On Sun, Oct 18, 2020, 10:33 PM Bruce Kellett <[email protected]> wrote:
> 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. > This is plainly false. Every 1 mile distance that particle is placed along the line encodes a unique number. Travel up to 2^N miles and you can encode N bits. With infinite range there's no upper bound. Or think of a grid of naughts and crosses, with a larger grid but fixed number of crosses, the number of possible combinations for drawing a fixed number of crosses still increases with more spaces to place them. > An arbitrary volume can only hold a limited amount of energy, or entropy, > as given by the Bekenstein bound. > Energy isn't the same thing as entropy. But the maximum entropy for a particular mass is given when that mass forms > a black hole -- which saturates the Bekenstein bound. > The bound is always satisfied. Black holes just reach the maximum of the bound at a given VOLUME. Increasing the volume does not increase the actual entropy unless you > simultaneously increase the mass. > You keep saying this but don't provide any justification or sources. I implore you to read the wikipedia article and if it is wrong, please point me to a source with the right/corrected equation. As explained on that page, the bound is not limited to black holes, it says something more general which relates entropy bounds to the product of spherical radius and mass. Jason 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 > <https://groups.google.com/d/msgid/everything-list/CAFxXSLSEGvVqnunZd%2BJAEirj3QKiwGO91NBXe6SCgqzsBpC7xg%40mail.gmail.com?utm_medium=email&utm_source=footer> > . > -- 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/CA%2BBCJUj36y0sHEpnRWTCXgse-90f6KaXgMJrpsjx3Ks0ZnVj2A%40mail.gmail.com.
