Chapter 12 Chapter 11 Is the Universe Finite or Infinite?

Before the space age, astronomy was considered the most mysterious of all sciences, but now it suddenly becomes a subject of great interest and a practical applied science.Since the first artificial satellites, many people who had never raised their curious eyes to the stars now do so.Topics such as the motion of the moon, the physics of the planets, and the like that for years were the domain of a handful of specialists living in remote observatories now fill the pages of newspapers and the screens of television. But the most exciting question in astronomy is utterly impractical; whatever its ultimate answer may be, it has absolutely no bearing on the practical affairs of mankind.This problem is the nature and structure of the universe. We live in the universe, and we ourselves are part of the universe.This mysterious question is without a doubt one of the greatest and most fundamental questions in science, and it has been asked over and over again since the time when man had leisure to think when he struggled to survive.The question is all the more fascinating precisely because it has nothing to do with human affairs; the human mind is often bewildered by ideas bordering on metaphysics.

Almost everyone is confronted in one way or another with an essentially unanswerable question of the opposition of the finite and the infinite.Of course, it is impossible for the human mind to conceive of infinitely small or infinitely large things; but the concept of finiteness is also inconceivable when applied to space or time.There is no third thought; if the universe is not finite, it must be infinite.This is the dilemma around which any discussion of the nature of our universe must revolve. Even a three-foot boy may come into contact with this problem.He might see in a chemist's window a large advertising bottle with a placard showing a dwarf with a white beard holding a bottle exactly like the large bottle but smaller.Of course, there is another sign on the bottle in this painting, which also shows a smaller dwarf with a bottle in his hand, and this smaller bottle still has a smaller dwarf with a bottle in his hand .Although the printing technique has not advanced to the point where even the invitation paper on the bottle of the third or fourth generation dwarves can be seen clearly, this drawing method implies that the graphics on the invitation paper can be reduced step by step, to infinity.After studying the original bottle, the children outside the window may ask: At what level should this pattern be repeated one level at a time?Obviously, the graphics can be reduced and reduced, endlessly!

At some point, of course, it must cease; the human mind recoils before this dreadful notion of infinity.But as far as the mind is concerned, there is no escape. It cannot but think of the dwarf and the bottle shrinking step by step.After the smallest figure there is always the possibility of an even tinier figure. This is only one end of infinity; things can also expand step by step.No matter how big something is, no matter if it is a house, a continent, the entire earth, the sun, the solar system, the galaxy, all the galaxies, the universe, there is always something bigger, if you can't see it, you can at least imagine it arrive.If we describe the farthest frontier of the universe as being surrounded by a fence with the words "Ultimate of the Universe" written on it in a big book, our minds will immediately jump over the fence and ask the question: What is beyond the fence?No matter how far we move the fence, we can always jump over it, and the concept of infinity reappears before us.

So far we have only discussed the extent of space.But when we think about time, the problem of the finite versus the infinite comes back to us.Is there a primordial one?If so, what was it before the beginning?Will there be an end to everything?Does time extend to an incomprehensible, endless length called eternity? These two conundrums of space and time become especially difficult when applied to the universe we inhabit.If the universe is finite in both space and time, then we have to ask: what is beyond the limit!What was before the beginning?What is after the end?But the human mind cannot give up the finite for the infinite, and cannot appreciate how the universe stretches infinitely in both space and time.A third possibility might be that both space and time are infinite, but matter exists in a finite portion of space and only for a certain amount of time.This third idea is no more satisfying than the first two possibilities, because it reduces the phenomenon of the physical universe to a mere insignificant event lost in the vast ocean of space and time.It seems utterly futile to even think about these mystical questions, since our normal ways of thinking cannot conceive of any solutions.We have an instinctive feeling that there is no evidence or counter-evidence to judge this dispute.But human nature is never content to be helpless in the face of difficulties.In ancient times, all kinds of conjectures were usually based on beliefs, religious dogmas, and even individual hobbies.The fact that everyone is free to pick and choose a theory may be fun, but it doesn't reveal the true nature of the universe.For thousands of years, there have been mostly fruitless debates.

Then the astonishing advances in science in the twentieth century suddenly changed the situation.Astronomy and theoretical physics now give us the tools to attack this problem from a new angle, using concepts and ideas that were previously unimaginable.The theory of relativity and the vastly improved astronomical apparatus of observation, such as the 200-inch telescope and the gigantic radio telescope (radio telescope), have given us the tools with which to probe the age-old question of the structure of the universe without relying on personal belief or belief. hobby.This is not necessarily to say that we are any closer to understanding the nature of the universe than ever before; but, at least, the problem and the possibility of solving it are far more exciting than ever before.

