What is space? An empty stage, where the physical world of matter acts out its drama? An equal participant, that both provides background and has a life of its own? Or the primary reality, of which matter is a secondary manifestation? Views on this question have evolved, and several times changed radically, over the history of science. Today, the third view is triumphant. Where our eyes see nothing, our brains, pondering the revelations of sharply tuned experiments, discover the Grid that powers physical reality.

PHILOSOPHICAL AND SCIENTIFIC IDEAS about what the world is made of continue to change. Many loose ends remain in today’s best world-models, and some big mysteries. Clearly the last word has not been spoken. But we know a lot, too—enough to draw some surprising conclusions that go beyond piecemeal facts. They address, and offer some answers to, questions that have traditionally been regarded as belonging to philosophy or even theology.

For natural philosophy, the most important lesson we learn from QCD is that what we perceive as empty space is in reality a powerful medium whose activity molds the world. Other developments in modern physics reinforce and enrich that lesson. Later, as we explore the current frontiers, we’ll see how the concept of “empty” space as a rich, dynamic medium empowers our best thinking about how to achieve the unification of forces.

So: What is the world made of? Subject, as ever, to addition and correction, here is the multifaceted answer that modern physics provides:

• The primary ingredient of physical reality, from which all else is formed, fills space and time.

• Every fragment, each space-time element, has the same basic properties as every other fragment.

• The primary ingredient of reality is alive with quantum activity. Quantum activity has special characteristics. It is spontaneous and unpredictable. And to observe quantum activity, you must disturb it.

• The primary ingredient of reality also contains enduring material components. These make the cosmos a multilayered, multicolored superconductor.

• The primary ingredient of reality contains a metric field that gives space-time rigidity and causes gravity.

• The primary ingredient of reality weighs, with a universal density.

There are words that capture different aspects of this answer. Ether is the old concept that comes closest, but it bears the stigma of dead ideas and lacks several of the new ones. Space-time is logically appropriate to describe something that is unavoidably there, everywhere and always, with uniform properties throughout. But space-time carries even more baggage, including a heavy suggestion of emptiness. Quantum field is a technical term that summarizes the first three aspects, but it doesn’t include the last three and it sounds, well, too technical and forbidding for use in natural philosophy.

I will use the word Grid for the primary world-stuff. That word has several advantages:

• We’re accustomed to using mathematical grids to position layers of structure, as in Figure 8.1.

Figure 8.1 Grid, old and new. a. A grid is often used to describe how various things are distributed in space. b. The Grid, which underlies our most successful world-model,has several aspects. The Grid, with these aspects, is present always and everywhere.Ordinary matter is a secondary manifestation of the Grid, tracing its level of excitation.

• We draw power for appliances, lights, and computers from the electric grid. The physical world of appearance draws its power, in general, from the Grid.

• A great developing project, driven in part by the needs of physics, ²⁰ is the technology to integrate many dispersed computers into functional units, whose total power can be accessed as needed from any point. That technology is known as Grid technology. It’s hot, and it’s cool.

• Grid is short.

• Grid is not Matrix. I’m sorry, but the sequels tarnished that candidate. And Grid is not Borg.

A Brief History of Ether

Debate about the emptiness of space goes back to the prehistory of modern science, at least to the ancient Greek philosophers. Aristotle wrote, “Nature abhors a vacuum,” whereas his opponents the atomists held, in the words of their poet Lucretius, that

All nature, then, as self-sustained, consists
Of twain of things: of bodies and of void
In which they’re set, and where they’re moved around.

That old speculative debate echoed at the dawn of modern science, in the Scientific Revolution of the seventeenth century. René Descartes proposed to ground the scientific description of the natural world on what he called primary qualities: extension (essentially, shape) and motion. Matter was supposed to have no properties other than those. An important consequence is that the influence of one bit of matter on another can occur only through contact; having no properties other than extension and motion, a bit of matter has no way of knowing about other bits than by touching them. Thus, to describe (for instance) the motion of planets, Descartes had to introduce an invisible space-filling “plenum” of invisible matter. He envisioned a complex sea of whirlpools and eddies, upon which the planets surf.

Isaac Newton cut through all those potential complexities by formulating precise, successful mathematical equations for the motion of planets, using his laws of motion and of gravity. Newton’s law of gravity does not fit into Descartes’s framework. It postulates action at a distance, rather than influence by contact. For example, the Sun exerts a gravitational force on Earth, according to Newton’s law, even though it is not in contact with Earth. Despite the success of his equations in providing an excellent, detailed account of planetary motion, Newton was not happy with action at a distance.

That one body may act upon another at a distance through a vacuum without the mediation of anything else, by and through which their action and force may be conveyed from one another, is to me so great an absurdity that, I believe, no man who has in philosophic matters a competent faculty of thinking could ever fall into it.

Nevertheless he left his equations to speak for themselves:

I have not been able to discover the cause of those properties of gravity from phenomena, and I frame no hypotheses; for whatever is not deduced from the phenomena is to be called a hypothesis, and hypotheses, whether metaphysical or physical, whether of occult qualities or mechanical, have no place in experimental philosophy.

Newton’s followers, of course, did not fail to notice that his system had emptied out space. Having fewer scruples, they became more Newtonian than Newton. Here is Voltaire:

A Frenchman who arrives in London, will find philosophy, like everything else, very much changed there. He had left the world a plenum, and he now finds it a vacuum.

Mathematicians and physicists, through familiarity and spectacular success, grew comfortable with action at a distance. So things stood, in essence, for more than 150 years. Then James Clerk Maxwell, consolidating everything that was known about electricity and magnetism, found that the resulting equations were inconsistent. In 1861, Maxwell found that he could repair the inconsistency by introducing an extra term into the equations—in other words, by postulating the existence of a new physical effect. Some years earlier, Michael Faraday had discovered that when magnetic fields change in time, they produce electric fields. To fix his equations, Maxwell had to postulate the converse effect: that changing electric fields produce magnetic fields. With this addition, the fields can take on a life of their own. Changing electric fields produce (changing) magnetic fields, which produce changing electric fields, and so forth, in a self-renewing cycle.

Maxwell found that his new equations—known today as Maxwell’s equations—have pure-field solutions of this kind, solutions that move through space at the speed of light. Climaxing a grand synthesis, he concluded that these self-renewing disturbances in electric and magnetic fields are light, a conclusion that has stood the test of time. For Maxwell, these fields that fill all space and take on a life of their own were a tangible symbol of God’s glory:

The vast interplanetary and interstellar regions will no longer be regarded as waste places in the universe, which the Creator has not seen fit to fill with the symbols of the manifold order of His kingdom. We shall find them to be already full of this wonderful medium; so full, that no human power can remove it from the smallest portion of Space, or produce the slightest flaw in its infinite continuity.

Einstein’s relationship with the ether was complex, and changed over time. It is also, I think, poorly understood, even by his biographers and historians of science (or quite possibly by me). In his first 1905 paper on special relativity,²¹ “On the Electrodynamics of Moving Bodies,” he wrote,

The introduction of a “luminiferous ether” will prove to be superfluous inasmuch as the view here to be developed will not require an “absolutely stationary space” provided with special properties, nor assign a velocity-vector to a point of the empty space in which electromagnetic processes take place.

