Bob Walance said:
Jacob Bekenstein asserts that the entropy of a black hole is proportional to its area rather than its volume. Wow.
Yup. This is accurate. The basic physical reasoning is that the area of its horizon is the only physical geometry-related quantity that a black hole can actually have. Its volume doesn't work because there's no way to measure it: the singularity at its center prevents this.
Chronos said:
A finite universe is a non-starter for me. Ir creates bigger problems that any it may resolve. Embedding our universe in an endless collage of multiverses smacks of 'turtles all the way down'.
I don't think that's a coherent argument. Heck, the argument works even if you don't like the many worlds interpretation.
The finite universe is ideal for a number of reasons, most particularly that it offers a neat solution to the measure problem which makes it otherwise basically impossible to compute probabilities in an expanding, infinite universe. One way to understand why it is such a neat solution to the problem is this:
If you assume that our universe has a non-zero cosmological constant, then it has a cosmological horizon. There are a finite (though very, very large) possible number of degrees of freedom within that horizon. If you imagined moving far away, to another location within the universe, that location would have the same cosmological horizon, with the same exact possible number of degrees of freedom.
Furthermore, in quantum theory, if we have a physical process which allows the universe to explore all of those degrees of freedom, then that means that the physical system inside one quantum horizon will necessarily describe
every possible configuration of the universe within that horizon. Since every region has the same possible configurations, they all describe the same possible configurations, such that adding a second region has added no new configuration states that haven't already been considered when examining the first.
What all of this means is that if you consider the volume inside one cosmological horizon using the many worlds interpretation, you have already considered the entire possible set of configurations of the entire universe. Adding nearby regions is superfluous.
And if you don't like the many worlds interpretation, it shouldn't be hard to see how this way of looking at the universe is absolutely identical to examining the universe as infinite with only one quantum state in any given volume, while counting each specific configuration once (that is, if any two volumes repeat, only one is counted). The states that are actually examined using this more classical interpretation are completely identical.
The construction described above, then, is going to be a valid way of examining the universe provided the following hold true:
1) The cosmological constant is a fundamental, positive, non-zero constant (note: this can be relaxed to the cosmological constant taking a finite number of positive values and the same basic result holds, though with larger numbers).
2) The laws of physics allow a complete exploration of the degrees of freedom available. This is equivalent to stating that the physical process which sets the initial conditions for the universe is homogeneous.
Nothing else is required. You don't need the many worlds interpretation at all: just consider the "single horizon" calculation to be a mathematical representation which provides a neat way of avoiding the double-counting of identical regions.
