Knocking on Heaven's Door: How Physics and Scientific Thinking Illuminate the Universe and the Modern World - Lisa Randall (2011)
Part IV. MODELING, PREDICTING, AND ANTICIPATING RESULTS
Chapter 18. BOTTOM-UP VERSUS TOP-DOWN
Nothing substitutes for solid experimental results. But we physicists haven’t just been sitting on our thumbs for the last quarter century waiting for the LHC to turn on and produce meaningful data. We’ve thought long and hard about what it is that experiments should look for and what the implications of the data are likely to be. We have also studied results from experiment s that have been operational during this time frame, and these have taught us details about known particles and interactions and helped orient our thinking.
This interim period has also been a tremendous opportunity to think more deeply about ideas that at least for the time being are more removed from data. Some of the more interesting and speculative models and theoretical insights of the last twenty-five years resulted from these more mathematical pursuits. I doubt that I, for one, would have thought about extra dimensions or more mathematical aspects of supersymmetry had data been more plentiful. Even if measurements that would ultimately support these ideas had been made, the implications would have taken a while to unravel without the luxury of previous mathematical pursuits.
Experiments and mathematics both lead to scientific advances. But the road to progress is rarely clear, and physicists have been divided as to the best strategy. Model builders use the “bottom-up” approach introduced in Chapter 15 to start with what is known from experiments and then address residual puzzling unexplained features—often employing more theoretical mathematical developments. The last chapter presented some specific examples of models and how they influence the searches experimenters at the LHC will perform.
Others, most notably string theorists, apply a “top-down” way of thinking, in which they start with the theory that they believe is true—namely string theory—and try to use its underlying concepts to formulate a consistent quantum theory of gravity. Top-down theories are defined at high energies and small distances. The label refers to the theoretical notion that everything can be derived from fundamental premises defined at high-energy scales. Although the name can be confusing since high energies correspond to short distances, recall that the ingredients at small distances are the fundamental building blocks of matter. In this way of thinking, everything can be derived from basic principles and fundamental ingredients, which are defined at small distances and high energies—hence the label “top-down.”
This chapter is about the top-down and bottom-up approaches and the ways in which they contrast with each other. We’ll explore the differences, but also reflect on how they occasionally converge to yield remarkable insights.
Unlike model builders, more mathematically inclined physicists try to work from pure theory. The hope is to start with a single elegant theory and derive the consequences, and only then apply the ideas to data. Most any attempt at a unified theory embodies such a top-down approach. String theory is perhaps the most prominent such example. It is a conjecture for the ultimate underlying framework from which all other known physics phenomena would in principle follow.
String theorists take a major leap in the physics scales they try to conquer—jumping from the weak scale to the Planck scale at which gravity becomes strong. Experiments probably won’t directly test these ideas anytime soon (although the extra-dimensional models of the last chapter might be an exception). But even though string theory itself is difficult to test, elements of string theory do provide ideas and concepts that potentially observable models have incorporated.
The question physicists ask when deciding on model building versus string theory is whether to follow the Platonic approach, which tries to gain insights from some more fundamental truth, or the Aristotelian one, rooted in empirical observations. Do you take the “top-down” or the “bottom-up” approach? The choice could also be phrased as “Old Einstein versus Young Einstein.” Einstein originally did thought experiments that were grounded in physical situations. Nonetheless, he also valued beauty and elegance. Even when an experimental result contradicted his ideas about special relativity, he confidently (and ultimately correctly) decided that the experiment had to be wrong since its implications would have been too ugly to believe.
Einstein became more mathematically inclined after mathematics helped him finally complete his theory of general relativity. Since mathematical advances were crucial to completing his theory, he had more faith in theoretical methods later in his career. Looking to Einstein won’t resolve the issue, however. Despite his successful application of mathematics to general relativity, his later mathematical search for a unified theory never reached fruition.
The Grand Unified Theory proposed by Howard Georgi and Sheldon Glashow was also a top-down idea. GUTs, as they were known, were rooted in data—the inspiration for their conjecture was the particular set of particles and forces that exist in the Standard Model and the strength with which they interact—but the theory extrapolated from what we know to what might be happening at very distant energy scales.
