7
What Is Real?

Why, sometimes I’ve believed as many as six impossible things before breakfast.

Lewis Carroll (Through the Looking-Glass)

WEIGHTY GEOMETRY

A baker would be astonished if every cookie he baked had exactly the same size, within thousandths of a millimeter. A sculptor would be amazed if every clay urn she hand molded had precisely the same shape. Yet nature’s artisan seems to have crafted untold quantities of protons (and other elementary particles) with identical rest masses. They are infinitely more “cookie cutter” than anything in a cookie manufacturer’s wildest dreams.

Why is the mass of a proton on Pluto the same as that of a proton in Pittsburgh? How do they “know” how to coordinate their attire, like soldiers in a vast army? And where does their mass originate anyway? Mass is a fundamental feature of objects in the cosmos. Any comprehensive model of the universe ought to explain how it arises and why it is doled out in identical amounts.

Let us start by examining theories of gravitation. Given the essential relationship between gravity and mass, one might presume that an explanation of one would also account for the other. Not



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Brave New Universe: Illuminating the Darkest Secrets of the Cosmos 7 What Is Real? Why, sometimes I’ve believed as many as six impossible things before breakfast. Lewis Carroll (Through the Looking-Glass) WEIGHTY GEOMETRY A baker would be astonished if every cookie he baked had exactly the same size, within thousandths of a millimeter. A sculptor would be amazed if every clay urn she hand molded had precisely the same shape. Yet nature’s artisan seems to have crafted untold quantities of protons (and other elementary particles) with identical rest masses. They are infinitely more “cookie cutter” than anything in a cookie manufacturer’s wildest dreams. Why is the mass of a proton on Pluto the same as that of a proton in Pittsburgh? How do they “know” how to coordinate their attire, like soldiers in a vast army? And where does their mass originate anyway? Mass is a fundamental feature of objects in the cosmos. Any comprehensive model of the universe ought to explain how it arises and why it is doled out in identical amounts. Let us start by examining theories of gravitation. Given the essential relationship between gravity and mass, one might presume that an explanation of one would also account for the other. Not

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Brave New Universe: Illuminating the Darkest Secrets of the Cosmos necessarily so. In general relativity the force of gravity results from the curvature of space-time by matter. But it does not explain where the mass in the universe comes from. Einstein’s theory merely assumes that the mass came into existence when the universe came into being and has since remained unaltered. Einstein himself was dissatisfied by the dichotomy between the vibrant, flowing geometries on the left-hand side of his gravitational equations and the stultified stuff on the right. The mass terms seemed positioned on the right-hand side as necessary but awkward ballast. Like the counterweights on an elevator, they helped lift the geometric side to ethereal heights. It would be nice, Einstein felt, if everything were lofty and dynamic and there were no need for extra bulk. As he wrote in an essay, “Physics and Reality”: [General relativity] is sufficient—as far as we know—for the representation of the observed facts of celestial mechanics. But it is similar to a building, one wing of which is made of fine marble (left part of the equation), but the other wing of which is built of low-grade wood (right side of equation). The phenomenological representation of matter is, in fact, only a crude substitute for a representation which would do justice to all known properties of matter. Thus, one of Einstein’s principal goals in the latter half of his life was to perform the alchemy of turning wood into marble. His motivation for this effort stemmed largely from his strong belief in Machian ideals. Mass, Einstein felt, should draw its nature from the relationships between all objects in the universe. Pure geometry would be the proper mechanism for conveying such information. Although Einstein first explored such notions in the 1920s, they were hardly new. In the early 1870s the British mathematician William Clifford caused quite a stir with his proposal that matter represents lumps in the carpet of space. His article, “On the Space Theory of Matter,” postulated that empty space is completely smooth

