The Hidden Reality_ Parallel Universes and the Deep Laws of the Cosmos - Brian Greene [188]
You might still wonder about the barrier to building a device capable of measuring a particle’s position with ever greater precision. It too is a matter of energy. As in the text, if you want to measure a particle’s position with ever greater precision, you need to use an ever more refined probe. To determine whether a fly is in a room, you can turn on an ordinary, diffuse overhead light. To determine if an electron is in a cavity, you need to illuminate it with the sharp beam of a powerful laser. And to determine the electron’s position with ever greater accuracy you need to make that laser ever more powerful. Now, when an ever more powerful laser zaps an electron, it imparts an ever greater disturbance to its velocity. Thus, the bottom line is that precision in determining particles’ positions comes at the cost of huge changes in the particles’ velocities—and hence huge changes in particle energies. If there’s a limit to how much energy particles can have, as there always will be, there’s a limit to how finely their positions can be resolved.
Limited energy in a limited spatial domain thus gives finite resolution on both position and velocity measurements.
14. The most direct way to make this calculation is by invoking a result I will describe in nontechnical terms in Chapter 9: the entropy of a black hole—the logarithm of the number of distinct quantum states—is proportional to its surface area measured in square Planck units. A black hole that fills our cosmic horizon would have a radius of about 1028 centimeters, or roughly 1061 Planck lengths. Its entropy would therefore be about 10122 in square Planck units. Hence the total number of distinct states is roughly 10 raised to the power 10122, or 1010122.
15. You might be wondering why I’m not also incorporating fields. As we will see, particles and fields are complementary languages—a field can be described in terms of the particles of which it’s composed, much like an ocean wave can be described in terms of its constituent water molecules. The choice of using a particle or field language is largely one of convenience.
16. The distance that light can travel in a given time interval depends sensitively on the rate at which space expands. In later chapters we will encounter evidence that the rate of spatial expansion is accelerating. If so, there is a limit to how far light can travel through space, even if we wait an arbitrarily long time. Distant regions of space would be receding from us so quickly that light we emit could not reach them; similarly, light they emit could not reach us. This would mean that cosmic horizons—the portion of space with which we can exchange light signals—would not grow in size indefinitely. (For the mathematically inclined reader, the essential formulae are in Chapter 6, note 7.)
17. G. Ellis and G. Bundrit studied duplicate realms in an infinite classical universe; J. Garriga and A. the quantum context.
Chapter 3: Eternity and Infinity
1. One point of departure from the earlier work was Dicke’s perspective, which focused on the possibility of an oscillating universe that would repeatedly go through a series of cycles—big bang, expansion, contraction, big crunch, big bang again. In any given cycle there would be remnant radiation suffusing space.
2. It is worth noting that even though they don’t have jet engines, galaxies generally do exhibit some motion above and beyond that arising from the expansion of space—typically the result of large-scale intergalactic gravitational forces as well as the intrinsic motion of the swirling gas cloud from which stars in the galaxies formed. Such motion is called peculiar velocity and is generally small enough that it can be safely ignored for cosmological purposes.
3. The horizon problem is subtle, and my description of inflationary cosmology’s solution slightly nonstandard, so