On Monday, September 16, 2019 at 1:23:09 AM UTC-6, Russell Standish wrote: > > On Sat, Sep 14, 2019 at 10:13:27PM -0700, 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 > > > > > > When I was an undergraduate I took a course in Classical Thermodynamics > and > > recall being satisfied that entropy was well-defined. I never took a > course in > > Classical Statistical Mechanics, but I've seen Boltzmann's equation for > S and > > wonder how N, the number of possible states is defined. If we have a gas > > enclosed in a container, we can divide it into occupation cells of fixed > volume > > to calcuate S. But why can't we double the number of cells by reducing > their > > volume by half? How then is S well defined in the case of Classical > Statistical > > Mechanics? TIA, AG > > It actually isn't. The point bothered me too. The number of states is > basically V/h, where V is the volume of phase space occupied by the > system, and h a cell size. Therefore, entropy is > > klog V - klog h > > For a large range of values of h, the second term is just a negligible > constant offset to the total entropy. However, as h→0, entropy blows > up. And that what classical statistical mechanics tells you. >
How could the second term be negligible for large values of h? AG > > Enter quantum mechanics. Heisenberg's uncertainty relation tells us > that ΔxΔp ≥ ℏ, so in the above entropy formula, h is constrained to be > larger than ℏ³. Quantum mechanics saves classical statistical physics' > bacon. Nothing blows up. > > -- > > ---------------------------------------------------------------------------- > > Dr Russell Standish Phone 0425 253119 (mobile) > Principal, High Performance Coders > Visiting Senior Research Fellow [email protected] > <javascript:> > Economics, Kingston University http://www.hpcoders.com.au > ---------------------------------------------------------------------------- > > -- 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/0a314df1-ffa8-4369-8045-e395c2e8d8db%40googlegroups.com.
