Warped Passages - Lisa Randall [99]
For similar reasons, a transformation that transformed only the gauge bosons that communicate a force, but not the particles that experience that force, could never preserve a symmetry. The internal symmetry that eliminates the spurious polarizations of the gluons requires the quarks to be interchangeable as well as the gluons. In fact, the symmetry transformation that interchanges quarks is the same one that interchanges the gauge bosons. The only way to preserve the symmetry is to mix up both together, just as the only way to preserve the Oreo cookie is to rotate the whole thing at the same time.
The force that will interest us most in this book is the weak force. The internal symmetry associated with the weak force treats the three weak gauge bosons as equivalent. It also treats particle pairs such as the electron and the neutrino, or the up and down quarks, as equivalent. This weak force symmetry transformation interchanges the three weak gauge bosons and also these pairs of particles. As with gluons and quarks, the symmetry is preserved only when everything is interchanged at once.16
What to Remember
Symmetries tell us when two different configurations behave the same way.
In particle physics, symmetries are useful as a way of forbidding certain interactions: those that don’t preserve the symmetries are not allowed.
Symmetries are important to the theory of forces because the simplest workable theory of forces includes a symmetry associated with each force. Those symmetries eliminate unwanted particles. They also eliminate the false predictions that the simplest theory of forces would otherwise make about high-energy particles.
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The Origin of Elementary Particle Masses: Spontaneous Symmetry Breaking and the Higgs Mechanism
One of these mornings the chain is gonna break.
Aretha Franklin
The stricter enforcement of speed limits made long-distance driving a nightmare for Icarus III. He longed to race as fast as he pleased, but police pulled him over nearly every half-mile. The cops never bothered with dull, neutral cars, but harassed only the lively, turbo-charged vehicles, like his own.
Ike resigned himself to driving only short distances, since that way he could avoid the police altogether. Within the half-mile-wide region around where he started, police never interfered and he could always drive impressively fast. Though the Porsche engine’s force was unknown outside his neighborhood, closer to home it became legendary.
Symmetries are important, but the universe usually doesn’t manifest perfect symmetry. Slightly imperfect symmetries are what makes the world interesting (but organized). For me, one of the most intriguing aspects of physics research is the quest for connections that make symmetry meaningful in an unsymmetric world.
When a symmetry is not exact, physicists say the symmetry is broken. Although broken symmetry is often interesting, it isn’t always aesthetically appealing: the beauty and economy of the underlying system or theory can be lost (or lessened). Even the very symmetric Taj Mahal doesn’t have perfect symmetry, since the builder’s parsimonious heir decided not to build a planned second monument, adding instead an off-center tomb to the original. This second tomb destroys the Taj Mahal’s otherwise perfect fourfold rotational symmetry, detracting slightly from its underlying beauty.
But fortunately for aesthetically minded physicists, broken symmetries can be even more beautiful and interesting than things that are perfectly symmetrical. Perfect symmetry is often boring. The Mona Lisa with a symmetric smile just wouldn’t be the same.
In physics,