As far as modern science understands, our comprehensive view of the universe no longer focuses on a moon, planet or star, but takes the Milky Way (Tianhe) as the basic unit of matter in the universe.These galaxies, formerly known as spiral nebulae, are very, very distant objects in the sky that astronomers have been baffled for years.Now in astronomy, the typical Milky Way is described as a huge mass of many stars combined to form a huge island-like universe, whose volume is equivalent to the Milky Way to which our solar system belongs.With Dutch astronomer Jan. H．In the words of Jan H. Oort:

Mankind has been in the situation for nearly two centuries as a watchman, watching a collection of strange objects coming towards him.At first these objects appeared as dim, fuzzy shadows.When more powerful telescopes brought them closer and closer, we realized that they were clusters of stars, and we further saw that they were divided into many systems, with different shapes and types; now we have been able to analyze the internal structure of many star clusters of the details. There may be as many as 100 billion stars in a single galaxy, and there are no less than billions of such galaxies recorded, all observed by powerful telescopes deep into space.

Interesting though the above details are, they need not be given too much attention when we study the fundamental question of the structure of the universe.The most important thing now is such a statement, that is, the galaxy is considered as the basic unit of the universe, which can be said to be the atoms that make up the universe. Two important discoveries have been made about the distribution of galaxies in the universe.The first is that, as seen by the most powerful telescopes, the Milky Way appears to be evenly distributed throughout space.The Milky Way has a tendency to form clusters and clusters, but this tendency to cluster is statistically similar everywhere in the universe as a whole.The second discovery was made in the early twentieth century by V. M．Slipper (VM Slipher) E. p.Hebo (EP Hubble) and M. l.Made by ML Humason.They found that the galaxies are moving away from each other, and the speed of any two galaxies is proportional to the distance between them.This phenomenon gave rise to the theory that the universe is expanding.The twentieth century was full of scientific surprises, and the theory of cosmic inflation may be the most significant and exciting discovery in astronomy in the twentieth century.

Clearly, a knowledge of the true nature of the galaxies and their strange transits must provide much food for thought to those who study the nature of the universe.But these great discoveries are useless without an overarching theory by which they can be understood within a larger system of thought.In one of the luckiest coincidences in science, just a few years before astronomers discovered the phenomenon of the expansion of the universe, theoretical physicists happened to deduce the same idea from their mathematical equations.These equations are all born out of the famous Special Theory of Relativity (Special Theory of Relativity), the Special Theory of Relativity is Albert.It was developed by Albert Einstein in 1905, and he promoted it in 1917.

The theory of relativity is said to be incomprehensible to laymen, but as long as the nature of the universe is discussed, it is impossible to talk about it without relying on Einstein's ideas.The theory of relativity has revolutionized our concepts of space, time, and matter, the basic entities of the universe.Einstein himself and mathematicians of his time soon realized that the theory of relativity was a uniquely powerful tool for solving the ancient unanswerable question of what happened to the universe around us.Unfortunately, there is a concept in the theory of relativity that is beyond the specific perception of human senses.The various concepts of the theory of relativity involve a factor that does not occupy a place in the structure of our thinking, that is: the fourth dimension (or translation dimension, degree).

