OSMOLOGY & RELATIVITY

From our vantage point at Earth, we see an abundance and variety of objects and phenomena. Among them are gassy nebulosities glowing with colorful light, explosive stars ejecting matter and energy, and powerful galaxies spinning in the depths of space. Through a telescope on a dark, moonless night, celestial objects present superb examples of astronomical architecture—real jewels of the night. But astronomical bodies are more than works of art, more than objects of elegance. Each is a rich repository of light illuminating a material aspect of our Universe. To the cosmic evolutionist, planets, stars, nebulae, novae, galaxies, and all the rest are of vital significance if we are to realize our human place in the big picture. This intellectual placement of humankind in the wider cosmos will emerge later in this Web site; for now, we focus on the grand issues addressed by cosmologists.

Terrestrial vs. Extraterrestrial Light is only one type of radiation—namely, that type to which our human eyes are sensitive. As light enters our eye, the cornea and lens focus it onto the retina, whereupon small chemical reactions triggered by the incoming light send electrical impulses to the brain, producing the sensation of sight. By contrast, radio, infrared, and ultraviolet waves, as well as x rays and gamma rays, all comprise invisible radiation, each of which goes undetected by human eyes. But regardless of the type, radiation is energy, that physical property best characterizing (and driving) change. Radiation is also information—a primitive form of information that moves from one point to another, such as from a star to our eyes. It is only by means of such one-way information flows that we can hope to fathom the depths of space.

Practitioners of astrophysics acquire information about cosmic objects by interpreting their emitted radiation. We say “astrophysics” because that word best defines the basis on which the interpretations are made. These days, the emphasis is on physics: astro is a mere prefix. The space scientist of today who doesn’t have a firm grounding in physics is hardly a space scientist at all. Gone are the romantic evenings when individual astronomers made fundamental discoveries by peering through long telescopes and marveling at the sights; gone also are the thick catalog tabulations and stacks of exposed photographic plates. The modern astrophysicist wants to know more than just where objects are, or what their brightness and colors may be. Contemporary astronomy has become more of an applied physics than the classical astronomy of old.

Astrophysicists are driven more than most by a need to understand how Nature functions. We not only want to perceive what lurks beyond the range of human eyesight, what the Universe “looks” like in the invisible domain—which is, by the way, where most matter radiates. We also seek to know how the myriad celestial objects came to be, how they operate in detail, how matter and radiation interact, and especially how energy guides the ceaseless changes among all known cosmic systems. We are intellectually transitioning from addressing only what questions to the more penetrating how questions.

In a way, astronomers and astrophysicists have been commissioned by society to keep an eye on the Universe. Our job is to inventory the cosmos, to seek a complete account of the state and nature of all the different types of matter beyond planet Earth. Likewise, the newly emerging field of “astrobiology” seeks to inventory life in the Universe, although thus far life on Earth is our only confirmed example. In contrast to the abundant databases of modern astrophysics, astrobiology is a subject for which there are as yet no data. If and when life is found elsewhere beyond Earth, the interpretive emphasis will shift to biology in a cosmic setting.

Note the essential difference between the majority of scientists, who study terrestrial matter in laboratories on Earth, and astroscientists, who investigate remote, alien matter far from our home planet. On Earth, scientists can control their experiments as an aid to discovering a wealth of properties among terrestrial matter. They can both tangibly manipulate the matter under scrutiny and tinker with the experimental equipment used to inspect it. In the case of a new rocky ore, for example, laboratory scientists could examine its properties by sampling a variety of rocks, each having a different size, shape, or composition. They could probe the ore in many ways—vigorously heating it or cryogenically cooling it, and even subjecting it to varying amounts of electricity and magnetism. Or they could just hit it with a hammer, which geologists often do. All the while, researchers would learn a great deal about the rock by testing its responses to many environmental changes. In short, the medium in which a terrestrial experiment operates can be intentionally altered in various ways in order to enhance the study of localized matter.

Distant matter far beyond our planet, however, cannot be so directly examined and massaged, not even with the very best tools of modern civilization. Remote extraterrestrial environments can be neither controlled nor manipulated. For the most part, astronomers are restricted to working with intangible radiation emitted by cosmic matter—radiation occasionally intercepted by human eyes or detected by earthly instruments, signals momentarily captured while traveling from faraway objects to faded oblivion elsewhere in the dim recesses of the Universe.

Technological advances have recently provided a few exceptions to these statements, enabling space scientists to perform guided experiments on a handful of specimens from nearby extraterrestrial regions: interplanetary meteorites discovered buried in Earth’s crust and especially its icy polar caps, lunar rocks retrieved from our dead neighbor via the American and Russian space programs, a few specks of cometary dust sampled by spacecraft and returned to Earth, and Martian soil examined by robots now parked on the plains of that alien planet. Yet it’s likely to be centuries before our descendants gain the means to conduct hands-on exploration of matter beyond our own Solar System. For now and a good long time to come, the bulk of cosmic matter must be inventoried and analyzed by extracting information veiled within its naturally emitted radiation that just happens to be captured by equipment on or near Earth.

For the time being at least, radiation is the only means whereby we know of the existence of virtually any celestial object.

Looking Out, Looking Back A further restriction comes to mind when contemplating distant extraterrestrial matter. Not only are we prohibited from studying celestial objects at their present locations in space, but we are also denied the chance to examine them now in time. The reason is that radiation does not travel infinitely fast; it moves at a finite speed—the velocity of light. Consequently, it takes time—often lots of time—for light or any type of radiation to travel through the vast expanses of space separating objects in the Universe. Yet, few people realize the enormous time intervals needed even for light to traverse the great realms beyond our home in space.

The bright red star easily visible in the northern winter constellation Orion provides a classic example. Betelgeuse is known to be about 420 light-years away—a surely lengthy range given that a light-year is the distance traveled by light in a full year at the fastest velocity known. One light-year equals about 10 trillion kilometers, or 6 trillion miles; even a light-day measures some 30 billion kilometers. So radiation moves fast, there is no doubt—which makes the distance to this relatively nearby star all the more impressive. To be sure, Betelgeuse’s radiation takes more than 4 centuries to travel to Earth. Since nothing known surpasses the velocity of light, its radiation simply couldn’t get here any quicker. Expressed another way, the light we see while looking at Betelgeuse tonight left that star before the invention of the telescope. It has been cruising through the near void of outer space ever since.

The nearest spiral galaxy, called Andromeda for short and shown in Figure S.3, provides an even more dramatic example of light’s finite speed. It, too, can be seen with the naked eye as a fuzzy “cotton ball” just south of the bright, sharp stars of the big-W constellation Cassiopeia in the northern summer sky. Roughly 2.5 million light-years distant, this galaxy’s radiation takes ~25,000 centuries to reach us—meaning that Andromeda’s light that we see tonight left that galaxy well before Homo sapiens emerged on planet Earth. And yet it’s the nearest major galaxy to us!

Radiation from distant objects, therefore, harbors clues to the past—but not to the present. The farther an object is from Earth, the longer its light takes to reach us. In the case of the truly remote galaxies, some of which are billions of light-years away, radiation left those objects well before the Earth or the Sun even formed. In fact, radiation now reaching us from the most distant cosmic objects was launched in earlier epochs of the Universe when none of the familiar stars and planets yet existed.

