Relativity Lite

78 | Relativity Lite pr esent time 7 billion year s ago near the time of the big bang 1 million light year s between galax ies near infinite density of galax ies an infinite number of galax ies to the r ight t Figure 5. Even in the case of a universe that always was of infinite size, one can see an infinitely dense early universe by projecting present galactic density backward in time. For the k = 0 or k = −1 cases, we can again ask, “What is the universe expanding into?” Well, for these cases time is not synonymous with the radius of a sphere. In figure 5, time points straight up and the galaxies are moving rightward. So the expansion is not into the future, nor does the universe create the universe it is expanding into. We can say, “The uni- verse was already infinite at the start so there is plenty of universe for the universe to expand into, is there not?” This is best explicated by part of a story of two travelers checking into a hotel, modeled on David Hilbert’s ideas of infinity: “We’re completely full, sir. Not even a dog kennel to spare. In fact, the dog seems to have double-­ booked his kennel to a pack of huskies.” Smith gestured at their huge pile of luggage. “Well, we’re not equipped for camping on the beach. We’ve got to stay somewhere!” The receptionist nodded in sympathy. “Mmm, . . . I’ve got an idea, sir. But it will mean a bit of disruption . . . Let me check with the Manager.” She hurried off. About ten minutes later she returned, smiling broadly. “You’re in luck, Room 1 has just become vacant.” “Brilliant.” A thought occurred to Smith. “Where are they going, then? You said the airport’s closed.” “Into Room 2.” “But Room 2 is occupied.” “No, they’re moving into Room 3.”