Discrete mechanics, time machines and hybrid systems

Abstract

Modifying the discrete mechanics proposed by T.D. Lee, we construct a class of discrete classical Hamiltonian systems, in which time is one of the dynamical variables. This includes a toy model of time machines which can travel forward and backward in time and which differ from models based on closed timelike curves (CTCs). In the continuum limit, we explore the interaction between such time reversing machines and quantum mechanical objects, employing a recent description of quantum-classical hybrids.

14 pages; invited talk at the conference The Time Machine Factory (Torino, October 2012)

References in corpus (12)

• Closed timelike curves via post-selection: theory and experimental demonstration
• Linear dynamics of quantum-classical hybrids
• The quantum mechanics of time travel through post-selected teleportation
• Consistent classical and quantum mixed dynamics
• Entangled quantum states in a local deterministic theory
• Open timelike curves violate Heisenberg's uncertainty principle
• Does quantum mechanics tell an atomistic spacetime?
• Statistical ensembles in Hamiltonian formulation of hybrid quantum-classical systems
• Four questions for quantum-classical hybrid theory
• Proliferation of observables and measurement in quantum-classical hybrids
• Classical-Quantum Coexistence: a `Free Will' Test
• Non-adiabatic Non-cyclic Generalization of the Berry Phase for a Spin-1/2 Particle in a Rotating Magnetic Field

Cited by in corpus (11)

• Action principle for cellular automata and the linearity of quantum mechanics
• A derivation of a microscopic entropy and time irreversibility from the discreteness of time
• Are nonlinear discrete cellular automata compatible with quantum mechanics?
• Quantum models as classical cellular automata
• Ontological states and dynamics of discrete (pre-)quantum systems
• Qubit exchange interactions from permutations of classical bits
• Schroedinger vs. Navier-Stokes
• On the time continuous evolution of the universe if time is discrete and irreversible in nature
• The irreversible quantum
• On the Einstein-Podolsky-Rosen paradox using discrete time physics
• Distinguishing quantum states using time travelling qubits in a presence of thermal environments