Warped Passages - Lisa Randall [109]
Through this indirect route, Athena was told Ike’s remark, “The influence of forces depends on where you are.” Ike’s uncharacteristic pronouncement completely mystified Athena until she realized that the message must have been distorted along the way. After thinking about it awhile, she decided that Ike’s real remark must have been, “The performance of Porsches depends on the model of car.”
We’ll see that the statement Athena originally heard is true. This chapter is about how physical processes that take place between particles at one separation can be related to those that take place at another separation and why physical quantities, such as a particle’s mass or interaction strength, depend on the particle’s energy. This dependence on energy and distance is over and above the classical separation dependence of forces. For example, classically, the strength of electromagnetism, like that of gravity, decreases in proportion to the square of the interacting objects’ separation (the inverse square law). But quantum mechanics changes this distance dependence by influencing the strength of the interaction itself so that particles at different separations (and energies) seem to interact with different charges.
Forces become weaker or stronger with increasing distance as a result of virtual particles—short-lived particles that exist as a consequence of quantum mechanics and the uncertainty principle. Virtual particles interact with gauge bosons and alter forces so that their effect depends on distance, much as Athena’s friends distorted Ike’s message as they passed it along.
Quantum field theory tells us how to compute the effect of virtual particles on the distance and energy dependence of forces. One triumph of such calculations was that they explained why the strong force is so strong. Another interesting fallout was the potential existence of a Grand Unified Theory, in which the three nongravitational forces, which are so different at low energies, merge into a single unified force at high energies. We’ll explore both of these results and the quantum field theory ideas and calculations that underlie them.
When you are reading the next few chapters, bear in mind the very disparate energy scales we are discussing. The unification energy is about one thousand trillion GeV, and the Planck scale energy, where gravity gets strong, is about a thousand times greater than that. The weak scale energy, which is the energy where experiments currently operate, is a whole lot smaller: it is only about a hundred to a thousand GeV. The weak scale energy is about as small relative to the unification energy as a marble’s size is compared with the distance between the Earth and the Sun. I’ll therefore sometimes call the weak scale energy low even though it’s a high energy from the perspective of experiments,* as it’s so much smaller than both the unification and the Planck scale energies.
Zooming In and Out
Effective field theories apply the effective theory idea that we learned about in Chapter 1 to quantum field theory. They focus only on those energy and length scales you can hope to measure. The effective field theory that applies at a particular energy or distance scale “effectively” describes those energies or distances we need to take into account. It concentrates on those forces and interactions that can occur when particles have that particular energy (or lower)* and ignores any energies that are inaccessibly higher. It doesn’t ask for the details of physical processes or particles that occur only with higher energy than you can achieve.
One advantage of an effective field theory is that even if you don’t know what interactions take place over short distances, you can still study the quantities that matter at the scales that interest you. You really need only to think about the quantities that you can