I believe some models of physics require the universe to be infinite
These are dependent on certain assumptions, the most general of which is the fact that the laws of physics be the same everywhere (the universe is seen as “isotropic and homogeneous”). But those sort of principles arise from observation.
And we can never be entirely sure that they are true. Now, normally this doesn’t matter—the probability of them being false is so tiny that we can consider them true. But infinity is nasty. Let’s put an probability estimate on “There are more stars than X in the universe”, and let X grow. We expand the universe beyond the visible domain, beyond that where we have any information. And we have to assume that the universe remains “isotropic and homogeneous” beyond our ability to measure that it is so. The uncertainty in that will grow, and swamp our estimate.
More mathematically, I distribute a bayesian prior over all the finite and infinite universes that can exist. Unless we can somehow put a nice measure on this “space of possible universes”, then finite amounts of observations will always leave many radically different possibilities for the universe. More worryingly, the prior will determine our results for us; the estimate will not converge to comparable result for different priors (if the space of possible universes is sufficiently pathological, then it will not converge on comparable results even after infinitely many observations).
For this reason I feel that philosophical arguments that depend on infinite universes should be generally avoided. But if someone knows a way round this issue, I’d be pleased to hear it—I want my universe to be infinite. So much more elegant that way.
The idea that the universe is “isotropic and homogeneous” does not require it to be infinite. For example, the universe could be shaped like a sphere’s surface, which is closed and finite. The size and shape of the universe, and its ultimate fate, are answered by the question “What is the sum of the angles of a very large triangle?” (this turns out to be equivalent to measuring Omega, the density parameter of the universe).
If Omega > 1, then the universe is closed, shaped like a sphere, finite, and will collapse in a Big Crunch. If Omega = 1, then the universe is flat (but could still be finite, eg doughnut-shaped, or infinite, like the Cartesian plane), and end in heat death. If Omega < 1, then the universe is open, shaped like an infinite saddle, and will end in a Big Rip. To the best of our knowledge, Omega appears to be 1, plus or minus Omega might actually be bigger or smaller than 1.
I believe some models of physics require the universe to be infinite
These are dependent on certain assumptions, the most general of which is the fact that the laws of physics be the same everywhere (the universe is seen as “isotropic and homogeneous”). But those sort of principles arise from observation.
And we can never be entirely sure that they are true. Now, normally this doesn’t matter—the probability of them being false is so tiny that we can consider them true. But infinity is nasty. Let’s put an probability estimate on “There are more stars than X in the universe”, and let X grow. We expand the universe beyond the visible domain, beyond that where we have any information. And we have to assume that the universe remains “isotropic and homogeneous” beyond our ability to measure that it is so. The uncertainty in that will grow, and swamp our estimate.
More mathematically, I distribute a bayesian prior over all the finite and infinite universes that can exist. Unless we can somehow put a nice measure on this “space of possible universes”, then finite amounts of observations will always leave many radically different possibilities for the universe. More worryingly, the prior will determine our results for us; the estimate will not converge to comparable result for different priors (if the space of possible universes is sufficiently pathological, then it will not converge on comparable results even after infinitely many observations).
For this reason I feel that philosophical arguments that depend on infinite universes should be generally avoided. But if someone knows a way round this issue, I’d be pleased to hear it—I want my universe to be infinite. So much more elegant that way.
The idea that the universe is “isotropic and homogeneous” does not require it to be infinite. For example, the universe could be shaped like a sphere’s surface, which is closed and finite. The size and shape of the universe, and its ultimate fate, are answered by the question “What is the sum of the angles of a very large triangle?” (this turns out to be equivalent to measuring Omega, the density parameter of the universe).
If Omega > 1, then the universe is closed, shaped like a sphere, finite, and will collapse in a Big Crunch. If Omega = 1, then the universe is flat (but could still be finite, eg doughnut-shaped, or infinite, like the Cartesian plane), and end in heat death. If Omega < 1, then the universe is open, shaped like an infinite saddle, and will end in a Big Rip. To the best of our knowledge, Omega appears to be 1, plus or minus Omega might actually be bigger or smaller than 1.
Shape of the Universe
Fate of the Universe