Interestingly, even though the unification would happen at an energy much higher than a particle accelerator could achieve, the initial model for a GUT made a prediction that was potentially observable. The Georgi-Glashow GUT model predicted that the proton would decay. The decay would take a long time, but experimenters set up giant vats of material with the hopes that at least one of the protons inside would decay and leave a visible signal. When that didn’t happen, the original GUT model was ruled out.
Since that time neither Georgi nor Glashow has chosen to work on any top-down theory that makes such a dramatic leap in energies from those we can directly access in accelerators to those so far removed that they might have only subtle experimental consequences—or likelier still, not any. They decided it would just be too ridiculously unlikely to make a correct guess about a theory so many orders of magnitude away in distance and energy from anything we currently understand.
Despite their reservations, many other physicists decided that a top-down approach was the only way to attack certain difficult theoretical issues. String theorists chose to work in a netherworld that isn’t clearly traditional science but has led to a rich, if controversial, set of ideas. They understand some aspects of their theory, but they are still piecing it together—looking for the key underlying principles as they go along and develop their radical ideas.
The motivation for string theory as a theory of gravity didn’t come from data, but from theoretical puzzles. String theory provides a natural candidate for the graviton, the particle quantum mechanics tells us should exist and communicate the force of gravity. It is currently the leading candidate for a fully consistent theory of quantum gravity—a theory that includes both quantum mechanics and Einstein’s theory of general relativity, and that works at all conceivable energy scales.
Physicists can use known theories to reliably make predictions at small distances, such as the inside of an atom, where quantum mechanics plays a big role and gravity is negligible. Because gravity has such feeble influence on atomic-mass particles, we can use quantum mechanics and safely ignore gravity. Physicists can also make predictions about phenomena at large distances, such as inside galaxies, where gravity dominates predictions and quantum mechanics can be ignored.
However, we lack a theory that includes both quantum mechanics and gravity—and works at all possible energies and distances. In particular, we don’t know how to calculate at enormously high energies and extremely short distances—comparable to the Planck energy or length. Because the influence of gravity is bigger for heavier and more energetic particles, gravity acting on Planck mass particles would play an essential role. And at the tiny Planck length, quantum mechanics would too.
Although this problem doesn’t spoil any calculations for observable phenomena—certainly not those at the LHC—it does mean theoretical physics is incomplete. Physicists don’t yet know how to consistently include quantum mechanics and gravity at extremely high energies or short distances where both have comparable importance for predictions and neither can be neglected. This important gap in our understanding could potentially point the way forward. Many think string theory could be the resolution.
The name “string theory” derives from the fundamental oscillating string that formed the core of the initial formulation. Particles exist in string theory, but they arise from the vibrations of a string. Different particles correspond to different oscillations, much as different notes arise from a vibrating violin string. In principle, experimental evidence for string theory should consist of new particles that would correspond to the many additional vibrational modes that a string can produce.
However, most such particles are likely to be much too heavy to ever observe, and that’s why it’s so difficult to experimentally verify whether string theory is realized in nature. String theory’s equations describe objects that are so incredibly tiny and that possess such extraordinarily high energy that any detector we could even imagine would be unlikely to ever see them. It is defined at an energy scale that is about 10 million billion times larger than those we can experimentally explore with current instruments. At present, we still don’t even know what will happen when the energy of particle colliders increases by a factor of 10.
String theorists can’t uniquely predict what happens at experimentally accessible energies since the particle content and other properties depends on the as yet undetermined configuration of fundamental ingredients in the theory. String theory’s consequences in nature depend on how the elements arrange themselves. As it is currently formulated, string theory contains more particles, more forces, and more dimensions than we see in our world. What is it that distinguishes those particles, forces, and dimensions that are visible from those that are not?
