That was a major problem for early string theory, since tachyons don't exist, and if they did they would flagrantly violate the incredibly successful special theory of relativity. It also required the existence of particles that travel faster than the speed of light, called tachyons. It was fiendishly difficult to work with, making predictions nearly impossible. In the end, this early version of string theory, known as baryonic string theory for the kinds of particles it tried to explain, didn't quite cut the mustard. These strings appeared to be the basic building block of the strong force, with their quantum mechanical vibrations determining their properties in the microscopic world - in other words, their vibrations made them look and act like tiny little particles. And there they found something surprising: in order to describe the strong force, it had to be carried by tiny, vibrating strings. Other theoretical physicists dived in, and couldn't resist the urge to give the framework a traditional interpretation in terms of time and space and following the evolution of particles. Reviving this approach to the newfound strong nuclear force, theorists extended and developed the s-matrix idea, finding that certain mathematical functions that repeated themselves were especially powerful. It was a cool idea but proved too difficult for anybody to get excited about, and it died on the vine - until physicists got desperate in the '60s. That machine encodes all the interaction in a giant box without actually worrying about the evolution of the system. Instead, he argued, why don't we just skip all that work and develop a machine, called the scattering matrix, or s-matrix, that immediately jumps from the initial state to the final state, which is what we really want to measure. In the 1930s, Heisenberg suggested a rather extreme idea: instead of taking the normal classical physics approach of 1) write down the starting positions of all the particles involved in an interaction, 2) have a model of that interaction, and 3) follow the evolution through time of those particles, using your model to predict a result. In the early days of quantum mechanics (the first half of the 20th century), it wasn't exactly clear what would be the best mathematical approach to explain all that weirdness.
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