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Seth Lloyd proposed an alternative approach to time travel with closed timelike curves (CTCs), based on "post-selection" and path integrals. [21] Path integrals are a powerful tool in quantum mechanics that involve summing probabilities over all possible ways a system could evolve, including paths that do not strictly follow a single timeline. [22]
A linear matrix difference equation of the homogeneous (having no constant term) form + = has closed form solution = predicated on the vector of initial conditions on the individual variables that are stacked into the vector; is called the vector of initial conditions or simply the initial condition, and contains nk pieces of information, n being the dimension of the vector X and k = 1 being ...
An objection to the practicality of building a Tipler cylinder was discovered by Stephen Hawking, who argued that according to general relativity it is impossible to build a time machine in any finite region that satisfies the weak energy condition, meaning that the region contains no exotic matter with negative energy. The Tipler cylinder, on ...
For instance, an object located at position p at time t 0 can only move to locations within p + c(t 1 − t 0) by time t 1. This is commonly represented on a graph with physical locations along the horizontal axis and time running vertically, with units of t {\displaystyle t} for time and ct for space.
A plot of Lorenz' strange attractor for values ρ=28, σ = 10, β = 8/3. The butterfly effect or sensitive dependence on initial conditions is the property of a dynamical system that, starting from any of various arbitrarily close alternative initial conditions on the attractor, the iterated points will become arbitrarily spread out from each other.
[9]: 184 This only applies to initial conditions outside of the chronology-violating region of spacetime, [9]: 187 which is bounded by a Cauchy horizon. [10] This could mean that the Novikov self-consistency principle does not actually place any constraints on systems outside of the region of space-time where time travel is possible, only ...
The systems studied in chaos theory are deterministic. If the initial state were known exactly, then the future state of such a system could theoretically be predicted. However, in practice, knowledge about the future state is limited by the precision with which the initial state can be measured, and chaotic systems are characterized by a strong dependence on the initial condit
A sample solution in the Lorenz attractor when ρ = 28, σ = 10, and β = 8 / 3 The Lorenz system is a system of ordinary differential equations first studied by mathematician and meteorologist Edward Lorenz. It is notable for having chaotic solutions for certain parameter values and initial conditions.