For example, space in string theory is not necessarily the space we see around us—space with three dimensions. Instead, string theory’s gravity describes six or seven additional dimensions of space. A workable version of string theory has to explain how the invisible extra dimensions are different from the three we know. As fascinating and remarkable as string theory is, puzzling features like its extra dimensions obscure its connection to the visible universe.
To get from the high energy at which string theory is defined to predictions about measurable energies, we need to deduce what the original theory will look like with the heavier particles removed. However, there are many possible manifestations of string theory at accessible energies, and we don’t yet know how to distinguish among the enormous range of possibilities, or even how to find the one that looks like our world. The problem is that we don’t yet understand string theory sufficiently well to derive its consequences at the energies we see. The theory’s predictions are hindered by its complexity. Not only is the challenge mathematically difficult, it is not even always clear how to organize string theory’s ingredients and determine which mathematical problem to solve.
On top of that, we now know that string theory is much more complex than physicists originally thought and involves many other ingredients with different dimensionalities—notably branes. The name string theory still generally survives, but physicists also talk about M-theory, although no one really knows what the “M” stands for.
String theory is a magnificent theory that has already led to profound mathematical and physical insights, and it might well contain the correct ingredients to ultimately describe nature. Unfortunately, an enormous theoretical gulf separates the theory as it is currently understood from predictions that describe our world.
Ultimately, if string theory is correct, all the models that describe real-world phenomena should be derivable from its fundamental premises. But its initial formulation is abstract, and its connection to observable phenomena is remote. We would have to be very lucky to find all the correct physical principles that will make string theoretical predictions match our world. That is string theory’s ultimate goal, but it is a daunting task.
Although elegance and simplicity can be the hallmarks of a correct theory, we can only really judge a theory’s beauty when we have a reasonably comprehensive understanding of how it works. Discovering how and why nature hides string theory’s extra dimensions would be a stunning achievement. Physicists want to figure out how this occurs.
As I joked in Warped Passages, most attempts to make string theory realistic have had something of the flavor of cosmetic surgery. In order to make string theory conform to our world, theorists have to find ways to hide the pieces that shouldn’t be there, removing particles from view and tucking dimensions demurely away. But although the resulting sets of particles come tantalizingly close to the correct set, you can nonetheless tell that they aren’t quite right.
More recent attempts to make string theory realistic have something of the flavor of a casting call. Although most ingenues can’t act very well and some have frozen faces that don’t let them emote, with enough auditions, a beautiful talented actor might show up.
Similarly, some ideas about string theory also rely on our universe being the rare but ideal configuration of its ingredients. Even if string theory does ultimately unify all the known forces and particles, it might contain a single stable basin representing a particular set of particles, forces, and interactions, or more likely, a more complicated landscape with many possible hills and valleys and a variety of possible implications.
According to recent research, string theory can manifest itself in many possible universes in a scenario corresponding to a multiverse. The different universes can be so far apart that they never interact—even through gravity—over their lifetimes. In that case, completely different evolution can occur in each of these universes, and we would end up in only one of them.
If these universes existed and there were no way of populating them, we would be justified in ignoring all but our own. But cosmological evolution provides ways to create all of them. And the different universes can have significantly different properties, with different matter, forces, or energy.
Some physicists employ the idea of the landscape in conjunction with the anthropic principle to try to address the particularly thorny questions in string theory and particle physics. The anthropic principle tells us that since we live in a universe that permits galaxies and life, certain parameters must take values at or near the values they do—or we would never be here to ask the question. For example, the universe couldn’t have so much energy that it would expand at a rate too quickly for matter to collapse into cosmic structures.
If this is the case, we need to determine what physical features, if any, favor one configuration of particles and forces and energy over another. We don’t even know which properties should be predictable and which are simply necessary for us to be sitting around discussing science in the first place. Which properties have fundamental explanations and which are an accident of location?
Personally, I believe a landscape of many possible configurations where we might reside is reasonably likely since there are many possible solutions to any set of equations for gravity we write down, and I don’t see any reason why what we observe should be all there is. But I find the anthropic principle as a way of explaining observed phenomena unsatisfying. The problem is we never know whether the anthropic principle suffices. Which phenomena should we be able to uniquely predict and which are determined by “just so” stories? On top of that, an anthropic explanation cannot be tested. It might turn out to be correct. But it will certainly be abandoned if a more fundamental explanation from first principles comes along.
