I want to understand the universe

[Looh]

Hello!

As I'm new on the forum, I might as well 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 & Lifgarbagez - 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 Lifgarbagez - 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]

Mary Boas - Mathematical Methods in the Physica Sciences
That book will get you started on the basic maths you need to know
Landau & Lifgarbagez - 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 Lifgarbagez - 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!

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]

The motivation for Lagrangian and Hamiltonian mechanics would be better appreciated if he/she first understands the usual Newtonian formulation.

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]

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.

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 Feynman 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]

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.

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.

I'm also very interested in uncertainty and quantum mechanics, but I know close to nothing about those subjects.

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.

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.

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.

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.

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]

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.

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.

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

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]

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.

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]

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.

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.

 

[Looh]

Wonderful, I was close to completing my answer to the thread when I accidently closed down the tab and lost all my text. A less elaborate answer will have to suffice, I'm sorry.

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.

I actually wouldn't mind learning maths - but I generally feel that the more advanced concepts are, I don't know, scary. However, I think that acquiring a general overview over the subjects is a pretty good idea. As twofish-quant wrote, it's pointless in trying to understand every subject to the fullest. My best bet would probably be to get an overview and then start digging in the subject I find most interesting.
As for the book you suggested, I'll definitely check it out. Hopefully I can find it in my local library. Do you think that Brain Greene's The Elegant Universe is a good choice to read for an overview of string theory? I've heard good things about it.

Thank you for your answer.

Anyway, here's a book list:

Looks like a wonderful compilation, thanks! I'll see if I can get a hold of some of the books.

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.

Yes, I was thinking of starting with classic mechanics. I did have a book about it, but unfortunately I've lost it.

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.

Yes, the best thing is probably to just enroll in a university. But there are some problems.
First, I'm not done with high school yet. And as such, I don't have enough grades to enroll. Secondly, there is no university in the city I live in. I'm not sure if I have the luxury of choosing, so I don't know where I might end up (I live in Sweden, by the way).

I was actually going to enroll for some courses now during the summer (distance), but I needed my final grades from high school so I couldn't do it.

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*.

Something I didn't mention in my introduction is that I'm quite experienced with computers and IT-security; and as such, I do know several languages (including C/C++). But why would C++ be good for physics or even maths in general?


Thank you all for the help! I really appreciate it.

 

[Karimspencer]

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.

:) Well of course he is going to learn new stuff + the basics.

 

[BruceW]

Something I didn't mention in my introduction is that I'm quite experienced with computers and IT-security; and as such, I do know several languages (including C/C++). But why would C++ be good for physics or even maths in general?

algorithms. Computers have the kind of processing power that is often useful. If you think about it, lots of physics research requires programs to be written. e.g. astronomical data, data from particle detecting equipment, data from most sophisticated equipment really. And then there's also the ability to run a model of some physical situation and see what happens, and maybe make predictions about what would happen in the real-life physical situation.

 

[kloptok]

Now I don't know how good you are in maths but I would suggest starting with Introductory Linear Algebra and Calculus, as every physics university student would. Sure you've learned some stuff in high school (=gymnasium?) but there's a LOT more to learn out there. Which takes me to my second piece of advice: patience and stubbornness! You will not learn physics in a couple of months or a year. It takes years of studying to get to the advanced topics you are interested in, string theory is something you usually don't begin to study until master's level at university or even later. And general relativity is also quite advanced, tensors are tricky and require a mathematical "maturity" as people call it. Although you could very well grasp the basics if you first study special relativity.

A normal physics bachelor's curriculum starts with about two years of basic mathematics and physics courses, the first year contains a lot of maths (linear algebra, single- and multivariable calculus, probability/statistics). After this you are ready to tackle quantum mechanics and relativity (actually special relativity is not that difficult and can be done with high school algebra, but you will understand it better the more physics and maths you know). So if you do not have the patience to go through the basics before diving into relativity and quantum physics, I would not suggest studying physics at university. However, from your recent posts it sounds like you have an interest in the things encountered along the way and are interested in maths and physics in a more general sense. Then physics might just be for you.