That forceful declaration from Einstein puzzled me for a long time, for the following reason. In 1905, the problem facing physics was not that there was no theory of relativity. The problem was that there were two mutually inconsistent theories of relativity. On one hand was the relativity theory of mechanics, obeyed by Newton’s equations. On the other was the relativity theory of electromagnetism, obeyed by Maxwell’s equations.

Both of these relativity theories showed that their respective equations display boost symmetry—that is, the equations take the same form when you add a common, overall velocity to everything. In more physical terms, the laws of physics (as stated by the equations) look the same to any two observers moving at a constant velocity relative to one another. To get from one observer’s account of the world to the other, however, you have to relabel positions and times. An observer on a plane from New York to Chicago, for instance, would in a couple of hours label Chicago as “distance 0,” whereas Chicago would still be “distance 500 miles west” (roughly) for the observer on the ground. The problem was that the relabeling required for mechanical relativity was different from that required for electromagnetic relativity. According to mechanical relativity you must relabel spatial positions but not times; whereas according to electromagnetic relativity you had to relabel both, in a rather more complicated way that mixes space and time together. (The equations of electromagnetic relativity had, by 1905, already been derived by Hendrik Lorentz and perfected by Henri Poincaré; today they are known as Lorentz transformations.) Einstein’s great innovation was to assert the primacy of electromagnetic relativity, and work out the consequences for the rest of physics.

So it was the venerable theory of Newtonian mechanics, not the upstart theory of electromagnetism, that required modification. The theory based on particles moving through empty space gave way, not the theory based on continuous, space-filling fields. Maxwell’s field equations were not modified by the special theory of relativity; on the contrary, they supplied its foundation. One still had the space-filling, potentially self-regenerating electric and magnetic fields that sent Maxwell into raptures. Indeed, the ideas of special relativity almost require space-filling fields and, in that sense, explain why they exist, as we’ll discuss momentarily.

Why, then, did Einstein express himself so strongly to the contrary? True, he had undermined old ideas about a mechanical ether, made of particles following Newton’s laws—in fact he had undermined those laws altogether. But far from eliminating space-filling fields, his new theory elevated their status. He might have said with more justice (I’ve always thought) that the idea of an ether that looks different to moving observers is wrong but a reformed ether, that looks the same to observers moving at a constant velocity relative to one another, is the natural setting for special relativity.

At the time he was hatching special relativity, in 1905, Einstein was also brooding over the problem of what later became known as light quanta. A few years earlier, in 1899, Max Planck had put forward the first idea of what eventually became quantum mechanics. Planck suggested that atoms could exchange energy with electromagnetic fields—that is, emit and absorb electromagnetic radiation, such as light—only in discrete units, or quanta. Using that idea, he was able to explain some experimental facts about blackbody radiation. (Very roughly speaking, the problem is how the color of a hot body, such as a red-hot poker or a glowing star, depends on its temperature. Less rough, but still far from smoothly polished: a hot body emits a whole range of colors, with different intensities. The challenge was to describe the whole spectrum of intensities and how it changes with temperature.) Planck’s idea worked, empirically, but it wasn’t very satisfactory intellectually. It was just tacked on to the other laws of physics, not derived from them. In fact, as Einstein (but not Planck) clearly realized, Planck’s idea was inconsistent with the other laws.

In other words, Planck’s idea was another of those things—like the original quark model, or partons—that works in practice but not in theory. It wouldn’t pass muster at the University of Chicago, and it didn’t pass muster with Einstein. But Einstein was very impressed with the power of Planck’s idea to explain experimental results. He extended it in a new direction, hypothesizing that not only did atoms emit and absorb light (and electromagnetic radiation generally) in discrete units of energy, but light always came in discrete units of energy, and also travelled carrying discrete units of momentum. With these extensions, Einstein was able to explain more facts, and even to predict new ones—including the photoelectric effect, which was the primary work cited in his 1921 Nobel Prize. In his mind, Einstein had cut the Gordian knot: Planck’s idea is inconsistent with existing physical laws, but it works—therefore those laws must be wrong!

And if light travels in lumps of energy and momentum, what could be more natural than to consider these lumps—and light itself—to be particles of electromagnetism? Fields might be more convenient, as we’ll see, but Einstein was never one to value convenience over principle. With this issue occupying his mind, I suspect that Einstein took an unusual perspective on what lessons to draw from special relativity. For him, the idea of a space-filling entity that looks the same when you move past it at finite velocity (as special relativity shows the “luminiferous ether” must) was counterintuitive and therefore suspect. This perspective, which cast a shadow over Maxwell’s electromagnetic field theory of light, reinforced his intuitions from Planck’s work, and from his own, on blackbody radiation and the photoelectric effect. Einstein thought that these developments—the ether had become counterintuitive, and it seemed to take form, physically, only in lumps—together made a strong case for abandoning fields and going back to particles.

In a 1909 lecture Einstein speculated publicly along these lines:

Anyway, this conception seems to me the most natural: that the manifestation of light’s electromagnetic waves is constrained at singularity points, like the manifestation of electrostatic fields in the theory of the electron. It can’t be ruled out that, in such a theory, the entire energy of the electromagnetic field could be viewed as localized at these singularities, just like the old theory of action-at-a-distance. I imagine to myself, each such singular point surrounded by a field that has essentially the same character of a plane wave, and whose amplitude decreases with the distance between the singular points. If many such singularities are separated by a distance small with respect to the dimensions of the field of one singular point, their fields will be superimposed, and will form in their totality an oscillating field that is only slightly different from the oscillating field in our present electromagnetic theory of light.

In other words, by 1909—and even, I suspect, in 1905—Einstein did not think that Maxwell’s equations expressed the deepest reality of light. He did not think the fields truly had a life of their own; instead, they arose from “singularity points.” He did not think that they truly filled space: they are concentrated in packets near the singularity points. These ideas of Einstein were, of course, tied up with his concept that light comes in discrete units: today’s photons.

Just as Newton had misgivings about the natural implication of his theory, that it emptied space, Einstein had misgivings about the natural implication of his theory, that it filled space. Like Columbus, who found the New World while seeking a way to the Old, explorers who make landfall on unexpected continents of ideas are often unprepared to accept what they have found. They continue to seek what they were looking for.

By 1920, after he developed the theory of general relativity, Einstein’s attitude had changed: “More careful reflection teaches us, however, that the special theory of relativity does not compel us to deny ether.” Indeed, the general theory of relativity is very much an “ethereal” (that is, ether-based) theory of gravitation. (I’m saving Einstein’s own declaration on that score for use later in this chapter.) Nevertheless, Einstein never gave up on eliminating the electromagnetic ether:

If we consider the gravitational field and the electromagnetic field from the standpoint of the ether hypothesis, we find a remarkable difference between the two. There can be no space nor any part of space without gravitational potentials; for these confer upon space its metrical qualities, without which it cannot be imagined at all. The existence of the gravitational field is inseparably bound up with the existence of space. On the other hand a part of space may very well be imagined without an electromagnetic field. . . .²²

Around 1982, I had a memorable conversation with Feynman at Santa Barbara. Usually, at least with people he didn’t know well, Feynman was “on”—in performance mode. But after a day of bravura performances he was a little tired, and eased up. Alone for a couple of hours, before dinner, we had a wide-ranging discussion about physics. Our conversation inevitably drifted to the most mysterious aspect of our model of the world—both in 1982 and today—the subject of the cosmological constant. (The cosmological constant is, essentially, the density of empty space. Anticipating a little, let me just mention that a big puzzle in modern physics is why empty space weighs so little even though there’s so much to it.)

