ABSTRACT
This chapter shows the math used in modern physics. It examines first relativity and then quantum mechanics. The discussion of special relativity opens with the Michelson-Morley experiment that disproved the existence of the ether. There is then a discussion of space-time and the idea of non-positive-definite metrics. Hyperbolic functions are examined and employed. Discussion of the space-time point of view leads to the twin paradox and its resolution. Examination of energy leads to E = mc2 which rounds out special relativity. General relativity begins with examination of gravity which led Einstein to learn differential geometry and use it to describe motion in space-time with gravity. We then shift to quantum mechanics. We begin with particle-wave duality and from them follow Schrodinger's approach to generate his quantum wave equation. We then explore the meaning of solutions to Schrodinger's equation in terms of the probability distributions that they give rise to. We move on to Heisenberg's algebraic approach to quantum mechanics, including his uncertainty principle. We end with a discussion of quantum field theory and the question of what math will be needed to help unify modern physics.
