However, in the universe at large gravity cannot be neglected. Wherever there is a piece of matter, it warps the space-time continuum. The larger the piece of matter, the more pronounced the warp.
In the example of the revolving circles, the variation of velocity in different parts of the co-ordinate system caused the ruler to change size. With that in mind, remember that acceleration (change in velocity) is the equivalent of gravity. Therefore, changes in the strength of a gravitational field will produce the same contractions of the ruler as changes in velocity. “Acceleration” and “gravity” are two ways of saying the same thing. That means that if a ruler is subjected to gravitational fields of different strength, it changes length.
Of course, it is impossible to travel through our solar system, much less our galaxy, without encountering gravitational fields of varying intensity, which would cause any maps that we somehow could produce to look distorted like the stretched piece of india rubber. The terrain of the space-time continuum in which our earth moves is like a hilly countryside with a mountain (the sun) dominating the geography.
According to Newton, the earth wants to continue forever in a straight line, but forever is deflected from its inclination by the gravitational force of the sun. A balance of the two keeps the earth in orbit around the sun. According to Einstein, the earth’s orbit is simply the easiest path for the earth to take as it moves through the space-time continuum, warped as it is in this neighborhood by the sun.
Imagine how complex is the geography of the space-time continuum which is our universe with its solar systems, star systems, galaxies, and galaxy clusters, each of them causing major and minor bumps, curves, hills, valleys, and mountains in the four-dimensional space-time continuum.
Would it be possible to navigate under such circumstances?
Yes. Although it is a crude example, sailors navigate under somewhat analogous circumstances. We cover the earth with squares which are formed by lines of latitude and longitude. The size of these squares varies depending upon where they are located. The closer they are to the equator, the larger they are. (If this is unclear, look at a globe). Nonetheless, we still can locate physical points on the surface of the earth by designating the intersection of a line of latitude and a line of longitude. Knowing the number of squares between us and where we want to sail does not give us the distance to our destination because the squares may vary in size. However, if we know the nature of our terrain (a globe) we can calculate distances on it (using spherical trigonometry).
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 the
ir 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.
If the black hole is not rotating, the object will be pulled directly to the center of the black hole to a point called the singularity. There it literally will be squeezed out of existence, or as physicists say, to zero volume. At the black hole singularity all of the laws of physics break down completely, and even space and time disappear. It is speculated that everything which is sucked into a black hole is spilled out again on “the other side”—the “other side” being another universe!
If the black hole is rotating, an object that is sucked into the event horizon could miss the black hole singularity (which is shaped like a “ring” in a rotating black hole) and emerge into another time and another place in this universe (through “wormholes”), or into another universe (through “Einstein-Rosen bridges”). In this way, rotating black holes may be the ultimate time machines.
Although black holes are almost invisible, we can search for observable phenomena that may be characteristic of them. The first of these is a large amount of electromagnetic radiation. A black hole continuously attracts hydrogen atoms, cosmic particles, and everything else to it. As these particles and objects are drawn to the black hole, they steadily accelerate through its gravitational field until they approach the velocity of light itself. This causes tremendous amounts of electromagnetic radiation. (Any accelerating charged particle creates electromagnetic radiation.)
The second observable characteristic of an invisible black hole is its effect on a nearby visible star. If a visible star can be found which moves as though it were revolving around an invisible star (i.e., as though it were half of a binary star system), we might speculate that it actually is revolving around an invisible star, and that its invisible partner is a black ho
le.
The search for black holes consequently became the search for these two phenomena. In 1970, the satellite Uhuru located both of them in one area. It pinpointed a high-energy x-ray source in the constellation Cygnus which emits a million times more energy than the sun. This high-energy source of electromagnetic radiation, which came to be known as Cygnus X-1, is very close to a visible blue-hot supergiant star. Scientists now believe that this blue supergiant forms a binary system with the black hole, Cygnus X-1.
As the visible star and the invisible black hole orbit each other, the blue supergiant literally is being sucked into the black hole. As material is torn away from its surface, it plunges into the black hole at tremendous speed, emitting x-rays. Incredible as Cygnus X-1 is, more than one hundred similar objects have been detected within our own Milky Way galaxy since its discovery. Although black holes stretch our imagination to the limit, the evidence is mounting that they actually do exist.
For example, if black holes are as we have speculated them to be, whatever disappears in them reappears somewhere. Is it possible, therefore, that there are black holes in other universes which are sucking matter from those universes into our universe? This is a seriously considered possibility. There are objects in our universe that appear to be the reverse of black holes. They are called white holes (of course). These objects are quasi-stellar radio sources, or quasars for short.
Quasars are extraordinarily intense energy sources. Most of them are only several times the diameter of our solar system, yet they emit more energy than an entire galaxy of over 150 billion stars! Some astronomers believe that quasars are the most distant objects ever detected, yet their incredible brightness allows us to see them clearly.