I asked Feynman, “Doesn’t it bother you that gravity seems to ignore all we have learned about the complications of the vacuum?” To which he immediately responded, “I once thought I’d solved that one.”

Then Feynman became wistful. Ordinarily he would look you right in the eye, and speak slowly but beautifully, in a smooth flow of fully formed sentences or even paragraphs. Now, however, he gazed off into space; he seemed transported for a moment, and said nothing.

Gathering himself again, Feynman explained that he had been disappointed with the outcome of his work on quantum electrodynamics. It was a startling thing for him to say, because that brilliant work was what brought Feynman graphs to the world, as well as many of the methods we still use to do difficult calculations in quantum field theory. It was also the work for which he won the Nobel Prize.

Feynman told me that when he realized that his theory of photons and electrons is mathematically equivalent to the usual theory, it crushed his deepest hopes. He had hoped that by formulating his theory directly in terms of paths of particles in space-time—Feynman graphs—he would avoid the field concept and construct something essentially new. For a while, he thought he had.

Why did he want to get rid of fields? “I had a slogan,” he said. Racheting up the volume and his Brooklyn²³ accent, he intoned it:

The vacuum doesn’t weigh anything [dramatic pause] because there’s nothing there!

Then he smiled, seemingly content, but subdued. His revolution didn’t quite come off as planned, but it was a damned good try.

Special Relativity and the Grid

The theory of special relativity, historically, came out of the study of electricity and magnetism, which culminated in Maxwell’s field theory. Thus special relativity arose from a description of the world based on the concept of entities—the electric and magnetic fields—that fill all space. That sort of description was a sharp break from the world-model inspired by Newton’s classical mechanics and gravity theory, which dominated earlier thinking. Newton’s world-model was based on particles that exert forces on one another through empty space.

The claims of special relativity, however, go beyond electromagnetism. The essence of special relativity is a postulate of symmetry: the laws of physics should take the same form after you boost everything appearing in them by the same, constant velocity. This postulate is a universal claim, grown beyond its electromagnetic roots. That is, the boost symmetry of special relativity applies to all the laws of physics. As we noted above, Einstein had to change Newton’s laws of mechanics so that they obeyed the same boost symmetry as electromagnetism.

While the ink was drying on special relativity, Einstein started looking for a way to include gravity in the new framework. It was the beginning of a ten-year search, of which Einstein later said,

. . . the years of searching in the dark for a truth that one feels, but cannot express; the intense desire and the alternations of confidence and misgiving, until one breaks through to clarity and understanding, are only known to him who has himself experienced them.

In the end he produced a field-based theory of gravity, general relativity. We’ll have much more to say about that theory later in this chapter. Several other clever people, including notably Poincaré, the great German mathematician Hermann Minkowski, and the Finnish physicist Gunnar Nordström, were also in the hunt, trying to construct theories of gravity consistent with the concepts of special relativity. All were led to field theories.

There’s a good general reason to expect that physical theories consistent with special relativity will have to be field theories. Here it comes:

A major result of the special theory of relativity is that there is a limiting velocity: the speed of light, usually denoted c. The influence of one particle on another cannot be transmitted faster than that. Newton’s law for the gravitational force, according to which the force due to a distant body is proportional to the inverse square of its distance right now, does not obey that rule, so it is not consistent with special relativity. Indeed the concept “right now” itself is problematic. Events that appear simultaneous to a stationary observer will not appear simultaneous to an observer moving at constant velocity. Overthrowing the concept of a universal “now” was, according to Einstein himself, by far the most difficult step in arriving at special relativity:

[A]ll attempts to clarify this paradox satisfactorily were condemned to failure as long as the axiom of the absolute character of times, viz., of simultaneity, unrecognizedly was anchored in the unconscious. Clearly to recognize this axiom and its arbitrary character really implies already the solution of the problem.

This is fascinating stuff, but it is well covered in dozens of popular books on relativity, so I won’t go further into it here. For present purposes, what’s important is simply that there’s a limiting velocity, c.

Now consider Figure 8.2. In Figure 8.2a, we have the world-lines of several particles. Their positions in space are indicated on the horizontal axis, and the value of time is indicated on the vertical axis. As time progresses, the particles’ positions change. The positions for any one particle, followed through time, make that particle’s world-line. Of course we should really have three spatial dimensions, but even two are too many to fit on a flat page, and fortunately one is enough to make our point. In Figure 8.2b, you see that if influence propagates at a finite speed, then the influence of particle A (say) on particle B depends on where particle A was in the past. So to get the total force on a particle, we have to sum up the influences from all the other particles, coming from different earlier times. This leads to a complicated description, as emphasized in Figure 8.2b. An alternative, also shown in Figure 8.2c, is to forget about keeping track of the individual past positions, and instead focus on the total influences. In other words, we keep track of a field representing the total influence.

That move from a particle description to a field description will be especially fruitful if the fields obey simple equations, so that we can calculate the future values of fields from the values they have now, without having to take past values into account. Maxwell’s theory of electromagnetism, general relativity, and QCD all have this property. Evidently, Nature has taken the opportunity to keep things relatively²⁴ simple by using fields.

Figure 8.2 How special relativity leads to fields. a. Here we have the world-lines of several particles, indicating how their positions (horizontal axis) change with time (vertical axis). b. If there’s a limiting velocity, then the total force felt by any given particle will depend on where the other particles were in the past. The “lines of influence” corresponding to propagation of influence at the limiting speed c are sketched in. c. To get the total force, we can either keep track of where everybody’s been in the past, or just focus on the summed influences. The first procedure corresponds to a particle theory, the second—potentially much simpler—to a field theory.

Gluons and the Grid

Einstein and Feynman were not unaware of the logic that suggests the inevitability of a field description for fundamental physics. Yet as we’ve seen, each of them was ready—even eager—to go back to a particle description.

That these two great physicists, at different times and for different reasons, could question the existence of fields that fill all space (a crucial aspect of the Grid) shows that the case for their existence did not appear overwhelming even well into the twentieth century. There was room for doubt, because hard evidence that fields have a life of their own was scanty. In my arguments around Figure 8.2, I made the case that fields are convenient. That’s very different from their being necessary ingredients of ultimate reality.

