Knocking on Heaven's Door - Lisa Randall [14]
“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.
One of the most important aspects of an effective theory is that while it describes what we can see, it also categorizes what is missing—be it small scale or large.