipline). Getting a job at the end of it however is a different matter, you pretty much need a university degree for that part.

Good luck!

Looh

Thank you very much for your suggestions, genericusrnme, I'll check them out immediately!

Nabeshin

I'll say that this is a very ambitious book list, especially for a high school student. Most of these books are written for 3rd or 4th year university students, and some for graduate students.

Furthermore, if it's physics you're interested in, I wouldn't recommend most of these either. They are very heavy on (abstract) mathematics, which isn't really the core of physics. Sure, many of us find it interesting in its own right, or as a means to an end, but if you just start out reading Boas, Strang, Apostol, etc. you don't really see where the material is applicable to the real world. I'd say this is a way to get demotivated fast. This is maybe a list of books one should have read to start approaching string theory from a more formal perspective, which is itself a tall goal even for a university student.

I don't really see anything terribly wrong with the standard textbooks used in university. I don't really have the time to list them off here, or to come up with a list of my own, but there are tons of threads on the subject here. So, for example, if you want a book for an introduction to quantum mechanics, search in this forum and you'll see dozens of threads with people asking the same question. There are also some free books online if you're unable or unwilling to get texts from the library. I'm not too familiar with them, but Ben Crowell who posts here at PF has his own set of free books you might be interested in checking out: http://www.lightandmatter.com/books.html

micromass

Anyway, here's a book list:

For mathematics:

A first course in calculus - Lang
Like the title says, it's quite a good introduction to calculus. You said you know calculus, so this book might not be necessary.

Calculus - Spivak
OK, this is a pure math book. But knowing calculus is so very important in everything you will do, so I guess it's better to do it right. If you want to do physics, then understanding this book isn't necessary. But there might come a time that you want to know the math behind physics. For example, you might want to study functional analysis for QM or manifolds for relativity. This involves pretty heavy math. Understanding this book is a very good tool.

Introduction to linear algebra - Lang
An excellent treatise on linear algebra with lots of motivation from geometry and algebra. It has many computational exercises, but also conceptual proofy questions.

Vector Calculus, Linear Algebra, and Differential Forms: A Unified Approach - Hubbard
One of the best calculus 3 books out there, and not terribly difficult. It also contains a unique view on linear algebra and develops differential forms in view of that.

Elementary differential equations - Boyce, Diprima
This is a bit of a cookbook text. Got this equation? Do that. But unfortunately, most differential equations texts are like this. Still, I think it's a very decent book.

Mathematical methods for the physical sciences - Boas
An extremely good book, but you need some prerequisite knowledge to fully appreciate it. Knowledge of calculus and linear algebra would be good and probably some knowledge of physics. But this book contains about all the math you need to appreciate most of physics (of course, if the physics becomes more advanced, so does the math!!)

As for physics, I can't give you much advice as I'm no physicist. But here are two books:

Physics for scientists and engineers - Halliday and Resnick
This book, or books like it, are very good starters if you want to begin in physics. They a very basic knowledge of calculus, but no advanced math. Personally, I find books like this pretty boring, but you have to got through them. You will likely not understand more advanced texts if you don't get the basics.

Classical Mechanics - Taylor
A very good and comprehensive text on classical mechanics. A very good second book to read.

phinds

I agree w/ Nabeshin that genericusrnme's list is too heavy for someone at your level, too much focused on the math, and could well be demotivating. Depending on how quickly you want to jump into the math, or rather, I should say, if you want to AVOID jumping into the math too quickly but get a broad perspective on the subjects you name, I'd suggest you start out with the more accessible popularizations that are light on math. Try a book or two in each of several fields (cosmology, string theory, quantum mechanics, etc) to get an overview and see where you might be most interested in jumping into more rigorous detail. I'd suggest Steven Weinberg's "The First Three Minutes" as a good starting point.

Should you take that approach, BE CAREFUL about one thing --- even the really serious professional physicists sometimes make VERY poor choices of terminology and make overly simplified statements, so take everything with a grain of salt. The point would be to get an overview, not to feel that you have learned the details.

WannabeNewton

Halliday and Resnick "Fundamentals of Physics" is a great textbook for the Physics I, II level. Its "calculus" based but all the calculus problems in the book tend to be very easy and not too insightful; the very annoying / difficult problems tend to be algebraic. Its a pretty standard text. I think Landau would be a bit of a stretch for a person starting out with physics. The motivation for Lagrangian and Hamiltonian mechanics would be better appreciated if he/she first understands the usual Newtonian formulation.

Nabeshin

This is a true point, but even if one understands the Newtonian formulation, L&L is not the best place to start learning Lagrangians and Hamiltonians. It's very terse, which I can see giving a lot of students (ESPECIALLY self-studying ones) a very difficult time. Something like Thornton & Marion, Goldstein, or Taylor would be better in my opinion.

BruceW

yes, it's probably best to get very familiar with the Newtonian formulation first, then go on to Lagrangian. I agree with Nabeshin really. The best way to learn stuff is by reading through the recommended university physics textbooks. Just google a couple of universities and have a look at their reading lists.