I’m not sure that Einstein was ever convinced about the electromagnetic ether. One of his greatest strengths as a theoretical physicist could also be a weakness: his stubbornness. Stubbornness served him well when he insisted on resolving the contradictions between the two relativities, mechanical versus electromagnetic, in favor of the latter; again when he insisted on taking Planck’s ideas seriously and extending them, despite their conflict with existing theory; and again when he struggled with the difficult and unfamiliar mathematics needed for general relativity. On the other hand, stubbornness kept him from participating in the tremendous successes of modern quantum theory after 1924, when uncertainty and indeterminism took root, and it kept him from accepting one of the most dramatic consequences of his own theory of general relativity, the existence of black holes.

Einstein’s difficulties in reconciling the quantum discreteness of photons with continuous space-filling fields, which since Maxwell have been used with great success to describe light, are overcome in the modern concept of quantum fields. Quantum fields fill all space, and the quantum electric and magnetic fields obey Maxwell’s equations.²⁵ Nevertheless, when you observe the quan-tum fields, you find their energy packaged in discrete units: photons. I’ll have much more to say about the strange but very successful concepts at the root of quantum field theory in the next chapter.

As for Feynman, he gave up when, as he worked out the mathematics of his version of quantum electrodynamics, he found the fields, introduced for convenience, taking on a life of their own. He told me he lost confidence in his program of emptying space when he found that both his mathematics and experimental facts required the kind of vacuum polarization modification of electromagnetic processes depicted—as he found it, using Feynman graphs—in Figure 8.3. Figure 8.3a corresponds to a sophisticated way of summarizing the same physics we saw in Figure 8.2. Here the influence of one particle on another is conveyed by the photon. Figure 8.3b adds something new. Here the electromagnetic field gets modified by its interaction with a spontaneous fluctuation in the electron—or, in other words, by its interaction with a virtual electron-positron pair. In describing this process, it becomes very difficult to avoid reference to space-filling fields.

The virtual pair is a consequence of spontaneous activity in the electron field. It can occur anywhere. And wherever it occurs, the electromagnetic field can sense it. Those two activities—fluctuations both occurring everywhere and being sensed everywhere—appear quite directly in the mathematical expressions that go with Figure 8.3b. They lead to complicated, small but very specific modifications of the force you would calculate from Maxwell’s equations. Those modifications have been observed, precisely, in accurate experiments.

In QED vacuum polarization is a small effect, both qualitatively and quantitatively. In QCD, by contrast, it is all-important. In Chapter 6, we saw how it leads to asymptotic freedom and thereby permits a successful description of jet phenomena. In the next chapter, we’ll see how QCD is used to calculate the mass of protons and other hadrons. Our eyes were not evolved to resolve the tiny times (10^-24 second) and distances (10^-14 centimeter) where the action is. But we can “look” inside the computers’ calculations, to see what the quarks and gluon fields are up to. To nimbler eyes, space would look like the ultrastroboscopicmicronano lava lamp you see in Color Plate 4. Creatures with such eyes wouldn’t share the human illusion that space is empty.

Figure 8.3 The force between electrically charged particles. Part a summarizes, in the language of Feynman graphs, the physics of Figure 8.2. At this level, the electric and magnetic fields are given by Maxwell’s equations, but they could also be traced back to the influence of charged particles. The fields are convenient, but perhaps we could do without them. Part b gives something new. In this contribution to the force, the electromagnetic fields are affected by spontaneous activity (virtual particle-antiparticle pairs) in the electron field.

Material Grid

Besides the fluctuating activity of quantum fields, space is filled with several layers of more permanent, substantial stuff. These are ethers in something closer to the original spirit of Aristotle and Descartes—they are materials that fill space. In some cases, we can even identify what they’re made of and even produce little samples of it. Physicists usually call these material ethers condensates . One could say that they (the ethers, not the physicists) condense spontaneously out of empty space as the morning dew or an all-enveloping mist might condense out of moist, invisible air.

The best understood of these condensates consists of quark-antiquark pairs. Here, we are talking about real particles, beyond the ephemeral, virtual particles that spontaneously come and go. The usual name for this space-filling mist of quarks and antiquarks is chiral symmetry-breaking condensate, but let’s just call it after what it is:

(pronounced “Q-Q bar”), for quark-antiquark.

For

, as for the other condensates, the two main questions are

• Why do we think it exists?

• How can we verify that it’s there?

Only in the case of

do we have good answers to both questions.

forms because perfectly empty space is unstable. Suppose we clean out space by removing the condensate of quark-antiquark pairs—something we can do more easily in our minds, with the help of equations and computers, than in laboratory experiments. Then, we compute, quark-antiquark pairs have negative total energy. The mc² energy cost of making those particles is more than made up by the energy you can liberate by unleashing the attractive forces between them, as they bind into little molecules. (The proper name for these quark-antiquark molecules is σ mesons.) So perfectly empty space is an explosive environment, ready to burst forth with real quark-antiquark molecules.

Chemical reactions usually start with some ingredients A, B and produce some products C, D; then we write

and, if energy is liberated,

(This is the equation for an explosion.)

In that notation, our reaction is

—no starting ingredients (other than empty space) required! Fortunately, the explosion is self-limiting. The pairs repel each other, so as their density increases it gets harder to fit new ones in. The total cost for producing a new pair includes an extra fee, for interacting with the pairs that are already there. When there’s no longer a net profit, production stops. We wind up with the space- filling condensate,

, as the stable endpoint.

An interesting story, I hope you’ll agree. How do we know it’s right?

One answer is that it’s a mathematical consequence of equations—the equations of QCD—that we have many other ways of checking. But although that may be a perfectly logical answer (the checks, as we’ve discussed, are very detailed and convincing), it’s not exactly science at its best. We’d like the equations to have consequences we can see reflected in the physical world.

A second answer is that we can calculate the consequences of 026

itself, and check whether they match things we see in the phys ical world. To be more specific, we can calculate whether 027

, considered as a material, can vibrate, and what the vibrations should look like. This is very close to what “luminiferous ether” fans once wanted to have for light: a good old-fashioned material, more sub stantial than electromagnetic fields. Vibrations of 028

aren’t visible light, but they do describe something quite definite and observable, namely π mesons. Among the hadrons, π mesons have unique properties. They are by far the lightest, for example,²⁶ and they never fit comfortably within the quark model. So it’s very satisfying—and after you study the details in depth, it’s very convinc ing—that they arise in quite a different way, as vibrations of 029

A third answer is the most direct and dramatic of all, at least in principle. We started by considering the thought experiment of cleaning out space. How about doing it for real? Scientists at the relativistic heavy ion collider (RHIC) at Brookhaven National Laboratory, on Long Island, have been working on it, and more such work will be going on at the LHC. What they do is accelerate two big collections of quarks and gluons moving in opposite directions—in the form of heavy atomic nuclei, such as gold or lead nuclei—to very high energy, and make them collide. This is not a good way to study the basic, elementary interactions of quarks and gluons or to look for subtle signs of new physics, because many many such collisions will happen at once. What you get, in fact, is a small but extremely hot fireball. Temperatures over 10¹² degrees (Kelvin, Celsius, or Fahrenheit—at this level, you can take your pick) have been measured. This is a billion times hotter than the surface of the Sun; temperatures this high last occurred only well within the first second of the big bang. At such tempera tures, the condensate 030

vaporizes: the quark-antiquark molecules from which it’s made break apart. So a little volume of space, for a short time, gets cleaned out. Then, as the fireball expands and cools, our pair-forming, energy-liberating reaction kicks in, and 031

is restored.

