## Quantum Physics

In the early twentieth century, experimental physicists discovered that subatomic particles, the smallest constituents of matter, obey entirely different laws of nature than macroscopic objects. Classical physics, as proscribed by Isaac Newton, conceives of a deterministic universe, where the future behavior of objects can be predicted exactly. Baseballs, for example, follow a well-defined Newtonian trajectory, and the future positions of the orbiting planets can be precisely predicted with basic physics.

However, quantum physics, the framework describing small particles, rests on a foundation of

The next step forward for quantum theory came in the 1940s, when Richard Feynman discovered another mathematical technique for predicting quantum probabilities. The

However, quantum physics, the framework describing small particles, rests on a foundation of

*probability*. Unlike planets, for example, whose future positions can be predicted precisely, electrons exist in a probabilistic haze. Quantum theory can only determine the probability that a particle will behave in a particular way. Erwin Schrodinger, in 1926, first conceived of a mathematical equation that can predict these quantum odds. The eponymous Schrodinger equation tells us the probability that a particle will be found in a particular location.The next step forward for quantum theory came in the 1940s, when Richard Feynman discovered another mathematical technique for predicting quantum probabilities. The

*path-integral formulation*asserts that particles, when moving from one location to another, travel along all possible paths between these two locations. Thus, their overall motion is a sort of average over all possible trajectories. Calculating this average requires a mathematical tool called a*limit*, where successively precise approximations approach an answer. The end result of this*path-integral*is the probability that a particle will be found in a certain location.