In mathematical terms, a dimension is a great extension of space.An infinitely thin line only stretches in one direction, so it is one-dimensional.A plane, such as a flat piece of paper, extends in two directions; it has only length and width, if we ignore the thickness of the paper.Therefore, the plane is two-dimensional.A box stretches height, length and width in three directions so the space is three-dimensional.The two dimensions of the plane form a right angle, which is immediately visible from each corner of a sheet of paper.The same goes for the three dimensions of space: each corner of the box is formed by combining three sides that form three right angles. When we talk about a box from a piece of paper, we add one more dimension, that is, change from two dimensions to three dimensions.With the usual limits of our thinking, things can only go so far.It is impossible for us to feel concretely that this box is increased by another dimension.There is no room for us to add another side to the corner of the box, forming a right angle with the original three sides.In other words, the concept of the fourth dimension simply does not fit the innate state of our sentience. Many people believe that the fourth dimension is an extremely difficult problem that only the greatest mathematicians or scientists can understand it, just as ordinary people can understand or concretely feel a box.This thinking is not true.No matter how clever and dexterous the human mind is, it cannot specifically feel the fourth dimension, because the space occupied by our own body is three-dimensional.The impressions received by our senses and all our experience are distributed in three dimensions only, and our thinking and our idea of ​​space must correspond to our experience.Knowledge of the properties of the four-dimensional world can be obtained only by one means, and that is by logic and reasoning.Of course, some special mathematics must be used to thoroughly study the strange properties of four-dimensional things, but this does not mean that the door to the four-dimensional world must always be closed, denying entry to anyone who does not have the mathematical key.In fact, anyone who is willing to pay a little thought can enter this strange place for a swim. Our journey starts from the world of two dimensions, and enters the world of three dimensions.When we make such a transition, we pay careful attention to all the changes that occur.We can easily understand and physically feel all these changes, because the world we depart from and the world we arrive in is within the sphere of our sensory abilities.There is nothing mysterious about these changes, since they are all related to our everyday, three-dimensional experience.We will then set off into the fourth dimension and try to gain some understanding of this strange range by comparing it with our earlier observations. We start from the realm of two dimensions, which can be said to be an infinitely thin piece of paper.We draw a circle on this piece of paper, and this circle is of course also a two-dimensional image.Then, we enter the three-dimensional realm of space, which is the world of our experience. We build a sphere in this space; it is related to the three-dimensional, just like the circle mentioned above is related to the two-dimensional.These two forms are cousins, and their close blood relationship can be seen only by looking at their nature.In fact, we should give them both the same family name, to indicate their close relationship; we may call this circle a sub-sphere.The same blood relationship also exists between the square and the cube, we can call the square a sub-cube. Now that we are ready to jump into the fourth dimension, we will put a geometric shape that corresponds to a sphere and a circle into the fourth dimension.In other words, the relationship between the four-dimensional body and the sphere must be the same as the relationship between the sphere and the circle.We have no way to describe such a shape, just like there is no way to express the realm of the four dimensions.We can only draw a box to represent the four-dimensional strange land, and write the names of the four-dimensional objects we put into this world in this box.Since this body is also a cousin of the other two figures, it deserves the same family name; we call it a hypersphere.Now we must determine the nature of this hypersphere. Let's review the circle for a moment.Its boundary is a line, and the line itself has only one dimension.But this line