Knocking on Heaven's Door (33 page)

For public policy, decision points can be even less clear. Public opinion usually occupies a gray zone where people don’t necessarily agree on how accurately we should know something before changing laws or implementing restrictions. Many factors complicate the necessary calculations. As the previous chapter discussed, ambiguity in goals and methods make cost-benefit analyses notoriously difficult, if not impossible, to reliably perform.

As
New York Times
columnist Nicholas Kristof wrote in arguing for prudency about potentially dangerous chemicals (BPA) in foods or containers, “Studies of BPA have raised alarm bells for decades, and the evidence is still complex and open to debate. That’s life: in the real world, regulatory decisions usually must be made with ambiguous and conflicting data.”
⁵¹

None of these issues mean that we shouldn’t aim for quantitative evaluations of costs and benefits when assessing policy. But they do mean that we should be clear about what the assessments mean, how much they can vary according to assumptions or goals, and what the calculations have and have not taken into account. Cost-benefit analyses can be useful but they can also give a false sense of concreteness, certainty, and security that can lead to misguided applications in society.

Fortunately for physicists, the questions we ask are usually a lot simpler—at least to formulate—than they are for public policy. When we’re dealing with pure knowledge without an immediate eye to applications, we make different types of inquiries. Measurements with elementary particles are a lot simpler, at least in principle. All electrons are intrinsically the same. You have to worry about statistical and systematic error, but not the heterogeneity of a population. The behavior of one electron is representative of them all. But the same notions of statistical and systematic error apply, and scientists try to minimize these whenever feasible. However, the lengths to which they will go to accomplish this depends on the questions they want to answer.

Nonetheless, even in “simple” physics systems, given that measurements won’t ever be perfect, we need to decide the accuracy to aim for. At a practical level, this question is equivalent to asking how many times an experimenter should repeat a measurement and how precise he needs his measuring device to be. The answer is up to him. The acceptable level of uncertainty depends on the question he asks. Different goals require different degrees of accuracy and precision.

For example, atomic clocks measure time with stability of one in 10 trillion, but few measurements require such a precise knowledge of time. Tests of Einstein‘s theory of gravity are an exception—they use as much precision and accuracy as can be attained. Even though all tests so far demonstrate that the theory works, measurements continue to improve. With higher precision, as-yet-unseen deviations representing new physical effects might appear that were impossible to see with previous less precise measurements. If so, these deviations would give us important insights into new physical phenomena. If not, we would trust that Einstein’s theory was even more accurate than had been demonstrated before. We would know we can confidently apply it over a greater regime of energy and distances and with a higher degree of accuracy. If you were sending a man to the Moon, on the other hand, you would want to understand physical laws sufficiently well that you aim your rocket correctly, but you wouldn’t need to include general relativity—and you certainly would not need to account for the even smaller potential effects representing possible deviations.

ACCURACY IN PARTICLE PHYSICS

In particle physics, we search for the underlying rules that govern the smallest and most fundamental components of matter we can detect. An individual experiment is not measuring a mishmash of many collisions happening at once or repeatedly interacting over time. The predictions we make apply to single collisions of known particles colliding at a definite energy. Particles enter the collision point, interact, and fly through detectors, usually depositing energy along the way. Physicists characterize particle collisions by the distinctive properties of the particles flying out—their mass, energy, and charges.

In this sense, despite the technical challenges of our experiments, particle physicists have it lucky. We study systems that are as basic as possible so that we can isolate fundamental components and laws. The idea is to make experimental systems that are as clean as existing resources permit. The challenge for physicists is reaching the required physical parameters rather than disentangling complex systems. Experiments are difficult because science has to push the frontiers of knowledge in order to be interesting. They are therefore often at the outer limit of the energies and distances accessible to technology.

In truth, particle physics experiments aren’t all that simple, even when studying precise fundamental quantities. Experimenters presenting their results face one of two challenges. If they do see something exotic, they have to be able to prove it cannot be the result of mundane Standard Model events that occasionally resemble some new particle or effect. On the other hand, if they don’t see anything new, they have to be certain of their level of accuracy in order to present a more stringent new limit on what can exist beyond known Standard Model effects. They have to understand the sensitivity of the measuring apparatus sufficiently well to know what they can rule out.

To be sure of their result, experimenters have to be able to distinguish those events that can signal new physics from the
background
events that arise from the known physical particles of the Standard Model. This is one reason we need many collisions to make new discoveries. The presence of lots of collisions ensures enough events representing new physics to distinguish them from “boring” Standard Model processes they might resemble.

Experiments therefore require adequate statistics. Measurements themselves have some intrinsic uncertainties necessitating their repetition. Quantum mechanics tells us that the underlying events do too. Quantum mechanics implies that no matter how cleverly we design our technology, we can compute only the probability that interactions occur. This uncertainty exists, no matter how we make a measurement. That means that the only way to accurately measure the strength of an interaction is to repeat the measurement many times. Sometimes this uncertainty is smaller than measurement uncertainty and too small to matter. But sometimes we need to take it into account.

Quantum mechanical uncertainty tells us, for example, that the mass of a particle that decays is an intrinsically uncertain quantity. The principle tells us that no energy measurement can possibly be exact when a measurement takes a finite time. The time of the measurement will necessarily be shorter than the lifetime of the decaying particle, which sets the amount of variation expected for the measured masses. So if experimenters were to find evidence of a new particle by finding the particles it decayed into, measuring its mass would require that they repeat the measurement many times. Even though no single measurement would be exact, the average of all the measurements would nonetheless converge to the correct value.

