Celebrating Einstein

“The General Theory of Relativity”

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E.  Further Tests

The reality checks didn't stop there.  In his early discussions of general relativity, Einstein described several other consequences of the theory.  Observations of some of these consequences commenced soon after Einstein's early publications, and have continued since.

One interesting consequence was that everything, including light, should be affected by gravity in the same way.  One of Einstein's thought-experiments with the "space elevator" involved shining a light as the elevator moved in various ways.  If the elevator were in steady, unaccelerated motion, any beam of light shining inside the elevator would be straight.  If the elevator accelerated upward, the beam would still be straight as seen by an unaccelerated outside observer, but from the perspective of the elevator's passengers, any non-vertical beam would be deflected downward.

Since the elevator's acceleration produces the same basic effects as gravity,  Einstein realized that an ordinary gravitational field should also deflect a light beam.  The earth's gravity, like accelerations small enough to simulate it, deflects light too little to make the deflection obvious, but larger accelerations or masses greater than the earth's can produce a measurable effect.  For instance, the sun should deflect any light skimming its surface by just over 3 microradians (1.7 arcseconds)—a very small angle, but measurable.  The sun would thus focus any beams of light that passed near its surface, like a magnifying lens, thereby making the sources of such beams look as though they were spread further apart than they really were.  It's difficult to see beams of light graze the sun when the sun is out, unless the sun is eclipsed.  Photographs of the May 1919 solar eclipse provided the first confirmation that light was deflected by gravity.  Today, astronomers take this effect for granted.  When they find multiple similar images close together in the sky, they recognize that some large mass is bringing two or more different sets of light waves from the same object into view, much as a lens would, and they calculate the location and size of the "lens" mass from measurements of the multiple images.

Figure 7

Figure 7.  On the left, rays of light converging toward the earth from different stars undeflected by the sun's gravity (top); if the sun were between the stars and the earth, and the sun's gravity had no effect on the rays, the sun would block these particular stars from view (bottom).  On the right, with the sun between the same stars and the earth, the rays from the stars are deflected by the sun (top), and (bottom) the resulting view from the earth (assuming the sun is eclipsed to make the stars visible).  The deflection is exaggerated here to make it obvious; on the scale of this figure, the actual repositioning of the stars' images between the bottom left and bottom right would be on the order of one micrometer.

Einstein found that not only does gravity curve the paths of light as it does the paths of everything else, it also desynchronizes time.  Where spacetime isn't curved, time passes at the same rate everywhere.  Where gravity exists, and spacetime is curved, time runs faster wherever the curvature is weaker.

This effect manifests itself in several ways, some of them involving things that vibrate at some steady rate.  Atoms in the outer layers of the sun absorb light waves that vibrate at particular frequencies.  This makes the sunlight of these frequencies that we get on Earth less intense than it would be otherwise.  We find that the same types of atoms on Earth also absorb light waves, but at slightly higher frequencies.  This is what general relativity theory leads us to expect.  The gravity at the sun's surface is stronger than that at Earth's surface, so the spacetime curvature near the sun is greater, and time near the sun proceeds at a slower rate.  From the perspective of an atom that moved between Earth and the sun, the frequencies of light it could absorb are the same in both places; but to us on Earth, since time on the sun flows more slowly, the atom's "same frequency" is to us a lower frequency.  An identical effect can be observed in the light from other stars--the frequencies absorbed by atoms near their surfaces are lower than those absorbed by the same types of atoms in Earth's weaker gravity.

Although Earth's gravity is much weaker, with the right instruments we can see the same effect here.  In the late 1950s and mid 1960s, Robert Pound, Glen Rebka, and Joseph Snider demonstrated that gamma rays increased their frequencies by 2.4 parts per quadrillion as they rose 74 feet through a tower against gravity. This indicated that time flowed 1.000 000 000 000 002 4 times faster at the top of the tower than at the bottom, the difference again matching what Einstein's equation G = 8 πκ T/c4 implies for the curvature of spacetime near Earth's surface.

A more precise test, known as Gravity Probe A, was conducted in 1976, when a hydrogen maser clock was taken on a 115-minute rocket flight with a maximum altitude of 10,000 kilometers.  As the rocket rose and fell through the earth's gravitational field, its clock registered more time than a similar clock on the ground, the difference matching the prediction of general relativity for the different rates of time flow in the different regions of the gravitational field.

