Fear of Physics (22 page)

By measuring the CMB and attempting to observe such lumps and determine their angular size, knowing their intrinsic physical size, astrophysicists were finally able in 1998 to attempt to directly constrain the geometry of the universe. And the answer (see figure below) was, perhaps surprisingly, precisely what theorists had imagined it needed to be. We appear, with reasonably high precision, to live in a flat universe.

 

Upper image shows a false color image of the Cosmic Microwave Background in a small region of the sky as observed by the Boomerang Microwave Detector, launched in Antarctica in 1998. Below it are shown three computer-generated images showing the expected mean-size of temperature fluctuations predicted if the universe was closed (left), open (right) and flat (middle).

However, at the same time direct determinations of the total matter content associated with galaxies and clusters, including dark matter, has definitively shown that it comprises only 30 percent of the total energy density needed to result in a flat universe. Remarkably, the mysterious missing 70 percent is precisely what is suggested to exist in empty space in order to account for the acceleration of the universe described in the last chapter. All the data holds together if we live in a wacky universe in which 99 percent of the total energy is hidden from view, with 30 percent being in the form of dark matter and almost 70 percent existing as dark energy, distributed throughout empty space!

It is remarkable how far our understanding of space and time has developed since Einstein first unearthed the hidden connections between them. We now understand that the universe of our experience is actually four dimensional, in which each observer must define his or her own
now
and, in so doing, partition space-time into the separate entities we perceive as space and time. We understand that space and time are also inextricably linked to matter and energy, and that the curvature of space-time near massive objects results in what we perceive as gravity. And we have just measured the curvature of our universe, shedding new light on its makeup and its future evolution. We may live in a metaphorical cave, but the shadows on the wall have so far provided unerring evidence that there exist remarkable new connections that make our universe more comprehensible and ultimately more predictable.

 

 

Before I wax too profound, I want to arrive back at the world of everyday phenomena to end this chapter. I promised examples that are close to home, and even though I started out with something simple like space and time, I ended up talking about the
whole universe. But it is not just at the forefront of microscopic and macroscopic scales where hidden connections lie in wait to simplify our picture of the universe. Even as the grand discoveries about space, time, and matter that I have described in this chapter were being made, new connections have been unearthed about the nature of materials as exotic as oatmeal, and as diverse as water and iron. As I shall describe in the final chapter, while the subject of these discoveries is everyday physics, the ramifications include changing the way we picture the search for the “ultimate” theory.

Everyday materials appear extremely complicated. They must be because they differ widely in their behavior. One of the reasons why chemical engineering and materials science are such rich fields, and why industry supports significant materials research, is because substances can be designed to satisfy almost any property that might be required. Sometimes new materials are developed by accident. High-Temperature Superconductivity, for example, a subject of intense current interest, began almost as an alchemic accident by two researchers at IBM laboratories who were exploring a new set of materials in hopes of finding a new superconductor, but with no solid theoretical reasons behind their approach. On the other hand, more often than not, materials are developed based on a combination of empirical expertise and theoretical guidance. Silicon, for example, the main component in the semiconductor devices that run our computers (and our lives) spawned a research field to search for new materials with properties that might be more amenable to certain semiconductor applications. One such material is gallium, which is playing a key role in the next generation of semiconductors.

Even the simplest and most commonplace materials have exotic behaviors. I will always remember my high school physics
teacher telling me, tongue in cheek, of course, that there are two things in physics that prove the existence of God. First, water, almost alone of all materials, expands when it freezes. If this rare characteristic were not so, lakes would freeze from the bottom up instead of the top down. Fish would not survive the winter, and life as we know it would probably not have developed. Next, he pointed to the fact that the “coefficient of expansion”—that is, the amount by which a material expands when heated—of concrete and steel are virtually identical. If this were not the case, then modern large buildings would not be possible because they would buckle in the summer and winter. (I must admit that I found the second example a little less compelling, because I am sure that if concrete and steel did not have the same coefficient of expansion, some building materials could have been developed that did.)

Back to the first example, the fact that water, perhaps the most common substance on Earth, reacts differently than most other materials when it freezes is interesting. In fact, aside from the fact that water expands when it freezes, it provides in every other sense a paradigm for how materials change as external physical conditions change. At temperatures that exist on Earth, water both freezes and boils. Each such transition in nature is called a “phase transition” because the phase of the material changes—from solid to liquid to gas. It is fair to say that if we understand the phases and the conditions that govern the phase transitions for any material, we understand most of the essential physics.

