On Mon, Oct 19, 2020 at 1:09 PM Jason Resch <[email protected]> wrote:
> On Sun, Oct 18, 2020, 8:47 PM Bruce Kellett <[email protected]> wrote: > >> >> Remember that entropy is basically related to the volume of phase space, >> not of ordinary space. And phase space relates to the number of particles >> (hence mass-energy). Spatial volume is essentially irrelevant for volumes >> greater than that of the corresponding black hole. >> > > No. Consider an infinite length. With a single atom you can encode > infinite information through placement of the atom along that length. This > is with finite mass energy, but unrestricted spatial volume. > That does not encode infinite information. There is, after all, only one particle, and it can have only one position. If you want to encode more information, you need more particles. You might need an infinite number of bits to encode the position of one particle as a real number, but the single particle cannot encode this. An arbitrary volume can only hold a limited amount of energy, or entropy, as given by the Bekenstein bound. But the maximum entropy for a particular mass is given when that mass forms a black hole -- which saturates the Bekenstein bound. Increasing the volume does not increase the actual entropy unless you simultaneously increase the mass. In terms of the cosmological problem, the initial state has a particular total mass, and that does not increase with the expansion of the universe. Consequently, the maximum possible entropy does not increase either. The point of the Past Hypothesis is that the initial state of this mass was of low entropy since the gravitational degrees of freedom were not saturated (it did not form a black hole), so there is a large amount of room available for the entropy to increase. Bruce -- 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/CAFxXSLSEGvVqnunZd%2BJAEirj3QKiwGO91NBXe6SCgqzsBpC7xg%40mail.gmail.com.