By collecting radiation, astronomers can learn what the conditions were like long ago when distant objects emitted their light. The light itself resembles a letter mailed some time earlier; the letter’s contents grow no older while being delivered, thus bringing to the recipient information about the time when the letter was written. Likewise, light embodies data about earlier times when the light was launched; light itself does not age. Deciphering the information within that radiation, we can not only determine the general conditions in the Universe before the dawn of the Sun and Earth, but we can also specify values for the two most important factors—temperature and density—characterizing the Universe in some of those ancient times.

Our perspective of the Universe is therefore delayed. We see the Universe as it was, not as it is. Even more useful than many philosophers’ wish that light speed be infinite so as to reveal the whole Universe presently, it’s precisely because light speed is finite that we can discover a fascinating record of many past events, including perhaps knowledge of our own cosmic origins.

Astronomers, then, are the ultimate historians; our telescopes, effectively, are time machines. We go all the way back (or nearly so) into “deep time,” indeed we probe times much, much earlier than those studied by scholars traditionally called historians—before Rome, before Egypt, to be sure well before any recorded history. Looking out from Earth, we see a natural history of the Universe arrayed before us, including epochs early enough to reveal the ways and means that may have created our being. Much like anthropologists who sift through ancient rubble for bones and artifacts containing hints and clues about the origin and evolution of human culture, astrophysicists dissect radiation only now arriving at Earth, seeking to interpret its embedded information about the origin and evolution of matter itself.

So note well the cosmologists’ dictum: Looking out in space is equivalent to probing back in time. We do not perceive the Universe as it is now, rather we see it progressively younger the farther out we probe. Since our telescope-aided fields of view extend for billions of light-years into space, we necessarily explore billions of years earlier in time. By examining deep space and capturing radiation from the most distant objects, researchers gain an increasingly better picture of what the Universe was like long ago, including near the time when time itself began. This is the task before us—to construct a chronological narrative that relates, using the best science available, how all things came to be.

Universal Expansion Cosmic activity permeates the Universe, yet so does quiescence. Perspective often determines which dominates. Surveyed casually, celestial objects usually display stability. Yet higher resolution often reveals some violence. Generally, the larger the perspective, the more stable things seem. For example, that our Earth is ruptured by quakes and volcanoes is obvious to those of us who live on it and witness its daily activity up close; but our planet appears tranquil when viewed from afar in those striking lunar earthrise photos taken by the Apollo astronauts. Likewise, telescopic studies of our Sun show it to be peppered with bright flares, dark spots, and surface explosions, as are presumably all stars; yet to the naked eye, the Sun and most stars assume a rather peaceful, steady pose.

We might then expect that, while pockets of violence will be surely occur here and there throughout the fabric of the Universe, the largest possible, cosmic perspective would display perfect quiescence. Not so, however. In bulk, the Universe is not calm and stable. Surprisingly, the whole Universe in toto displays much dynamism.

Knowing, then, that the Universe harbors a certain verve, we might further expect the largest material structures—among them the galaxies—to have random, disordered motions, some hurtling one way and some others another. Chaotic motions of fireflies trapped in a jar come to mind, or the nearly scattered motions of hockey players in a skating rink. For the Universe at large, however, these are not good analogies. Our expectations are wrong again, for the galaxies are not moving chaotically. The Universe on the largest scales is indeed active, but in an awesomely ordered fashion.

For well more than half a century now, scientists have realized that galaxies have some definite organized movement in space—a universal traffic pattern of sorts. Surprisingly, virtually all the galaxies are steadily receding, propelled away from us as though we had a kind of cosmic plague. (Only a few nearby galaxies, including neighboring Andromeda, are known to have a component of their velocity toward us, but that’s due to the random, small-scale motions that all galaxies display in addition to their more directed, large-scale recession—like confused fireflies in a jar that has been heaved away, which is a good analogy.) What’s more, the galaxies are also receding in a grand overall manner. Each one drifts away at a velocity proportional to its distance from Earth. This is an observational finding of great significance: the greater the distance of an object from us, the faster that object recedes. These two quantities—velocity and distance—are highly correlated.

Astronomers know this because the galaxies’ light displays a red shift—that is, a stretching to longer wavelengths because of the Doppler effect. Just as sound waves from a police car’s siren (or speeding train) produces a higher pitch when the vehicle (or train) approaches and a lower pitch when moving away, so light waves from an approaching object are squeezed to shorter wavelengths—toward the blue part of the spectrum—and stretched to longer wavelengths—toward red—as it recedes. The extent of the shift, which occurs in light much as it does in sound, reveals how fast the object is traveling. To be sure, the Doppler effect is also used to spot speeders on the highway and to measure the speed of a pitch at the ballpark.

Hubble’s Relation How do we know the galaxies share this net, direction motion away from us? The answer is that spectroscopy proves that galaxies' spectral lines are red shifted. Figure 1.1 shows some representative examples of optical spectra observed toward several galaxies. Interpreted as a Doppler effect, these shifts indicate that the galaxies are steadily receding. Furthermore, the extent of the red shift increases progressively from top to bottom in the figure. And since the distance also increases in the same way—from top to bottom—we conclude that there must be a connection between Doppler shift and distance. This trend of greater red shifts for objects farther away holds valid for virtually all known galaxies in the Universe. (Two galaxies in our Local Group of galaxies, including the Andromeda Galaxy, and a few galaxies in the Virgo Cluster display blue shifts and hence have some motion toward us, but this results from their random motions within these nearby galaxy clusters.)

So not only are the galaxies receding, but they recede at velocities proportional to their distances. A linear relationship—a tight correlation—connects velocity and distance. The greater the distance of an object from us, the faster it recedes.

IGURE 1.1

FIGURE 1.1 – Optical spectra (at left) observed toward several different galaxies (at right). The extent of red shift (denoted by horizontal arrows at left) and the distance to each galaxy increase from top to bottom. (Adapted from Palomar Observatory data; Caltech.)

Figure 1.2(a) shows a diagram of recessional velocity plotted against distance for the five galaxies in Figure 1.1. Figure 1.2(b) is a similar plot for numerous galaxies within 4 billion light-years. Diagrams like these were published in the 1920s by the American astronomer Edwin Hubble (and his colleagues) and hence bear his name; the resultant statistical fit (dashed line) is sometimes called Hubble's law. We could make such a diagram for any group of galaxies provided that their distances can be found and their radial velocities measured by spectroscopy.

Note the implications for Figure 1.2. As can be read directly from the plot, galaxies at the remote distance of 4 billion light-years speed away with velocities of nearly 90,000 km/s. This is a fair fraction of the velocity of light. The ratio, 90,000/300,000, implies that such a distant galaxy has a recessional velocity of 30 percent of light velocity. That's fast, very fast—but it does not mean that the galaxy per se is moving through space that fast, rather that space itself is rapidly expanding and the galaxies are along for the ride.

IGURE 1.2

FIGURE 1.2 – Plots of recessional velocity against distance (a) for the galaxies shown in Figure 1.1, and (b) for numerous other galaxies within 4 billion light-years.

Note also that Hubble's law is an empirical finding. By "empirical" we mean one based strictly on observational results. Its central relationship—a statistical correlation between velocity and distance—is well documented to at least 4 billion light-years. Yet there is no basic physical reason for this relationship. No law of physics demands that all galaxies recede. And no physical law requires distance and velocity to be correlated. Consequently, astronomers are currently unsure if this relationship holds true for cosmic objects beyond several billion light-years. In this sense, then, it's not really a "law" at all.

