ethan@utastro.UUCP (05/24/84)
[Herewith the bugkiller] This is my last article before I leave (promise!). Alan Silverstein writes: >1: Whether the universe expanded from a point or from a small area, it > had sufficent energy density to warp space around itself at some > point in time, right? E.g. the whole universe is inside a black > hole, at least from the point of view of the people inside, right? > So, what is this talk about the universe being open if the current > total mass is lower than some magic value? Did the hole open up? The mass density of the universe is sufficient to cause significant curvature over the size of the observed universe. However this is not the same as being inside a black hole. The topology is different. Not all curvatures are equal. In particular, the expansion of the universe means that the time direction has significant curvature associated with it. For a a longer explanation see N. Sharp's article in net.astro.expert. >2: How can the horizon distance ever be larger than the size of the > universe? No matter how fast it expanded, even 10^50 in a short > time as the article suggests, matter can't go faster than > lightspeed. Hence we should be able to see all the way to the other > end of the universe if it came from a single point, right? First of all, the fact that nothing can go faster than light is a local limitation on motion. That is to say that nothing can rip by me at faster than the speed of light. The distance between two points *can* expand at rate such that change in distance/time interval >> speed of light. Consider three observers, two moving in opposite directions at very fast (close to speed of light) velocities and one who is stationary. Each carries a clock and communicates with the other two. They have agreed to set up a coordinate system defined by an expanding spatial coordinate set (such that each of them is stationary in these coordinates) and use their clocks to define the local time. The person in the center says: "If I used my definitions of time and distance everywhere I would see my friends living at a slower pace (time is slowed down from mine) and each is receding from me at the speed of light in either direction. However, I can't say this without violating our agreement to consider local measurements of distance definitive. I am constrained to measure the difference of distance between us according to some smooth mapping from my definition of an inch to my friend's definition. This makes the distance between us longer than if we used my definitions throughout. Moreover, "simultaneity" is defined as when our clocks read the same time. Since either of my friend's clock is slow (in my coordinate system) this implies that I must bend my definition of time so that "simulataneous" things are things that happen later to them (according to my naive coordinates) than to me. The total effect is that our compromise coordinate system has them moving away from me at faster than the speed of light." A similar monologue could be carried on by either of the other two observers. Now, if space is flat (like a critically bound model universe) then there is a global coordinate system in which nobody is moving "faster than light" i.e. there are no two points whose increase in spatial separation per unit time is greater than the speed of light. If space is curved then all bets are off. No such global coordinate system need exist. Ultimately the problem is that velocity is a local measurement (whose value depends on your choice of coordinates) and the "speed" of a cosmologically distant object is a nonlocal quantity (whose value also depends on your choice of coordinates) whose possible values are not limited in the same way as a local velocity. One final point, as long as the universe has an equation of state such that the average pressure is positive (in fact greater than minus one third the energy density) the universe was *never* pointlike in the sense that all places in the universe could communicate with all other places. The observed homogeneity of the universe is a complete mystery in such a model. This is why models of the *very* early universe with large negative pressures are so popular. "Cute signoffs are for Ethan Vishniac perverts" {charm,ut-sally,ut-ngp,noao}!utastro!ethan Department of Astronomy University of Texas Austin, Texas 78712