Knocking on Heaven's Door (5 page)

One of the most important features of physics is that it tells us how to identify the range of scales relevant to any measurement or prediction—according to the precision we have at our disposal—and then calculate accordingly. The beauty of this way of looking at the world is that we can focus on the scales that are relevant to whatever we are interested in, identify the elements that operate at those scales, and discover and apply the rules that govern how these components relate. Scientists average over or even ignore (sometimes unwittingly) physical processes that occur on immeasurably small scales when formulating theories or setting up calculations. We select relevant facts and suppress details when we can get away with it and focus on the most useful scales. Doing so is the only way to cope with an impossibly dense set of information.

When appropriate, it makes sense to ignore minutiae in order to focus on the topic of interest and not to obscure it with inessential details. A recent lecture by the Harvard psychology professor Stephen Kosslyn reminded me how scientists—and everyone else—prefer to keep track of information. In a cognitive science experiment that he performed on the audience, he asked us all to keep track of line segments he presented on a screen one after the other. Each of the segments could go “north” or “southeast,” and so on, and together they formed a zigzagging line. (See Figure 2.) We were asked to close our eyes and say what we had seen. We noticed that even though our brains allow us to keep track of only a few individual segments at a time, we could remember longer sequences by grouping them into repeatable shapes. By thinking on the scale of the shape rather than the individual line segment, we could keep the figure in our heads.

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FIGURE 2
]
You might choose as your component the individual line segment or a larger unit, such as the group of six segments that appears twice.

For almost anything you see, hear, taste, smell, or touch, you have a choice between examining details by looking very closely or examining the “big picture” with its other priorities. Whether staring at a painting, tasting wine, reading philosophy, or planning your next trip, you automatically parcel your thoughts into the categories of interest—be they sizes or flavor categories, ideas, or distances—and the categories that you don’t find relevant at the time.

The utility of focusing on the pertinent questions and ignoring structures too small to be relevant applies in many contexts. Think about what you do when you use MapQuest or Google maps or look at the small screen on your iPhone. If you were traveling from far away, you would first get some rough idea where your destination is. Subsequently, when you have the big picture, you would zoom into a map with more resolution. You don’t need the additional detailed information in your first pass. You just want to have some sense of location. But as you begin to map out the details of your journey—as your resolution becomes finer in seeking out the exact street you will need—you will care about the details on the finer scale that were inessential to your first exploration.

Of course, the degree of precision you want or need determines the scale you choose. I have friends who don’t pay much attention to hotel location when visiting New York City. For them, the gradations in character of the city’s blocks is irrelevant. But for anyone who knows New York, those details matter. It’s not enough to know you are staying downtown. New Yorkers care if they are above or below Houston Street, or east or west of Washington Square Park, or even whether they are two or five blocks away.

Although the precise choice of scale might differ among individuals, no one would display a map of the United States in order to find a restaurant. The necessary details won’t be resolvable on a computer screen displaying such an overly large scale. On the other hand, you don’t need the details of a floor plan just to know that the restaurant is there in the first place. For any question you ask, you choose the relevant scale. (See Figure 3 for another example.)

The Eiffel Tower

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FIGURE 3
]
Different information becomes more obvious when viewed at different scales.

In a similar manner, we categorize by size in physics so we can focus on the questions of interest. Our tabletop looks solid—and for many purposes we can treat it as such—but in reality it is made up of atoms and molecules that collectively act like the hard impenetrable surface we encounter at the scales we experience in our daily lives. Those atoms aren’t indivisible, either. They are composed of nuclei and electrons. And the nuclei are made of protons and neutrons that are in turn bound states of more fundamental objects called quarks. Yet we don’t need to know about quarks to understand the electromagnetic and chemical properties of atoms and elements (the field of science known as atomic physics). People studied atomic physics for years before there was even a clue about the substructure beneath. And when biologists study a cell, they don’t need to know about quarks inside the proton either.

I remember feeling a tad betrayed when my high school teacher, after devoting months to Newton’s Laws, told the class those laws were wrong. But my teacher was not quite right in his statement. Newton’s laws of motion work at the distances and speeds that were observable in his time. Newton thought about physical laws that applied, given the accuracy with which he (or anyone else in his era) could make measurements. He didn’t need the details of general relativity to make successful predictions about what could be measured then. And neither do we when we make the sorts of predictions relevant to large bodies at relatively low speeds and densities that Newton’s Laws apply to. When physicists or engineers today study planetary orbits, they also don’t need to know the detailed composition of the Sun. The laws that govern the behavior of quarks don’t noticeably affect the predictions relevant to celestial bodies either.

