The Flatness Problem
When I was a first-year graduate student in astrophysics at Harvard University in 1958, I encountered two problems that have remained with me all these years. One I might have called the "equilibrium problem," although today it is the fundamental problem of information philosophy - What creates the information structures in the universe?" At Brown I had studied physics and especially the second law of thermodynamics. There I had read Arthur Stanley Eddington's wonderful 1927 book The Nature of the Physical World, his Gifford Lectures, and took away two ideas - that entropy had something to do with values, and that Werner Heisenberg's then new uncertainty principle had put a crack in the idea of determinism, through which he could see a "chink of daylight" in the problem of free will. I thought I would solve two related problems starting with Eddington's ideas - libertarian free will and the problem of values. In my philosophy classes at Brown I learned that continental existentialists thought that we are radically free, but that our freedom is absurd, because there are no objective values to help us make choices. Logical positivists had the very opposite idea. There are values, either utilitarianism or a consequence of our human emotions. But Anglo-American philosophy was solidly determinist, certain that laws of nature explained the workings of the universe and so clearly could explain the human mind. There was no free will for them. If freedom without values is absurd, I thought, values without freedom are useless. The problems need to be solved together. Back in astrophysics, I saw cosmology and the second law about the inevitable increase of entropy seemed to be in serious conflict. The best opinion about the beginning of the universe in 1958 was that it had started in a state of equilibrium about ten billion years ago. The "equilibrium problem" I saw at that time was this. "If the universe began in a state of equilibrium, and the second law says that entropy can only increase, why aren't we still in a state of equilibrium?" I asked anyone who might be interested, "How can we be here having this conversation?" At that time, the universe was thought to be positively curved. Hubble's red shifts of distant galaxies showed that they did not have enough kinetic energy to overcome the gravitational potential energy. Textbooks likened the universe to the surface of an expanding balloon decorated with galaxies moving away from one another. That balloon popped for me when Walter Baade came to Harvard to describe his wartime work at Mount Wilson. During the war, lights in California cities were blacked out and astronomical seeing was great. There was little competition for observing time, as most astronomers were doing defense work. As a German national, Baade was exempt. He took many images with long exposures of nearby galaxies and discovered there are two distinct populations of stars. And in each population there was a different kind of Cepheid variable star. The period of the Cepheid's curve of light variation indicated its absolute brightness, so they could be used as "standard candles" to find the distances to star clusters in the Milky Way. Baade then realized that the Cepheids being used to calculate the distance to Andromeda were 1.6 magnitudes brighter than the ones used in our galaxy. Baade said Andromeda must be twice as far away as Hubble had thought. As I listened to Baade, for me the universe went from being positively curved to negatively curved. It jumped right over the flat universe! I used to draw a line with tick marks for powers of ten in density around the critical density ρc. We could increase the density of the universe by thirty powers of ten before it would have the same density as the earth (too dense!). But on the lighter side, there are an infinite number of powers of ten. We can't exclude a universe with average density zero, which still allows us to exist, but little else in the distance. Couldn't we live happily in a universe with 10-35 grams per cubic centimeter, or even 10-40? I asked myself how likely is it that the universe is so close to flat that the observational error bars include the flat case? I started telling friends that if the universe is exactly flat, future observations alone could never resolve the question of positive versus negative curvature. We needed a theory of why the universe is exactly flat! In a Newtonian universe, the flat case is when the kinetic and potential energies exactly balance, when there is no net energy in the universe. The 1/r2 potential goes to zero at infinity, at which point/time (never reached) the asymptotic kinetic energy is zero. What I did see is that the universe might consist of equal and opposite amounts of something, such that before t = 0, it was nothing. This would neatly answer Leibniz' great philosophical question, "Why is there something rather than nothing?"Normal | Teacher | Scholar
The Flat Universe TodayThe standard model of cosmology now assumes that the universe is exactly flat, but that the amount of matter needed is not available in the form of the ordinary matter (baryons, electrons, photons, etc.) that makes up the visible (luminous) universe. The luminous matter can account for only a few percent of the critical density of matter needed for a flat universe. Another 25% or so of an unknown form of dark matter, plus 70% of a "dark energy," thought to be quantum vacuum energy, makes up the balance of the critical density. Information philosophy can contribute little to the standard model, but it can support an early universe with very little information (negative entropy). As long as the maximum possible entropy increases with the universe expansion, the cosmic creation process can provide the information (negative entropy) in the galaxies, stars, planets, terrestrial life, etc.