Don't be confused here. There are good and valid reasons for the red shift as an indicator of recessional velocity. This is the Doppler effect that is well established in physics; the larger the spectral-line shift, the greater the net motion between the observer and the observee. But the Doppler effect in no way relates velocity and distance. In particular, the Doppler effect doesn’t predict Hubble's law at all. Hubble's law is merely a compact way of noting the observational fact that any galaxy's recessional velocity is directly related to its distance from us.

Hubble's law can be quantified in order to make it more useful. This is relatively simple since velocity and distance are linearly related. The data of Figure 1.2 obey the following equation:

recessional velocity = Hubble's constant x distance.

Here the proportionality factor between velocity and distance is called Hubble's constant. We can derive the value of this constant by estimating the slope of the dashed line in Figure 1.2. That slope measures nearly 90,000 kilometers/second divided by 4 billion light-years, or ~22 km/s/million light-years. (In units commonly used by professional astronomers, this would equal ~70 km/s/Megaparsecs, where there are 3.26 light-years in a parsec, a dreadful unit that does nothing but help keep the beginners out.) Thus for every additional million light-years of distance from us, cosmic objects race away with an added speed of some 22 km/s.

This is the best current value for Hubble's constant. We say "current" because Hubble's constant is a statistical solution to the data plotted in the Hubble diagram. Over the years, newer methods (and better calibration of older methods) used to determine distances have repeatedly forced astronomers to revise the value of Hubble's constant; 75 years ago, it was thought to be some 10 times larger. Even today, researchers suspect that its value might be skewed a bit by the drift of our Local Group of galaxies toward the much bigger Virgo Cluster of galaxies; this net drift amounts to ~600 kilometers/second and might be nothing more than the random motions of our Local Group in the outskirts of a larger galaxy supercluster. At any rate, today's researchers regard the current value of Hubble's constant to be accurate to within 10% of the correct value, and thus do not anticipate the need for further major revision.

Throughout the past few decades, astronomers have striven to refine the accuracy of Hubble's diagram and the resulting estimate of Hubble's constant. That's because Hubble's constant is one of the most fundamental quantities in Nature, specifying the rate of movement of the grandest contents of the Universe. As such, Hubble's constant is a cornerstone in our study of the origin, structure, and destiny of the entire Universe.

Now, if we think about it for a moment, the entire pattern of distant objects receding more rapidly than nearby ones implies that an “explosion” must have occurred at some time in the past. Visualizing the past by mentally reversing the outward flow of galaxies, we reason that all such galaxies were once members of a smaller, more compact, and hotter Universe. The more distant an object is from us, the more forcefully it—or whatever preceded it—must have been initially expelled; their greater distances result directly from their greater velocities. In other words, the faster-moving galaxies are by now farther away because of their high velocities. This is precisely the flight pattern of shrapnel fragments when a conventional bomb explodes. The galaxies are simply the debris of a primeval “explosion,” a cosmic bomb whose die was cast long ago.

The word explosion is in quotes above because, technically, most astronomers don’t like that description. Since there was no preexisting space, nor any matter per se at the start of the Universe, that word can be misleading. Yet if we keep this bomb-like interpretation in mind as merely artistic license—more properly interpreted as energy initially expelled into time, rather than matter into space—then the analogy serves a useful purpose.

This implied, titanic event is commonly known as the “big bang,” a derisive term introduced by skeptics who decades ago preferred a more steady, less violent Universe. But the term has stuck and is now synonymous with the standard model of cosmology—a widely accepted description of macroscopic phenomena on the largest scales. Note again and despite the word “bang” that primordial matter did not actually explode into any already existing space, nor are the galaxies now moving through space or rushing into “empty space” beyond. Rather, owing to the initial conditions at the moment of the big bang, space itself began expanding at high speed, much like a crumpled fabric rapidly unraveling or a balloon rapidly inflating. The galaxies now seen are merely part of that expanding fabric of space, or to employ an even better analogy more like raisins in a baking bread

Recessional motions of the galaxies virtually prove that the whole Universe itself is in motion. On the largest scale of all, the Universe is surprisingly active and by no means a pillar of stability. Instead, much like everything within it, the Universe changes with time—in short, it evolves.

Be assured that neither Earth nor the Solar System nor individual galaxies are physically swelling in size. Planets, stars, and galaxies are all gravitationally bound, intact systems. Only the largest framework of the Universe—the ever-increasing distances separating galaxies and especially clusters of galaxies—manifests cosmic expansion.

Deep Questions Astronomers, philosophers, theologians, as well as people from all segments of society would like to know if the Universe will continue to expand forever or whether its expansion will someday stop. It’s the destiny issue, hereby scientifically stated: If the Universe eternally expands, unimaginable amounts of time would be available for the continued evolution of matter and life. By contrast, if the Universe embodies enough matter, the combined pull of gravity could conceivably bring the expansion to a halt, and even reverse it into contraction.

Several questions come to mind: How long has the Universe been expanding? How much more time will elapse before it ceases expanding? If the Universe does start to contract, what will happen upon its eventual collapse? Will the Universe simply end as a small, dense point much like that from which it began? Or will it perhaps bounce and begin expanding anew? If the Universe has rebounded in this way before, might we inhabit a cyclically expanding and contracting Universe—one having a continuous cycle of birth, death, and rebirth, though neither a true beginning nor an ultimate end?

These are the basic large-scale fates of the Universe in bulk: It can expand forever. It can expand and then contract to a virtual point and end. Or it can cyclically expand and contract indefinitely. Each model represents a hypothesis—a theory based on available data and awaiting further tests. But unless we take that final step in the scientific method and put these models to the experimental test, we cannot know which one, if any, is correct.

We also welcome more information about the nature of the primeval event that triggered the expanding pattern in the first place. What was the original, primordial state that gave rise to the energy that would later help form galaxies, stars, planets, and life? Can we really expect to probe all the way back in time? After more than 10,000 years of civilization, indeed after many cultures had earlier invented their own worldviews based on beliefs and thoughts, modern science now seems ready to provide some data-rich insight into the origin of all things.

As tricky a task as this may seem, several cosmological models are now being subjected to observational tests by today’s astrophysicists. We live at a remarkable time when genuinely fundamental issues can be addressed, if not yet solved, by empirical means. Our experiments, together with the theories underlying them, seek direct answers to many of the above questions. Even a superficial understanding of the current status of the solutions, though, requires a deep appreciation for the nature of space and time on the grandest scale. And to gain this appreciation, we need a tool of deep and powerful insight—Einstein’s theory of relativity.

Relativity Theory Some people become hot, bothered, and tense upon hearing the word relativity. This subject is surrounded by a mystique implying that only geniuses can understand it—and that might well be true at the mathematical level. But, conceptually, relativity theory is relatively simple. Its foundations are clear and explicit, provided we are willing to forgo common sense and human intuition. Indeed, that’s the key: to put aside our everyday, Newtonian (even Aristotelian) ways of reasoning and adopt a broader, innovative stance that allows for unorthodox thinking.

Relativity is simple in its symmetry, its beauty, its elegant ways of describing grandiose aspects of the Universe. To be sure, it employs higher mathematics—advanced calculus and beyond—to quantify its application to the real Universe, yet everyone should strive to gain at least a non-mathematical feeling for some of the underlying concepts of relativity theory. In this way, we shall be better positioned to appreciate, albeit only qualitatively, some of the weird physical effects encountered while modeling the Universe, exploring black holes, and even contemplating the origin of all things.

