Tune shift with amplitude of the system. When the tune reaches resonant values, it can be unstable, and thus a tune-shift with amplitude can limit the stability region, or dynamic aperture. In classical mechanics, a simple example of a system with tune shift with amplitude is a pendulum. In accelerator physics, both the transverse and the longitudinal dynamics show tune shift with amplitude. A simple model of the transverse dynamics is of an oscillator with a single sextupole, it is referred to as the Hénon map. Another model for this case is the Standard Map. An important example is the typical case of distributed
The Trouble with Physics formulation; and that it has not been mathematically proved finite. Some experts in the theoretical physics community disagree with these statements. Smolin states that to propose a string theory landscape having up to 10 string vacuum solutions is tantamount to abandoning accepted science: The scenario of many unobserved universes plays the same logical role as the scenario of an intelligent designer. Each provides an untestable hypothesis that, if true, makes something improbable seem quite probable. The book generated much controversy and debate about the merits of string theory, and was criticised by some prominent physicists including Sean Carroll and string