Knocking on Heaven's Door - Lisa Randall [107]
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