Sciences

Space Time Theory

Observations of spacetime bending light

Gravity and light

Einstein was very lucky because data that fit predictions of his new mathematical model was observed in light from stars a solar eclipse in 1919, very soon after his model became public. The deflection of light around the Sun was one such predictive success of General Relativity.
The figure to the left shows three different possible (mathematical) paths for a pulse of light travelling around the Sun: the path with no gravity, the path as predicted by Newtonian gravity, and the path as predicted by Einstein's General Theory of Relativity.
The deflection angle df tells us how far away from a straight line the path of the light pulse in question was deflected by the Sun. The deflection angle is by definition zero when there is no gravity. We need to compare the deflection angles calculated using the Newtonian and relativistic models for gravity and spacetime.
The turning point R₀ is the closest distance that the light pulse gets to the Sun. We'll standardize our coordinate system so that f=0 corresponds to R = R₀, and calculate df that way.

No gravity

Without gravity, both Newtonian and relativistic models say the path is a straight line. The path of a straight line in polar coordinates centered at the center of the Sun would be: 1/r = (1/R₀) cos(f) where R₀ is the turning point mentioned above. First we want to find Df, which is the total angle swept out by the light pulse from the start to the end of its journey across spacetime. Look at the figure to the left and imagine the straight line path extending infinitely far to the right and left of your screen. When r = infinity, by symmetry of our coordinate system we have 0 = (1/R₀) cos(Df/2). Therefore Df = p is the total difference in angle swept out by the light pulse as it comes in from infinitely far away and travels back out infinitely far away.
The deflection angle here is df = Df - p = 0, as it should be for a straight line.

Newtonian gravity

Newtonian gravity doesn't work well for describing the properties of light, which can be modeled like the propagation of a massless particle. But it is possible to fake it by using the equation for a Newtonian hyperbolic orbit: 1/r = (G M(m/L)²)(1 + e cos(f)), e = (1 + (2E/m)(L/GMm)²))^1/2 where the eccentricity e is a function of the incoming particle's energy E, mass m and angular momentum L. The turning point R₀ = (L/m)²/(G M (1 + e)).
If we want to fake the propagation of light in Newtonian gravity, we can set the energy E = m v²/2 = m c²/2 so that (2 E/m) = c². The angular momentum per unit incoming mass (L/m) becomes L/m = R₀ c. The total angular sweep Df = p + df is given by 0 = (1/R₀) cos(Df/2) + (G M/c²)/R₀²,
- cos(p/2 + df/2) = sin(df/2) ~ df/2 = (G M/c²)/R₀ so finally df_N = 2 (G M/c²)/R₀ is the deflection angle for light found by naively using the Newtonian model for a particle with velocity c.

Einstein's General Theory of Relativity

In General Relativity, the path of a light pulse is described as a null geodesic satisfying the geodesic equation for the Schwarzschild metric, the distance function that solves the Einstein equations around a massive object in outer space such as the Sun. An approximate equation for the trajectory is 1/r = (1/R₀) cos(f) + ((G M/c²)/R₀²) (2 - cos²(f)). The term cos²(f) can be neglected if the deflection angle df is very small and Df/2 is close to p/2. Therefore, to lowest order in df we get 0 = (1/R₀) cos(Df/2) + 2 (G M/c²)/R₀²,
- cos(p/2 + df/2) = sin(df/2) ~ df/2 = 2 (G M/c²)/R₀. Therefore df_E = 4 (G M/c²)/R₀ = 2 df_N is the deflection angle for light found by using null geodesics in the Schwarzschild metric according to General Relativity.
Observations of starlight deflected around the Sun were made during solar eclipses beginning in 1919, and the measurements supported Einstein's model, not Newton's which predicts an angular deflection of half the size that was observed.

Multiple images from graviational lensing

We've already shown that paths of light are bent by gravity. Another way of stating this is spacetime curvature acts like a lens, hence the term gravitational lensing.
Under certain circumstances, gravitational lensing can fool us into thinking we are seeing several spacetime events, when in fact we're seing several images of a single spacetime event. The figure below shows how a single flash of light behind a very massive object M in two space dimensions can be perceived as two simultaneous flashes of light coming from opposite directions by a viewer in front of M.
Gravitational lensing means that the light cone of an event can be distorted by matter and energy. The possibility of distorting light cones is crucial to the possibility for nontrivial time travel. In the case of multiple images, the light cone of the event in question has developed a crease in it, it has overlapped with itself. We will see more of this later, in the next section.
Multiple images are observed in our Universe today. The next frame has a picture of a very complex multiple image system photographed by the Hubble Space Telescope in 1995.

A real gravitational lens

The image was taken with the Wide Field Planetary Camera 2. Credits: W.Couch (University of New South Wales), R. Ellis (Cambridge University), and NASA

The above photo of a real gravitational lens was taken by the Hubble Space Telescope. More images of observed gravitational lenses are available at the Gravitational Lensing Home Page. And here is the press release that accompanied the above photo:

HUBBLE VIEWS DISTANT GALAXIES THROUGH A COSMIC LENS

This NASA Hubble Space Telescope image of the rich galaxy cluster, Abell 2218, is a spectacular example of gravitational lensing. The arc-like pattern spread across the picture like a spider web is an illusion caused by the gravitational field of the cluster.
The cluster is so massive and compact that light rays passing through it are deflected by its enormous gravitational field, much as an optical lens bends light to form an image. The process magnifies, brightens and distorts images of objects that lie far beyond the cluster. This provides a powerful "zoom lens" for viewing galaxies that are so far away they could not normally be observed with the largest available telescopes.
Hubble's high resolution reveals numerous arcs which are difficult to detect with ground-based telescopes because they appear to be so thin. The arcs are the distorted images of a very distant galaxy population extending 5-10 times farther than the lensing cluster. This population existed when the universe was just one quarter of its present age. The arcs provide a direct glimpse of how star forming regions are distributed in remote galaxies, and other clues to the early evoution of galaxies.
Hubble also reveals multiple imaging, a rarer lensing event that happens when the distortion is large enough to produce more than one image of the same galaxy. Abell 2218 has an unprecedented total of seven multiple systems.
The abundance of lensing features in Abell 2218 has been used to make a detailed map of the distribution of matter in the cluster's center. From this, distances can be calculated for a sample of 120 faint arclets found on the Hubble image. These arclets represent galaxies that are 50 times fainter than objects that can be seen with ground-based telescopes.
Studies of remote galaxies viewed through well-studied lenses like Abell 2218 promise to reveal the nature of normal galaxies at much earlier epochs than was previously possible. The technique is a powerful combination of Hubble's superlative capabilities and the "natural" focusing properties of massive clusters like Abell 2218.