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Brave New Universe: Illuminating the Darkest Secrets of the Cosmos and that deviations from such smoothness manifest themselves as physical materials. Since space is three-dimensional, these bumps would need to poke out along an additional dimension. Decades before Minkowski, Clifford based his theory on space, not space-time. Hence, the extra dimension of his theory was the fourth. Today, we’d call it the fifth, including time. Clifford’s radical conception of mass was debated for years in the pages of Nature and other journals. Readers pondered ways to fathom his multidimensional vision. Sadly, he had little time to develop it further. Pulmonary illness took his life in 1879, when he was only 33. Although neither Clifford, nor Einstein, succeeded in geometrizing matter, many others have since tried their luck. Like Brigadoon, the shining city of marble has periodically reawakened—enticing eager adventurers to explore its beauty. In the 1950s and 1960s, for example, John Wheeler attempted to describe all particles as geometric twists, called “geons.” Think of geons as whirlpools arising, moving, and interacting in the ocean of space-time connections. Recently, physicists Dieter Brill, James Hartle, Fred Cooperstock, and others have revived Wheeler’s notion—attempting to stir up various material configurations from the froth of gravitational waves. Finding a mathematical explanation for the solid forms around us is a vision too vital to ignore. INDUCED MATTER New five-dimensional cosmologies suggest an intriguing way of achieving Einstein’s dream of describing matter through geometry. Let’s consider a variation of Kaluza-Klein theory in which the fifth dimension is not compact but rather of observable proportions. We’ve seen such an assumption put to good use in brane-world models, leading, for example, to the Ekpyrotic and Cyclic cosmologies. While such models account for differences between the properties of various interactions, they do not furnish a geometric explanation

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Brave New Universe: Illuminating the Darkest Secrets of the Cosmos of mass’s origin. Rather, they introduce matter (in terms of strings) as an extra element—not intrinsic to the universe itself. There is, though, an alternative way of approaching higher dimensions, which naturally incorporates matter into the structure of the cosmos itself. In “induced matter theory,” the fifth dimension turns out to be mass. Space, time, and matter comprise an inseparable whole. Induced matter theory and membrane theory are similar mathematically but clearly different conceptually. One of the main distinctions between the two theories is how they handle energy. This might be the garden-variety type of energy present in the rest masses and motions of particles or exotic forms associated with the “vacuum” (which we know is not really empty). In induced matter theory, the starting equations look like those for five-dimensional empty space but break down naturally into four-dimensional relationships that correctly describe matter and its fields. Hence, the fifth dimension is all around us: It is the energy of the world, whether in the rest masses of particles, the kinetic energy of their velocities, the potential energy of their interactions, or extra contributions involving what has traditionally been called the vacuum. According to membrane theory, in contrast, the extra parts of the manifold are not apparent to the eye. Rather, like the Wizard of Oz, they operate behind the screen. Furtively, these unseen regions control the gravitational interactions of particles and therefore ultimately the matter of everyday existence. Thus, unlike induced matter theory, what you see is not what you get. Let’s examine the procedure in induced matter theory by which geometry can give birth to mass. In the manner of Kaluza and Klein, we first extend conventional general relativity by adding an extra dimension. We make sure to use the vacuum version of Einstein’s theory, with no explicit source terms (matter and energy put in by hand). This ensures that no slivers of wood are tracked into our elegant marble foyer. We also insist that the fifth dimension remain noncompact. Unlike Kaluza, we don’t mathematically dismiss it and, unlike Klein,

