No time machines in classical general relativity

Irrespective of local conditions imposed on the metric, any extendible spacetime U has a maximal extension containing no closed causal curves outside the chronological past of U. We prove this fact and interpret it as impossibility (in classical general relativity) of the time machines, insofar as the latter are defined to be causality-violating regions created by human beings (as opposed to those appearing spontaneously).Comment: A corrigendum (to be published in CQG) has been added to correct an important mistake in the definition of localit

Group Chase and Escape

We describe here a new concept of one group chasing another, called "group chase and escape", by presenting a simple model. We will show that even a simple model can demonstrate rather rich and complex behavior. In particular, there are cases in which an optimal number of chasers exists for a given number of escapees (or targets) to minimize the cost of catching all targets. We have also found an indication of self-organized spatial structures formed by both groups.Comment: 13 pages, 12 figures, accepted and to appear in New Journal of Physic

The Bond-Algebraic Approach to Dualities

An algebraic theory of dualities is developed based on the notion of bond algebras. It deals with classical and quantum dualities in a unified fashion explaining the precise connection between quantum dualities and the low temperature (strong-coupling)/high temperature (weak-coupling) dualities of classical statistical mechanics (or (Euclidean) path integrals). Its range of applications includes discrete lattice, continuum field, and gauge theories. Dualities are revealed to be local, structure-preserving mappings between model-specific bond algebras that can be implemented as unitary transformations, or partial isometries if gauge symmetries are involved. This characterization permits to search systematically for dualities and self-dualities in quantum models of arbitrary system size, dimensionality and complexity, and any classical model admitting a transfer matrix representation. Dualities like exact dimensional reduction, emergent, and gauge-reducing dualities that solve gauge constraints can be easily understood in terms of mappings of bond algebras. As a new example, we show that the (\mathbb{Z}_2) Higgs model is dual to the extended toric code model {\it in any number of dimensions}. Non-local dual variables and Jordan-Wigner dictionaries are derived from the local mappings of bond algebras. Our bond-algebraic approach goes beyond the standard approach to classical dualities, and could help resolve the long standing problem of obtaining duality transformations for lattice non-Abelian models. As an illustration, we present new dualities in any spatial dimension for the quantum Heisenberg model. Finally, we discuss various applications including location of phase boundaries, spectral behavior and, notably, we show how bond-algebraic dualities help constrain and realize fermionization in an arbitrary number of spatial dimensions.Comment: 131 pages, 22 figures. Submitted to Advances in Physics. Second version including a new section on the eight-vertex model and the correction of several typo

Schroedinger equation for joint bidirectional motion in time

The conventional, time-dependent Schroedinger equation describes only unidirectional time evolution of the state of a physical system, i.e., forward or, less commonly, backward. This paper proposes a generalized quantum dynamics for the description of joint, and interactive, forward and backward time evolution within a physical system. [...] Three applications are studied: (1) a formal theory of collisions in terms of perturbation theory; (2) a relativistically invariant quantum field theory for a system that kinematically comprises the direct sum of two quantized real scalar fields, such that one field evolves forward and the other backward in time, and such that there is dynamical coupling between the subfields; (3) an argument that in the latter field theory, the dynamics predicts that in a range of values of the coupling constants, the expectation value of the vacuum energy of the universe is forced to be zero to high accuracy. [...]Comment: 30 pages, no figures. Related material is in quant-ph/0404012. Differs from published version by a few added remarks on the possibility of a large-scale-average negative energy density in spac

Association between hemodynamic activity and motor performance in six-month-old full-term and preterm infants: a functional near-infrared spectroscopy study

FAPEMIG - FUNDAÇÃO DE AMPARO À PESQUISA DO ESTADO DE MINAS GERAISFAPESP - FUNDAÇÃO DE AMPARO À PESQUISA DO ESTADO DE SÃO PAULOThis study aimed to assess task-induced activation in motor cortex and its association with motor performance in full-term and preterm born infants at six months old. A cross-sectional study of 73 sixmonth- old infants was conducted (35 full-term and 38 preterm infants). Motor performance was assessed using the Bayley Scales of Infant Development third edition-Bayley-III. Brain hemodynamic activity during motor task was measured by functional near-infrared spectroscopy (fNIRS). Motor performance was similar in full-term and preterm infants. However, differences in hemodynamic response were identified. Full terms showed a more homogeneous unilateral and contralateral activated area, whereas in preterm-born the activation response was predominantly bilateral. The full-term group also exhibited a shorter latency for the hemodynamic response than the preterm group. Hemodynamic activity in the left sensorimotor region was positively associated with motor performance measured by Bayley-III. The results highlight the adequacy of fNIRS to assess differences in task-induced activation in sensorimotor cortex between groups. The association between motor performance and the hemodynamic activity require further investigation and suggest that fNIRS can become a suitable auxiliary tool to investigate aspects of neural basis on early development of motor abilities.5118FAPEMIG - FUNDAÇÃO DE AMPARO À PESQUISA DO ESTADO DE MINAS GERAISFAPESP - FUNDAÇÃO DE AMPARO À PESQUISA DO ESTADO DE SÃO PAULOFAPEMIG - FUNDAÇÃO DE AMPARO À PESQUISA DO ESTADO DE MINAS GERAISFAPESP - FUNDAÇÃO DE AMPARO À PESQUISA DO ESTADO DE SÃO PAULO215502012/02500-82013/07559-

Time as an operator/observable in nonrelativistic quantum mechanics

The nonrelativistic Schroedinger equation for motion of a structureless particle in four-dimensional space-time entails a well-known expression for the conserved four-vector field of local probability density and current that are associated with a quantum state solution to the equation. Under the physical assumption that each spatial, as well as the temporal, component of this current is observable, the position in time becomes an operator and an observable in that the weighted average value of the time of the particle's crossing of a complete hyperplane can be simply defined: ... When the space-time coordinates are (t,x,y,z), the paper analyzes in detail the case that the hyperplane is of the type z=constant. Particles can cross such a hyperplane in either direction, so it proves convenient to introduce an indefinite metric, and correspondingly a sesquilinear inner product with non-Hilbert space structure, for the space of quantum states on such a surface. >... A detailed formalism for computing average crossing times on a z=constant hyperplane, and average dwell times and delay times for a zone of interaction between a pair of z=constant hyperplanes, is presented.Comment: 31 pages, no figures. Differs from published version by minor corrections and additions, and two citation

Unsuitability of the moving light clock system for the Lorentz factor derivation

The moving light clock system was analyzed with respect to the orientation of the wavefront of the light pulse observed in the moving and stationary frames of reference. The plane wavefront of the light pulse was oriented horizontally in both the frames. The wavefront observed in the stationary frame was not perpendicular to the direction of the light pulse propagation. This showed different characteristics of the light pulse than that assumed in the Lorentz factor derivation. According to the horizontal orientation of the wavefront, velocity c was determined as the vertical component of the light pulse motion observed in the stationary frame. Application of this velocity distribution in the Lorentz factor derivation showed the same travel time for the light pulse observed in the moving and stationary frames of reference. The moving light clock system was therefore found to be unsuitable for the Lorentz factor derivation and illustration of time dilation, and shown to illustrate the relativity of the observation of light rather than the relativity of time.Comment: 4 pages, 5 figure