On Saturday, September 14, 2019 at 10:07:28 AM UTC-5, Alan Grayson wrote: > > > > On Saturday, September 14, 2019 at 7:12:34 AM UTC-6, Alan Grayson wrote: >> >> If the early universe, say before the emergence of the CMBR, consisted of >> a random collection of electrons and photons, wouldn't this correspond to a >> *high*, not low entropy? Wouldn't it be analogous to gas with many >> possible states? Yet cosmologists seem hard pressed to explain an initial >> or early state assuming the entropy is low. AG >> > > Here's an easier question: when Boltzmann defined entropy as S = k * log > N, why the log; why not just k*N? AG >
Think of the case where you have binary strings of length n. How many possible binary string are there with that length? There are N = 2^n. The Boltzman log(N) is just the size of the macrostate, where there are 2^n possible microstates. This is where the entropy S = kn comes from, for the units of Planck area on the horizon count microstates. We have S = k ln(N) = k ln(2^n) = k n ln(2). With the black hole horizon or any horizon this linear chain is replaced by a two dimensional table or matrix. The same argument carries over. LC -- You received this message because you are subscribed to the Google Groups "Everything List" group. To unsubscribe from this group and stop receiving emails from it, send an email to [email protected]. To view this discussion on the web visit https://groups.google.com/d/msgid/everything-list/d15a4c00-0b00-46a8-81ab-37aecb901b9a%40googlegroups.com.