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Brave New Universe: Illuminating the Darkest Secrets of the Cosmos we don’t curl it up. This creates a bevy of extra terms on the left-hand (geometric) side of the generalized form of Einstein’s equation. These turn out to be a blessing, not a curse. By moving these to the right-hand (matter-energy) side of the generalized Einstein equation, we can generate matter and energy terms. We can identify these extra quantities, for example, as the density and pressure of actual materials. Now, let’s stand back to see what we have created. On the left-hand side of the equation, we witness the geometric part of ordinary four-dimensional general relativity. On the right-hand side, we find expressions for matter and energy. Where has the fifth dimension gone? Instead of being wrapped up in a cocoon, it is flitting around as the wondrous things we see in space. What a stunning metamorphosis indeed. If higher dimensions are merely inventions, they are uncannily clever ones. They offer ways of encapsulating complex aspects of nature into simple expressions. Now we see that they can replicate matter and energy. If something looks like reality and acts like reality, perhaps it is reality. A hidden diamond unearthed and polished, the fifth dimension could well be authentic. MAPPING OUT REALITY If matter in the cosmos arose through a fifth dimension, how could we best envision the mathematics behind this novel concept? Our brains are ill equipped to accommodate realms beyond the perceptual delimiters of length, width, breadth, and time. How could we best become familiar with the roads and byways of a five- (or higher) dimensional topography? The answer is that we need a map. Specifically, we need a way of rendering a portrait of five-dimensional interactions in four-dimensional space-time. The latter, in turn, naturally breaks up into a three-dimensional ordinary space, as well as time. We know that on large scales the three-dimensional space is flat because of WMAP

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Brave New Universe: Illuminating the Darkest Secrets of the Cosmos and other measures of the cosmic microwave background. These considerations of uniformity and spatial flatness turn out to be very lucky in our quest to map out the universe. They make it easier for us to embed (represent in a higher-dimensional space) the universe in a five-dimensional manifold that is also flat. This picture helps us visualize directly the universe’s geometry. Mathematicians distill lower-dimensional images of higher dimensions through either slicing or projection. Slicing involves carving out lower-dimensional segments like a butcher thinly divides up ham. Thus, cubes can be sliced into squares, hypercubes into cubes, and so forth. In any given slicing, connections are broken, and certain types of information can be lost. Projection, on the other hand, attempts to grasp the whole picture at once. This is done by a process akin to the creation of shadows. For example, by shining light on a hollow cube, we can explore its image on a flat screen. (We can readily see why flat screens would be easier to handle than curved ones.) Similarly, we could imagine illuminating a hypercube to see how it would appear. Such a projection provides a “map” of the higher-dimensional surface. Constructing such a map is not as simple as it sounds. To see that the problem is nontrivial, consider the map maker’s task of rendering the curved surface of Earth onto a flat page. The Mercator projection, used in many school atlases, is very useful for this purpose. However, it distorts the areas of land masses, making regions near the poles appear larger than those near the equator. (It is said that the 19th century British liked this mapping because it exaggerated the size of Canada, Australia, and other parts of their empire.) Equal-area projections, used by many geographers, address this problem but look rather odd. There are indeed an infinite number of ways of making a map, either for Earth or the universe. The value of a map depends on how it will be used. To visualize a higher-dimensional cosmos, we have a clear plan. First, we express flat three-dimensional space as part of a curved

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Brave New Universe: Illuminating the Darkest Secrets of the Cosmos four-dimensional space-time. Then we embed the latter in a flat five-dimensional manifold. The mathematical justification for this arises from a theorem proved by the early 20th century Irish geometrist John Edward Campbell. Campbell’s theorem states that a certain simple multidimensional manifold can properly represent any surface within it of one fewer dimension. Consequently, the five-dimensional equivalent of a plane can well house any four-dimensional occupants—no matter what their shape or size. Because we are trying to represent the real universe and not some hypothetical construct, we have to ensure that we do not contradict the physics involved. The physics is encapsulated in field equations that relate to particular equations of state. Recall that an equation of state defines the precise connection between the pressure and density of a material. Radiation, dust (loose material), and tightly packed matter each have different relationships, reflecting varying types of movement in response to forces. When the universe was very young, its particles were extremely energetic, and its equation of state was close to that of photons, where the pressure is one-third of the energy density. In the present epoch the energy in the microwave background is many orders less than that in galaxies and dark matter. This means that currently the equation of state is analogous to that of dust; that is, pressure effectively equals zero. According to induced-matter theory, the properties of three-dimensional matter, evolving in time, arise as a “shadow” of five-dimensional geometry. Hence, the universe’s equation of state during various epochs stems from specific relationships between sets of geometric terms in the five-dimensional extension of general relativity. These extra terms result from an uncurled fifth coordinate in Kaluza-Klein theory. In 1988, Jaime Ponce de Leon, a young theorist from Puerto Rico, solved the five-dimensional field equations for a noncompact fifth dimension. His results were most remarkable. Finding the pres-

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Brave New Universe: Illuminating the Darkest Secrets of the Cosmos sure and density relationship between various classes of solutions, he discovered that they precisely matched the known equations of state for specific types of matter and radiation during different universal epochs (inflation, radiation era, and so on). In other words, shadows of the fifth dimension had profiles similar to those of the familiar faces of cosmology. This impressive correspondence boded well for the theory. With reasonable solutions in hand, we can now map the terrain. Curiously, the relationship between these four-dimensional profiles (technically known as hypersurfaces) and the five-dimensional world that surrounds them resembles that of blobs in a 1960s lava lamp. Imagine a blob of oily material floating in water. The physical properties of the blob’s surface determine its changes in shape over time. Similarly, the physical characteristics of four-dimensional space-time determine its dynamic relationship with the five-dimensional manifold in which it is embedded. One striking feature culled from this exercise in higher-dimensional cartography concerns the shape of the Big Bang. While in four dimensions the Big Bang has an unavoidable singularity, in five dimensions the singularity vanishes. Rather, the five-dimensional topography is as smooth as crystal. No blemish marks the initial burst of the universe—permitting a fuller and more satisfying description. Another fascinating result of these studies could bear on the dark-matter question. Particular solutions comprise durable mathematical structures known as solitons. If five-dimensional solitons exist, they could well provide an important piece of the puzzle of why so much of the material in space cannot be directly observed. SOLITONS FROM THE DEEP The curiously persistent forms called solitons were discovered by the Scottish engineer John Scott Russell during a survey of boats floating along a canal. While observing a barge’s motion, he noticed “a

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Brave New Universe: Illuminating the Darkest Secrets of the Cosmos rounded, smooth and well-defined heap of water, which continued its course along the channel apparently without change of form or diminution of speed. I followed it on horseback, and overtook it still rolling on at a rate of some eight or nine miles an hour, preserving its original figure some thirty feet long and a foot to a foot and a half in height. Its height gradually diminished, and after a chase of one or two miles I lost it in the windings of the channel. Such, in the month of August 1834, was my first chance interview with that singular and beautiful phenomenon which I have called the Wave of Translation.” What Russell witnessed was a particular phenomenon that can appear in a shallow body of water. The dynamics of such a system, governed by what is now called the Korteweg-deVries equation, permits “solitary waves” that do not diminish in amplitude or spread out in space as they move along. Such solitons spontaneously appear if hydrodynamic conditions are just right. Since Russell’s time, solitons have assumed an important role in topology and other branches of mathematics. A number of noteworthy equations have distinct soliton solutions that do not dissipate over time. Rather, they maintain their shape indefinitely as they propagate. In physics, solitons have offered hope for representing particles as “kinks” in the fabric of field theories—in a manner akin to Wheeler’s geon model. By taking the well-known Klein-Gordon equation and replacing a term with the sine function, the result is the “Sine-Gordon equation,” which produces soliton waves in quantum physics. Given that Kaluza-Klein theories harbor many modes of behavior, it is not surprising that among these are five-dimensional solitons that represent nondissipative solutions in the induced-matter scenario. Discovered in the early 1990s, they constitute higher-dimensional generalizations of the Schwarzschild model. As noted, the Schwarzschild solution, published in 1916, describes the properties of nonspinning black holes of neutral charge.