Nowadays, though, it doesn't take special experiments to demonstrate a relation between gravity and the flow of time; two modern utilities demonstrate it every day in their normal operation.  The worldwide system of timekeeping is based on atomic clocks stationed at different places on Earth.  The clocks at Boulder, Colorado, which are at a much higher altitude than others in the United States, measure the faster rate of their local time; these clocks require adjustment to keep the slower pace of the worldwide "official" time.  A newer utility, the Global Positioning System, has to deal with a more pronounced manifestation of the same effect.  This location system is based on time signals from atomic clocks in Earth orbit, where time flows faster still.  If the difference in the rate of time between the satellites and the ground were not taken into account, the system would give wildly inaccurate location readings within only one day of operation.

Modern space technology has provided other tests of relativity that Einstein hadn't proposed.  One test is similar to that of our imaginary two-dimensional man's survey.  Just as curvature in his two-dimensional space can alter distances, like the diameters of his circles, curvature can change distances in our spacetime.  Irwin Shapiro noted in 1964 that if spacetime is curved near massive objects as Einstein's formula predicts, signals sent through the spacetime around those objects will take longer to reach their destinations than they would without the curvature.  This had been checked by radar signals reflected from the plants Mercury and Venus, and by radio communications with space probes elsewhere in the solar system, when the line of sight to each passed near the sun.  The signals' round trips take about 200 microseconds longer than they would have if the spacetime near the sun weren't curved—a small difference in our ordinary experience, but a significant difference in our modern age of devices that readily measure durations of nanoseconds (thousandths of a microsecond).

Figure 8




Figure 8.  In this figure, the position of two different radar signals moving from the earth, then past the sun, then reaching a space probe, and then moving back the other way, is represented by points on straight or (slightly) curved lines.  The horizontal direction represents the signal's position in space; the vertical direction represents the passage of time.  The lower line in each direction (earth to probe, probe to earth) shows how the signal would proceed in straight lines if spacetime were not curved.  Near the sun, spacetime is curved more, which means the straightest possible path for the radar signal is itself a curve—scarcely different from a straight line at large distances from the sun, but less like a straight-line signal close to the sun.  Because of this curvature, the signal takes longer than it otherwise would to make a round trip from the earth to the space probe and back again.  Observing how the signal's travel time varies as the earth and the space probe both move and change their alignment with the sun reveals that when the radar signal passes near the sun, the signal's trip to the probe and back is lengthened by some 200 microseconds—the equivalent of 60 extra kilometers.

At this writing, the newest space-based test (Gravity Probe B) measures a quite different effect of curvature.  If spacetime were not curved, any device set up to point in a fixed direction could be taken on any round trip one chose, and as long as no torques were ever applied to the device, it would still point in the same direction when it returned to where it started.  But try to move a similar device through a curved spacetime, and the right kind of round trip would end up changing the device's orientation, even if the device never underwent a torque.  This aspect of spacetime curvature has recently been sought near the earth with a set of gyroscopes placed on a satellite known as "Gravity Probe B".  Gyroscopes keep their orientation as long as there are no torques on them and there is no curvature in the spacetime they move through.  The gyroscopes on the satellite were carefully kept from undergoing significant torque, but their orbit is through a region of spacetime that, according to Einstein's formula, is curved enough to reorient them by a known, measurable amount.  If it turns out that their orientation has changed by this amount, the experiment will have shown us a new type of evidence for the reality of spacetime curvature.



Figure 9

Figure 9.  An arrow made to slide over a globe without being twisted clockwise or counterclockwise can still change direction simply because of the globe's own curvature (top left)—something that would not happen if the arrow slid over a plane without being twisted (top right).  Similarly, a gyroscope's axis can change as the gyroscope moves through a curved spacetime (bottom).  The axis of a gyroscope orbiting over the earth's north and south poles would gradually change its orientation, mostly within the plane of the gyro's orbit (as shown), but also with some precession about an axis parallel to that of the earth's rotation.  The gyroscopes on Gravity Probe B would have to keep spinning for about 4000 centuries for their axes to make the first kind of change by the amount shown here (π/6 radians); on this scale, the second kind of change would make the gyroscope's axis point just a few micrometers out of the page.  Over the 16 months of the actual experiment, the angle of the gyro's axis should have changed by only a few tens of microradians in the plane of its orbit, and a few tenths of a microradian perpendicular to this plane.


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Date Modified: 01/15/2008
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