S-matrix

The S-matrix (or Scattering Matrix) theory was a proposed principle of particle interactions. The approach was started by Werner Heisenberg in 1943, who was building on work by John Archibald Wheeler, from the previous decade. 

Why should theoretical physicists have any business in knowing the inner workings of hadrons? The advocates of the S-matrix wanted to keep the physics as close to the experimental data as possible. They didn't want to speculate too much about the inner workings of the proton. The input of this S-matrix is some specified collection of particles that are about to collide. These are some composite particles (hadrons), such as protons, neutrons, mesons or even some atomic nuclei. Each of these particles, has properties, such as: momentum, spin and electric charge. When these particles enter the S-matrix, they disappear. However, groups of particles will come out of the S-matrix. These are the byproducts of the collision, which also have their own properties. But what exactly was happening in the S-matrix? Physicists were afraid to look inside to see. What were it's underlying mechanisms? The S-matrix went from the initial, right to the final state particles. The S-matrix would be a table of quantum mechanical probabilities. For each input, the S-matrix, will give you the probability of the output. The S-matrix would make these quantum mechanical predictions based on the direction and momentum of the incoming and outgoing particles. 

The S-matrix approach, was proposed to replace the standard techniques of quantum field theory, as it could answer some phenomenon at strong coupling. One of the reasons that the S-matrix approach was abandoned was because of the obscurity of it's mathematical methods. The S-matrix, did not rely on local notions of space and time. This makes it difficult to formulate a physical theory. Space and time were avoided and were replaced with some of the S-matrix's mathematical properties. Instead, the infinite past was related to the infinite future. This was done in one step. It could not be reduced to slices of time or to intermediate steps. On a related note, Werner Heisenberg believed that space and time broke down at the nuclear scale. The proton and neutron, are not point like particles, like the electron. This was beginning to be suspected at the time. If only had they known that the application of the S-matrix theory to strongly interacting particles would lead to the birth of string theory! That being said, the S-matrix was completely abandoned in the 1970s, when it was discovered that Quantum chromodynamics is the proper theory of strongly interacting particles.