Simple Nature - Light and Matter

An Einstein’s ring. Thedistant object is a quasar,MG1131+0456, and the onein the middle is an unknownobject, possibly a supermassiveblack hole. The intermediateobject’s gravity focuses the raysof light from the distant one.Because the entire arrangementlacks perfect axial symmetry, thering is nonuniform; most of itsbrightness is concentrated in twolumps on opposite sides.deviation from Euclidean behavior depends on gravity.Since the noneuclidean effects are bigger when the system beingstudied is larger, we expect them to be especially important in thestudy of cosmology, where the distance scales are very large.Einstein’s ring example 24An Einstein’s ring, figure b, is formed when there is a chancealignment of a distant source with a closer gravitating body. Thistype of gravitational lensing is direct evidence for the noneuclideannature of space. The two light rays are lines, and they violate Euclid’sfirst postulate, that two points determine a line.One could protest that effects like these are just an imperfectionof the light rays as physical models of straight lines. Maybe thenoneuclidean effects would go away if we used something better andstraighter than a light ray. But we don’t know of anything straighterthan a light ray. Furthermore, we observe that all measuring devices,not just optical ones, report the same noneuclidean behavior.CurvatureAn example of such a non-optical measurement is the GravityProbe B satellite, figure d, which was launched into a polar orbitin 2004 and operated until 2010. The probe carried four gyroscopesmade of quartz, which were the most perfect spheres ever manufactured,varying from sphericity by no more than about 40 atoms.Each gyroscope floated weightlessly in a vacuum, so that its rotationwas perfectly steady. After 5000 orbits, the gyroscopes hadreoriented themselves by about 2 × 10 −3◦ relative to the distantstars. This effect cannot be explained by Newtonian physics, sinceno torques acted on them. It was, however, exactly as predicted byEinstein’s theory of general relativity. It becomes easier to see whysuch an effect would be expected due to the noneuclidean nature ofspace if we characterize euclidean geometry as the geometry of a flatplane as opposed to a curved one. On a curved surface like a sphere,figure c, Euclid’s fifth postulate fails, and it’s not hard to see thatwe can get triangles for which the sum of the angles is not 180 ◦ .By transporting a gyroscope all the way around the edges of such atriangle and back to its starting point, we change its orientation.The triangle in figure c has angles that add up to more than180 ◦ . This type of curvature is referred to as positive. It is alsopossible to have negative curvature, as in figure e.In general relativity, curvature isn’t just something caused bygravity. Gravity is curvature, and the curvature involves both spaceand time, as may become clearer once you get to figure k. Thus thedistinction between special and general relativity is that general relativityhandles curved spacetime, while special relativity is restricted424 Chapter 7 Relativity