BACK ON SOLID GROUND
String theory very likely contains some deep and promising ideas. It has already given us insights into quantum gravity and mathematics and provided interesting ingredients for model builders to pursue. But it will most likely be a long time before we can solve the theory sufficiently to answer the questions we would most like to solve. Deriving string theory’s consequences for the real world directly from scratch might just be too difficult. Even if successful models ultimately arise from string theory, the clutter of superfluous elements makes them very difficult to find.
The model-building approach in physics is fueled by the instinct that the energies at which string theory makes definite predictions are too remote from those we can observe. As with many phenomena that have different descriptions on different scales, it could be that the mechanisms that address questions in particle physics are best studied at the relevant energies.
Physicists share common goals, but we have different expectations about how best to achieve them. I prefer the model-building approach because it is more likely to receive experimental guidance in the near future. My colleagues and I might use ideas from string theory, and some of our research might have string theory implications, but applying string theory is not my primary goal. Understanding testable phenomena is. Models can be described and subjected to experimental tests, even before any connection to a more fundamental theory is made.
Model builders pragmatically admit that we can’t derive everything at once. A model’s assumptions could be part of the ultimate underlying theory, or they might simply illuminate new relationships that have still deeper theoretical underpinnings. Models are effective theories. Once a model proves correct, it can provide direction for string theorists, or anyone attempting a more top-down approach. And models already benefit from the rich set of ideas that string theory provides. But models primarily focus on lower energies, and experiments that apply at these scales.
Models that go beyond the Standard Model incorporate its ingredients as well as the results at energies that have already been explored, but they also contain new forces, new particles, and new interactions that can be seen only at shorter distances. Even so, fitting everything we know is difficult, and the resulting precise model that I or anyone else works on often loses much of its initial elegance. For this reason, model builders need to have open minds.
People are often puzzled when I tell them that I work on many different models when I know that they can’t all be correct and that the LHC should tell us more about which could be right. They are even more surprised when I explain that I don’t necessarily assign huge probabilities to any particular model I am thinking about. Nonetheless, I choose projects that illuminate a genuinely new explanatory principle or new type of experimental search. The models I consider generally have some interesting feature or mechanism that provides interesting potential explanations for mysterious phenomena. Given the many unknowns—and uncertain criteria for progress—predicting and interpreting reality poses formidable challenges. It would be miraculous to get it all right from the get-go.
One of the beautiful aspects of the extra-dimensional theories is that ideas from both the top-down and bottom-up camps converged to produce them. String theorists recognized the critical role of branes in their theoretical formulations. And model builders realized that by reinterpreting the hierarchy problem as a question about gravity, they could find alternative solutions.
The Large Hadron Collider is now testing such ideas. Whatever the LHC discovers will guide and constrain model building in the future. With its higher-energy experimental results, we’ll be able to piece together observations to determine what is right. Even if observations don’t conform to any one particular proposal, the lessons we learned from constructing those models will help narrow down the possibilities for which theory is ultimately correct.
Model building helps us recognize the possibilities, suggest experimental searches, and interpret data once they are available. We might be lucky and get it right. But model building also gives us insights into what to look for. Even if no particular model’s predictions turn out to be completely correct, they will help us deduce the implications of any new experimental result. The results will distinguish among the many ideas and determine which—if any—of the specific implementations correctly describes reality. If no current proposal works, data will nonetheless help determine what the right model might be.
High-energy experiments are not merely searching for new particles. They are searching for the structure of underlying physical laws with even greater explanatory power. Until experiments help determine the answers, we are all just making guesses. For now we’ll apply aesthetic criteria (or prejudice) to favor certain models. But when experiments reach the energies or distances and statistics necessary to distinguish among models, we will know much more. Experimental results, such as those we hope that the LHC will provide, will determine which of our conjectures are correct and help us establish the underlying nature of reality.