The ‘Dramatic Picture’ of Richard Feynman by Freeman Dyson
….Feynman’s picture of the world starts from the idea that the world has two layers, a classical layer and a quantum layer. Classical means that things are ordinary. Quantum means that things are weird. We live in the classical layer. All the things that we can see and touch and measure, such as bricks and people and energies, are classical. We see them with classical devices such as eyes and cameras, and we measure them with classical instruments such as thermometers and clocks. The pictures that Feynman invented to describe the world are classical pictures of objects moving in the classical layer. Each picture represents a possible history of the classical layer. But the real world of atoms and particles is not classical. Atoms and particles appear in Feynman’s pictures as classical objects, but they actually obey quite different laws. They obey the quantum laws that Feynman showed us how to describe by using his pictures. The world of atoms belongs to the quantum layer, which we cannot touch directly.
The primary difference between the classical layer and the quantum layer is that the classical layer deals with facts and the quantum layer deals with probabilities. In situations where classical laws are valid, we can predict the future by observing the past. In situations where quantum laws are valid, we can observe the past but we cannot predict the future. In the quantum layer, events are unpredictable. The Feynman pictures only allow us to calculate the probabilities that various alternative futures may happen.
The quantum layer is related to the classical layer in two ways. First, the state of the quantum layer is what is called “a sum-over-histories,” that is, a combination of every possible history of the classical layer leading up to that state. Each possible classical history is given a quantum amplitude. The quantum amplitude, otherwise known as a wave function, is a number defining the contribution of that classical history to that quantum state. Second, the quantum amplitude is obtained from the picture of that classical history by following a simple set of rules. The rules are pictorial, translating the picture directly into a number. The difficult part of the calculation is to add up the sum-over-histories correctly. The great achievement of Feynman was to show that this sum-over-histories view of the quantum world reproduces all the known results of quantum theory, and allows an exact description of quantum processes in situations where earlier versions of quantum theory had broken down….