Brian Greene is quite good, but as with all popularizations things soon gets very loosely described and there is sometimes a tradeoff between accuracy and "understandability". I do not say that you should avoid these books, they are still a fun read, especially at your level, and can give you a feeling for the ideas involved and if you like them. But to understand the maths behind string theory you will have to study many years. There are some books by Hans-Uno Bengtsson which introduce a bit more mathematics which you might be able to find in your local library ("Kvarken och universum", "Bengtsson om ..."-serien) . I would recommend you to take a look at the science shelf there and see what you find, there are sometimes also university textbooks available.

By the way, I'm also from Sweden (the Hans-Uno Bengtsson reference was a bit of a giveaway I guess =P ). I'll happily give more advice if you want!

 

[phinds]

As for the book you suggested, I'll definitely check it out. Hopefully I can find it in my local library. Do you think that Brain Greene's The Elegant Universe is a good choice to read for an overview of string theory? I've heard good things about it.

Yeah, I'd say Green is a good intro on string theory BUT I would caution you to put string theory at the bottom of your list. It MAY turnout to be the be-all and end-all, but right now it's been worked on by a LOT of very bright people for over 20 years and it really hasn't produced anything despite all the promise that was seen about 25 years ago. I recommend cosmology (including SR and GR) and quantum mechanics as being QUITE enough to bite off for a while.

I agree w/ kloptok about the need to be wary about the details in popularizations. Even Weinberg, for example, makes the EGREGIOUS mistake of referring to the big bang as a POINT when he really does know better. Also, be wary of INTERPRETATIONS. Quantum mechanics has several of them, each contradictory and yet each with its own covey of adherents.

BUT ... I still say that several such popularizations will give you a good broad picture and help you decide where you might want to focus your energies.

THere is some tension between what I just said and the very correct fact that you won't undersand much of any of it in detail without the math (which leads some people to insist that you HAVE to start with the math) ... BUT ... here's the real point: the math for some areas will appear more difficult than that for others, but that's a distraction. What is IMPORTANT is that you first figure out what you love to do and go there. If you do it that way, the degree of difficulty of the math will be irrelevant.

 

[Nabeshin]

Regarding reading Brian Greene, I agree more or less with what phinds has said above. Two points I think are worth making (or restating). The first is that a book like The Elegant Universe actually has some decent descriptions of established physics (chiefly relativity and quantum mechanics) for the first ~100 pages or so. So even though it's about string theory, you can learn these more fundamental pillars as well. Secondly, you really do have to caution against taking what is written in a book like this at face value. I suspect that if you were to just read this in a vacuum, you would assume from Greene's language that string theory is the only thing in theoretical physics that anyone is working on, that we're right around the corner from a breakthrough, and that everyone agrees this is the correct direction. Of course, none of these are really true. So while it's fine to read about these things, try not to lose context of what they are.

Another general note about popular science books is that if this is all you read, you have to resign yourself to taking a lot of things at face value. For example, you could 'understand' the expansion of the universe via the ants on the surface of an expanding balloon analogy. You might even be able to talk about some predictions and outcomes of this as it relates to our physical universe. But as far as why this is a somewhat accurate description of reality, essentially all you can say is 'because someone told me so'. It's not a terrible state of affairs though, it's one in which essentially you are not ignorant, but also not intelligent on the subject matter.

 

[Nano-Passion]

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.

Can you elaborate on this statement.

 

[twofish-quant]

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

Undergraduate level physics books typically assume the ability to do partial differential equations. For GR and cosmology, they are typically aimed at juniors and seniors.

The thing about popular books is that the usually assume zero mathematical ability. If you have someone that can do algebra, or better yet basic calculus, you can do lots of explanations that wouldn't otherwise be available.

This wouldn't be that much use for physics majors, but the target audience would be say a civil engineering major that is interested in general relativity.

 

[twofish-quant]

My best bet would probably be to get an overview and then start digging in the subject I find most interesting.

Something that you might be interested in galaxy formation, turbulence, statistical mechanics, and magnetic fields. Personally, I find those things more interesting than string theory.

Do you think that Brain Greene's The Elegant Universe is a good choice to read for an overview of string theory? I've heard good things about it.

I'm actually pretty negative about string theory because we've dumped twenty years of effort into it, and gotten nada. The reason I'm more interested in galaxy formation is that it's likely that we'll know more about galaxy formation in 2015 than we do today. This isn't necessarily true for string theory.

String theory has some interesting mathematics, but there's very little useful physics.