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Brave New Universe: Illuminating the Darkest Secrets of the Cosmos In particular, it specifies at what particular radii their event horizons lie—as determined by their masses. As far as researchers know, all black holes have event horizons that serve the vital function of clothing points of indeterminate properties—in other words, singularities. Otherwise, such singularities are said to be “naked.” Compared to the Schwarzschild solution, five-dimensional solitons are quite different beasts altogether. Each represents a concentrated, spherically symmetric form of induced matter. Unlike ordinary, pointlike black holes, typically these clouds of material are extended objects with densities that sharply decrease with radius. Moreover, their pressures are generally anisotropic—different in each direction. They possess equations of state characteristic of ultrahigh-speed particles. Because we have yet to predict the properties of their light spectra, we do not know what range of temperatures they could have. Like unmarked faucets of energy, they could run hot or cold. One of the most important distinctions between these “fireballs from the fifth dimension” and ordinary black holes is that the former do not possess event horizons. No space-time garment covers up their singularities. If they exist, they are astronomical streakers, displaying their entire selves for any telescope powerful enough to see them. However, it’s quite possible, if the five-dimensional solitons are cold enough, that they’ll emit little-to-no discernable radiation. In that case, only indirect means—such as their interactions with visible stars, their influence on the development of galaxies, or their gravitational effects on passing light rays—would potentially distinguish them from the void. This third means, gravitational lensing, would likely provide the best opportunity for finding them. Astronomers could probe for patterns in the emissions of quasars, distant galaxies, and other objects, as distorted by the unseen presence of intermediate bodies. Then they could match these results to soliton profiles. If Kaluza-Klein solitons turn out to be plentiful enough, they would be prime suspects for the hidden material that fills the uni-

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Brave New Universe: Illuminating the Darkest Secrets of the Cosmos verse. Moreover, five-dimensional theories also allow for other kinds of matter and predict that space is permeated by a kind of vacuum field. The latter arises directly from the scalar field connected with the fifth dimension and acts like a variable cosmological “constant.” Thus, the five-dimensional theory agrees with the COBE and WMAP observations in describing the universe as consisting of ordinary (visible) matter, dark matter, and dark energy. BURGEONING MASS One of the curious features of induced-matter theory is that mass has the same units as length. At first glance this would seem strange. If you took your child to the doctor’s office for repeated check-ups, you would be perplexed if the tape measure and scale always read the same. Remember, however, that the length corresponding to mass extends along the fifth dimension and is independent of three-dimensional space. Thus, a physician could delicately report to the mother of an overweight child: “My, your son has grown—even in the fifth dimension.” Physicists perform a similar conversion in standard relativity when they convert time into distance using the speed of light. In the metric system the speed of light has units of meters per second. Hence, multiplying time (in seconds) by the speed of light “magically” converts it into distance units (meters). This procedure provides time with the proper membership card to join the club of spatial dimensions as its fourth member. The conversion factor that transforms mass into distance and allows it to become the fifth member of the dimensionality club is the ratio of the gravitational constant to the speed of light squared. That is, if you combine the units of these parameters with those of mass (kilograms), you end up with distance units. Many theoreticians set various constants equal to one to simplify their calculations and make the math more readable. By setting

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Brave New Universe: Illuminating the Darkest Secrets of the Cosmos the gravitational constant and speed of light each equal to one, mass and length now have precisely the same units. They simply constitute perpendicular ways of measuring the world—the former along the fifth dimension and the latter along any direction of the spatial threesome. This lends itself to an intriguing reinterpretation of the notion of a changing gravitational constant. Current tests, such as laser measurements of the Earth-Moon distance and investigations of the Sun’s luminosity, place strict limits on alterations in the strength of gravity as the universe ages. However, this force depends on objects’ masses as well as the gravitational constant, G. What if the masses of elementary particles are themselves changing over time? Brans and Dicke pointed out in their seminal paper that, if you construct a representation of mass in length units (ordinary mass times the gravitational constant divided by the speed of light squared), it is natural to imagine that this quantity would grow with the size of the Hubble radius (the boundary of the visible universe). Just as distances between galaxies increase with time, according to this hypothesis, masses would as well. This is completely equivalent to the theory of varying G. Instead of mass being constant and G variable, mass would alter and G would remain constant. As Brans and Dicke emphasized, “There is no fundamental difference between the alternatives of constant mass or constant G.” According to the induced-matter hypothesis, mass derives from dynamic solutions of the five-dimensional extension of general relativity. Therefore, it is not surprising that solutions exist in which particle masses vary slowly over time. For instance, according to some solutions, the rest masses of quarks, electrons, and other subatomic particles began as zero some time in the very distant past and have been growing ever since. If we identify such an instant as the “creation moment,” we find a natural way of describing the origin of mass. Instead of emerging all at once in the Big Bang, mass would accrue dynamically over the eons, starting at time zero. Conceivably, an epoch in which all the masses in the cosmos were somehow nega-

