Tuesday, February 01, 2005

Chewing on S and ICs

Finished "Cosmic Inflation and the Arrow of Time", (Albrecht, 2003). He's at Davis, I wonder if Sara knows him.
I am still struggling with the origins and meaning of a common statement in "time" cosmology,
"The origin of the Second Law is traced back to initial conditions: the early universe had an extremely low entropy, allowing it to continue to increase thereafter." (Carroll et. al. 2004)

After lots of reading I still fail to see how this "ultimate initial condition" is elevated to explanans for the monotomic increasing state function that is the entropy, as if the initial condition causes the law. I think that maybe there is a subtle confusion of wording here, or at least reading. We observe that any system with an arrow of time must begin in an "abnormal" state, that is, of lower entropy than the state which we consider to be macro-equilibrium. Ok, so what they really mean is that we need the right ICs.
I am thinking about what the measurement of entropy entails, what kind of information we need to get a number for "S". We need to know not only the state of the system, but also all the other available micro-states, or rather what the system can do. In the case of the gas in the box, this is equivalent to knowing the equilibrium macro-state. Only most consider the chance that the Universe is finite and bounded unlikely. So to treat the question of entropy we have to understand both limits of evolution of the system. This appears to be an open and contentious question. Albrecht lists ten theories of initial conditions; theories of available states (or t->inf evolution) are even more plentiful.
I think I will take this time to hand out the award for most readable paper in the past 5 or so to Andreas Albrecht. His examples were simple and insightful. His definition of the thermodynamic arrow is clear and well illustrated. I finally understand the inner workings of inflation and the definition of a deSitter space. Now when someone says "slow roll" I have a picture to think about.
New things I need to understand.
  • the anthropic principle (has something to do with number of parameters in a theory)
  • potential dominance (how does the inflaton field couple to matter?)
  • emergent things (what does it mean?
Leftovers from Price
  • No Boundary Condition (wavefunction of the universe)
  • Weyl curvature
  • how can one use the word "obtain"? eg "Notice here that there are two possible models of the connections that might obtain between the products of two low entropy boundary condtions..."
  • Cf. (Does it mean, "refer to"?)
  • bilking argument
  • pre-emption

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