needs a second dimension to bend through in order to form a circle, otherwise it can only be a straight line and never form a circle.It is the curved nature of this line that makes it possible for the circle to be a closed, two-dimensional figure.The outer boundary of this circle, that is, the line, has neither beginning nor end; but though it is infinite, it has a definite length, which may be represented by dimensions.If we put a point into the circle, this point will be limited by the one-dimensional boundary line and be within the two-dimensional range of the circle. What has been said above is very clear and easy to see.Now we are going to go to the sphere and do the same.Since the transition from a circle to a sphere requires adding a dimension, when we explain the sphere, we only need to repeat what was said in the previous paragraph, and add one more dimension wherever we talk about dimensions. .The statements about the circle and about the sphere agree exactly in every respect except one more dimension. Let's move on to the sphere.Its boundary is a surface, which itself has only two dimensions.But in order to form a sphere, this surface must have a third dimension so that it can be bent through, otherwise it can only be a plane of a flat plate, and it will never become a sphere.It is precisely because of the curvature of the surface that the sphere can be a closed, three-dimensional shape.The outer boundary of the sphere, that is, the surface of the sphere, has neither beginning nor end; but though it is infinite, it has a definite area, which may be expressed in square inches.If we put a point into a sphere, the point will be within the three-dimensional range of the sphere limited by the two-dimensional boundary surface. The explanation in the previous paragraph just copied the explanation about the circle in the previous paragraph word for word, without thinking about its meaning at all.Spheres were not in mind when these instructions were written.As long as a dimension is added wherever dimensions are mentioned in the explanation about circles, this explanation can be changed into an explanation about spheres.When I reread this mechanically written explanation, I find it to be perfectly correct.This shows that some of the apparent properties of the sphere are truly and unmistakably stated, and we acquire this knowledge without looking at the sphere at all.The above explanation can be made by assuming a person living in a realm of only two dimensions, who has no sense of the third dimension.Despite this severe restriction on the structure of his thoughts, he was able to describe a sphere correctly. Now that we are ready to describe the hypersphere, we shall again apply the above explanation.This time we're going to borrow the statement about the sphere, and wherever it talks about dimensions, we'll add a dimension.The result must be a statement describing some properties of the hypersphere. Let's talk about hyperspheres.The boundary of the hypersphere is a space, and the space itself has only three dimensions.In order to form a hypersphere, this space must have a fourth dimension, so that it can be bent and passed through, otherwise it can only be a space of a flat plate, and can never become a hypersphere.It is this curvature of space that makes it possible for a hypersphere to be a closed, four-dimensional shape.The outer boundary of the hypersphere, which is space, has neither beginning nor end; but though it is infinite, it has a definite volume, expressed in cubic inches.If we put a point into the hypersphere, this point will be limited by the three-dimensional boundary space and be within the scope of the four-dimensional hypersphere. The above descriptions may seem meaningless, but we must realize that these descriptions are meaningful.It is impossible for us to feel the curved space concretely.We can draw curved lines and curved surfaces, but not curved spaces.This is a very meaningful concept, and we can only obtain this concept by transfer.We cannot feel the fourth dimension, since the space must have a fourth dimension in order to be curved and pass through, the curved space is beyond the domain of human thought.Likewise, it is difficult for us to recognize areas beyond the human mind.Similarly, it is difficult for us to recognize that the outer boundary of a hypersphere is not something like a wall, because it means that it is a boundary, but it is a space.In our language, space has the meaning of allowing people to come and go freely without