The mathematics is way too difficult

[seriously disabled]

I tried to understand quantum mechanics, general relativity and quantum field theory on my own, learning just from books, without having to go to University to study it but the mathematical machinery is just too complicated for me to understand.

 

So my impression is that unless you are very very good at math you have no chance of ever understanding quantum mechanics, general relativity and quantum field theory in this lifetime.

Edited February 8, 2013 by seriously disabled

[x(x-y)]

I agree - however, fortunately, I am fairly competent in mathematics (and I have studied basic quantum mechanics thus far on my degree, but not GR - looking forward to it though). Anyway, if you just keep on practising the maths and build yourself up from the very basics, then you have a fair shot at being able to understand the likes of QM and GR eventually; however, of course it does help to have some sort of lecturer/teacher/tutor.

[elfmotat]

Once you're familiar with Vector Calculus, Linear Algebra, and Differential Equations you're ready to start tackling the more complicated fields of physics. Most physics textbooks assume you're already competent in those three areas and will introduce any additional math as needed. And, of course, you need to be familiar with Classical Mechanics, including the Lagrangian and Hamiltonian formulations. I like John Taylor's book for Classical Mechanics.

 

You'll need to study Special Relativity before anything else. It's definitely the easiest to learn, and really doesn't require too much math. Taylor and Wheeler's Spacetime Physics would be my recommendation for SR.

 

From a math standpoint, QM is probably the next easiest. Griffiths' book would be my recommendation.

 

You don't actually need to know any differential geometry before you start studying GR (though it would be invaluable) because most intro textbooks will introduce the math as you go along. Schutz's book would be my recommendation for a beginner.

 

Once you're familiar with all of those + Classical Field Theory (the short intro in Carroll's GR textbook should be enough CFT) you'll be ready to start tackling QFT. Peskin and Schroeder's text is generally recommended here.

[beefpatty]

I tried to understand quantum mechanics, general relativity and quantum field theory on my own, learning just from books, without having to go to University to study it but the mathematical machinery is just too complicated for me to understand.

 

So my impression is that unless you are very very good at math you have no chance of ever understanding quantum mechanics, general relativity and quantum field theory in this lifetime.

 

What level of maths are you at?

 

The QM book titled "Principles of Quantum Mechanics" by R. Shankar commits the entire first chapter to the mathematical machinery necessary to understand QM. It's a graduate level text, but the maths is easy enough to understand, as long as you don't skip any steps. In my opinion, when working through a textbook you need to be very methodical. Don't skip problems, and if the author makes a derivation and skips some steps (which they almost always do), fill those in yourself. You cannot learn from a text just by reading, you have to work alongside it with pencil and paper.

[Enthalpy]

It all depends on what one calls "difficult mathematics"...

 

QM is all about waves, and accordingly is as complicated as waves are: optics, acoustics, radiocomms... It does add some formal operators, which are linear algebra. Nothing tragic, even an engineer can hope to grasp it.

 

That's maths created over a century ago (Fourier). Present-day maths are horribly more difficult.

[Robert Clark]

I tried to understand quantum mechanics, general relativity and quantum field theory on my own, learning just from books, without having to go to University to study it but the mathematical machinery is just too complicated for me to understand.

 

So my impression is that unless you are very very good at math you have no chance of ever understanding quantum mechanics, general relativity and quantum field theory in this lifetime.

You would certainly need to have an undergraduate level understanding of math and physics. But if you major in those fields you should be able to understand it.

 

Bob Clark