Relativity theory has two principal tenets, both enunciated in 1905 by the German-Swiss-American physicist Albert Einstein. Together they lead to the famous E = mc2 equation, where E, m, and c are symbols representing energy, mass, and light velocity, respectively. The first tenet is straightforward: Nature’s laws are the same everywhere and for all observers. Regardless of where a person is, or how fast a person may be moving, the basic physical laws are invariant.

The second tenet of relativity is a little more subtle: There is a 4th dimension—time—which in every way is equivalent to the usual three spatial dimensions. In other words, by using the three well-known dimensions of space, an object’s position can be generally described as either right or left, either up or down, and either in or out. Three dimensions are sufficient to describe where any object is in space. A 4th dimension of time is needed to describe when—either past or future—an object exists in that space. By coupling time together with the three dimensions of space, Einstein was able to reconcile previous inconsistencies in Isaac Newton’s post-Renaissance view of our world by arguing that the velocity of light is an absolute constant number at all times and to all observers, regardless of when, where, or how radiation is measured. Space and time are in fact so thoroughly intertwined within Einstein’s thinking that he urged us to regard these two quantities not as space and time, but as one—spacetime.

Many important consequences of relativity theory can be qualitatively explained only by analogy. Here is one of them, as illustrated in Figure 1.3: Suppose we are in an elevator having no windows. As it rises, we feel the floor pushing, especially on our feet. It’s easy to attribute this pushing sensation to the upward acceleration of the elevator. Now, imagine such a windowless elevator in outer space far from Earth. Normally, we would experience the weightlessness made familiar by watching astronauts floating around in the absence of any net forces. But if we did experience a sensation of pushing on our bodies, we could draw one of two conclusions: Perhaps the elevator is accelerating upward in the absence of gravity, thus pinning us to the floor. Or maybe the elevator is at rest in the presence of gravity, which is pulling us from below. There is actually no way to tell which of these explanations is correct without performing an experiment—that is, without observing objects outside the hypothetical elevator. In either case, pendulum clocks swing normally, released stones fall just as Galileo taught us, water pours from a glass in customary fashion, and so on. If we did build a window to look out, we would have no trouble establishing whether the elevator is really at rest or really accelerating. Relative to the Universe outside the elevator, it’s easy to assess the real status of that elevator.

IGURE 1.3

FIGURE 1.3 – A windowless elevator accelerating through empty space in the absence of gravity (right) is indistinguishable from one at rest in the presence of gravity (left). (Lola Chaisson)

The important point is that the effect of gravity on an object and the effect of acceleration on that object are indistinguishable. Physicists call this keystone of relativity theory the Principle of Equivalence: The pull of gravity and the acceleration of objects through spacetime can be viewed as conceptually and (almost) mathematically equivalent. Consequently, Einstein postulated as unnecessary the Newtonian view of gravity as a force that pulls. Not only is that view obsolete, but Newton’s theory is today known to be less accurate than Einstein’s.

Let’s briefly examine how the notion of an accelerated object can replace the commonsense idea of gravity. The upshot is this: Einstein’s theory of relativity allows us to inquire how it is that matter, which conventionally gives rise to Newton’s theory of gravity, alters the nature of spacetime. Bypassing the details (for they are formidable, going well beyond the technical level of this Web site), matter effectively shapes the geometry of spacetime. Put another way, mass is said to “curve” or “warp” spacetime.

Ordinary Euclidean geometry—the type learned in high school—holds valid when the extent of curvature is zero, that is, when spacetime is flat. Even when that curvature is slight, Euclidean geometry of flat space is approximately correct. At any one location on Earth’s surface, for instance, an architect can design a building, or a contractor build one, using the procedures laid down 25 centuries ago by the Greek mathematician Euclid. However, although terrestrially familiar flat-space geometry is used regularly in our daily tasks, it’s not absolutely correct. The Earth, after all, is not flat; it’s curved. On the surface of a sphere, flat Euclidean geometry works satisfactorily at any small locality, but that’s because it’s nearly impossible to perceive our planet’s curvature from any single place on its surface. Once the curvature of Earth becomes discernable, as in the case of intercontinental aircraft travel or global ship navigation, for example, a more sophisticated geometry must be used—a curved-space geometry.

And so it is at selected locations in the Universe. In the absence of matter, the curvature of spacetime is zero, the appropriate geometry is flat, and objects move undeflected in straight lines. Newtonian dynamics and Euclidean geometry are fine, for all practical purposes, wherever spacetime is unappreciably curved. To be sure, flat space isn’t entirely hypothetical, since well beyond the reaches of galaxies matter is extraordinarily sparse. As noted later in this PARTICLE EPOCH, the Universe itself, on average and in sum, may well be flat.

On the other hand, the geometry of spacetime is strongly warped near massive objects. It’s not the object or the surface of the object that is warped, just the near-void of spacetime in which the object exists. The larger the amount of matter at any given location, the larger the extent of curvature or the warp of spacetime there. By contrast, far from a massive object, the warp lessens. As with gravity, the extent of curvature depends upon both the amount of matter and the distance from that matter. But, since this newer, innovative notion of warped spacetime is more accurate than the older, traditional idea of gravity, the universal worldview of Newton must be replaced by that of Einstein.

No one ever said that relativity wasn’t strange. How can a curve replace a force? The answer is that the topography of spacetime influences celestial travelers in their choice of routes much as Newton imagined gravity to hold an object in its path. Just as a pinball cannot traverse a straight path once shot along the inside of a bowl or a golfball conforms to the undulated topology of a putting green, so the shape of space causes objects to follow curved paths (called geodesics). And any object whose motion changes direction, even though its speed remains steady, is said to be accelerated. Earth, for example, accelerates while orbiting the Sun—not because of gravity, as Newton maintained, but because of the curvature of spacetime, as Einstein preferred.

To see this, consider another analogy—not an example, an analogy, as illustrated in Figure 1.4. Imagine a pool table with a playing surface made of a thin rubber sheet, rather than the usual felt-covered slate. Such a rubber sheet would become distorted if a large weight were placed on it. A heavy rock, for instance, would cause the sheet to sag or warp. The otherwise flat rubber sheet would become curved, especially near the rock. The heavier the rock, the greater the curvature. Trying to play billiards, we would quickly find that balls passing near the rock are deflected by the curvature of the tabletop.

IGURE 1.4

FIGURE 1.4 – The “fabric” of spacetime can be visualized to be curved near a massive star (c) in much the same way that a rubber sheet distorts when a heavy rock is placed on it (b). The response of a billiard ball to the rock’s dimple in the (hypothetically frictionless) rubber sheet, or of the Earth to the Sun’s warp in (real) spacetime, mimics the conventional view of our planet orbiting the Sun under the commonsense influence of gravity (a). (Lola Chaisson)

In much the same way, both matter and radiation are deflected by the curvature of spacetime near massive objects. For example, Earth is deflected from a straight-line path by the slight spacetime curvature created by our Sun. The extent of the deflection is large enough to cause our planet to circle the Sun repeatedly. Likewise, the Moon or a baseball responds to the spacetime curvature created by Earth and they, too, move along a curved path. The deflection of the distant Moon is slight, causing it to orbit Earth endlessly. The deflection of a small baseball is much larger, causing it to return to Earth’s surface.