hindrance, which conflicts with the meaning of the word boundary.Moreover, we acquire a new concept by appropriation.The two-dimensional plane can restrict the movement of a point in the third dimension, but in the two-dimensional space of the plane itself, the point can come and go freely without hindrance.In the same way, space can indeed be used as a boundary to limit a point to move within the fourth dimension, but within the three dimensions of the space itself, this point can come and go freely. We cut the sphere in half, and looking at the cut, we see a circle.In terms of mathematics, cutting is equivalent to reducing a dimension.Cutting a sphere produces a secondary sphere, the circle.What happens if we cut a hypersphere?Since cutting is equal to reducing one dimension, the cut surface of a hypersphere is a sphere! Let us go back to the realm of the second dimension, assuming that the people living in the second dimension are not ordinary people, but subhumans.They have no way of feeling the third dimension because their experience and their way of thinking are limited to two dimensions.Yet you are a three-dimensional being, and you have a sphere that you intend to show these subhumans.You take the sphere over their world, and the subhumans can't see it at all, because they can't look beyond their world.When your sphere touches their world, the subhumans only know that there is one point where the sphere touches their flat world.Now you push the sphere through, through their world, and the subhumans just see a disk appear.The disk becomes bigger and bigger, so that the equator part of the sphere passes through the plane world, and then the disk shrinks and shrinks, and finally shrinks to a point, completely away from the plane world.People will be amazed the first time they see this, and if you try to explain to them that what they have just seen is a sphere penetrating their world, they will not know what you mean.They will admire you greatly for your ability to perform such inexplicable tricks; but it seems to you that such things are extremely simple. Now, compared with the fourth dimension, we human beings are also planar creatures.We'd also be amazed if a four-dimensional Superman had a hypersphere and decided to push it through our world.Suddenly, out of nowhere, a point appears where the hypersphere meets our world.This point will become a sphere, getting bigger and bigger, so that the equator of this hypersphere appears, which is the largest part, and then it will gradually shrink until there is a small point, and finally it will leave our world completely . We can play another trick on the subhumans in the two-dimensional world.Suppose in that world a criminal is thrown into prison by the police.This prison is of course a closed square or rectangular frame.The criminal is a prisoner as soon as he is in a prison; he cannot escape, because his two-dimensional world is surrounded by walls and borders on all sides.We can set him free without rushing into the prison, which is no trick at all, because the frame seems to us to be open both above and below.We have only to grab him from above, lift him out of the prison, and carry him away through the third dimension.From the point of view of the prison guards, there was no sign of a break-in in the prison, but the prisoner disappeared. This is really a magical escape event. In the same way, in the eyes of the four-dimensional superhuman jailbreaker, all closed, three-dimensional boxes that we have built as prisons are seen by him as open both above and below.He can take the offender out of prison without breaking doors or walls.Four-dimensional superhuman doctors can perform truly astonishing surgeries.Such a doctor can remove a dangerous foreign object, such as a pin, from a baby without incision or pain at all. Everything we know so far about hyperspheres and the fourth dimension seems to be nothing more than amusing mathematical theories that have nothing to do with the reality of the physical world.Indeed, the initial guesses about the nature of the four-dimensional world appeared in the form of mathematical games.Later, Einstein discovered that this kind of puzzle game for mathematicians can be used for extremely valuable practical purposes, and he used this mathematical game as part of his famous theory of relativity.Einstein intended to explain the structure of the universe by means of curved space in the theory of relativity. Since curved space requires a fourth dimension in order to bend through