He also recognized that these relations might be useful in computing observables for the case of strong interaction physics. Heisenberg's proposal was revived in 1956 when Murray Gell-Mann recognized that dispersion relations-like those discovered by Hendrik Kramers and Ralph Kronig in the 1920s (see Kramers–Kronig relations)-allow the formulation of a notion of causality, a notion that events in the future would not influence events in the past, even when the microscopic notion of past and future are not clearly defined. But without extra assumptions on the high-energy behavior, unitarity is not enough to determine the scattering, and the proposal was ignored for many years. #STRINGS THEORY TRIO SERIES#This property can determine the amplitude in a quantum field theory order by order in a perturbation series once the basic interactions are given, and in many quantum field theories the amplitudes grow too fast at high energies to make a unitary S-matrix. In all conceivable situations, the sum of the squares of the amplitudes must equal 1. Heisenberg proposed to use unitarity to determine the S-matrix. In this proposed S-matrix theory, there are no local quantities at all. In quantum field theory, the intermediate steps are the fluctuations of fields or equivalently the fluctuations of virtual particles. But when transitions from the far-past to the far-future occur in one step with no intermediate steps, it becomes difficult to calculate anything. Heisenberg proposed to study the S-matrix directly, without any assumptions about space-time structure. The S-matrix is the quantity that describes how a collection of incoming particles turn into outgoing ones. The physical quantity he proposed as fundamental is the quantum mechanical amplitude for a group of incoming particles to turn into a group of outgoing particles, and he did not admit that there were any steps in between. Heisenberg proposed that even when space and time are unreliable, the notion of momentum state, which is defined far away from the experimental chamber, still works. The objects that fly to infinity are stable particles, in quantum superpositions of different momentum states. An experiment only sees a microscopic quantity if it can be transferred by a series of events to the classical devices that surround the experimental chamber. Heisenberg proposed a solution to this problem: focusing on the observable quantities-those things measurable by experiments. Without space and time, it becomes difficult to formulate a physical theory. Heisenberg proposed that the strongly interacting particles were in fact extended objects, and because there are difficulties of principle with extended relativistic particles, he proposed that the notion of a space-time point broke down at nuclear scales. Their interactions were so strong that they scattered like a small sphere, not like a point. Their magnetic moment differed greatly from that of a pointlike spin-½ charged particle, too much to attribute the difference to a small perturbation. By the 1940s it had become clear that the proton and the neutron were not pointlike particles like the electron. The theory presented a radical rethinking of the foundations of physical laws. Physicists neglected it because some of its mathematical methods were alien, and because quantum chromodynamics supplanted it as an experimentally better-qualified approach to the strong interactions. The field became marginalized and discarded in the mid 1970s and disappeared by the 1980s. Many prominent theorists picked up and advocated S-matrix theory, starting in the late 1950s and throughout the 1960s. String theory represents an outgrowth of S-matrix theory, a research program begun by Werner Heisenberg in 1943 following John Archibald Wheeler's 1937 introduction of the S-matrix. 6 1994–2003: Second superstring revolution.5 1984–1994: First superstring revolution.4 1974–1984: Bosonic string theory and superstring theory.2 1959–1968: Regge theory and bootstrap models.
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