2,137 research outputs found
Closed Timelike Curves in Relativistic Computation
In this paper, we investigate the possibility of using closed timelike curves
(CTCs) in relativistic hypercomputation. We introduce a wormhole based
hypercomputation scenario which is free from the common worries, such as the
blueshift problem. We also discuss the physical reasonability of our scenario,
and why we cannot simply ignore the possibility of the existence of spacetimes
containing CTCs.Comment: 17 pages, 5 figure
Quantum mechanics of time travel through post-selected teleportation
This paper discusses the quantum mechanics of closed-timelike curves (CTCs) and of other potential methods for time travel. We analyze a specific proposal for such quantum time travel, the quantum description of CTCs based on post-selected teleportation (P-CTCs). We compare the theory of P-CTCs to previously proposed quantum theories of time travel: the theory is inequivalent to Deutsch's theory of CTCs, but it is consistent with path-integral approaches (which are the best suited for analyzing quantum-field theory in curved space-time). We derive the dynamical equations that a chronology-respecting system interacting with a CTC will experience. We discuss the possibility of time travel in the absence of general-relativistic closed-timelike curves, and investigate the implications of P-CTCs for enhancing the power of computation.This paper discusses the quantum mechanics of closed-timelike curves (CTCs) and of other potential methods for time travel. We analyze a specific proposal for such quantum time travel, the quantum description of CTCs based on post-selected teleportation (P-CTCs). We compare the theory of P-CTCs to previously proposed quantum theories of time travel: the theory is inequivalent to Deutsch's theory of CTCs, but it is consistent with path-integral approaches (which are the best suited for analyzing quantum-field theory in curved space-time). We derive the dynamical equations that a chronology-respecting system interacting with a CTC will experience. We discuss the possibility of time travel in the absence of general-relativistic closed-timelike curves, and investigate the implications of P-CTCs for enhancing the power of computation
NP-complete Problems and Physical Reality
Can NP-complete problems be solved efficiently in the physical universe? I
survey proposals including soap bubbles, protein folding, quantum computing,
quantum advice, quantum adiabatic algorithms, quantum-mechanical
nonlinearities, hidden variables, relativistic time dilation, analog computing,
Malament-Hogarth spacetimes, quantum gravity, closed timelike curves, and
"anthropic computing." The section on soap bubbles even includes some
"experimental" results. While I do not believe that any of the proposals will
let us solve NP-complete problems efficiently, I argue that by studying them,
we can learn something not only about computation but also about physics.Comment: 23 pages, minor correction
The Computational Power of Minkowski Spacetime
The Lorentzian length of a timelike curve connecting both endpoints of a
classical computation is a function of the path taken through Minkowski
spacetime. The associated runtime difference is due to time-dilation: the
phenomenon whereby an observer finds that another's physically identical ideal
clock has ticked at a different rate than their own clock. Using ideas
appearing in the framework of computational complexity theory, time-dilation is
quantified as an algorithmic resource by relating relativistic energy to an
th order polynomial time reduction at the completion of an observer's
journey. These results enable a comparison between the optimal quadratic
\emph{Grover speedup} from quantum computing and an speedup using
classical computers and relativistic effects. The goal is not to propose a
practical model of computation, but to probe the ultimate limits physics places
on computation.Comment: 6 pages, LaTeX, feedback welcom
The Quantum Propagator for a Nonrelativistic Particle in the Vicinity of a Time Machine
We study the propagator of a non-relativistic, non-interacting particle in
any non-relativistic ``time-machine'' spacetime of the type shown in Fig.~1: an
external, flat spacetime in which two spatial regions, at time and
at time , are connected by two temporal wormholes, one leading from
the past side of to t the future side of and the other from the
past side of to the future side of . We express the propagator
explicitly in terms of those for ordinary, flat spacetime and for the two
wormholes; and from that expression we show that the propagator satisfies
completeness and unitarity in the initial and final ``chronal regions''
(regions without closed timelike curves) and its propagation from the initial
region to the final region is unitary. However, within the time machine it
satisfies neither completeness nor unitarity. We also give an alternative proof
of initial-region-to-final-region unitarity based on a conserved current and
Gauss's theorem. This proof can be carried over without change to most any
non-relativistic time-machine spacetime; it is the non-relativistic version of
a theorem by Friedman, Papastamatiou and Simon, which says that for a free
scalar field, quantum mechanical unitarity follows from the fact that the
classical evolution preserves the Klein-Gordon inner product
Simulations of closed timelike curves
Proposed models of closed timelike curves (CTCs) have been shown to enable
powerful information-processing protocols. We examine the simulation of models
of CTCs both by other models of CTCs and by physical systems without access to
CTCs. We prove that the recently proposed transition probability CTCs (T-CTCs)
are physically equivalent to postselection CTCs (P-CTCs), in the sense that one
model can simulate the other with reasonable overhead. As a consequence, their
information-processing capabilities are equivalent. We also describe a method
for quantum computers to simulate Deutschian CTCs (but with a reasonable
overhead only in some cases). In cases for which the overhead is reasonable, it
might be possible to perform the simulation in a table-top experiment. This
approach has the benefit of resolving some ambiguities associated with the
equivalent circuit model of Ralph et al. Furthermore, we provide an explicit
form for the state of the CTC system such that it is a maximum-entropy state,
as prescribed by Deutsch.Comment: 15 pages, 1 figure, accepted for publication in Foundations of
Physic
Dynamics and stability of the Godel universe
We use covariant techniques to describe the properties of the Godel universe
and then consider its linear response to a variety of perturbations. Against
matter aggregations, we find that the stability of the Godel model depends
primarily upon the presence of gradients in the centrifugal energy, and
secondarily on the equation of state of the fluid. The latter dictates the
behaviour of the model when dealing with homogeneous perturbations. The
vorticity of the perturbed Godel model is found to evolve as in almost-FRW
spacetimes, with some additional directional effects due to shape distortions.
We also consider gravitational-wave perturbations by investigating the
evolution of the magnetic Weyl component. This tensor obeys a simple plane-wave
equation, which argues for the neutral stability of the Godel model against
linear gravity-wave distortions. The implications of the background rotation
for scalar-field Godel cosmologies are also discussed.Comment: Revised version, to match paper published in Class. Quantum Gra
Dirac four-potential tunings-based quantum transistor utilizing the Lorentz force
We propose a mathematical model of \textit{quantum} transistor in which
bandgap engineering corresponds to the tuning of Dirac potential in the complex
four-vector form. The transistor consists of -relativistic spin qubits
moving in \textit{classical} external electromagnetic fields. It is shown that
the tuning of the direction of the external electromagnetic fields generates
perturbation on the potential temporally and spatially, determining the type of
quantum logic gates. The theory underlying of this scheme is on the proposal of
the intertwining operator for Darboux transfomations on one-dimensional Dirac
equation amalgamating the \textit{vector-quantum gates duality} of Pauli
matrices. Simultaneous transformation of qubit and energy can be accomplished
by setting the -operators attached on the
coupling between one-qubit quantum gate: the chose of \textit{cyclic}-operator
swaps the qubit and energy simultaneously, while \textit{control}-operator
ensures the energy conservation.Comment: 23 pages, 10 figures: Typo corrections. A new Subsection with
massless Dirac-fermions in a uniform magnetic field is include
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