All this almost certainly happens. “Almost” comes in, though, because what we actually get to observe is the flotsam and jetsam thrown off as the fireball cools. Color Plate 5 is a photograph of what it looks like. Obviously, the photograph doesn’t come labeled with circles and arrows telling you what’s responsible for each aspect of this spectacularly complicated mess. You have to interpret it. In this case, even more (actually, much more) than with the pictures of proton interiors and jets that we discussed in Chapter 6, the interpretation is a complicated business. Today, the most accurate and complete interpretations build in the process of 032

melting and re-formation we’ve been discussing, but they’re not yet as clear and convincing as we might hope for. People continue to work at it—both the experiments and the interpretation.

For the next-best-understood condensate, we have good circumstantial evidence that it exists, but only guesses about what it’s made up of. The evidence comes from a part of fundamental physics we haven’t mentioned so far, the theory of the so-called weak interaction.²⁷ We have a good theory of the weak interaction that’s gone from triumph to triumph since the early 1970s. Notably, this theory was used to predict the existence, mass, and detailed properties of the W and Z bosons before they were observed experimentally. The theory is usually called the standard model, or the Glashow-Weinberg-Salam model, after Sheldon Glashow, Steven Weinberg, and Abdus Salam, three theorists who played key roles in formulating it (for which they shared the Nobel Prize in 1979).

In the standard model, the W and Z bosons play leading roles. They satisfy equations very similar to the equations for gluons in the quantum chromodynamics. Both are symmetry-based expansions of the equations for photons in quantum electrodynamics (namely, Maxwell’s equations). Activity in the W and Z boson fields creates the weak interactions, in the same sense that activity in the photon field is responsible for electromagnetism, and activity in the color gluon fields is responsible for the strong interaction.

The striking similarities among our fundamental theories of superficially very different forces hint at the possibility of a synthesis, in which all of them will be seen as different aspects of a more encompassing structure. Their different symmetries might be sub-symmetries of a larger master symmetry. Extra symmetry allows the equations to be rotated into themselves in even more ways; that is, there are more ways of making “distinctions without differences.” Thus it opens new possibilities for making connections among patterns that previously seemed unrelated. If our fundamental equations describe partial patterns that we can make more symmetric, by making additions, we’re tempted to think that maybe they really are just facets of the larger, unified structure. Anton Chekhov famously advised,

If in Act One there is a rifle hanging over the mantelpiece, it must have been fired by the fifth act.

Now I’ve hung the rifle of unification.

Returning to the standard model: The W and Z bosons are attractive lead players, but they need help to fit the parts they’re meant to play. Left to themselves, according to the equations that define them, they’d be massless, like the photon and the color gluons. Reality’s script, however, calls for them to be heavy. It’s as if Tinkerbelle had been cast as Santa Claus. To enable the sprite to impersonate the plumpkin, we’ve got to pad her out in a pillowy costume.

Physicists know how to do this trick—that is, to make the W and Z bosons acquire mass. We think. In fact Nature showed us how, by giving us a demonstration. My wife, who’s an accomplished writer and a fountain of good advice, gave me a list of cliché words to avoid, including amazing, astonishing, beautiful, breathtaking, extraordinary , and others you can probably guess. I mostly follow her advice. But I have to say that I find what I’m about to tell you amazing, astonishing, beautiful, breathtaking, and, yes, extraordinary.

The model Nature gives us for making force-carrying particles heavy is superconductivity. For inside superconductors, photons become heavy! I’ve offloaded a more detailed discussion of this to Appendix B, but here’s the essential idea. Photons, as we’ve discussed, are moving disturbances in electric and magnetic fields. In a superconductor, electrons respond vigorously to electric and magnetic fields. The electrons’ attempt to restore equilibrium is so vigorous that they exert a kind of drag on the fields’ motion. Instead of moving at the usual speed of light, therefore, inside a superconductor photons move more slowly. It’s as if they’ve acquired inertia. When you study the equations, you find that the slowed-down photons inside a superconductor obey the same equations of motion as would particles with real mass.

If you happened to be a life-form whose natural habitat was the interior of a superconductor, you’d simply perceive the photon as a massive particle.

Now let’s turn the logic around. Humans are a life-form that observes, in its natural habitat, photon-like particles, the W and Z bosons, that are massive. So perhaps we humans should suspect that we live inside a superconductor. Not, of course, a superconductor in the ordinary sense, that’s supergood at conducting the (electric) charge that photons care about, but rather a superconductor for the charges that W and Z bosons care about. The standard model is based on that idea; and, as we’ve said, the standard model is very successful at describing reality—the reality we find ourselves inhabiting. Thus we come to suspect that the entity we call empty space is an exotic kind of superconductor.

Where you have superconductivity, there’s got to be a material that does the conducting. Our exotic superconductivity works everywhere, so the job requires a space-filling material ether.

Big Question: What is that material, concretely? What is it that, for the cosmic superconductor, plays the role that electrons play in ordinary superconductors?

Unfortunately, it can’t be the material ether we understand well, 033

. Actually 034

is an exotic superconductor of the right kind, and it does contribute to the W and Z boson masses. But it falls short quantitatively by a factor of about a thousand.

No presently known form of matter has the right properties. So we don’t really know what this new material ether is. We know its name: the Higgs condensate, after Peter Higgs, a Scots physicist who pioneered some of these ideas. The simplest possibility, at least if you equate simplicity with adding as little as possible, is that it’s made from one new particle, the so-called Higgs particle. But the cosmic superconductor could be a mixture of several materials. In fact, as we’ve mentioned, we already know that 035

is part of the story, though a small part. As we’ll see later, there are good reasons to suspect that a whole new world of particles is ripe for discovery, and that several among them chip in to the cosmic superconductor, a.k.a. the Higgs condensate.

Taken at face value, the most promising unified theories²⁸ seem to predict the existence of all kinds of particles we haven’t yet observed. Additional condensates might save the day. New condensates can make the unwanted particles very heavy—just as the Higgs condensate does for the W and Z bosons, only more so. Particles with very large mass are hard to observe. It takes more energy, and hence bigger accelerators, to produce them as real particles. Even their indirect influence, as virtual particles, is diminished.

Of course, it would be cheap speculation to add new stuff into your equations just because you know how to make excuses when it isn’t observed. What makes the unified field theories interesting is that they explain features of the world that we observe, and—better yet—predict new ones. Now I’ve told you that the rifle is loaded.

The entity we perceive as empty space is a multilayered, multicolored superconductor. What an amazing, astonishing, beautiful, breathtaking concept. Extraordinary, too.

The Mother of All Grids: Metric Field

Here’s the Einstein quotation I saved up. In 1920 he wrote,

According to the general theory of relativity space without ether is unthinkable; for in such space there not only would be no propagation of light, but also no possibility of existence for standards of space and time (measuring-rods and clocks), nor therefore any space-time intervals in the physical sense.