Something I didn't mention in my introduction is that I'm quite experienced with computers and IT-security; and as such, I do know several languages (including C/C++). But why would C++ be good for physics or even maths in general?

Templates. It turns out that you can write extremely efficient numerical code in C++. Also, a lot of physics code turn out to be huge CS projects with millions of lines of code.

Something that you might want look at is lattice gauge theory or numerical relativity.

 

[twofish-quant]

Can you elaborate on this statement.

Sure. You write the equations of GR, you get ten non-linear partial differential equations. No one fully understands the properties of those equations. What people do in practice is to take those PDE's and the make approximations and simplifications to get you something that you can calculate.

However, if you write those 10 equations in their full glory, there are some basic mathematical questions that are not answers. For example, can you have a wormhole or can you have a "realistic" naked singularity? No one really knows.

It turns out that GR is too complex to handle fully. What people do is to write approximations to actually solve problems. The simplest approximation is Newtonian gravity. If it turns out that this won't work, then you go for simple extensions.

The same turns out to be true for quantum mechanics. Except for the hydrogen atom, the equations are not fully solvable, so a lot of getting numbers involves making approximations.

 

[Feodalherren]

I don't know if anybody already mentioned it but Khan Academy is an excellent resource if you want to catch up on physics and/or mathematics.

You're pursing a noble goal. Although physics is far too wide for you to specialize in all of the mentioned fields, expertise in anyone of them should give you sufficient understanding to satisfy your curiosity (although the theoretical physicists specializing in relativity would sometimes argue that other physicists only THINK they understand relativity). Who knows, maybe you will be the one to finally unlock the secrets that bind the quantum and astronomical worlds together?
I wish you the best of luck on your road, it will be filled with many difficult challenges. Start training that logical part of your brain, physics = math.

 

[twofish-quant]

Although physics is far too wide for you to specialize in all of the mentioned fields, expertise in anyone of them should give you sufficient understanding to satisfy your curiosity (although the theoretical physicists specializing in relativity would sometimes argue that other physicists only THINK they understand relativity).

And by and large other physicists would agree. I just know enough general relativity to show that general relativity turns out to be unimportant in modelling supernova, and that's enough for me. It turns out that the amount of relativity that you have to know in order to do useful things in most fields of astrophysics (including black hole physics and cosmology) is pretty low.

Who knows, maybe you will be the one to finally unlock the secrets that bind the quantum and astronomical worlds together?

Something that you quickly learn is that there isn't one secret. There are thousands of secrets out there, and it's not hard to find a niche in which you can discover something useful. One thing that I'm trying to get the OP to avoid doing is to get so focused on string theory, than you lose sight of other "mysteries of the universe." (Such as the fact that we don't know how globular clusters, type II supernova, type Ia supernova, galaxies, or black jets work.)

The other thing is that "binding quantum physics and astrophysics" is "just an ordinary day in the office". If you do anything in astrophysics, then you'll constantly be thinking in terms of quantum mechanics.

I wish you the best of luck on your road, it will be filled with many difficult challenges. Start training that logical part of your brain, physics = math.

In fact, physics *isn't* math. Physics uses math, but it's not the same thing. A physicist is to a mathematician what a novelist is to a linguist.

 

[Feodalherren]

And by and large other physicists would agree. I just know enough general relativity to show that general relativity turns out to be unimportant in modelling supernova, and that's enough for me. It turns out that the amount of relativity that you have to know in order to do useful things in most fields of astrophysics (including black hole physics and cosmology) is pretty low.

Then you know much more than I do and I will take your word for it :).

Something that you quickly learn is that there isn't one secret. There are thousands of secrets out there, and it's not hard to find a niche in which you can discover something useful. One thing that I'm trying to get the OP to avoid doing is to get so focused on string theory, than you lose sight of other "mysteries of the universe." (Such as the fact that we don't know how globular clusters, type II supernova, type Ia supernova, galaxies, or black jets work.)

Aren't those the kinds of things that you bump into along the road anyway? People in general don't start out knowing what a black jet even is (I sure don't).

In fact, physics *isn't* math. Physics uses math, but it's not the same thing. A physicist is to a mathematician what a novelist is to a linguist.

What I was getting at was that you need to be an excellent linguist in order to be a good novelist. If you're not good at math you're going to be crippled physicist.