The commonsense notion of gravity, then, is just a convenient word for the natural behavior of objects responding to the curvature of spacetime. Accordingly, we can use a knowledge of spacetime to predict the motions of objects traveling through space and time. More appropriately, we can turn the problem around: By studying the accelerated motions of objects, we can learn something about the geometry of spacetime near those objects.

And so it is with the whole Universe. When seeking the size, shape, and structure of the entire Universe—the biggest picture of all—we need to consider, in principle, the net effect of spacetime curvature caused by each and every massive object in the cosmos. By studying the motions of representative pieces of matter within the Universe, we can discover much about the curvature of the whole Universe. In practice, it’s a lot more difficult.

By infusing relativity’s basic tenets throughout a full-blown, mathematical treatment of Einstein’s theory, researchers have learned to map various ways that matter warps spacetime. This is the area where relativity theory becomes notoriously complex; here, theorists scamper away, leaving us in an imponderable dust. What we glean from their labored calculations can only be appreciative. The results, in a nutshell, are the so-called Einstein field equations—a dozen or so equations that must be solved simultaneously to determine how the Universe is grandly structured, namely, how spacetime is curved by all the matter present. On the one hand these equations are nearly intractable to solve quantitatively, yet on the other hand they contain remarkable symmetry qualitatively. Much like works of art, they often inspire a sense of wonder, a certain awe. Their complexity arises largely because, in addition to the field equations specifying the shape of the Universe, astrophysicists using relativity must also solve several geodesic (geometrical) equations to determine how it is that any individual object behaves dynamically at any given place amongst all the other matter in the Universe. The bottom line of much technicality is this: Matter determines how space is curved, and space determines how matter moves.

Spacetime Curvature To illustrate further the curvature of spacetime, ponder the following hypothetical example, illustrated in Figure 1.5. Imagine two planets, each inhabited by equally advanced technological civilizations capable of launching identical rockets. Earth can be one and the less massive planet Mars the other. For the sake of discussion, let’s assume that these rockets can achieve only a fixed amount of thrust at launch, after which they glide freely through space. When the rockets are launched from both planets, the shapes of their paths differ. In the Newtonian view of space, the rocket paths are determined by the gravitational interaction between the rocket and each planet. In the Einsteinian view of spacetime, these trajectories are determined by the response of the rocket to the spacetime warp produced by each planet.

IGURE 1.5

FIGURE 1.5 – The paths of identical rockets launched from two different planets—a more massive Earth and a less massive Mars—can be explained either in terms of (Newton's) gravitational pull of the planets on the rockets, or in terms of (Einstein's) spacetime curvature that causes the rockets' paths to change. (Lola Chaisson)

Consider first a typical path of the rocket launched from the more massive Earth. Here the initial thrust is large enough to place the rocket into an elliptical orbit. Like gravity, whose strength decreases with increasing distance from a massive object, the curvature of spacetime is also greater close to the massive planet. The rocket accordingly speeds up (or accelerates) when close by and slows down (or decelerates) when far away. General relativity thus agrees with Kepler’s laws of planetary motion empirically discovered a few centuries ago by the German astronomer Johannes Kepler. Relativity maintains that the rocket accelerates near massive objects, owing to the greater degree of spacetime curvature there.

The ellipse, a “closed” geometric path, is only one possible type of motion. It’s an orbital trajectory of minimum energy, so labeled because this rocket doesn’t have enough energy to escape the planet’s influence. It keeps orbiting endlessly like an artificial satellite.

Rockets can travel on other paths as well. Consider the trajectory taken by an identical rocket after launch from the less massive planet Mars. The same thrust used to launch the Earth rocket into an elliptical orbit is now great enough to propel the Mars rocket entirely away from that planet. Less energy is used in the launch from Mars than in the one from Earth, and thus more energy can be imparted to the motion of the rocket. The rocket escapes the influence of Mars because, as Newtonian classicists would say, Mars has less gravitational pull than Earth. By contrast, Einsteinian relativists claim that such a rocket escapes Mars because the less-massive Mars warps spacetime less than does Earth. The two views—Newtonian and Einsteinian—predict virtually identical paths for the rocket as it recedes toward regions of spacetime progressively less curved by Mars.

The resultant path away from Mars is called a hyperbolic trajectory. This is the type of flight path taken by robot spacecraft that have been exploring other planets of our Solar System in recent years. Its geometry is said to be “open,” in contrast to the closed, elliptical path around Earth. Any object traveling along such a hyperbolic path has more energy than one on an elliptical trek, either because the initial thrust needed to achieve a hyperbolic trajectory was large or because the mass of the parent object from which the launch was made is small. In this particular example, the rockets are identical, so the increased energy of the hyperbolic case results from the relatively small mass of Mars.

Even while receding far from its parent planet, a rocket is still affected by the pull of gravity or the warp of spacetime created by the mass of that planet. Although large only in the immediate vicinity of the planet itself, Mars’ influence over the rocket never diminishes to zero. Mathematical analyses predict that, in the idealized absence of all other astronomical objects, such a hyperbolically launched rocket should approach infinity.

The hyperbolic path contrasts slightly with another type of trajectory conceivably taken by an escaping rocket. A third geometrical path, also open in form and called a parabola, is one taken by a rocket from some hypothetical planet having a mass between that of Earth and Mars. The parabolic path closely mimics the hyperbolic one in that they both approach infinity, though they differ a little in energy content. Mathematicians distinguish between the two open paths by saying that a parabolically moving rocket will have a velocity of zero when it gets to infinity—and will then stop!—whereas its hyperbolic counterpart will theoretically reach infinity with some finite velocity—and move beyond! The academic language of mathematics not withstanding, no object can ever really reach infinity, thus this is tantamount to saying that the rocket will continue to recede forevermore.

The above cases conveniently describe the motion of any object in terms of its energy content and its response to the curvature of spacetime. The intermediate case of the parabolic path is a very special, precisely balanced one for which the net energy is zero, the overall geometry of space flat, and Euclid would have loved it. These cases will be useful analogies when later considering (below) the essentials of cosmology, for then the “object” will be the entire Universe itself.

Einstein’s Early Ideas Einstein, as the originator of relativity, clearly had an advantage in initially using his equations to deduce the nature and structure of the Universe; he knew them better than anyone else. His equations predicted in 1917 that the curvature of the entire Universe must indeed be large owing to all the matter contained within it. The flat geometry of Euclid just didn’t seem to work when examining the bulk properties of the whole Universe. Unfortunately, Einstein’s most popular solution—one of many possible at the time—can be cast only in terms of nearly unimaginable 4-dimensional spacetime. It’s quite imaginable mathematically, but it’s tricky verbally and hard to illustrate. Even if we suspect now, nearly a century later, that the Universe in toto is not much curved (in fact may be flat, on average), what follows is useful conceptually.

To visualize the essence of this solution, we employ another analogy. This one is sketched in Figure 1.6. Since no one has ever built a viewable model of anything in 4 dimensions, in this analogy we suppress 1 of those 4 dimensions and imagine consolidating the 3 dimensions of space into only 2 dimensions. Then, with time as the remaining dimension, we can construct a 3-dimensional analogue of Einstein’s 4-dimensional Universe. That analogue is a sphere, sometimes colloquially termed “Einstein’s curveball.” Here, all of space is taken to be spread on the surface of this sphere. The other dimension—time—is represented by the radius, or depth, of the sphere.