it, the scholar must determine where this fourth dimension can be found in our physical universe.Einstein concluded that the fourth dimension is time.However, space and time are two different entities.The two cannot be interchanged immediately, unlike the dimensions of two spaces (for example, length and height can be interchanged immediately, like a box, as long as it is placed on its side, its length will become its height, height becomes long).Einstein changed time mathematically, making it equal to three dimensions of space (length, width, height) in form.He called this four-dimensional world the four-dimensional continuum, and said that this is indeed the universe in which we live.With this concept, the curvature of space is related to the existence of matter in the universe. Einstein's original idea was a little incoherent.These places were given to the Russian mathematician Alexander.Friedman (Alexander Friedman) corrected it, and he further studied the four-dimensional continuum full of galaxies mathematically, and his mathematical formula represented our real universe.But he discovered based on mathematical reasoning that such a universe would be unstable and would have to expand like an inflated balloon.Friedman made the above discovery in 1922.This is indeed a peculiar discovery, because no one had ever dreamed that the universe would behave like a balloon.However, just two years later, Erdwin S., a scientist at the Mount Wilson Observatory in California, USA,Edwin Powell Hubble found evidence that the galaxies were flying away from each other like fragments of exploding cannonballs.This discovery was immediately connected to a curious result of the speculation of mathematicians who have been trying to apply Einstein's equations to explain the structure of the universe.It was immediately clear to everyone that the motion of the Milky Way was the observational evidence for the conclusive evidence of an expanding universe as advocated by Einstein and Friedman. To illustrate this, we might as well assume that the Milky Way is like a pattern of circles on the outer surface of an inflated balloon.Since we are in a dot-like galaxy, we are surrounded by these dots.As the balloon inflates gradually, other dots will move away from us, and the farther away they are from us, the faster they will move away from us.This is exactly the mode of motion described above: since the spots on the surface of the balloon are all equal, the speed at which they move away from each other increases in proportion to their distance.Since the flight of the Milky Way was first discovered, people have observed the speed at which the Milky Way, which is the most distant frontier of the observable universe, is moving away from each other.The galaxy, so far away, is moving away from us at ninety thousand miles per second, nearly half the speed of light.Obviously, we should say that we live in an exploding universe, not just use the word expansion to describe it. The rosettes on the surface of the balloon give us only a model of a curved, three-dimensional universe.In fact, the universe is a four-dimensional continuum. As for the three-dimensional space of the Milky Way, it is just the boundary of the universe, just like the three-dimensional boundary of a hypersphere.The problem still exists to determine the four-dimensional shape of the universe, that is, the structure of the universe. Let us again subtract a dimension from everything, as we did before, in order to provide useful metaphors for shape and curvature.One dimension is subtracted from the space of the Milky Way, and it becomes a two-dimensional surface, and the Milky Way itself becomes a flat point on this surface.There are now three ways to represent the curvature of our space.First, it could be flat, and if so, space would have no curvature and would extend to infinity.The second way is: space may have a positive curvature, like the surface of a sphere; if so, it would form a closed volume, and would be finite.In the third way, space is curved according to the shape of the saddle (see the illustrations on the following pages); this curvature is negative, and the surface extends to infinity, since the saddle does not form a closed volume.How can we decide which of the three ways the real universe fits into? Unfortunately, the equations derived from the theory of relativity are not helpful in this matter.These cosmological equations are not like the simple equations learned in middle school, which only have one unknown, but only