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Brave New Universe: Illuminating the Darkest Secrets of the Cosmos tive preceded that moment, which would render the creation moment merely a transition between eras—from negative to positive mass—rather than an abrupt singularity. In other words, the bang would become a blur. Whether or not the effects of changing mass could be detected through experimentation depends on the rate of growth. The slower the increase, the less noticeable the effect. Therefore, in the limit in which mass changes by an infinitesimal amount, the five-dimensional theory would reproduce known results for standard four-dimensional relativity. There would be no detectable difference between the two theories. If, say, the rate of increase were approximately seven-billionth of a percent per year, the effect still couldn’t be measured in the laboratory. Nevertheless, over the 13.7-billion-year history of the observable universe, it would amount to an increase of 100 percent in each particle—that is, from masses of zero to their current values. This dramatic increase could potentially be detected through astronomical measures. The idea of changing mass offers an intriguing solution to several of the conceptual problems that plague conventional cosmology. Mass is not created in a sudden “big bang” singularity. Rather, it grows naturally with time, much like the familiar Hubble expansion. To prove this conjecture, however, would require new and delicate tests. INSTANTANEOUS TIME If the solidity of mass is a phantom, a consequence of the viewing of five-dimensional geometry through four-dimensional spectacles, could the passage of time be an illusion as well? A number of thinkers, including Fred Hoyle, J. G. Ballard, Arthur Eddington, Julian Barbour, David Deutsch, and even Einstein, have suggested that time as we know it is purely an ordering device and that the real universe is in some fundamental sense timeless.

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Brave New Universe: Illuminating the Darkest Secrets of the Cosmos In his science fiction novel, October the First Is Too Late, Hoyle offered a fictional account of some of his serious perspectives on the illusory nature of time. “There’s one thing quite certain in this business,” he wrote. “The idea of time as a steady progression from past to future is wrong. I know very well we feel this way about it subjectively. But we’re all victims of a confidence trick. If there’s one thing we can be sure about in physics, it is that all times exist with equal reality.” J. G. Ballard, the well-known science fiction writer, echoed this view. In his short story “Myths of the Near Future,” a character suggests that we should “think of the universe as a simultaneous structure. Everything that’s ever happened, all the events that will ever happen, are taking place together…. Our sense of our own identity, the stream of things going on around us, are a kind of optical illusion.” Eddington proposed that time was subjective, a construct of the human mind. “General scientific considerations,” he wrote, “favour the view that our feeling of the going on of time is a sensory impression; that is to say, it is as closely connected with stimuli from the physical world as the sensation of light is. Just as certain physical disturbances entering the brain cells via the optic nerves occasion the sensation of light, so a change of entropy… occasions the sensation of time succession, the moment of greater entropy being felt to be the later.” Oxford physicists Julian Barbour and David Deutsch have independently developed models in which each instant of time (in Barbour’s terminology, “Nows”) represents its own reality—a separate world, so to speak. These Nows are linked up through records of what we call the past. Thus, the only reason we say that one moment is later than another is because the “later time” contains particular information about the “earlier time.” This is analogous to a film, in which each frame comprises a separate photograph. Nevertheless, if the movie is coherent, then even if these frames were cut up and placed randomly in a box, one could sort out the order of the segments.