In many cases, the quantum mechanical mass uncertainty is less than the systematic uncertainties (intrinsic error) of the measuring devices. When that is true, experimenters can ignore the quantum mechanical uncertainty in mass. Even so, a large number of measurements are required to ensure the precision of a measurement due to the probabilistic nature of the interactions involved. As was the case with drug testing, large statistics help get us to the right answer.

It’s important to recognize that the probabilities associated with quantum mechanics are not completely random. Probabilities can be calculated from well-defined laws. We’ll see this in Chapter 14 in which we discuss the
W
boson mass. We know the overall shape of the curve describing the likelihood that this particle with a given mass and a given lifetime will emerge from a collision. Each energy measurement centers around the correct value, and the distribution is consistent with the lifetime and the uncertainty principle. Even though no single measurement suffices to determine the mass, many measurements do. A definite procedure tells us how to deduce the mass from the average value of these repeated measurements. Sufficiently many measurements ensure that the experimenters determine the correct mass within a certain level of precision and accuracy.

MEASUREMENTS AND THE LHC

Neither the use of probability to present scientific results nor the probabilities intrinsic to quantum mechanics imply that we don’t know anything. In fact, it is often quite the opposite. We know quite a lot. For example, the
magnetic moment of the electron
is an intrinsic property of an electron that we can calculate extremely accurately using
quantum field theory,
which combines together quantum mechanics and special relativity and is the tool used to study the physical properties of elementary particles. My Harvard colleague Gerald Gabrielse has measured the magnetic moment of the electron with 13 digits of accuracy and precision, and it agrees with the prediction at nearly this level. Uncertainty enters only at the level of less than one in a trillion and makes the magnetic moment of the electron the constant of nature with the most accurate agreement between theoretical prediction and measurement.

No one outside of physics can make such an accurate prediction about the world. But most people with such a precise number would say they definitely know the theory and the phenomena it predicts. Scientists, while able to make much more accurate statements than most anyone else, nonetheless acknowledge that measurements and observations, no matter how precise, still leave room for as-yet-unseen phenomena and new ideas.

But they can also state a definite limit to the size of those new phenomena. New hypotheses could change predictions, but only at the level of the present measurement uncertainty or less. Sometimes the predicted new effects are so small that we have no hope of ever encountering them in the lifetime of the universe—in which case even scientists might make a definite statement such as “that won’t ever happen.”

Clearly Gabrielse’s measurement shows that quantum field theory is correct to a very high degree of precision. Even so, we can’t confidently state that quantum field theory or particle physics or the Standard Model is all that exists. As explained in Chapter 1, new phenomena whose effects appear only at different energy scales or when we make even more precise measurements can underlie what we see. Because we haven’t yet experimentally studied those regimes of distance and energy, we don’t yet know.

LHC experiments occur at higher energies than we have ever studied before and therefore open up new possibilities in the form of new particles or interactions that the experiments search for directly, rather than through only indirect effects that can be identified only with extremely precise measurements. In all likelihood, LHC measurements won’t reach sufficiently high energy to see deviations from quantum field theory. But they could conceivably reveal other phenomena that would predict deviations to Standard Model predictions for measurements at the level of current precision—even the well-measured magnetic moment of the electron.

For any given model of physics beyond the Standard Model, any predicted small discrepancies—where the inner workings of an as-yet-unseen theory would make a visible difference—would be a big clue as to the underlying nature of reality. The absence of such discrepancies so far tells us the level of precision or how high an energy we need to find something new—even without knowing the precise nature of potential new phenomena.

The real lesson of effective theories, introduced in the opening chapter, is that we only fully understand what we are studying and its limitations at the point where we see them fail. Effective theories that incorporate existing constraints not only categorize our ideas at a given scale, but they also provide systematic methods for determining how big new effects can be at any specific energy.

Measurements concerning the electromagnetic and weak forces agree with Standard Model predictions at the level of 0.1 percent. Particle collision rates, masses, decay rates, and other properties agree with their predicted values at this level of precision and accuracy. The Standard Model therefore leaves room for new discoveries, and new physical theories can yield deviations, but they must be small enough to have eluded detection up to now. The effects of any new phenomena or underlying theory must have been too small to have been seen already—either because the interactions themselves are small or because the effects are associated with particles too heavy to be produced at the energies already probed. Existing measurements tell us how high an energy we require to directly find new particles or new forces, which can’t cause bigger deviations to measurements than current uncertainties allow. They also tell us how rare such new events have to be. By increasing measurement precision sufficiently, or doing an experiment under different physical conditions, experimenters search for deviations from a model that has so far described all experimental particle physics results.

Current experiments are based on the understanding that new ideas build upon a successful effective theory that applies at lower energies. Their goal is to unveil new matter or interactions, keeping in mind that physics builds knowledge scale by scale. By studying phenomena at the LHC’s higher energies, we hope to find and fully understand the theory that underlies what we have seen so far. Even before we measure new phenomena, LHC data will give us valuable and stringent constraints on what phenomena or theories beyond the Standard Model can exist. And—if our theoretical considerations are correct—new phenomena should eventually emerge at the higher energies the LHC now studies. Such discoveries would force us to extend or absorb the Standard Model into a more complete formulation. The more comprehensive model would apply with greater accuracy over a larger range of scales.