one simple solution: X∥a.There are many solutions to these cosmic philosophical equations, and painstaking research on the behavior of galaxies in the real universe is required to reveal what kind of universe we live in. Every possible solution of a cosmological equation is called a model of the universe.We have already talked about three kinds: one is the spherical universe, which is finite; the other is flat, and the third is the saddle-shaped universe, all of which are infinite.There are other factors to consider.We must also determine the change of the universe with time.Since the universe is not fixed and is clearly expanding, we must try to discover what has happened to the universe in the past and what will happen in the future.Will the universe continue to expand?Or will it finally start shrinking? Clearly, there are a large number of possible universes at our disposal.Einstein's equations may not only have several unstable models of the universe as solutions, but may also have a completely different solution.This kind of answer was proposed by the British scientist Fred.He Yier (Fred Hoyle), Herman.Bondi (Herman Bondi) and Thomas.Developed by Thomas Gold.They proposed a so-called steady-state universe, which is infinite in both space and time; more importantly: a universe that does not change over time, but remains essentially the same forever. Advocates of a steady-state universe must answer the question of how to reconcile galactic flight with their steady-state principles.The flight of the galaxy will make the galaxies in the universe thinner, because the galaxies diverge from each other and disperse, disappearing into the far-reaching infinite space.But according to the steady-state universe theory, this dispersion of galaxies is exactly offset by the automatic and continuous generation of hydrogen atoms in the increasingly expanding space between galaxies.This newly created matter condenses and forms new galaxies, replacing those that have vanished into infinity. The idea that matter can be created automatically in unobstructed space sounds weird and incredible at first, but it probably isn't.We can explain it in terms of the laws of physics, which apply the laws of indestructibility of matter and energy to the entire universe.This idea was proposed in 1945 by the German physicist Pasquale.Jordan (Pascual Jordan) first proposed, does not violate the known laws of nature. Steady-state theories of the universe have enormous appeal.According to this theory, the creation of matter, stars, and even galaxies has been going on since time immemorial; it is still going on today, and it will go on forever.The steady-state universe connects the idea of ​​perpetual change, birth and death, with the never-changing backdrop upon which the drama of the world is reflected.In this respect, the calm of the steady-state universe is almost the most elegant, in sharp contrast to those models of the unstable, evolving universe. The steady-state universe and the various types of evolutionary universes are theoretically correct solutions to the equations of cosmology.Which one is right and which one is wrong cannot be determined by theory alone.If we are to make a choice, we must study a feature of the evolved universe, namely the ancient situation, which we have not discussed.Now that the galaxies are moving away from each other, and the discrete velocities have been measured with considerable precision, it is easy to work out how long ago they must all have been in the same place.If there were a movie that recorded the history of the universe from the beginning, if we could rewind the movie and play it back, we would see the galaxies speeding and coming together; since the farthest flies the fastest, they will all be in the same place. time to arrive at a place.This dramatic beginning, when all matter in the universe condensed into an impossibly hot, compact ball, must have occurred about six billion years ago, according to astronomers, physicists and mathematicians who advocate the theory of evolution.They believe that the universe was created in a cataclysm, out of which all space, time and matter came into being. One of the main defenders of the theory of evolution was the American physicist George W.Jia Mao (George Gamow).According to Jia Mao, in the beginning, extremely hot matter formed a huge mass, which was the birthplace of hydrogen and helium. Ninety-nine percent of the mass of the universe is composed of hydrogen and helium.The unresolved questions of where, when