Knocking on Heaven's Door - Lisa Randall [106]
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