Time-travelling billiard-ball clocks: a quantum model
arXiv:2007.12677 · doi:10.1103/PhysRevA.103.042223
Abstract
General relativity predicts the existence of closed timelike curves (CTCs), along which an object could travel to its own past. A consequence of CTCs is the failure of determinism, even for classical systems: one initial condition can result in multiple evolutions. Here we introduce a new quantum formulation of a classic example, where a billiard ball can travel along two possible trajectories: one unperturbed and one, along a CTC, where it collides with its past self. Our model includes a vacuum state, allowing the ball to be present or absent on each trajectory, and a clock, which provides an operational way to distinguish the trajectories. We apply the two foremost quantum theories of CTCs to our model: Deutsch's model (D-CTCs) and postselected teleportation (P-CTCs). We find that D-CTCs reproduce the classical solution multiplicity in the form of a mixed state, while P-CTCs predict an equal superposition of the two trajectories, supporting a conjecture by Friedman et al. [Phys. Rev. D 42, 1915 (1990)].
arXiv comment15 pages, 8 figures
References in corpus (25)
- Quantum interferometric visibility as a witness of general relativistic proper time
- Closed timelike curves via post-selection: theory and experimental demonstration
- The quantum mechanics of time travel through post-selected teleportation
- Localized closed timelike curves can perfectly distinguish quantum states
- Quantum computation with indefinite causal structures
- Path Integrals, Density Matrices, and Information Flow with Closed Timelike Curves
- Information Flow of quantum states interacting with closed timelike curves
- Relativistic quantum information and time machines
- Quantum state cloning using Deutschian closed timelike curves
- Perfect state distinguishability and computational speedups with postselected closed timelike curves
- Quantum state cloning in the presence of a closed timelike curve
- Billiard in the space with a time machine
- Treating Time Travel Quantum Mechanically
- Existence and uniqueness theorems for massless fields on a class of spacetimes with closed timelike curves
- Reversible time travel with freedom of choice
- Reversible dynamics with closed time-like curves and freedom of choice
- Quantum Interactions with Closed Timelike Curves and Superluminal Signaling
- Quantum fields on closed time-like curves
- Cauchy Problem on Non-globally Hyperbolic Spacetimes
- Quantum Theory Looks at Time Travel
- Three-Dimensional Billiards with Time Machine
- Reply to comment on "Information Flow of quantum states interacting with closed timelike curves"
- Time travel without paradoxes: Ring resonator as a universal paradigm for looped quantum evolutions
- Ralph's equivalent circuit model, revised Deutsch's maximum entropy rule and discontinuous quantum evolutions in D-CTCs
- Klein-Gordon Solutions on Non-Globally Hyperbolic Standard Static Spacetimes