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The time loop is a popular trope in Japanese pop culture media, especially anime. [15] Its use in Japanese fiction dates back to Yasutaka Tsutsui's science fiction novel The Girl Who Leapt Through Time (1965), one of the earliest works to feature a time loop, about a high school girl who repeatedly relives the same day.
A "time loop" or "temporal loop" is a plot device in which periods of time are repeated and re-experienced by the characters, and there is often some hope of breaking out of the cycle of repetition. [31] Time loops are sometimes referred to as causal loops, [30] [31] but these two concepts are distinct. Although similar, causal loops are ...
The "predestination paradox" is a concept in time travel and temporal mechanics, often explored in science fiction. It occurs when a future event is the cause of a past event, which in turn becomes the cause of the future event, forming a self-sustaining loop in time.
A closed timelike curve can be created if a series of such light cones are set up so as to loop back on themselves, so it would be possible for an object to move around this loop and return to the same place and time that it started. An object in such an orbit would repeatedly return to the same point in spacetime if it stays in free fall.
is the initial density matrix of the system before the time loop. is a transformation operator derived from the trace operation over the CTC, applied to the unitary evolution operator . The transformation relies on the trace operation, which summarizes aspects of the matrix.
This closed-loop gain is of the same form as the open-loop gain: a one-pole filter. Its step response is of the same form: an exponential decay toward the new equilibrium value. But the time constant of the closed-loop step function is τ / (1 + β A 0), so it is faster than the forward amplifier's response by a factor of 1 + β A 0:
This list of films featuring time loops in which characters experience the same period of time which is repeatedly resetting: when a certain condition is met, such as a death of a character or a clock reaches a certain time, the loop starts again, with one or more characters retaining the memories from the previous loop.
This is the case of the Wilson loop, which is defined as a path-ordered exponential to guarantee that the Wilson loop encodes the holonomy of the gauge connection. The parameter σ that determines the ordering is a parameter describing the contour , and because the contour is closed, the Wilson loop must be defined as a trace in order to be ...