IGURE 1.6

FIGURE 1.6 – A finite but unbounded sphere is one way to visualize a model of the entire Universe. All 3 dimensions of space are consolidated onto the (2-dimensional) surface of the sphere, while the 4th dimension, time, is represented by the radius of that sphere. On the surface of such a sphere, there is no boundary, edge, center, or special location. (Lola Chaisson)

To counter an oft-misunderstood aspect of this analogy, note that the Universe and all its contents are not envisioned to be scattered inside the sphere. Rather, they are distributed just on its surface. All three dimensions of space are warped—in this special case, all the way around into a perfect sphere. Thus, all the galaxies, stars, planets, and people, and even all the radiation reside only on the surface of this model Universe.

Note also that since the radius of this model sphere represents time, this spherical analogue grows with time. After all, the galaxies are observed to be receding; the Universe is expanding. As time marches on, the radius of the sphere increases and so does its surface area. In this way, our 3-dimensional analogue mimics cosmic expansion.

Actually, Einstein didn’t know in 1917 that the Universe is expanding. Astronomers hadn’t established that observational fact until the 1930s. Einstein’s own equations allowed cosmic expansion (or contraction), but he didn’t believe it. He was probably fooled by the then still-popular Aristotelian philosophy that few things change in the Universe at large. So he tinkered with his equations, introduced an additional factor that offset the predicted expansion, and thereby forced his Universe models to remain static. Einstein later came to think that he was wrong in doing this, calling this “cosmological constant” the biggest mistake of his career. Ironically, in the early 21st century, this poorly understood factor has again become fashionable, implying that Einstein may well have been onto something truly fundamental, yet truly odd, that no one has yet deciphered. We shall return to discuss the implications of the cosmological constant later in this PARTICLE EPOCH.

Even if not a good model for the Universe, this spherical analogue enabled Einstein and his colleagues to recognize many important features of curved spacetime. One of their key findings is known as the cosmological principle—the notion that all observers perceive the Universe in roughly the same way regardless of their actual locations. To be sure, all our large-scale studies to date strongly suggest that the Universe is homogeneous (the same everywhere) and isotropic (the same in all directions). Excluding directions obscured by our Milky Way and considering scales larger than a billion light-years, the contents of the Universe look virtually identical. On the grandest scales of all, then, the cosmos seems smooth, even, and a bit boring.

To grasp the essence of the cosmological principle, consider a sphere again. It can be any sphere, so let it be Earth. Imagine ourselves at some desolate location on Earth’s surface, perhaps in the midst of the Pacific Ocean. To validate this analogy, we must confine ourselves to two dimensions of space; we can look east or west, and north or south, but not up or down—the life of a fictional “flatlander.” Perceiving our surroundings, we note a very definite horizon everywhere. The surface appears flat and pretty much identical in all directions. Accordingly, we might get the impression of being at the center of something. But we’re not really at the center of Earth’s surface at all. The surface of a sphere has no center. Such is the cosmological principle: There is no preferred, special, or central location on the surface of any sphere.

Likewise, regardless of our position in the real, 4-dimensional Universe, we observe roughly the same spread of galaxies as any other observer would note from any other vantage point in the Universe. Despite our observation that galaxies literally surround us in the sky, this need not mean that we reside at the center of the Universe. In fact, if our spherical analogy is valid, then the Universe has no center. Nor does it have any edge or boundary. The case of a flatlander roaming on the surface of a 3-dimensional sphere is completely analogous to a space traveler voyaging through the real 4-dimensional Universe. Neither ever reaches a boundary or an edge. Proceeding far enough in a single direction on the surface of the sphere, the traveler (or any radiation) would eventually return to the starting point, just as Magellan’s crew proved long ago by circumnavigating planet Earth. In much the same way, if 4-dimensional spacetime is structured according to this spherical analogue, an astronaut could be launched in one direction, only to return at some future date from the opposite direction. Einstein’s curveball, indeed.

Modern Ideas Today, we realize that the Universe is not static. The recessional motions of the galaxies make its expansion indisputable. Following the lead in the 1920s of the Russian meteorologist Alexander Friedmann and the Belgian priest Georges Lemaitre, modern relativists seek more realistic models of the Universe, especially ones that take account of the measured rate of cosmic expansion. In this way, observations of galaxy recession become a boundary condition, or demanding constraint, on any plausible model of the Universe, helping refine our 21st-century view of the big picture.

The cosmological principle is likely valid even though the Universe is expanding. As with any static sphere, the surface of an expanding sphere has no center, edge, or boundary. To see this, imagine a sphere again, though now one that can swell like a balloon—as shown in Figure 1.7. For example, visualize the entire Earth to be expanding, causing the surface area of our planet to increase as time advances. Standing on such a hypothetically expanding “Earth,” we would see familiar objects moving away. Surface objects all around—whether trees, homes, or mountains—would appear to recede. Now, more than ever, we may want to conclude that our position is special—that we exist at the center of some explosion. But we do not. Our position is no more special than anyone else’s on the sphere’s surface. In fact, everyone everywhere on an expanding surface would observe their surroundings to be receding. Who is correct, then? Everyone is correct. Recessional motions are observed from any and all positions on the surface of an expanding sphere.

IGURE 1.7

FIGURE 1.7 – Galaxies in an expanding Universe appear to recede from one another regardless of the galaxy inhabited. This can be illustrated by inflating a balloon; spots, drawn here as spirals on the surface of the balloon, recede from one another as the balloon inflates. Every observer in any galaxy would perceive all the other galaxies to be drifting away—and at roughly the same rate too. Thus, the cosmological principle holds valid even for a dynamically changing Universe. (Lola Chaisson)

Another popular way of visualizing the same concept is to tape small coins onto the surface of a balloon. The coins are meant to represent the galaxies, and the balloon the “fabric” of space itself. As the balloon inflates, space expands and all the coins recede from one another (though the coins themselves do not expand). Regardless of which galaxy we inhabit, we would see all the other galaxies receding (though the galaxies themselves, as bound entities, are also not expanding). The galaxies would appear to recede for any and all observers in the Universe. Nothing is special or peculiar about the fact that all the galaxies are receding from us. Such, again, is the cosmological principle: No observer anywhere in the Universe has a privileged position.

And so it is in the real, 4-dimensional Universe—a more accurate representation of which is attempted in Figure 1.8. Although the galaxies recede from us, this is not a peculiarity of our vantage point. All observers everywhere in the Universe witness essentially the same sort of galaxy recession. Neither we nor anyone else reside at the center of the expanding Universe. There is no center in space—no position on the sky that we can ever hope to identify as the location from which the cosmic expansion began.

igure 1.8

FIGURE 1.8 – As shown in this cutaway painting, the expanding Universe can be visualized better as a concentric series of spheres, each one representing a different epoch in time. The innermost sphere, closest in time to creation, is the brightest; the outer spheres have become progressively darker (save for the galaxies of stars) as the cosmos cooled and thinned. The outermost sphere represents today, from our perspective on Earth, but we cannot look along this “current” sphere. Since “looking out is looking back,” we rather observe objects as they existed in earlier spheres farther inside “Einstein’s curveball.” (Lola Chaisson)

Do note that all these analogies have their shortcomings and this one is no different. The issue here is that we must imagine the balloon, whose surface is a 2-dimensional analogue of space, expanding into a third dimension. That might suggest that, in the real world of three spatial dimensions, the Universe is expanding into some additional spatial realm—which, as noted earlier, is wrong. In our analogy, that balloon is properly visualized as expanding into time—namely, into the future. As best we can tell, even if higher dimensions of space do exist at sub-microscopic domains, they are likely irrelevant to the macroscopic models of the Universe discussed here.

