Basic Physical Concepts

Abstract

The physical ingredients of an astrophysical gravitational lens system are explicitly designated and described in Section 3.1: spacetime geometry (Section 3.1.1 and 3.1.3), cosmic distances (Section 3.1.2), matter deflectors (Section 3.1.4), light rays (Section 3.1.5), and light sources (Section 3.1.6). All relevant assumptions and approximations are spelled out. The lensing ingredients and approximations also provide a physical setting within which time delay and lensing maps can be explicitly defined. These mappings are at the heart of the theory of optics for gravitational lenses (Section 3.2). Section 3.2.1 introduces the concept of time delay using Fermat’s principle, while Section 3.2.2 derives an explicit expression for time delay. Section 3.2.3 presents the lens equation, which relates a light source’s position to the impact positions of its light rays passing through the lens plane. In Section 3.2.4, the physical variables of gravitational lensing are converted into dimensionless form. These dimensionless variables are then used throughout the rest of the book. Section 3.2.5 introduces the magnification of light sources and discusses magnification as it relates to flux conservation. Section 3.2.6 treats the locus of all formally infinitely magnified images (critical curves) and corresponding positions (caustics) from which a source has at least one such image. Light curves (i.e., the plot of a moving light source’s magnification versus time) due to single and binary point-mass lenses are also discussed in Section 3.2.6. Section 3.2.7 treats the distortion of an extended source by lensing, including how convergence and shear are involved. The chapter ends with a discussion of two important families of lens models (Section 3.3) and observable lensing properties (Section 3.4). In the latter, we not only list the observables, but also discuss a family of transformations — “degeneracies” — of the lens system that leave the observables unchanged. The chapter closes with a discussion of weak lensing (no multiple images, but distortions of background galaxies) by the large scale structure of the universe (Section 3.5).

The minute we begin to talk about this world, however, it somehow becomes transformed into another world, an interpreted world, a world delimited by language…. What we say about the world, our theories, are like garments—they fit the world to a greater or lesser degree, but none fit perfectly, and none are right for every occasion…. Einstein described the nature of physics in the following way:

‘Physical concepts are free creations of the human mind, and are not, however it may seem, uniquely determined by the external world. In our endeavor to understand reality we are somewhat like a man trying to understand the mechanism of a closed watch. He sees the face and the moving hands, even hears it ticking, but he has no way of opening the case. If he is ingenious he may form some picture of the mechanism which could be responsible for all the things he observes, but he may never be quite sure his picture is the only one which could explain his observations. He will never be able to compare his picture with the real mechanism and he cannot even imagine the possibility of the meaning of such a comparison.’ Bruce Gregory