WannabeNewton

Oh yeah I agree I just stated Landau because the other poster mentioned it. Taylor is an awesome text not to mention it has a great cover haha.

chiro

Hey Looh and welcome to the forums.

I'd actually suggest reading the Feynmann lectures if you want some physics intuition. It's a three volume set and covers a lot of stuff. It's not complete with regards to todays thinking, and knowledge but it's really good for getting the intuition.

twofish-quant

One bit of advance. Start with Newtonian mechanics. It's critical that you have a firm understanding how Newtonian mechanics works before doing anything else. One thing is that quantum mechanics and GR is in fact not more complicated then Newtonian mechanics. The difference is that people have "inituition" with Newtonian mechanics that doesn't exist in GR or QM.

Another bit of advance, is give up trying to understand everything. There's just too much for one human being to understand. You'll be doing great if you just find one bit of knowledge that interests you and work on that. One mental picture that I have is one of "mining truth". You just find a tiny bit of ground, and then start digging to see if you can find bits of diamond there.

With your current background, special relativity shouldn't be a problem. To understand special relativity completely takes some algebra, and nothing more.

General relativity is a bit trickier. To understand how to come up with the basic equations, you can get there with a few months of work. Now to understand the full *consequences* of these equations is something no one does. What people usually do is to work with simplications of the full GR equations.

You are about two years away from developing a "working knowledge" of quantum mechanics. The critical bit of mathematics is partial differential equations and a little linear algebra.

For "complete knowledge", no one has that. With about five years of work, you can understand everything that is known about QM, and end up on the frontier of knowledge at which point, you have to figure something out. Or you can use "basic knowledge" of QM and go off in a different direction.

Or it could be a waste of time. If you mine the same patch of dirt for two decades and come up with nothing, it could be that there is nothing there.

One thing is that there is this philosophy called "reductionism" which is that if you understand the basic processes of the universe, you understand everything. Personally, I think that's nonsense, which means that there is a whole bunch of other things to understand. Statistic mechanics for example.

The easy thing to do is to enroll in the local university, become a physics major, and then go to graduate school. A lot of the knowledge that is there is "tacit knowledge" which isn't something that you can easily get by reading books. One knowledge is "knife skills". Something that's very important in being a chef is to be able to use a knife to very quickly chop vegetables. This is somethng that you just have to practice at. There are similar bits of knowledge in doing physics.

A lot of physics involves problem solving. Someone gives you a problem, you break it up and solve it. The important thing is to be able to do it quickly and efficiently, and to do that, you just need practice.

The interesting thing is that I do believe that there is enough stuff on the internet now so that someone that is *extremely* motivated and unable to attend university for whatever reasons could self-teach themselves undergraduate physics. But no one has yet packaged that together. Someone will....

twofish-quant

A lot depends on the personality of the person looking at the books. Personally, I find looking at those sorts of books to be quite *motivating*. It's a "I don't have a clue what these greek symbols mean but I'll ram my head against the wall until I find out". After about two months of this, the book comes from 100% incomprehensible to 95% incomprehensible, at which point i feel good.

One thing I did when I was in high school was that I took out a book on general relativity, and started crashing my head against it. I took me about five years before I was able to finally make sense of it. The cool thing was that when I finally understood what a Christoffel symbol was, and the difference between covariant and contravariant vectors, and how tensors work, I figured out how I would have explained it to a 16 year old me. I also found that GR isn't terribly useful in the types of physics I was interested in. :-) :-) :-)

But people are different. One important thing that's missing is the "social aspect" of learning physics. It's important to get yourself in some sort of community in which you can learn the "psychology of physics" from someone else.

Also it's a good idea to look at multiple textbooks. One cool thing is to look at different textbooks and figure out that the authors are approaching the topic from completely different angles.

The other thing is that there is a huge missing step in textbooks. There are textbooks for graduate students. There is "popular literature." There isn't much in between.

twofish-quant

I also like Peter Szerkes "A Course in Modern Mathematical Physics"

It's not a great book for directly learning the material, but I think it's good as something of an "checklist" of the material that you should learn.

The other must read if you are into numerical stuff is "Numerial Recipes for C++". It's a cookbook. One thing to note is that the text is great, but the code examples are *terrible*.

Nabeshin

What exactly do you mean? What would you call undergraduate level books, if not 'something in between'?

Karimspencer

I suggest starting over with physics. Even revise some of the things that you already know about. Go through some of the physics books given above and start with really basic calculus or even go over all of algebra again for it'll help. Get a good understanding about the history of physics(Greek Philosophers to the modern researchers of today) Read some published books written physics and math professors. Take some tutoring by honor students in your class. Try getting a complete understanding of basic physics so you can go up the ladder with a great understanding of out universe.

phinds

This is a really nice ideal scenario but it posits a degree of patience that I think is unrealistic. Much more reasonable would be to do what you suggest IN PARALLEL with learning new stuff to keep the juices flowing.