Surprisingly, there is a center in time—at least in our analogy. This is the origin of time, and it corresponds in our 3-dimensional spherical analogue to a sphere having zero radius. In other words, at the beginning of the Universe, the 3-dimensional sphere was a mere point. This marked the beginning of time, the moment of the big bang. It’s proper to think of it as the edge of time. But there’s no edge in space.

Basic and profound queries come fluxing forward: When did the sphere have zero radius—a minute point? That is, how long ago were all the contents of the Universe squashed into a single speck? Fundamentally put, when did time begin?

To appreciate answers to these questions, imagine that time can be reversed. Not that we have any evidence that time actually does reverse, or flow backward; rather, this is another mental exercise to visualize when all the galaxies in space (or all the coins on our analogous balloon above) were effectively piled one upon another. To do this, we imagine reversing the expansion of the Universe by contracting it backward at the same rate as we currently observe it expanding forward. The galaxies would then come together, eventually touch, and finally mix. If we can estimate how long it would take for the whole Universe to shrink back to its starting point, we shall then have a measure of the time it took to reach its present state—the age of the Universe.

This problem can be quantified in very simple terms. Since the distance traveled by any object equals the product of its velocity and the time traveled, Hubble's law can then be re-expressed as

velocity = Hubble's constant x velocity x time.

Canceling the velocity terms from each side of the equation, we find that

time = 1 / Hubble's constant.

The answer, as best we can determine (being sure to work the right units in Hubble's constant), is about 14 billion years. Thus, the singular, compact region of space often associated with the origin of the Universe must have existed about 14 billion years ago. Alternatively stated, 14 billion years have passed since the expanding debris of universal matter raced out to the places where they are now observed.

Evolutionary Universe Models At the origin of time, the Universe burst forth. Like an inflated balloon, it flowed out into the future—the Universe expands and the galaxies recede. Initially, it changed at a rate dependent on the density of matter contained within it. After all, each clump of matter in the Universe gravitationally pulls on all the other clumps. Since the gravitational force is always attractive, it tends to oppose the expansion. So a tightly packed Universe is expected to cause a strong gravitational pull and eventually a slowing of the universal expansion. (Notice that we’ve returned to the notion of gravity; though warped space is more correct, the familiar concept of gravity often makes the argument easier to comprehend, given our commonsense bias.)

Figure 1.9 graphs these simple ideas. By plotting the size of the Universe against cosmic time, we can graph the greatest possible temporal perspective. By "size of the Universe," we mean either (in principle) the total four-dimensional region of spacetime in which all the galaxies reside, or (in practice) the average distance separating the galaxy clusters, which are the largest organized entities known. Either notion is valid, but only the latter can be observationally measured.

FIGURE 1.9 – A graph of the size of the Universe plotted against cosmic time. The drawn curve represents the expansion of the Universe from its origin to the present. (Lola Chaisson)

At face value, universal expansion is not unlike what happened with the rockets noted earlier. Each rocket departed from its parent planet at a rate dependent on that planet’s mass. Mars, for example, pulled on the launched rocket, but was unable to slow the rocket’s escape; the more massive Earth exerted a stronger pull on the rocket and was able to halt its escape. The parallel between the orbital dynamics of a rocket and the cosmic dynamics of the Universe is quite a good one. As for rockets, there are two diametrically opposed models of a dynamic, changing Universe—and one perfectly balanced between the two extremes.

The first model Universe is one that evolves from a powerful initial “explosion”—again, a bang of some sort at the origin of time. The Universe then expanded from what must have been an exceedingly dense primeval clump. As time progressed, space diluted the matter throughout the Universe, causing its average density to decline. In this first model, insufficient matter exists to counteract the expansion. Accordingly, the Universe simply expands forever, with the density of matter thinning eventually to nearly zero. It’s specifically analogous to the rocket moving away from Mars; this type of Universe has too little mass ever to halt the matter’s outward motion. Since this model Universe will theoretically arrive at infinity with some finite (non-zero) velocity, some astronomers term this case the hyperbolic model of the Universe, for that is the trajectory such a Universe takes while racing toward infinity. Represented diagrammatically in Figure 1.10, its spacetime is actually curved like that of a saddle.

IGURE 1.10

FIGURE 1.10 – Both the hyperbolic and parabolic galaxy motions imply an open Universe. As illustrated by the curves in (a), an open Universe will expand forever. The frames below in (b) diagram the change of this type of Universe with time (Lola Chaisson).

A hyperbolic model is said to imply an “open Universe.” It’s open in the sense that the initial bang was large enough and the contained matter spread thinly enough to ensure that this type of Universe will never stop expanding. Although matter everywhere mutually pulls on all other parts of the Universe, such a Universe will never collapse back on itself. There’s simply not enough matter.

Of course, the Universe can never really become infinitely large. An infinite amount of time would be needed to reach infinity. This is just a mathematician’s way of saying that a hyperbolic, or open, Universe will expand endlessly. Properly stated, an open Universe approaches infinity.

Should this model be correct, the galaxies will recede forevermore. With time, for an observer on Earth, they will fade away toward invisibility, their radiation weakening with increasing distance. Eventually, even some of the closest galaxies will become so remote as to be hardly visible. Someday, all the galaxies might become unobservable; they will be too distant, their radiation too faint. Our home Milky Way Galaxy will then be the only object within the observable Universe. All else, even through the most powerful telescopes, will be dark and quiet. And even beyond that in time, the Milky Way too will someday peter out as its fuel supply is consumed, the hydrogen in all its stars totally spent. This type of Universe and all its contents eventually experience a “cold death.” The radiation, matter, and life in such a Universe are destined to freeze.

Quite a different fate awaits the Universe if it has a larger matter density. As for the open Universe, this model also expands with time from a superdense, superhot original point. But unlike the open Universe, this model contains enough matter to halt the cosmic expansion before reaching infinity. That is, once the bang had initially pushed out the Universe, the galaxies gradually lost so much momentum that they will eventually skid to a stop sometime in the future. Astronomers everywhere—on any planet within any galaxy—would then announce that the galaxy recession has ended as their radiation is no longer red shifted. The cosmological principle guarantees that this new view will prevail everywhere. The bulk motion of the Universe, and of all the galaxies within, will be stilled—at least momentarily.

Cosmic expansion may well stop, but gravitational pull does not. Gravity is relentless. Accordingly, this type of Universe will necessarily contract. It cannot stay motionless; nothing fails to change. Astronomers will witness the galaxies’ red shift gradually change to a blue shift. The contraction of this model Universe is a mirror image of its expansion. Not an instantaneous collapse, it’s rather a steady movement toward an ultimate end, requiring just as much time to fall back as it took to rise up. Figure 1.11 shows this model diagrammatically, whose spacetime is curved like the surface of a sphere.

IGURE 1.11

FIGURE 1.11 – The elliptical, or closed, universal model (a) has a beginning, an end, and a finite lifetime. The frames in (b) further illustrate this type of Universe. (Lola Chaisson)

This model in many ways resembles the rocket trajectory for which, in our earlier example, the gravitational pull was great enough to cause the rocket’s path to become elliptical. Since it has a similar geometrical pattern, a cosmic model containing enough matter to reverse the expansion is often called an elliptical Universe. It’s also sometimes termed a “closed Universe”—closed because it represents a Universe finite in size and in time. It has a beginning and it has an end.

