Relativity Lite

Cosmology | 83 Note that the vacuum state of the bar magnet is generally in one of these trough posi- tions, such as to the right in figure 6, and not in the state of zero magnetization at the center of what has come to be a peak. But there is a slight chance that should the “ball” be at rest in the center of the high-temperature bowl shape as the temperature drops, it could stay at rest at this point that becomes the peak as the bowl slumps on either side of it, though the slight- est “breeze” or other perturbation would knock it off. We would say that the ball at rest on the peak would then be in a “false vacuum” state, because this is not the lowest-energy state of the system. The ball would be in an unstable position and the slightest disturbance would cause it to roll off the peak and down into the trough. BREAKING THE HIGGS SYMMETRY This discussion of symmetry breaking as temperature falls when the universe expands applies as well in the case of the Higgs fields, with two crucial twists in the story. As Guth first proposed it, the central peak that develops in figure 6 has a dimple in it that would allow the universe (the ball) to remain at that central position as the universe cools. (The models of Linde and of Albrecht and Steinhardt have a very broad plateau, instead of a dim- ple, that nevertheless lets the universe stay in the false vacuum state for a long time before it “rolls off.”) The consequences of this are profound. A photon is a bundle of energy whose energy is contained in oscillations in its electric and magnetic fields. If one were to put photons in a piston with reflective walls and pull the plunger outward, the energy per unit volume—the energy-density—would diminish as the oscillations spread out in the larger volume. The same argument holds for the quan- tum fields associated with material particles like electrons. These sorts of particles will shove outward on the plunger as they ricochet around inside the piston. They will exert pressure. Were you to have your hand on the piston, you would have to resist its movement outward, just as you need to hold down the lid of a popcorn popper as it is randomly knocked upward by exploding kernels. The latter analogy helps us understand what keeps a star from collapsing under its own weight: the balancing of gravity by the outward pressure of extremely hot gasses ricocheting off each other, as we discussed in the last chapter. But there is a subtlety in this balancing the inward gravitational force with the outward heat pressure if we move from the Newtonian idea of gravitational force to the Einsteinian warpage of spacetime. Just like mass and energy, pressure is a quantity that causes spacetime to warp downward into the time direction. That is, the pressure that keeps a star’s gasses from collapsing inward—from rolling down that funnel toward its center—also causes a deeper funnel that will cause gasses to more readily roll down that slope toward its center. This snake eating its tail in Einstein’s theory of gravity is what makes the equations so difficult to solve for specific problems. But given the right resources, one can show that there will