From Eternity to Here

by Sean Carroll

For comparison’s sake, the entropy of a macroscopic object like a cup of coffee is about 1025. That’s related to Avogadro’s Number, 6.02 • 1023, which is approximately the number of atoms in a gram of hydrogen. The number of grains of sand in all the Earth’s beaches is about 1020. The number of stars in a typical galaxy is about 1011, and the number of galaxies in the observable universe is also about 1011, so the number of stars in the observable universe is about 1022—a bit larger than the number of grains of sand on Earth. The basic units that physicists use are time, length, and mass, or combinations thereof. The shortest interesting time is the Planck time, about 10—43 seconds. Inflation is conjectured to have lasted for about 10—30 seconds or less, although that number is extremely uncertain. The universe created helium out of protons and neutrons about 100 seconds after the Big Bang, and it became transparent at the time of recombination, 380,000 years (1013 seconds) after that. (One year is about 3 • 107 seconds.) The observable universe now is 14 billion years old, about 4 • 1017 seconds. In another 10100 years or so, all the black holes will have mostly evaporated away, leaving a cold and empty universe. The shortest length is the Planck length, about 10—33 centimeters. The size of a proton is about 10—13 centimeters, and the size of a human being is about 102 centimeters. (That’s a pretty short human being, but we’re only being very rough here.) The distance fro...