It serves as a suitable introduction to the mother of all Grids: the metric field.

Let’s begin with something simple and familiar: maps of the world. Because maps are flat, whereas the thing they’re meant to depict—the surface of Earth—is (approximately) spherical, obviously the maps require interpretation. There are many ways of making a map that represents the geometry of the surface it depicts. All use the same basic strategy. The crucial thing is to lay down a grid of instructions for how to do geometry locally. More specifically, in each little region of the map, you lay down which direction corresponds to north and which direction corresponds to east (south and west will be the opposite directions, of course). You also specify, in each direction, what interval on the map corresponds to a mile—or kilometer, or lightmillisecond, or whatever—on Earth.

For example, maps based on the standard Mercator projection maintain north vertical and east horizontal. Then the surface of Earth can be fit to a rectangle. Going “around the world” from west to east takes you horizontally from one side of the map to the other, whether you follow the equator or the arctic circle. Back on Earth the equator covers a much longer distance than the arctic circle, so taking the map at face value gives a distorted impression: the polar regions appear, relatively, much larger than they are on Earth. But the grid instructs you how to get the distances right. In the polar regions you should use bigger rulers! (Things get a little crazy right at the poles. The whole top line on the map corresponds to a single point on Earth, namely the North Pole, and the whole bottom line corresponds to the South Pole.)

All the information you need to reconstruct the geometry of Earth’s surface from the map is contained in the grid of instructions. ²⁹ For example, here’s how you can tell the map describes a sphere. First pick a point on the map. Then, for each direction, measure off a fixed distance r from the reference point (following the grid instructions), and make a dot. The dotted places on the map now correspond to all places on Earth that are distance r from the reference point. Connect the dots. Generally (for instance, if your map is constructed à la Mercator), the figure you get on the map won’t look like a circle, even though it represents a circle on Earth. Nevertheless, you can use the map to measure the distance around the circle on Earth that the figure represents. And you’ll find it’s less than 2πr. (For experts: It will be R sin(2πr/R), where R is the radius of Earth.) If the map depicted a flat surface—which might not be obvious, if you’re using a distorted grid—you’d get exactly 2πr. You could also find a circumference greater than 2πr. Then you’d have discovered that your map is describing a saddle-shaped surface. Spheres, naturally, are defined to have positive curvature; flat surfaces have zero curvature; saddles have negative curvature.

Although visualization becomes much more difficult, the same ideas apply to three-dimensional space. Instead of a grid of instructions for doing geometry on a sheet, we can consider a grid of instructions that fills out a three-dimensional region. Such bulked-up “maps” contain (as slices) the sort of two-dimensional maps we have just discussed, as well as specs for putting the slices together. They define curved three-dimensional spaces.

So instead of working directly with complicated three-dimensional shapes that are (at best) extremely difficult to visualize, we can work in ordinary space, using grids of instructions. We can work with these maps without having to sacrifice any information.

The grid of instructions for doing geometry locally is called, in the scientific literature, the metric field. The lesson of maps is that the geometry of surfaces, or curved spaces of higher dimensions, is equivalent to a grid, or field, of instructions for how to set directions and measure distance locally. The underlying “space” of the map can be a matrix of points, or even an array of registers in a computer. With the proper grid of instructions, or metric field, either of those abstract frameworks can represent complicated geometry faithfully. Map makers and computer graphics wizards are expert at exploiting those possibilities.

We can also add time to the story. Special relativity tells us that one guy’s time is another guy’s mixture of space and time, so it’s natural to treat space and time on the same footing. To do that we need a four-dimensional array. The instruction grid, or metric field, at each point specifies which three directions are to be considered spatial directions—you can call them north, east, and up, although if you’re mapping deep space those names are quaint³⁰—and the standards of length in those directions. It also specifies that another direction represents time and gives a rule for translating map lengths in that direction into intervals of time.

In the general theory of relativity, Einstein used the concept of curved space-time to construct a theory of gravity. According to Newton’s second law of motion, bodies move in a straight line at constant velocity unless a force acts upon them. The general theory of relativity modifies this law to postulate that bodies follow the straightest possible paths through space-time (so-called geodesics). When space-time is curved, even the straightest possible paths acquire bumps and wiggles, because they must adapt to changes in the local geometry. Putting these ideas together, we say that bodies respond to the metric field. These bumps and wiggles in a body’s space-time trajectory—in more pedestrian language, changes in its direction and speed—provide, according to general relativity, an alternative and more accurate description of the effects formerly known as gravity.

We can describe general relativity using either of two mathematically equivalent ideas: curved space-time or metric field. Mathematicians, mystics, and specialists in general relativity tend to like the geometric view because of its elegance. Physicists trained in the more empirical tradition of high-energy physics and quantum field theory tend to prefer the field view, because it corresponds better to how we (or our computers) do concrete calculations. More important, as we’ll see in a moment, the field view makes Einstein’s theory of gravity look more like the other successful theories of fundamental physics, and so makes it easier to work toward a fully integrated, unified description of all the laws. As you can probably tell, I’m a field man.

Once it’s expressed in terms of the metric field, general relativity resembles the field theory of electromagnetism. In electromagnetism, electric and magnetic fields bend the trajectories of electrically charged bodies, or bodies containing electric currents. In general relativity, the metric field bends the trajectories of bodies that have energy and momentum. The other fundamental interactions also resemble electromagnetism. In QCD, the trajectories of bodies carrying color charge are bent by color gluon fields; in the weak interaction, still other types of charge and fields are involved; but in all cases the deep structure of the equations is very similar.

These similarities extend further. Electric charges and currents affect the strength of the electric and magnetic fields nearby—that is, their average strength, ignoring quantum fluctuations. This is the “reaction” of fields corresponding to their “action” on charged bodies. Similarly, the strength of the metric field is affected by all bodies that have energy and momentum (as all known forms of matter do). Thus the presence of a body A affects the metric field, which in turn affects the trajectory of another body B. This is how general relativity accounts for the phenomenon formerly known as the gravitational force one body exerts on another. It vindicates Newton’s intuitive rejection of action at a distance, even as it dethrones his theory.

Consistency requires the metric field to be a quantum field, like all the others. That is, the metric field fluctuates spontaneously. We do not have a satisfactory theory of these fluctuations. We know that the effects of quantum fluctuations in the metric field are usually—in our experience so far, always—small in practice, simply because we get very successful theories by ignoring them! From delicate biochemistry to exotic goings-on at accelerators to the evolution of stars and the early moments of the big bang, we’ve been able to make precise predictions, and have seen them accurately verified, while ignoring possible quantum fluctuations in the metric field. Moreover, the modern GPS system maps out space and time directly. It doesn’t allow for quantum gravity, yet it works very well. Experimenters have worked very hard to discover any effect that could be ascribed to quantum fluctuations in the metric field, or, in other words, to quantum gravity. Nobel Prizes and everlasting glory would attend such a discovery. So far, it hasn’t happened.³¹

Nevertheless, the Chicago objection—“That works in practice, but what about in theory?”—still holds. The problem that arises is much like the problems we saw with the quark model, and especially the parton model, in Chapter 6. Worrying about those theoretical problems eventually led to the concept of asymptotic freedom and to a complete, extremely successful theory of quarks and the (newly predicted!) color gluons. The analogous problem for quantum gravity hasn’t been solved. Superstring theory is a valiant attempt but very much a work in progress. At present it’s more a collection of hints about what a theory might look like than a concrete world-model with definite algorithms and predictions. And it hasn’t deeply incorporated the basic Grid ideas. (For experts: string field theory is clumsy at best.)

