next up previous contents
Next: Clocks in a gravitational Up: The General Theory of Previous: Gravitation vs acceleration


A very surprising corollary of the above is that light paths are bent by gravitational forces! I will argue this is true in a slightly round-about way.

Consider an elevator being pulled by a crane so that it moves with constant acceleration (that is its velocity increases uniformly with time). Suppose that a laser beam propagating perpendicular to the elevator's direction of motion enters the elevator through a hole on the left wall and strikes the right wall. The idea is to compare what the crane operator and the elevator passenger see.

The crane operator, who is in an inertial frame of reference, will see the sequence of events given in Fig. 7.5. Note, that according to him/her, light travels in a straight line (as it must be since he/she is in an inertial frame!).

Figure 7.5: Left: sequence of events seen by an crane operator lifting an elevator at constant acceleration (the speed increases uniformly with time). The short horizontal line indicates a laser pulse which, at the initial time, enters through an opening on the left-hand side of the elevator. At the final time the light beam hits the back wall of the elevator. Right: same sequence of events seen by a passenger in an elevator being hoisted by a crane. The line joining the dots indicates the path of a laser which, at the initial time, enters through an opening on the left-hand side of the elevator. At the final time the light beam hits the back wall of the elevator.
\centerline{ \vbox to 3.2 truein{\epsfysize=2.9 truein\epsfbox[50 170 662 962]{7.gtr/}} }\end{figure}

The elevator passenger will see something very different as shown in Fig. 7.5: the light-path is curved! Thus for this simple thought experiment light paths will be curved for observers inside the elevator.

Now we apply the equivalence principle which implies that we cannot distinguish between an elevator accelerated by a machine and an elevator experiencing a constant gravitational force. It follows that the same effect should be observed if we place the elevator in the presence of a gravitational force: light paths are curved by gravity

That gravity affects the paths of planets, satellites, etc. is not something strange. But we tend to think of light as being different somehow. The above argument shows that light is not so different from other things and is indeed affected by gravity in a very mundane manner (the same elevator experiment could be done by looking at a ball instead of a beam of light and the same sort of picture would result).

A natural question is then, why do we not see light fall when we ride an elevator? The answer is that the effect in ordinary life is very small. Suppose that the height of the elevator in Fig. 7.5 is 8 ft. and its width is 5 ft; if the upward acceleration is 25% that of gravity on Earth then the distance light falls is less than a millionth of the radius of a hydrogen atom (the smallest of the atoms). For the dramatic effect shown in the figure the acceleration must be enormous, more than 1016 times the acceleration of gravity on Earth (this implies that the passenger, who weights 70 kg on Earth, will weigh more than 1,000 trillion tons in the elevator).

This does not mean, however, that this effect is completely unobservable (it is small for the case of the elevator because elevators are designed for very small accelerations, but one can imagine other situations). Consider from example a beam of light coming from a distant star towards Earth (Fig. 7.6) which along the way comes close to a very massive dark object. The arguments above require the light beam to bend; and the same thing will happen for any other beam originating in the distant star. Suppose that the star and the opaque object are both prefect spheres, then an astronomer on Earth will see, not the original star, but a ring of stars (often called an ``Einstein ring). If either the star or the massive dark object are not perfect spheres then an astronomer would see several images instead of a ring (Fig. 7.7). This effect has been christened gravitational lensing since gravity acts here as a lens making light beams converge.

Figure 7.6: Diagram illustrating the bending of light from a star by a massive compact object. If both the bright objects and the massive object are prefect sphere, there will be an apparent image for every point on the ``Einstein ring''.  
\centerline{ \vbox to 3.4 truein{\epsfysize=6 truein\epsfbox[0 0 612 792]{7.gtr/}} }\end{figure}

Figure 7.7: The Einstein Cross: four images of a quasar GR2237+0305 (a very distant, very bright object) appear around the central glow. The splitting of the central image is due to the gravitational lensing effect produced by a nearby galaxy. The central image is visible because the galaxy does not lie on a straight line from the quasar to Earth. The Einstein Cross is only visible from the southern hemisphere.  
\centerline{\vbox to 3 truein{\epsfysize=5 truein\epsfbox[0 -180 612 612]{7.gtr/}} }\end{figure}

How do we know that the multiple images which are sometimes seen (Fig. 7.7) are a result of the bending of light? The argument is by contradiction: suppose they are not, that is suppose, that the images we see correspond to different stars. Using standard astronomical tools one can estimate the distance between these stars; it is found that they are separated by thousands of light years, yet it is observed that if one of the stars change, all the others exhibit the same change instantaneously! Being so far apart precludes the possibility of communication between them; the simplest explanation is the one provided by the bending of light. It is, of course, possible to ascribe these correlations as results of coincidences, but, since these correlations are observed in many images, one would have to invoke a ``coincidence'' for hundreds of observations in different parts of the universe.

The bending of light was one of the most dramatic predictions of the General Theory of Relativity, it was one of the first predictions that were verified as we will discuss below in Sect. 7.12.

next up previous contents
Next: Clocks in a gravitational Up: The General Theory of Previous: Gravitation vs acceleration
Jose Wudka