Relativity Lite

Cosmology | 81 ears and live for a short enough time, within the uncertainty principle, that they do not ultimately violate energy conversation. Dutch physicist Hendrik Casimir * predicted in 1948 that if one were to put two un- charged metal plates close enough together, the larger varieties of virtual particle pairs that can spring into being outside the plates, compared to those that can in between them, will tend to push the plates together. This prediction was confirmed in 1997 by S. K. Lam- oreaux. † The vacuum is, thus, not empty at all; it has energy. SYMMETRY BREAKING In 1918, a German mathematician named Emmy Noether discovered and published what is the most profound theorem on symmetry to date. She gave us a relation between symmetries and conservation laws. A spinning ice skater who pulls her arms in speeds up. Why is this? She has angular momentum as she spins, which is a product of her mass, the speed of her spin, and the distance of her mass from the spin axis. As she pulls her arms in, the distance of part of her mass from the spin axis decreases, and the only thing one may balance this change with to keep her angular momentum constant is to speed her up. But there is a deeper why to this. Noether showed that angular momentum conservation is a consequence of the symmetry (angular uniformity) of the space surrounding the skater. She showed that if you turn through an infinitesimal angle, the difference of kinetic and po- tential energies—which is called the Lagrangian —is unchanged. By adding up a bunch of zero changes for a bunch of these tiny angles, she showed that the Lagrangian is unaffected by any rotation of the entire system in a uniform space. If, on the other hand, an ice skater spinning to face a more northerly direction encountered a space that somehow made her more sluggish than spinning to face a more southerly direction, the Lagrangian would not be symmetrical and her angular momentum would not be conserved. Linear momentum conservation is a consequence of the uniformity of space before you (ignoring trees and rocks and such), and energy conservation is a consequence of the uni- formity of the flow of time. High energy physicists have applied Noether’s theorem to every Lagrangian they can find a symmetry for, many of which have nothing to do with space or time. What does this mean for the Higgs field? Consider again figure 6 of chapter 4, which modeled the transformation of potential energy into kinetic energy. We can also think of that figure as portraying a more abstract concept, symmetry. A marble rolling in the bowl has no preference for the left rim or the right; it just rolls back and forth. Likewise, an iron magnet that is heated above the Curie temperature, ‡ 770° C, loses its magnetization; the * H. B. G. Casimir, Proc. K. Ned. Akad. Wet. 51 , 793 (1948). † S. K. Lamoreaux, Phys. Rev. Lett. 78 , 5 (1997). ‡ Named after Marie Curie’s husband, Pierre.