Now, what makes this especially difficult is that in the region of a phase transition, matter appears as complicated as it ever gets. As water boils, turbulent eddies swirl, and bubbles explosively burst from the surface. However, in complexity there often lie the seeds of order. While a cow may seem hopelessly complex,
we have seen how simple scaling arguments govern a remarkable number of its properties without requiring us to keep track of all the details. Similarly, we can never hope to describe specifically the formation of every bubble in a pot of boiling water. Nevertheless, we can characterize several generic features that are always present when, say, water boils at a certain temperature and pressure, and examine their scaling behavior.

For example, at normal atmospheric pressure, when water is at the boiling point, we can examine a small volume of the material chosen at random. We can ask ourselves the following question: Will this region be located inside a bubble, or inside water, or neither? On small scales, things are very complicated. For example, it is clear that it makes no sense to describe a single water molecule as a gas or a liquid. This is because it is the configuration of many, many molecules—how close together they are on average, for example—that distinguishes a gas from a liquid. It is also clear that it makes no sense to describe a small group of molecules moving around as being in a liquid or a vapor state. This is because as they move and collide, we can imagine that at times a significant fraction of the molecules are sufficiently far apart that they could be considered as being in the vapor state. At other times, they might be close enough together to be considered a liquid. Once we get to a certain size region, however, containing enough molecules, it becomes sensible to ask whether they are in the form of a liquid or a gas.

When water boils under normal conditions, both bubbles of water vapor and the liquid coexist. Thus water is said to undergo a “first-order” transition at the boiling point, 212° Fahrenheit at sea level. A macroscopic sample after sufficient time at exactly the boiling point will settle down and can be unambiguously characterized as being in either the liquid or the gaseous state.
Both are possible at precisely this temperature. At a slightly lower temperature, the sample will always settle down in the liquid state; at a slightly higher temperature, it will settle down as vapor.

In spite of the intricate complexity of the local transitions that take place as water converts from liquid to gas at the boiling point, there is a characteristic volume scale, for a fixed pressure, at which it is sensible to ask which state the water is in. For all volumes smaller than this scale, local fluctuations in density are rapidly occurring that obscure the distinction between the liquid and gaseous states. For volumes larger than this, the average density fluctuates by a small enough amount so that this bulk sample has the properties of either a gas or a liquid.

It is perhaps surprising that such a complex system has such uniformity. It is a product of the fact that each drop of water contains an incredibly large number of molecules. While small groups of them may behave erratically, there are so many behaving in an average fashion that the few aberrant ones make no difference. It is similar to people, I suppose. Taken individually, everyone has his or her own reasons for voting for a political candidate. Some people even prepare write-in ballots for some local candidate of choice. There are enough of us, however, so barring hanky-panky with new electronic voting machines, or screw-ups with hanging chads or TV stations on the basis of exit polls, we can predict quite quickly who will win and often get it right. On average, all of our differences cancel out.

Having discovered such hidden order, we can exploit it. We can, for instance, ask whether the scale at which the distinction between water and liquid becomes meaningful changes as we change the temperature and pressure combination at which water boils. As we increase the pressure, and thus decrease the difference between the density of water vapor and water liquid, the
temperature at which water boils increases. If we now achieve this new temperature, we find, as you might expect after thinking about it, that because the difference in density between vapor and liquid is smaller, the size of the regions that regularly fluctuate between the two at the boiling point increases.

If we continue to increase the pressure, we find that at a certain conjunction of the pressure and temperature, called the
critical value,
the distinction between liquid and gas fails to have any meaning at all, even in an infinite sample. On all scales, fluctuations in density take place that are big enough to make it impossible to classify the bulk material as either liquid or gas. A little bit below this temperature, the density of the material is that appropriate to a liquid, and a little bit above the density is appropriate to a gas. But at this critical temperature, the water is neither or both, depending upon your point of view.

The specific configuration of water at the critical point is remarkable. On all scales, the material looks exactly the same. The material is “self-similar” as you increase the scale on which you examine it. If you were to take a high-magnification photograph of a small region, with differences in density appearing as differences in color, it would look the same as a photograph taken at normal magnification, with the same kind of variations but with the regions in question representing much bigger volumes. In fact, in water at the critical point, a phenomenon called
critical opulescence
occurs. Because the fluctuations in density are occurring at all scales, these fluctuations scatter light of all wavelengths, and suddenly the water no longer looks clear, but gets cloudy.

There is even something more fascinating about this state of water. Because it looks more or less exactly the same on all scales—what is called
scale invariance
—the nature of the microscopic
structure of the water (that is, the fact that water molecules are made of two hydrogen atoms and one oxygen atom) becomes irrelevant. All that characterizes the system at the critical point is the density. One could, for instance, mark +1’s for regions with a little density excess and–1’s for regions with a deficit. For all intents and purposes, the water on any scale would then look schematically something like this: