Einstein after Seven Decades

Why after almost eighty years do we still need to test Einstein's theory of general relativity? The answer is that although it is among the most brilliant creations of the human mind, weaving together space, time, and gravitation, and bringing an understanding of such bizarre phenomena as black holes and the expanding Universe, it remains one of the least tested of scientific theories. General relativity is hard to reconcile with the rest of physics, and even within its own structure has weaknesses. Einstein himself was dissatisfied, and spent many years trying to broaden his theory and unify it with just one other branch of physics, electromagnetism . Modern physicists seeking wider unification meet worse perplexities. Above all, essential areas of general relativity have never been checked experimentally.

Gravity, Relativity, and the Speed of Light

But surely Einstein's ideas must have been checked by now. Does not everyone believe that E=mc²? Yes, indeed; but Einstein advanced two distinct theories of relativity, the special and the general theory.

Special relativity weaves space and time together but does not touch gravitation. It states that no signal can be propagated faster than the speed of light. It leads to E=mc² and to phenomena such as changes in the mass and shape of a body with velocity, and changes in clock-rates seen by different moving observers. These predictions are verified every day in particle accelerators and nuclear power stations.

General relativity stands otherwise. This is Einstein's theory of gravitation. Once given special relativity Einstein faced an awkward problem. No signal can travel faster than light, but in Newton's time-honored theory of the Universe, gravity is a force transmitted instantaneously over vast distances. Something must be wrong. After ten years, Einstein produced in 1916 a new theory of gravity, interpreted not as a force but as a "field" distorting space and time. The planets in their courses, which seem to us to be moving in elliptic orbits around the Sun, are in reality following straight lines ("geodesics") through curved space-time.

Einstein's Two-and-a-Half Tests

Different as Einstein's and Newton's theories are, within the solar system their results are almost identical. Only on a cosmic scale, or near extremely dense objects such as black holes, does general relativity bring large changes. Einstein in 1916 could only think of three potential manifestations of general relativity, all minuscule.

	perihelion precession:	Mercury's orbit around the Sun should gradually turn in its plane through an angle minutely different from Newtonian prediction -- an effect called perihelion precession.
	starlight deflection:	Stars observed near the edge of the Sun should appear slightly displaced outward from their normal positions.
	gravitational redshift:	Light leaving a star should change color slightly, shifting toward the red.

For over forty years, these three effects -- weak both in what they tested and in how well they tested it -- were all there was. Starlight deflection proved frustratingly difficult to measure. Mercury's orbit, though better, was subject to Newtonian disturbances. Least satisfactory was the redshift, which was observationally messy and hinged on the assumption (the "Einstein equivalence principle") far short of general relativity. This was at most a half-test.

Worse, competing theories soon appeared giving the same predictions for Einstein's tests of general relativity.

New Technologies and Negative Experiments

The 1960s began a new era in experimental relativity, exploiting new technologies -- radar, lasers, inertial instrumentation, hydrogen maser clocks, space. Einstein's tests have been tightened, other tests proposed, and, unexpectedly, a special circumstance has produced experiments of a new kind that do discriminate between general relativity and some of its rivals.

General relativity is a minimalist theory. Its assumptions are few, and (more remarkably) often where other theories predict a non-Newtonian effect, it yields nothing. The theoretical log-jam can be broken by negative experiments -- searches for phenomena that are absent from general relativity and Newtonian gravitation but present in competing theories. An example is the Nordtvedt effect, a hypothetical 28-day non-Newtonian oscillation in the Earth-Moon distance as the two bodies orbit each other in the Sun's gravitational field. Limits on this effect have been set by bouncing laser beams from the Earth off retroreflectors planted on the Moon by the Apollo astronauts. The resulting measurements have demolished several theories.

The Problem of General Relativity and the Need for Further Tests

The demolition work from the negative experiments, valuable as it is, does not prove general relativity. If one asks for positive evidence, the story is in one view much better than it was, in another distinctly unsatisfactory.

The Einstein tests seem secure. The redshift has been confirmed -- notably in the elegant NASA program Gravity Probe A. The perihelion data have been strengthened, and supplemented by evidence from an astrophysical object, the Taylor-Hulse binary pulsar (though other astrophysical data from eclipsing binary stars conflict). Starlight deflection is established, while a closely related new test, the Shapiro time delay experiment, based on radar ranging measurements to planets and spacecraft, has been executed very precisely.

All of this indicates (what few physicists doubted) that Einstein was on the right track. Other more profound phenomena, however, remain untested. Save for some indirect evidence from the binary pulsar, no data exist on gravitational radiation. Even less is known about a vitally important relativistic effect -- "frame-dragging."

Moreover, deep theoretical problems -- some old and some new -- remain. Einstein himself remarked that the left-hand side of his field equation (describing the curvature of space-time) was granite, but that the right-hand side (connecting space-time to matter) was sand. The mathematical structures of general relativity and quantum mechanics, the two great theoretical achievements of 20th century physics, seem utterly incompatible. Some physicists, worried by this and by our continued inability to unite the four forces of nature -- gravitation, electromagnetism , and the strong and weak nuclear forces -- suspect that general relativity needs amendment.

One obstacle to creative amendment, however, is the paucity of experimental evidence. How will Gravity Probe B contribute to meeting the need for deeper tests of Einstein's wonderful but troubling theory?