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Brave New Universe: Illuminating the Darkest Secrets of the Cosmos Einstein offered his most revealing statement about the subject upon the death of his lifelong friend Michele Besso. “For us believing physicists,” he said, “the distinction between past, present and future is only an illusion, even if a stubborn one.” Yet even if time has ethereal qualities, leading many prominent thinkers to question its reality, no one could doubt its driving influence in human lives. Our ghostly taskmaster cracks its whip at every junction, forcing us ever forward toward old age and death. In his later years, as poor health took its toll, Einstein was well aware of this omnipresent tormenter yet stoically managed to channel his energies toward trying to develop a unified field theory. Perhaps he believed that the mathematical elegance of the universal equations would, in the scheme of things, outweigh the petty struggles of human existence. He fervently hoped to discover a timeless model of all reality, one that could describe all forces for eternity. Einstein’s hopes for a timeless “theory of everything” never came to pass for a variety of reasons, among which was his disregard for advances in nuclear and atomic physics. Like Kaluza and Klein in their 1920s papers, Einstein failed to incorporate the strong and weak nuclear forces into his unified models. With regard to quantum theory, Einstein refused to believe that random action could pervade the process of physical observation. Moreover, he found it absurd that observers could cause the collapse of wave functions (mathematical entities in quantum mechanics containing information about particles) from a mixed system (a distribution of possible positions, for example) to a particular state (a definite location). Such interactions break the chain of determinism and assign a direction to time. The universe takes on a different character than it had in the past, merely through the actions of a single observer. Until his dying days, Einstein refused to accept a cosmos steered by capriciousness. The collapse of quantum wave functions represents just one of many “arrows of time” in physics. Another arrow is the direction of entropy increase—the tendency for natural processes to operate

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Brave New Universe: Illuminating the Darkest Secrets of the Cosmos in the direction of increasing disorder. Third, on the grandest scale, it’s clear that the universe expands—and as recent results suggest, this expansion is eternal. It offers yet another critical distinction between past, present, and future. A fourth arrow, the direction of thought processes, may well be related to the first three—as suggested by Hawking, Penrose, and others with various models of conscious awareness. Some proof of such a connection between conscious thought and unidirectional physical processes would bolster the arguments of those who purport that all such arrows are illusions. Communication provides still another way of characterizing time. We send signals into the future but not the past. Lighthouses brighten passing vessels with their beams only after their beacons flash. One would be astonished if a ship became illuminated before the beacon was turned on. We can employ precision instrumentation to show that there must always be a delay between the time the beam leaves the lighthouse and when it touches the ship. The directionality of this lag would provide a signpost toward the future. All this, however, is from an external observer’s outlook. Suppose someone could actually ride on the beam and determine its time of flight. (In real life, of course, such a speed-of-light journey would be impossible—but let’s imagine one for the sake of argument.) According to special relativity, the time you’d experience would be the beam’s proper time. Light’s proper time is identical to its space-time interval—the shortest distance between two space-time events. As we discussed in Chapter 2, relativists define space-time intervals through a variation of the Pythagorean theorem: forming the sum of the squares of the spatial distances, then subtracting the square of the time difference. Performing such a calculation with light, we arrive at the quantity zero. In other words, according to our light-speed perspective, no time would have passed at all. Therefore, you might well conclude from your “bronco ride” that time is instantaneous—that there is no real past or future. From your point of view, everything would have happened at once.

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Brave New Universe: Illuminating the Darkest Secrets of the Cosmos When it comes to general relativity, things get even stranger. As Gödel pointed out in his rotating-universe model, this theory has solutions that violate the law of cause and effect. In the proper framework, an event could even represent its own cause. If an astronaut carefully whizzed around the axis of a rotating universe, he could potentially go back in time and offer himself directions on how best to take the spin. In that case, what would be the future and what would be the past? Moreover, Thorne and his colleagues have shown that traversable wormholes (interstellar connections) could potentially serve as time machines. He, Visser, and others have developed blueprints for such hypothetical devices. In light of such danger to causality’s tender threads, Hawking has proposed the “Chronology Protection Conjecture.” Could the uniqueness of history someday become an endangered concept? If the arrow of time is an artifice, would our minds be solid enough to cope with the alternative? Or like Billy Pilgrim, in Kurt Vonnegut’s classic novel Slaughterhouse Five, would we become unhinged? Time is complicated enough when partnered with space in a four-dimensional amalgam. Stirring extra dimensions into the mix (such as in the case of Kaluza-Klein theories) produces yet odder concoctions. Even with one extra dimension, we get strange new results, depending on the metric. Now, the metric is the specific form of the space-time interval equation, and its signature tells us how many of the terms are added (positive) and how many are subtracted (negative). Generally, positive corresponds to spacelike and negative to timelike. In a five-dimensional theory, we can in principle choose either sign for the extra part. Most researchers assume that the extra dimension is spacelike. In that case, not only do photons travel on paths with zero interval (or separation in five dimensions), but so do massive particles like protons, or even large objects like Earth, which implies that, in some sense, all of the objects in a five-dimensional universe are in causal