In the quotation that opened this section, Einstein said that space-time without the metric field is “unthinkable.” Taken literally, that’s obviously false—it’s easy to think about it! Let’s go back to our map. If the grid instructions are erased or get lost, the map still tells us things. It tells us which countries are next to which, for example. It just wouldn’t tell us, reliably, how big they are, or what shape. Even without information about size and shape, we still have what’s called topological information. That still leaves plenty to think about.

What Einstein meant is that it’s hard to imagine how the physical world would function without the metric field. Light wouldn’t know which way to move or how fast; rulers and clocks wouldn’t know what they’re supposed to measure. The equations Einstein had for light, and for the materials out of which you might make rulers and clocks, can’t be formulated without the metric field.

True enough, but a lot of things in modern physics are hard to imagine. We have to let our concepts and equations take us where they will. What Hertz said about this is so important (and so well expressed) that it bears repeating:

One cannot escape the feeling that these mathematical formulae have an independent existence and an intelligence of their own, that they are wiser than we are, wiser even than their discoverers, that we get more out of them than was originally put into them.

In other words, our equations—and more generally, our concepts—are not just our products but also our teachers.

In that spirit, the discovery that the Grid is filled with several materials, or condensates, raises an obvious question: Is the metric field a condensate? Might it be made from something more fundamental? And that question raises another: Could the metric field, like 036

, have vaporized at the origin of the universe, in the earliest moments of the big bang?

A positive answer would open up a new way of addressing a question that vexed Saint Augustine: “What was God doing before He created the world?” (Subtext: What was He waiting for? Wouldn’t it have been better to start sooner?) Saint Augustine gave two answers.

First answer: Before God created the world, He was preparing Hell for people who ask foolish questions.

Second answer: Until God creates the world, no “past” exists. So the question doesn’t make sense.

His first answer is funnier, but the second, spelled out at length in Chapter 10 of Augustine’s Confessions, is more interesting. Augustine’s basic argument is that the past no longer exists and the future does not yet exist; properly speaking, there is only the present. But the past has a sort of existence within minds, as present memory (as does of course the future, as present expectations). Thus the existence of a past depends on the existence of minds, and there can be no “before” in the absence of minds. Before minds were created, there was no before!

A modern, secular version of Augustine’s question is “What happened before the big bang?” And a version of his second answer based on physics might apply. Not that minds are necessary for time—I don’t think many physicists would accept that (and the equations of physics certainly don’t). But if the metric field vaporizes, with it goes the standard of time. Once no clocks exist (and this means an end not just to elaborate time-keeping devices, but to every physical process that could serve to mark time), time itself, along with the whole notion of “before,” loses any meaning. The flow of time commences with the condensation of the metric field.

Could the metric field change in some other way (crystallize?) under pressure, for example near the center of black holes? (We know that quarks will form weird condensates under pressure, with funny names like color-flavor locked superconductor, that are different from 037

Could the more fundamental material from which the metric field is made be the same material we need to unify the other forces?

Great questions, I hope you’ll agree! Unfortunately, we don’t have worthy answers yet. (I’m working on it. . . .) But it’s a sign of our progress, and of the growth of our ambition, that we can formulate questions and think seriously about possibilities that Einstein considered “unthinkable.” We have better equations now, and richer concepts, and we let them be our guides.

Grid Weighs

Mass traditionally has been regarded as the defining property of matter, the unique feature that gives substance to substance. So the recent astronomical discovery that Grid weighs—that the entity we perceive as empty space has a universal, nonzero density—crowns the case for its physical reality. Although it’s somewhat peripheral to the main thrust of this book, I’ll take a few pages to discuss the nature of that discovery and its cosmological implications, because it’s both fundamentally important and extremely interesting.³²

The concept of Grid density is essentially the same as Einstein’s cosmological term, which is essentially the same as “dark energy.” There are slight differences in interpretation and emphasis, which I’ll explain as they come up, but all three terms refer to the same physical phenomenon.

In 1917 Einstein introduced a modification of the equations he originally proposed for general relativity two years earlier. His motivation was cosmology. Einstein thought that the universe had constant density, both in time and (on average) in space, so he wanted to find a solution with those properties. But when he applied his original equations to the universe as a whole, he could not find such a solution. The underlying problem is easy to grasp. It was anticipated by Newton in 1692, in a famous letter to Richard Bentley:

. . . [I]t seems to me that if the matter of our sun and planets and all the matter of the universe were evenly scattered throughout all the heavens, and every particle had an innate gravity toward all the rest, and the whole space throughout which this matter was scattered was but finite, the matter on the outside of this space would, by its gravity, tend toward all the matter on the inside and, by consequence, fall down into the middle of the whole space and there compose one great spherical mass. But if the matter was evenly disposed throughout an infinite space, it could never converge into one mass; but some of it would converge into one mass and some into another . . .

Simply put: gravity is a universal attraction, so it is not content to leave things separate. Because gravity is always trying to bring things together, it’s not terribly surprising that you can’t find a solution where the universe maintains a constant density.

To get the kind of solution he wanted, Einstein changed the equations. But he changed them in a very particular way that doesn’t spoil their best feature, namely that they describe gravity in a way consistent with special relativity. There is basically only one way to make such a change. Einstein called the new term that he added to the equations for gravity the “cosmological term.” He didn’t really offer a physical interpretation of it, but modern physics supplies a compelling one, which I’ll describe momentarily.

Einstein’s motivation for adding the cosmological term, to describe a static universe, soon became obsolete, as evidence for the expansion of the universe firmed up in the 1920s, mainly through the work of Edwin Hubble. Einstein called the ideas that caused him to miss predicting the expansion of the universe his “greatest blunder.” (And it really was a blunder, because the model universe he produced, even with his new equations, is unstable. Strictly uniform density is a solution, but any small deviation from uniformity increases with time.) Nevertheless, the possibility he identified, of adding a new term to the equations of general relativity without spoiling the theory, was prophetic.

The cosmological term can be viewed in two ways. Like E = mc² and m = E/c², they are equivalent mathematically but suggest different interpretations. One way (the way Einstein viewed it) is as a modification of the law of gravity. Alternatively, the term can be viewed as the result of having a constant density of mass and also a constant pressure everywhere in space and for all time. Because both mass-density and pressure have the same value everywhere, they can be regarded as intrinsic properties of space itself. That’s the Grid viewpoint. If we take it as given that space has these properties, and focus exclusively on the gravitational consequences, we arrive back at Einstein’s viewpoint.

