A Variational Theory for Light Rays in Stably Causal Lorentzian Manifolds: Regularity and Multiplicity Results

1997 ◽  
Vol 187 (2) ◽  
pp. 375-415 ◽  
Author(s):  
Fabio Giannoni ◽  
Antonio Masiello ◽  
Paolo Piccione
Symmetry ◽  
2021 ◽  
Vol 13 (8) ◽  
pp. 1422
Author(s):  
Antonio Masiello

In this paper we present a survey of Fermat metrics and their applications to stationary spacetimes. A Fermat principle for light rays is stated in this class of spacetimes and we present a variational theory for the light rays and a description of the multiple image effect. Some results on variational methods, as Ljusternik-Schnirelmann and Morse Theory are recalled, to give a description of the variational methods used. Other applications of the Fermat metrics concern the global hyperbolicity and the geodesic connectedeness and a characterization of the Sagnac effect in a stationary spacetime. Finally some possible applications to other class of spacetimes are considered.


2017 ◽  
Vol 2019 (22) ◽  
pp. 6949-6987
Author(s):  
Peter Hintz ◽  
Gunther Uhlmann

Abstract On a time-oriented Lorentzian manifold (M, g) with nonempty boundary satisfying a convexity assumption, we show that the topological, differentiable, and conformal structure of suitable subsets S ⊂ M of sources is uniquely determined by measurements of the intersection of future light cones from points in S with a fixed open subset of the boundary of M; here, light rays are reflected at ∂M according to Snell’s law. Our proof is constructive, and allows for interior conjugate points as well as multiply reflected and self-intersecting light cones.


2020 ◽  
Vol 2020 (2) ◽  
pp. 100-1-100-6
Author(s):  
Takuya Omura ◽  
Hayato Watanabe ◽  
Naoto Okaichi ◽  
Hisayuki Sasaki ◽  
Masahiro Kawakita

We enhanced the resolution characteristics of a threedimensional (3D) image using time-division multiplexing methods in a full-parallax multi-view 3D display. A time-division light-ray shifting (TDLS) method is proposed that uses two polarization gratings (PGs). As PG changes the diffraction direction of light rays according to the polarization state of the incident light, this method can shift light rays approximately 7 mm in a diagonal direction by switching the polarization state of incident light and adjusting the distance between the PGs. We verified the effect on the characteristics of 3D images based on the extent of the shift. As a result, the resolution of a 3D image with depth is improved by shifting half a pitch of a multi-view image using the TDLS method, and the resolution of the image displayed near the screen is improved by shifting half a pixel of each viewpoint image with a wobbling method. These methods can easily enhance 3D characteristics with a small number of projectors.


Author(s):  
Olga Lemzyakova

Refraction of the eye means its ability to bend (refract) light in its own optical system. In a normal state, which is called emmetropia, light rays passing through the optical system of the eye focus on the retina, from where the impulse is transmitted to the visual cortex of the brain and is analyzed there. A person sees equally well both in the distance and near in this situation. However, very often, refractive errors develop as a result of various types of influences. Myopia, or short-sightedness, occurs when the light rays are focused in front of the retina as a result of passing through the optical system of the eye. In this case, a person will clearly distinguish close objects and have difficulties in seeing distant objects. On the opposite side is development of farsightedness (hypermetropia), in which the focusing of light rays occurs behind the retina — such a person sees distant objects clearly, but outlines of closer objects are out of focus. Near vision impairment in old age is a natural process called presbyopia, it develops due to the lens thickening. Both myopia and hypermetropia can have different degrees of severity. The variant, when different refractive errors are observed in different eyes, is called anisometropia. In the same case, if different types of refraction are observed in the same eye, it is astigmatism, and most often it is a congenital pathology. Almost all of the above mentioned refractive errors require correction with spectacles or use of contact lenses. Recently, people are increasingly resorting to the methods of surgical vision correction.


Author(s):  
David D. Nolte

Galileo Unbound: A Path Across Life, The Universe and Everything traces the journey that brought us from Galileo’s law of free fall to today’s geneticists measuring evolutionary drift, entangled quantum particles moving among many worlds, and our lives as trajectories traversing a health space with thousands of dimensions. Remarkably, common themes persist that predict the evolution of species as readily as the orbits of planets or the collapse of stars into black holes. This book tells the history of spaces of expanding dimension and increasing abstraction and how they continue today to give new insight into the physics of complex systems. Galileo published the first modern law of motion, the Law of Fall, that was ideal and simple, laying the foundation upon which Newton built the first theory of dynamics. Early in the twentieth century, geometry became the cause of motion rather than the result when Einstein envisioned the fabric of space-time warped by mass and energy, forcing light rays to bend past the Sun. Possibly more radical was Feynman’s dilemma of quantum particles taking all paths at once—setting the stage for the modern fields of quantum field theory and quantum computing. Yet as concepts of motion have evolved, one thing has remained constant, the need to track ever more complex changes and to capture their essence, to find patterns in the chaos as we try to predict and control our world.


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