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Brave New Universe: Illuminating the Darkest Secrets of the Cosmos contact. That would explain the astonishing uniformity of the universe, without even resorting to inflation. Because communication between any two regions of the cosmos would potentially be immediate, this would also bear on the search for extraterrestrial intelligence. However, a few researchers assume that the extra dimension of these extended theories is not spacelike but timelike. Then the results would be even weirder. Things could move faster than light, and the path of a single particle could weave in and out of space-time, like a sewing needle threading a piece of cloth. In the latter case, we could attribute the uniformity of the universe to the fact that it would consist of only a single particle—of which copies would appear everywhere as time progressed. This truly would be a grand illusion! We see that the statement “time is instantaneous” does carry some meaning. However, perhaps a more precise characterization would be “events in the universe happen at zero interval” or “the world is simultaneous.” If you doubt this statement, we’re sure that Einstein, Buddha, and other “contemporaneous” figures would be up for a grand debate. WHITHER CONSTANCY? Changing fundamental constants, matter from higher dimensions, simultaneous time, and hidden cosmic reaches—where is this world heading, anyway? Whatever happened to the simpler days of ruler and compass, when anything you needed for measurement could be found at the local hardware store? Yes, surveyors’ tools are still for sale. Two-dimensional maps will still do just fine for taking road trips. And, don’t worry, massive invisible solitons aren’t invading your local swimming pool as of yet. Mundane instruments work just fine for mundane tasks. Within the bounds of our middling planet and its relatively low speed and weak gravitation, Newton remains king. However, in two directions—the

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Brave New Universe: Illuminating the Darkest Secrets of the Cosmos extraordinarily large and the extremely small—we have long stepped beyond Sir Isaac’s domain. There we turn to the help of Einstein, Bohr, Feynman, Gamow, and others but find there is still much left unexplained. Our minds are incredible tools for pattern recognition. They have phenomenal abilities to fill in the gaps, even when accessible information is frustratingly sparse. It is wondrous, for example, how we are able to take a fact about Earth—its darkness at night, its relationship to the Moon, or its dearth of extraterrestrial signals— and extrapolate to sweeping conclusions about the cosmos itself. Yet we certainly must recognize that the same cognitive abilities that aid us in mapping out the greater realms also have the ability to manufacture “truths” that lack validity. A good example of this statement is Dirac’s Large Numbers Hypothesis. Dirac discovered what he thought was an unmistakable link between the large and the small. Nevertheless, as many present-day thinkers have concluded, his purported connection could well contain no more substance than a mirage in the desert. Or consider Kepler, who once believed that the orbits of planets were proscribed by the shapes of the regular Platonic solids (the tetrahedron, the cube, etc.). The logic seemed irrefutable and the mathematics brilliant. Nevertheless, through painstaking analysis of astronomical data he came to realize that he was wrong. His clever geometric mind had played a trick on him. The role of thought in the universe was a dominant theme of the work of Eddington. His view of physics presents an important lesson as we press out farther and farther in our search for universal truths. The world is objective, he argued, but the means by which it is described, including labels such as time and space, are subjective. Hence, it would not be surprising if concepts such as heaviness, solidity, durability, and other perceptual characterizations turn out to be phantoms—important on Earth as we conduct our daily affairs but not essential to the cosmos.

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