The change of density in a closed Universe is interesting—and ominous. From what must have been an enormously high initial value, the density thins dramatically by the time the Universe stops expanding, then returns again to a huge value when, at some future epoch, all matter collapses onto itself. Some astronomers call it the “big crunch.”

The expansion-contraction scenario of a closed Universe has many fascinating (and dire) implications. Life, in particular, which has evolved from simplicity to complexity during the expansion, will begin breaking down into simplicity again while inevitably heading toward its demise during the collapse. Toward the end of the contraction phase, the galaxies will collide frequently as the total amount of space in which they exist diminishes—and that means trouble for any life forms. For just as compressing air in a bicycle pump or rubbing our hands causes heating via friction, collisions among galaxies will generate heat as well. The entire Universe will grow progressively denser and hotter as the contraction approaches the end. Near total collapse, the temperature of the entire Universe will have become greater than that of a typical star. Everything everywhere will have become bright—so bright that stars themselves will cease to shine for want of contrasting darkness. This type of Universe will then shrink toward the superdense, superhot state of matter similar, if not identical, to the one from which it originated. In contrast to the open Universe that terminates as a frozen cinder, this closed Universe will experience a “hot death.” Its contents are destined to fry.

Cyclic Universe Cosmologists are uncertain of the fate of a closed Universe upon reaching this (perhaps infinitely) hot, dense, and small state, known among scientists as a singularity. The Universe might just end. Or it might bounce—into another cycle of expansion and contraction, as diagrammed in Figure 1.12. Frankly, the mathematics of singularities have not yet been solved; physical laws there are suspect and no one quite knows what happens at such ultra-points. This ultimate state of matter poses one of the hardest problems in all of science. Though they don’t like to hear it said out loud, astrophysicists are experimentally and theoretically ignorant of the physics of singularities.

Frontier research seeks to understand better the nature of such a singular state of matter, a topic to which we shall return when examining the Universe's origin more closely later in this first, PARTICLE EPOCH, and also when exploring black holes in the second, GALACTIC EPOCH. For now, suffice it to note that with both density and temperature increasing as such a contraction nears completion, pressure—the product of density and temperature, at least in classical physics—must increase phenomenally. The question as yet unanswered is, Will the Universe just end as a final miniscule speck, or will this pressure be sufficient to overwhelm the relentless pull of gravity, thereby pushing the Universe back out into another cycle of expansion and contraction? In other words, will a closed Universe bounce?

IGURE 1.12

FIGURE 1.12 – A cyclic, or oscillating, Universe (a) compromises the basic features of the open (indefinitely long) and closed (beginning and end) models. The frames in (b) further illustrate this grand evolutionary scheme having neither beginning nor end. (Lola Chaisson)

A certain aesthetic beauty pervades such a model of a “cyclic Universe.” Subjectively, it’s preferred by many researchers. For starters, there’s no need for a unique, once-and-for-all-time initial event—no need for a big bang. Nor does this model embody a definite beginning or a definite end. The cyclic model merely goes through phases—perhaps an infinite number of them—each initiated by a separate “bang,” each ending in another “bang,” ad infinitum. Such a cyclic Universe would presumably oscillate forever, each expansion a “day,” each contraction a “night.” But none of these bangs is unique, none of the origins any more significant than any other. Oscillation avoids the potential philosophical problem of what preceded a unique big bang of either a one-cycle closed Universe that has a real beginning and final end, or of an open Universe that expands indefinitely from a single event without any prospect of ever having an end.

Should the oscillating model be valid, we need not trouble ourselves with the concept of “existence” before the beginning of time. In this model, there is no beginning of time, no genuine start to the cosmos; its contents are endlessly recycled. Such a Universe always was and always will be.

Non-evolutionary Models The above models of the Universe stipulate evolutionary change as their guiding principle. Each is derivable from Einstein’s general theory of relativity and together they are favored, in one form or another and with some modifications, by the majority of today’s cosmologists. However, several other Universe models have been proposed over the years. Most of them don’t follow directly from relativity; some don’t even call for change with time or embrace evolution as their central theme. It’s worth considering one of the more prominent ones, for until a few decades ago it was favored by leading members of the scientific community.

The “steady-state” model stipulates not only that the Universe appears roughly the same to all observers, but also that such a Universe appears unchanging to all observers for all time. Its fundamental tenet is embodied within what is sometimes called the perfect Cosmological Principle: To any observer at any time, the physical state of the Universe is much the same. In other words, the average density of the Universe remains eternally constant. It holds steady.

Initial motivation for steady-state models was based as much on philosophy as on science. The cyclic Universe aside, many scientists and philosophers were (and still are) unwilling to concede that nothing could have existed prior to a unique big bang. Admittedly, it’s challenging indeed to inquire about time and events preceding the origin of the Universe. What existed before the big bang? Why was there a big bang? What or who caused it? These are queries unaddressable within the realm of modern science. When there are no data or ways to experimentally test ideas, the scientific method is useless. Philosophies, religions, and cults of all sorts can offer hypotheses to the Nth degree, but science remains mute. The steady-state model avoids these thorny questions, as does the oscillating model. For them, neither beginning nor end pertains. The Universe just is for all time.

Steady-state cosmologists concede that the Universe is expanding, for the recession of the galaxies seems irrefutable. They nonetheless demand that the bulk view of the Universe—the average density of matter—remains constant forever. Accordingly, since the recession of the galaxies demonstrates the distances among galaxies to be increasing, steady-state models require the emergence of additional matter. Otherwise, with the galaxies separating, the average density would inevitably dilute. Odd as it may seem, the steady-statist proponents argued that this new matter is created from nothing. Despite the observed recession of the galaxies, the creation of additional galaxies in just the right amount can keep constant the number of galaxies per unit volume, thus preserving the same universal density forever.

The most vexing problem with the steady-state model is its failure to specify how additional matter is created. Nor does it specify where. Some researchers theorized its injection in the voids well beyond the galaxies in intergalactic space, whereas others preferred infusion within the bright centers of galaxies. Not much new matter would be needed to offset the natural thinning as galaxies speed apart. Creation of a single hydrogen atom every few years in a volume the size of the New Orleans Superdome would suffice. Unfortunately, the sudden appearance of such a minute quantity of matter, either inside or outside galaxies, is currently quite impossible to detect and therefore to test.

Regardless of where matter is created, the real quandary is about how it’s created. The sudden appearance of new matter from absolutely nothing violates one of the most cherished concepts of modern science—the conservation of mass and energy. This widely embraced principle of physics maintains that the sum of all matter and all energy is constant in any closed system. Matter can in fact be created from energy (and energy from matter), but it’s tricky to understand how that matter can be spontaneously fashioned from nothing at all.

The grand puzzle of any steady-state model, then, is the process of material creation. Nonetheless, the lure of a Universe that always has existed and always will exist is strong, for it provides a way to skirt the need for a unique big bang and the awkward questions about the very start of an evolving Universe. All things considered, the big-bang model is as troubling for a steady-state cosmologist to swallow as is this continual-creation idea for an evolutionary cosmologist. At any rate, as we shall see in the next part of this PARTICLE EPOCH, current observations have virtually destroyed any possibility of a steady-state Universe, while fully embracing dynamism as key to the most feasible model of the Universe.


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