What knowledge of mathematics and or/ physics would I need to understand relativity and quantum mechanics?

Answer 1

Depends on how detailed you want to be. At the overview level, you can get by with ordinary algebra for Einstein's work. E = mc^2, for example, is easily solved via algebra. So are the mass inflation and time dilation equations like t = t0/sqrt(1 - (v/c)^2) and m = m0/sqrt(1 - (v/c)^2). But if you were wanting to derive these, in order to understand them better, you'd need linear algebra, matrices, vector analysis, and, probably, tensor analysis.

Quantum mechanics is a bit more difficult because even the fundamentals start with probability functions. So overviews tend to get a bit technical. And to confound the situation even further, something called the BRAKET notation was invented to make solving these probability relationships easier for those on the inside of QM, but harder to understand for those who are not immersed in QM.

Brian Greene's "The Elegant Universe" provides both a non-technical and a technical narrative about string theory and related stuff. He uses a lot of illustrations requiring no math at all to understand some aspects of string theory. But if you want the math, he also provides some of that...although not the really tough stuff.

Answer 2

Simple relativety doesn't require anything more than simple algebra. It's not complicated mathematically at all, just conceptually. General relativativety and Quantum mechanics are much harder, and to really be able to understand what the math means requires years of working with the math. You need to understand field theory, complex numbers, and linear algebra. A good starting block is Griffin's Electricy and Magnetism. If you can understand that, you'll have a fantastic start on a deeper understanding of the world around us (you'll need to understand calculus). Griffin also has a quantum text that's good for getting started on understanding the quantum world, though you'll really need a good grasp of linear algebra to get much out of it.

Answer 3

The mathematics behind relativity and quantum mechanics are pretty different.

To understand relativity, you must understand differential geometry. Working familiarity with tensor algebra is also important. The basic features of Special Relativity can be understood with basic algebra and geometry, though that is extremely limiting.

For quantum mechanics, to start you need to understand linear algebra, vector spaces, and partial differential equations. To get anywhere important, you need group theory, abstract algebra, and theory of special functions.

Answer 4

E=mc^2 is actualy a refinement of Newtons F=ma. Understanding "earth bound" energy concepts, like inertia, work, and kinetic energy are important pre requisites.

It turns out that when masses become very large, like stars, and velocities become large, like the speed of light, Newtons laws do not apply as well.

Einstein was the one that figured out why.

Also some basic concepts from calculus, like limits would help. This deals with what happens when quantities approach the infinite, or the infinitesimal (infinitly small, as in approacing nothingness)