Understanding the most basic components is rarely the most efficient way to understand the interactions at larger scales, where tiny substructure generally plays very little role. We would be hard pressed to make progress in atomic physics by studying the even tinier quarks. It is only when we need to know more detailed properties of nuclei that the quark substructure becomes relevant. In the absence of unfathomable precision, we can safely do chemistry and molecular biology while ignoring any internal substructure in a nucleus. Elizabeth Streb’s dance movements won’t change no matter what happens at the quantum gravity scale. Choreography relies only on classical physical laws.

Everyone, including physicists, is happy to use a simpler description when the details are beyond our resolution. Physicists formalize this intuition and organize categories in terms of the distance or energy that is relevant. For any given problem, we use what we call an
effective theory
. The effective theory concentrates on the particles and forces that have “effects” at the distances in question. Rather than delineating particles and interactions in terms of unmeasurable parameters that describe more fundamental behavior, we formulate our theories, equations, and observations in terms of the things that are actually relevant to the scales we might detect.

The effective theory we apply at larger distances doesn’t go into the details of an underlying physical theory that applies to shorter distance scales. It asks only about things you could hope to measure or see. If something is beyond the resolution of the scales at which you are working, you don’t need its detailed structure. This practice is not scientific fraud. It is a way of disregarding the clutter of superfluous information. It is an “effective” way to obtain accurate answers efficiently and keep track of what is in your system.

The reason effective theories work is that it is safe to ignore the unknown, as long as it won’t make any measurable differences. If the only unknown phenomena occur at scales, distances, or resolutions where the influence is still indiscernible, we don’t need to know about them to make successful predictions. Phenomena beyond our current technical reach, by definition, won’t have any measurable consequences aside from those that are already taken into account.

This is why, even without knowing about phenomena as substantial as the existence of relativistic laws of motion or a quantum mechanical description of atomic and subatomic systems, people could still make accurate predictions. This is fortunate, since we simply can’t think about everything at once. We’d never get anywhere if we couldn’t suppress irrelevant details. When we concentrate on questions we can experimentally test, our finite resolution makes this jumble of information on all scales inessential.

“Impossible” things can happen—but only in environments that we have not yet observed. Their consequences are irrelevant at scales we know—or at least those scales we have so far explored. What is happening at these small distances remains hidden until higher-resolution tools are developed to look directly or until sufficiently precise measurements differentiate and identify the underlying theory through the minuscule distinguishing features it provides at larger distances.

Scientists can legitimately ignore anything too small to be observed when we make predictions. Not only is it impossible to distinguish among the consequences of overly tiny objects and processes, but the physical effects of processes at these scales are interesting only insofar as they determine the physically measurable parameters. Physicists therefore characterize the objects and properties on measurable scales in an effective theory and use these to do science relevant to the scales at hand. When you do know the short-distance details, or the microstructure of a theory, you can derive the quantities in the effective description from more fundamental detailed structure. Otherwise these quantities are just unknowns to be experimentally determined. The observable larger-scale quantities in the effective theory are not giving the fundamental description, but they are a convenient way of organizing observations and predictions.

An effective description can summarize the consequences of any shorter-distance theory that reproduces larger-scale observations but whose direct effects are too tiny to see. This has the advantage of letting us study and evaluate processes using fewer parameters than we would need if we took every detail into account. This smaller set is completely sufficient to characterize the processes that interest us. Furthermore, the set of parameters we use are
universal
—they are the same independently of the more detailed underlying physical processes. To know their values we just have to measure them in any of the many processes in which they apply.

Over a large range of lengths and energies, a single effective theory applies. After its few parameters have been determined by measurements, everything appropriate to this range of scales can be calculated. It gives a set of elements and rules that can explain a large number of observations. At any given time, the theory we think of as fundamental is likely to turn out to be an effective theory—since we never have infinitely precise resolution. Yet we trust the effective theory because it successfully predicts many phenomena that apply over a range of length and energy scales.

Effective theories in physics not only keep track of short distance information—they can also summarize large distance effects whose consequences might also be too minute to observe. For example, the universe we live in is very slightly curved—in a way that Einstein taught us was possible when he developed his theory of gravity. This curvature applies to larger scales involving the large-scale structure of space. Yet we can systematically understand why such curvature effects are too small to matter for most of the observations and experiments that we perform locally, on much smaller scales. Only when we include gravity in our particle physics description do we need to consider such effects—which are too tiny to matter for much of what I will describe. In that case too, the appropriate effective theory tells us how to summarize gravity’s effects in a few unknown parameters to be experimentally determined.