The Dancing Wu Li Masters (26 page)

Similarly, once we know the properties of an area of the space-time continuum (by exploring it) we can determine not only the position of, but also the distance (interval) between two events in the
space-time continuum.
^*
The mathematical structure of the general theory of relativity, which Einstein created over a period of ten years, permits us to do just that.

The equations of the general theory of relativity are structural formulas. They describe the structure of changing gravitational fields. (Newton’s formula describes a situation between two objects at a given time. Einstein’s formulas relate a situation here and now to a situation in the immediate vicinity a little later.) By feeding the results of actual observations into these equations, they give us a picture of the space-time continuum in the neighborhood of our observations. In other words, they reveal the geometry of space-time in that area. Once we know that, our situation is roughly analogous to that of a sailor who knows that the earth is round and also knows spherical trigonometry.
^†

We have said, up to now, that matter distorts, or causes a curvature of, the space-time continuum in its vicinity. According to Einstein’s ultimate vision, which he never “proved” (demonstrated mathematically), a piece of matter
is
a curvature of the space-time continuum! In other words, according to Einstein’s ultimate vision, there are no such things as “gravitational fields” and “masses.” They are only mental creations. No such things exist in the real world. There is no such thing as “gravity”—gravity is the equivalent of acceleration, which is motion. There is no such thing as “matter”—matter is a curvature of the space-time continuum. There is not even such a thing as “energy”—energy equals mass and mass is space-time curvature.

What we considered to be a planet with its own gravitational field moving around the sun in an orbit created by the gravitational attraction (force) of the sun is actually a pronounced curvature of the
space-time continuum finding its easiest path through the space-time continuum in the vicinity of a very pronounced curvature of the space-time continuum.

There is nothing but space-time and motion and they, in effect, are the same thing. Here is an exquisite presentation, in completely western terms, of the most fundamental aspect of Taoist and Buddhist philosophies.

Physics is the study of physical reality. If a theory does not relate to the physical world, it may be pure mathematics, poetry, or blank verse, but it is not physics. The question is, does Einstein’s fantastic theory really work?

The answer is a slightly tentative, but generally accepted “Yes.” Most physicists agree that the general theory of relativity is a valid way of viewing large-scale phenomena, and at the same time, most physicists still are eager to see more evidence to confirm (or challenge) this position.

Since the general theory of relativity deals with vast expanses of the universe, its proof (or usefulness, not of “truth”—the watch is still unopenable) cannot come from observations of phenomena limited to the earth. For this reason, its verifications come from astronomy.

Thus far, the general theory of relativity has been verified in four ways. The first three ways are straightforward and convincing. The last way, if early observations are correct, may be more fantastic than the theory itself.

The first verification of the general theory of relativity came as an unexpected benefit to astronomers. Newton’s law of gravity purported to describe the orbits of the planets around the sun, and it did—all of them except Mercury. Mercury orbits the sun in such a way that some parts of its orbit bring it closer to the sun than others. The part of Mercury’s orbit closest to the sun is called its perihelion. The first verification of Einstein’s general theory of relativity turned out to be the long-sought explanation of the problem of Mercury’s perihelion.

The problem with Mercury’s perihelion—in fact, with Mercury’s entire orbit—is that it moves. Instead of continuously retracing its path around the sun relative to a co-ordinate system attached to the sun, Mercury’s orbit itself revolves around the sun. The rate of revolution is extremely slow (it completes one revolution around the sun every three million years). This still was enough to puzzle astronomers. Prior to Einstein, this precession in Mercury’s orbit had been attributed to an undiscovered planet in our solar system. By the time Einstein published his general theory of relativity, the search for this mysterious planet was well underway.

Einstein created his general theory of relativity without special attention to the perihelion of Mercury. However, when the general theory of relativity was applied to this problem, it showed that Mercury moves precisely as Mercury has to move through the space-time continuum in that vicinity of the sun! The other planets do not move significantly in this way because they are farther away from the sun’s gravity. Score one for the general theory.

The second verification of the general theory of relativity was the fulfillment of a prediction specifically made by Einstein. Einstein predicted that light beams are bent by gravitational fields. He also predicted exactly how much they are bent, and he suggested an experiment to test this prediction. Einstein suggested that astronomers measure the deflection of starlight by the gravitational field of the sun.

According to Einstein, the presence of the sun between a group of visible stars and the earth will cause an apparent change in the position of the stars because light coming from them will be bent by the gravitational field of the sun. In order to perform this experiment, it is necessary to photograph a group of stars at night, noting their positions relative to each other and other stars in their periphery, and then to photograph the same group during the day when the sun is between them and us. Of course, stars only can be photographed in the daytime during a total eclipse of the sun by the moon.

Astronomers consulted their star charts and discovered that May 29 is the ideal day for such an undertaking. This is because the sun, in its apparent journey across a varied stellar background, is in front of an exceptionally rich grouping of bright stars on that date. By incredible coincidence, a total eclipse of the sun occurred on May 29, 1919, only four years after the general theory was published. Preparations were made to use this event to test Einstein’s new theory.

Light signals from a star are bent in the neighborhood of the sun. Because we assume that starlight travels in a straight line, we assume that the star is in a position other than it actually is.

Although light was supposed to travel in a straight line in a vacuum, a certain amount of bending already was theorized before Einstein’s general theory of relativity. Newton’s law of gravity was used to calculate this bending, even though it could not explain it. Einstein’s theory predicted roughly
twice
the deflection that Newton’s
law predicted, and, in addition, it supplied an explanation for it. Physicists and astronomers alike eagerly awaited the outcome of this confrontation between the new theory and the old.

The 1919 eclipse was photographed by two different expeditions sent to two different parts of the world. These expeditions also took photographs of the same stellar background at times when the sun was not in the area. The results of both expeditions vindicated Einstein’s calculations, not Newton’s. Since 1919, the same verdict has been reached again and again during other eclipses. All of them confirm Einstein’s predictions. Score two for the general theory.

The third verification of the general theory of relativity is called gravitational red shift. Remember that gravity (because it is the equivalent of acceleration) not only causes rulers to contract, but it also causes clocks to run more slowly.

A clock is anything that repeats itself periodically. An atom is a type of clock. It vibrates at a certain frequency. When a substance, like sodium, is made to glow, the wavelength of the light that it emits can be measured accurately. This wavelength tells us exactly the frequency of the vibrations of the atoms that comprise the substance. If the frequency should vary, the wavelength also will vary.

If we want to compare the rhythm of a clock here on the earth with the rhythm of a clock that is influenced by an intense gravitational field, like that of the sun, we do not need to send a clock to the surface of the sun. The clocks already are in place.

Einstein predicted that any periodic process that takes place in an atom on the sun, where the gravity is very intense, must take place at a slightly slower rate than it does here on the earth. To test this prediction, all we need do is compare the wavelength of the radiation of a given element as it is found in sunlight and as it is found here on earth in the laboratory. This has been done many times. In each case, the wavelength measured from the sunlight was found to be longer than its laboratory counterpart. A longer wavelength means a lower (slower) frequency. Sodium atoms, for example, vibrate more slowly
under the influence of the sun’s strong gravitational field than they do on the earth. So do all the atoms.

This phenomenon is called gravitational redshift because the wavelengths involved appear to be shifted slightly toward the red end of the visible light spectrum where the wavelengths are the longest. Score three for the general theory.

Mercury’s moving perihelion, starlight deflection, and gravitational redshift are all observable phenomena. Now we come to an area where theory is still predominant and observation is minimal. Nonetheless, it is an area that is by far the most exciting and perhaps the most stimulating in the entire history of science. The fourth verification of the general theory of relativity appears to be the phenomenon of the black hole.

In 1958, David Finkelstein published a paper in which he theorized, on the basis of Einstein’s general theory of relativity, a phenomenon that he called a “one-way membrane.”
⁴
Finkelstein showed that under certain conditions involving an extremely dense gravitational field, an invisible threshold can occur into which light and physical objects can enter, but from which they never again can escape.
^*

The following year, a young graduate student at the University of London heard Finkelstein, who was speaking there as a guest lecturer, explain his one-way membrane. The idea caught his attention and then his imagination. The young student was Roger Penrose. Expanding on Finkelstein’s discovery, he developed it into the modern theory of the “Black Hole.”
^†

A black hole is an area of space which appears absolutely black
because the gravitation there is so intense that not even light can escape into the surrounding areas.
^*
Gravitation is negligible on the laboratory level, but quite important when bodies of large mass are concerned. Therefore, the exploration of black holes naturally became a joint venture of physicists and astronomers.

Astronomers speculated that a black hole may be one of several possible products of stellar evolution. Stars do not burn indefinitely. They evolve through a life cycle which begins with hydrogen gas and sometimes ends with a very dense, burned-out, rotating mass. The exact end product of this process depends upon the size of the star undergoing it. According to one theory, stars which are about three times the size of our sun or larger end up as black holes. The remains of such stars are unimaginably dense. They may be only a few miles in diameter and yet contain the entire mass of a star three times larger than the sun. Such a dense mass produces a gravitational field strong enough to pull everything in its vicinity into it, while at the same time allowing nothing, not even light, to escape from it.

Surrounding this remainder of a star is an “event horizon.” An event horizon is created by the enormous gravitational field of the burned-out star. It functions precisely like Finkelstein’s one-way membrane. Anything within the gravitational field of this mass quickly is pulled toward it, and once past the event horizon, never can return. It is the event horizon which constitutes the essential feature of the black hole. What happens to an object that passes through an event horizon is even more fantastic than the wildest (currently) science fiction.