A key relationship governing the physics of the cosmological term relates its density ρ to the pressure p it exerts, using the speed of light c. There’s no standard name for this equation, but it will be handy to have one. I’ll call it the well-tempered equation, because it prescribes the proper way to tune a Grid. The well-tempered equation reads

(1)

Where does it come from? What does it mean?

The well-tempered equation looks like a mutated clone of Einstein’s second law, m = E/c². The m has turned into a ρ, and the E into a p—and there’s that - sign—but you can’t help noticing a resemblance. And in fact they are deeply related.

Einstein’s second law relates the energy of an isolated body at rest to its mass. (See Chapter 3 and Appendix A.) It is a consequence of special relativity theory, though not an immediately obvious one. In fact it did not appear in Einstein’s first relativity paper; he wrote a separate note about it afterwards.

The well-tempered equation is likewise a consequence of special relativity, but now applied to a homogeneous, space-filling entity rather than to an isolated body. It’s not immediately obvious how a nonzero Grid density can be consistent with special relativity. To appreciate the problem, think about the famous Fitzgerald-Lorentz contraction, which we encountered in Chapter 6. To an observer moving at constant velocity, objects appear foreshortened in the direction of motion. It would seem, therefore, that the moving observer would see a higher Grid density. That’s contrary to relativity’s boost symmetry, which says she must see the same physical laws.

The pressure that goes with density, according to the well-tempered equation, provides a loophole. The weighing scales of the moving observer, according to the equations of special relativity, register a new density that is a mixture of the old density and the old pressure—just as, perhaps more familiarly, her clocks register time intervals that are mixtures of the old time intervals and the old space intervals. If—and only if—the old density and the old pressure are related in just the way prescribed by the well-tempered equation, then values of the new density (and the new pressure) will be the same as the old values.

Another, closely related consequence of the well-tempered equation is central to the cosmology of Grid density. In an expanding universe, the density of any normal kind of matter will go down. But the density of the well-tempered grid stays constant! If you’re up for a little exercise in first-year physics and algebra, here comes a pretty connection tying that constancy of density directly to Einstein’s second law. (If not, just skip the next paragraph.)

Consider a volume V of space, filled with grid density ρ. Let the volume expand by δV. Ordinarily, as a body expands under pressure it does work, and so loses energy. But the - sign in the equation for a well-tempered Grid gives us negative pressure p = -ρc². So by expanding, our well-tempered Grid gains energy δV × ρc². According to Einstein’s second law, therefore, its mass increases by δV × ρ. And that’s just enough to fill the added volume δV with density ρ, allowing the density of the Grid to remain constant.

Each of the Grid components we’ve discussed—fluctuating quantum fields of many sorts, 039

, Higgs condensate, unification-salvaging condensate, space-time metric field (or condensate?)—is well-tempered. Each of these space-filling entities obeys the well-tempered equation, because each is consistent with the boost symmetry of special relativity.

It’s possible to measure the cosmic density and the pressure separately, using quite different techniques. The density affects the curvature of space, which astronomers can measure by studying the distortion such curvature causes in images of distant galaxies, or—a powerful new technique—in the cosmic microwave background radiation. Using the new technique, by 2001 several groups were able to prove that there was much more mass in the universe than could be accounted for by normal matter alone. About 70% of the total mass appears to be very uniformly distributed, both in space and time.

The pressure affects the rate at which the universe is expanding. That rate can be measured by studying distant supernovae. Their brightness tells you how far away they are, while the redshift of their spectral lines tells you how fast they’re moving away. Because the speed of light is finite, when we observe the farther-away ones we’re looking at their past. So we can use supernovae to reconstruct the history of expansion. In 1998 two powerhouse teams of observers reported that the rate of expansion of the universe is increasing. This was a big surprise, because ordinary gravitational attraction tends to brake the expansion. Some new effect was showing up. The simplest possibility is a universal negative pressure, which encourages expansion.

The term dark energy became a shorthand for both of these discoveries: the additional mass and the accelerating expansion. It was meant to be agnostic about the relative values of density and pressure. If we simply called both of them the cosmological term, we’d be prejudging their relative magnitudes. But apparently we’d be right. The two very different quantities, cosmic mass density and cosmic pressure, observed in very different ways, do seem to be related by ρ = -p/c².

Is the astronomical discovery that space weighs, and seems to obey the well-tempered equation, a brilliant confirmation of the deep structures upon which we erect our best models of the world? Yes and no. To be honest, probably I should write yes and NO.

The problem is that the total density that astronomers weigh is far, far smaller than simple estimates of what any of our condensates provides. Here are simple estimates of the densities involved, as multiples of what the astronomers actually find:

• Quark-antiquark condensate: 10⁴⁴

• Weak superconducting condensate: 10⁵⁶

• Unified superconducting condensate: 10¹¹²

• Quantum fluctuations, without supersymmetry: ∞

• Quantum fluctuations, with supersymmetry: ³³ 10

• Space-time metric: ? (The physics here is too murky to allow a simple estimate.)

If any of these simple estimates were correct, the evolution of the universe would be much more rapid than what’s observed.

Why is the real density of space much smaller? Maybe there’s a vast conspiracy among these and possibly other contributions, some necessarily negative, to give a total that’s very much smaller than each individual contribution. Maybe there’s an important gap in our understanding of how gravity responds to Grid density. Maybe both. We don’t know.

Before dark energy was discovered, most theoretical physicists, looking at the enormous discrepancy between simple estimates of the density of space and reality, hoped that some brilliant insight would supply a good reason why the true answer is zero. Feynman’s “because it’s empty” was the best, or at least the most entertaining, idea I heard along those lines. If the answer really isn’t zero, we need different ideas. (It’s still logically possible that the ultimate density is zero, and that the universe is very slowly settling toward that value.)

A popular speculation today is that many different possible condensates contribute to the density, some positive, some negative. It’s only when the contributions cancel almost completely that you get a nice slowly evolving universe that is sufficiently user-friendly to be observed. An observable universe has to allow enough quality time for potential observers to evolve. Thus (according to this speculation) we observe an improbably small total Grid density because if the total were much larger, nobody would be around to observe it. Maybe that’s right, but it’s a diffi-cult idea to make precise, or to check. Sometimes we can leverage uncertainty into precision by gathering many samples. We do that when making insurance tables or applying quantum mechanics. But for the universe, we’re stuck with a sample size of one.

Anyway, in the one universe we’ve had a look at, Grid weighs. Fortunately, to clinch that conclusion, one universe is enough.

Recapitulation

At the beginning of this chapter, I advertised key properties of the Grid, that ur-stuff that underlies physical reality:

• The Grid fills space and time.

• Every fragment of Grid—each space-time element—has the same basic properties as every other fragment.

• The Grid is alive with quantum activity. Quantum activity has special characteristics. It is spontaneous and unpredictable. And to observe quantum activity, you must disturb it.

• The Grid also contains enduring, material components. The cosmos is a multilayered, multicolored superconductor.

• The Grid contains a metric field that gives space-time rigidity and causes gravity.

• The Grid weighs, with a universal density.

Now, after the sales pitch, I hope you buy it!