and how the various heavier elements formed are irrelevant to the image of the universe.It took 250 million years for this exploding mass of matter to form countless galaxies, and it continues to gallop away from the place where everything was born.Now these galactic flights still bear witness to the cataclysm that was the beginning of all things six billion years ago.Will this galloping go on forever, leaving our part of space virtually devoid of galaxies as they spread out into the ever-increasingly voluminous universe?This question remains unanswered.Since the density of matter in regions that can be observed in the universe is within a certain limit, the attractive force acting on these matter can be calculated.This force would act to slow the galaxy's outward flight.Here a question arises, namely, whether attraction can arrest the motion of the galaxies, reverse their direction, and at last bring them back to their original place of creation.It now appears that the galaxies moved too quickly, and their mutual attraction was too weak to draw them together again.然而我們對於宇宙所包含的物質的份量可能猜測錯了。假如這份量比我們所估計的龐大得多，銀河之間的相互吸引力就會比我們所猜想的更強大，可能延緩宇宙的膨脹。 M．赫馬孫（M. Humason）用二百吋直徑的望遠鏡進行的觀測，顯示這麼一種延緩可能真是在進行中。 說起來也許是件怪事：我們居然能夠查到銀河在十億年前運動的速度。這個道理非常簡單。用最大的望遠鏡觀察得到的許多銀河，離開我們大約有十億光年的路程。這就是說，從這些銀河發出的光，傳到我們的眼睛時，已在路上走了十億年；我們從這光所知道的銀河的情形，一定是它們在上古時代的情形。赫馬孫發現：這些遙遠的銀河似乎行得比它們應有的速度更快，意思就是說，它們在十億年前運動的速度比現在更大。以這個證據為基礎，我們必須達到一個結論，就是在最近的十億年裏，宇宙的膨脹已經顯著地延緩了。事實上，減速率似乎很大，膨脹將終於停止；然後銀河會開始走回頭的路。再過幾十億年後，它們會聚首於一起，作驚天動地的大碰撞，那時候，舊宇宙死亡，新宇宙誕生。假如真是這個樣子，在極遙遠的將來可能有另一種人類會觀察另一個宇宙的銀河，並且下結論說，每個宇宙不過是創世的脈搏跳動了一下而已。 顯然，證實了這種宇宙膨脹速率的減低，就會推翻穩定狀態的宇宙的理論。在穩定狀態的宇宙裏，膨脹的速率必須永遠是同一的。 我們觀察最外面的銀河時，的確就是在回顧上古的情況這個事實，給了我們另外一個可能性，足以斷定進化的宇宙和穩定狀態的宇宙究竟誰是誰非。這場測驗所用的工具，由一們新科學｜射電天文學提供。觀測表明：有些銀河是極強烈的無線電波的來源，儘管它們離開我們比光學望遠鏡所能達到的距離更遙遠得多，但發出的電波極強，我們還是可以錄取到。每個銀河都是個無線電波的源頭，但銀河同銀河相碰撞時發出的無線電波尤其特別強烈。講起兩個銀河的互撞，似乎是極富於戲劇的事件，其實一點也不奇怪。一個銀河裏的各個恒星之間的距離大極了，所以兩個銀河可以撞到一起而互相穿插過去，卻不致於讓任何兩顆恒星正面碰撞。然而每個銀河都包含由氫氣體形成的大塊雲；當這些雲塊迎頭相撞的時候，就會釋放大量的能，以無線電波的形式發出，雖然經過極遠距離的空間，歷過幾十億年的時間，還是能夠讓人偵察到。 十億年前，宇宙裏各個銀河的彼此距離比今天更接近得多；所以，那時候兩個銀河之間發生碰撞的情事必定比今天更加頻繁。秉著這樣的想法，英國的射電天文學家馬丁．瑞艾爾（Martin Ryle）一直在檢查宇宙，搜尋無線電波的來源這些電波可以給人辨明是二百吋望遠鏡所望不見的遙遠太空裏互相碰撞著的銀河發出來的。瑞艾爾獲得了驚人的結論：在太空的遙遠地區我們所知道的當地發生的事情都是發生於十多億年以前的這種銀河之間互相碰撞的情事，其發生的次數比今日更為頻繁。這個結論也趨向於推翻穩定狀態的宇宙的理論，依照這種理論，無論在什麼空間、什麼時間，銀河之間發生碰撞的頻繁程度必定是相同的。 倡導穩定狀態的宇宙理論的人說，銀河相撞和宇宙膨脹延緩的證據還是太靠不住，不足以斷定爭論的雙方誰是誰非。固然，已經作出的一切測算都是在僅僅可以容許測算的限度裏勉強作出的，而所得的結果也同可能的錯誤混在一起，必須慎重揀擇出來；但是有利於進化的宇宙的證據似乎在漸漸增加著。 穩定狀態的宇宙，依它的定義來說，在空間和時間方面都是無限的。進化的宇宙卻既可以是有限的，又可以是無限的；假如我們必須贊同這個理論，我們原先關於宇宙的性質的問題就得不到答案。於是我們又面臨三種可能性：一是無限的平的宇宙；二是有限的球形的宇宙；三是無限的馬鞍形的宇宙。 前面談到過的赫馬孫的研究，不但表示宇宙的膨脹已在逐漸延緩，也暗示宇宙是一種封閉的超球體，我們生活於有限的尺寸的宇宙裏。 但是還有另外一種辦法決定如何從平面形、球形和馬鞍形這三種形象的宇宙中選定一種。只要算一算銀河的數目就行了。我們不妨把宇宙看作一個表面，扁平的銀河就撒佈在這個表面上。現在我們以自己的銀河為圓心，畫一個大圓圈，計算一下在這個圈內的銀河總共有多少個。然後我們又畫第二個同心圓圈，其半徑為第一個圓圈的兩倍。我們又計算第二個圓圈所包含的銀河，當然包括第一個圓圈裏已經計算了的全部銀河在內，接著，我們又畫第三個圓圈，其半徑三倍於第一個圓圈，並又計算其中的銀河總數。現在我們得出三個數字，單憑這三個數字，就可查明我們的宇宙是怎樣彎曲的。我們必須假定銀河是均勻地分佈於宇宙各處的，但這是一個合理的假定。 我們可以首先看看平板的宇宙，它是沒有彎曲的。我們畫的三個圈，都在平面上，我們可以斷言，三個圈裏所包含的銀河的數目的比例必定是一比四比九，因為三個圈的面積的大小依照它們的半徑的正方１^2（＝１）、２^2（＝４）、３^2（＝９）成正比例地增長。 假如表面是彎曲的，這些簡單的比例就作不得數了。若彎曲是正的，不是負的，三個圓圈就是畫在一個球體上，它們的面積的增加率稍小於上文所說的。若要證明此事，只須將球體上畫了圈的部分切下來壓扁，攤開在平板上就行了。那時，切下來的球體部分的表面會有許多個地方裂開來，裂縫裏是沒有銀河的。所以，假如三個數字遞增時的比例少於一比四比九，我們的宇宙就必定是個有限的封閉的球體。反過來說，假如彎曲是負的而不是正的，我們的宇宙便是馬鞍形的，三個數字遞增的比例會大於一比四比九。這也可以證明，我們只要設法把馬鞍攤開在平面上就行。這時候，表面會起皺，某些地方會重疊起來，因此，在同一塊地區所包含的銀河的數目多過扁平的圈所包含的。 當然，我們剛才用來代表宇宙的那三種表面都缺了一個因次；但我們知道，同樣的結論可以適用於嵌在四因次連續裏的三因次空間的真實宇宙。扁平的世界相當於無限的直的空間；球體相當於一種有限的超球體，而馬鞍形相當於無限延伸的超鞍形。我們的關鍵性數學也會變更，因為我們現在必須計算越來越大的球體裏找得到的銀河的數目，而不是越來越大的圓圈裏銀河的數目。這些關鍵性數字變成了一、八和二十七。因為球體的體積依它們的半徑的立方而增加。（1^3為一、2^3為八、為3^3二十七。） 這樣一種計算銀河數目的工作確實進行過，數目遞增的速度似乎大過一比八比二十七的次序。這個結果表示宇宙的結構符合於某種超馬鞍形，也就是說，我們生活於一個無限延伸的宇宙裏。 不過，宇宙哲學的根本問題完全談不上已經獲得解決。事實上，天文學家們運用美國加里福尼亞州帕洛馬山上著名的二百吋赫爾望遠鏡，近來已經作出了一系列的發現，使宇宙科學像自古以來那樣流動而不確定但也同樣地令人醉心。一九六○年，艾倫． R．散德奇博士（Dr. Allan R. Sandage）發現了一叢黯弱的星，它們的年齡經他用靈敏的光電設備測定了。這些星屬於我們的銀河，據測定約莫有二百四十億歲。假如這個結果經過反覆核查後還站得住，我們可以預期宇宙在空間和時間的延伸範圍又會有重大的修正。 加里福尼亞理工學院的弗里茲．茲維克博士（Dr. Fritz Zwieky），把四十八吋的許密特望遠鏡加二百吋望遠鏡上使用，宣佈發現了銀河之際的物質的存在。許多年來，天文學家深信銀河與銀河之間的廣闊空間裏根本是沒有物質的。現在茲維克博士卻在一叢叢的銀河之間發現了一團團的銀河氣體和灰塵散佈著。這項發現對於一切的宇宙哲學理論都有重大的關係。根據宇宙哲學的方程式，宇宙中的物質的平均密度，對於宇宙的體積、它膨脹的速度和它的年齡，有著明確的關係。茲維克博士相信：宇宙中含有的物質，比往昔估計的份量要多一百至一萬倍。他這個結論如果獲得了證實，宇宙哲學的思想就必須作重大的變更。 英國數學家兼宇宙哲學家威廉． H．麥克瑞（Dr. William H. McCrea）甚至於認為：究竟進化的宇宙和穩定狀態的宇宙誰對誰錯，可能先天就是無從解答的。他認為我們對於宇宙極遙遠的空間和時間究竟是個什麼樣子，幾乎絲毫也不能有所斷言。他相信：這個看法似乎比近來的趨向認為整個宇宙的本質已經給人發現了更教人滿意。我們仍然不能確定我們關於宇宙的真正本質的結論究竟對不對，雖然有一段時期裏解答這個令人迷惑的問題的鑰匙好像幾乎可以被我們取得了。儘管如此，我們居然能夠作出很多有關這個問題的測定，也就足以教人驚奇了。 假如將來真有那麼一天，種種事實都讓人查明了。我們對於自己的結論能有確切的把握，這對於我們的日常生活也絕對不會發生什麼實際的影響。但那個最後的答案說不定是科學所能夠作出的最最激動人心的發現。人類的好奇心必定永遠以解答宇宙的偉大謎語為其最大的刺激。