The Hidden Reality_ Parallel Universes and the Deep Laws of the Cosmos - Brian Greene [192]
10. I will use the term “bubble universe,” although the imagery of a “pocket universe” that opens up within the ambient inflaton-filled environment is a good one too (that term was coined by Alan Guth).
11. For the mathematically inclined reader, a more precise description of the horizontal axis in Figure 3.5 is as follows: consider the two-dimensional sphere comprising the points in space at the time the cosmic microwave background photons began to stream freely. As with any two-sphere, a convenient set of coordinates on this locus are the angular coordinates from a spherical polar coordinate system. The temperature of the cosmic microwave background radiation can then be viewed as a function of these angular coordinates and, as such, can be decomposed in a Fourier series using as a basis the standard spherical harmonics, . The vertical axis in Figure 3.5 is related to the size of the coefficients for each mode in this expansion—farther to the right on the horizontal axis corresponds to smaller angular separation. For technical details, see for example Scott Dodelson’s excellent book Modern Cosmology (San Diego, Calif.: Academic Press, 2003).
12. A little more precisely, it is not the strength of the gravitational field, per se, that determines the slowing of time, but rather the strength of the gravitational potential. For instance, if you were to hang out inside a spherical cavity at the center of a massive star, you wouldn’t feel a gravitational force at all, but because you were deep inside a gravitational-potential well, time for you would run slower than time for someone far outside the star.
13. This result (and closely related ideas) was found by a number of researchers in different contexts, and was most explicitly articulated by Alexander Vilenkin and also by Sidney Coleman and Frank De Luccia.
14. In our discussion of the Quilted Multiverse, you may recall that we assumed particle arrangements would vary randomly from patch to patch. The connection between the Quilted and Inflationary Mulitverses also allows us to make good on that assumption. A bubble universe forms in a given region when the inflaton field’s value drops; as it does, the energy the inflaton contained is converted into particles. The precise arrangement of these particles at any moment is determined by the precise value of the inflaton during the conversion process. But because the inflaton field is subject to quantum jitters, as its value drops it will be subject to random variations—the same random variations that give rise to the pattern of slightly hotter and slightly colder spots in Figure 3.4. When considered across the patches in a bubble universe, these jitters thus imply that the inflaton’s value will display random quantum variations. And this randomness ensures randomness of the resulting particle distributions. That’s why we expect any particle arrangement, such as the one responsible for all we see right now, to be replicated as often as any other.
Chapter 4: Unifying Nature’s Laws
1. I thank Walter Isaacson for personal communications on this and a number of other historical issues related to Einstein.
2. In a little more detail, the insights of Glashow, Salam, and Weinberg suggested that the electromagnetic and weak forces were aspects of a combined electroweak force, a theory that was confirmed by accelerator experiments in the late 1970s and early 1980s. Glashow and Georgi went a step further and suggested that the electroweak and the strong forces were aspects of a yet more fundamental force, an approach that’s called grand unification. The simplest version of grand unification, however, was ruled out when scientists failed to observe one of its predictions—that protons should, every so often, decay. Nevertheless, there are many other versions of grand unification that remain experimentally viable since, for example,