On Mon, Oct 19, 2020 at 12:07 PM Jason Resch <[email protected]> wrote:
> On Sun, Oct 18, 2020, 7:31 PM Bruce Kellett <[email protected]> wrote: > >> On Mon, Oct 19, 2020 at 11:21 AM Jason Resch <[email protected]> >> wrote: >> >>> On Sun, Oct 18, 2020, 6:53 PM Bruce Kellett <[email protected]> >>> wrote: >>> >>>> On Mon, Oct 19, 2020 at 3:33 AM Jason Resch <[email protected]> >>>> wrote: >>>> >>>>> >>>>> But according to the Bekenstein bound, the maximum possible entropy of >>>>> a system is bound by its mass/enegy AND its volume. Two particles by >>>>> themselves can encode an infinite amount of information if given infinite >>>>> space to place them. >>>>> >>>>> Wouldn't expanding the available volume for a system increase the >>>>> number of bit-combinations you can work with? >>>>> >>>> >>>> >>>> The maximum entropy state for a given mass-energy occurs when the >>>> entire system forms a black hole. Increasing the volume of space around >>>> this BH does not affect the entropy -- it is already at its maximum. The >>>> only way to increase this maximum is to increase the amount of mass-energy >>>> available -- and simply expanding the universe (available volume) does not >>>> do this! >>>> >>> >>> >>> I think it's the other way around, a black hole is the maximum entropy >>> for a given volume, not for a given mass-energy. At least that's what >>> Bernstein's equation implies: >>> >>> Entropy is bounded by (Radius * Energy * (a constant)) >>> >>> https://en.m.wikipedia.org/wiki/Bekenstein_bound >>> >> >> >> Nah. You have interpreted that wrongly. If you compress a given amount of >> mass-energy into a smaller and smaller volume, when the radius reaches the >> Schwarzschild radius, a black hole will form. This then represents the >> maximum entropy state for that fixed amount of mass energy. Do not forget >> that entropy works rather differently in GR. >> > > You're contradicting the equation. R can increase arbitrarily which > increases the bound arbitrarily high. > The Bekenstein bound states that the maximum mass-energy that can be held in any particular volume is given when that volume is a black hole. The only way to increase the radius of a BH is to increase its mass. If you take a fixed energy, you can fit this in any volume larger than that of the related BH. But the entropy is maximum for that mass-energy if it is in the form of a black hole. The Bekenstein bound merely limits the amount of mass-energy (hence >> entropy) in a given volume (or the minimum volume that a fixed amount of >> mass-energy can be squeezed into). The only way to increase that minimum >> volume is to increase the mass-energy. The volume of the surrounding space >> is irrelevant. >> > > The black hole entropy equation is different from the bernstein bound. The > black hole is an edge case of the equation, which in its most general form > relates volume and energy to a maximum entropy. > The Bekenstein bound simply refers to the maximum energy in any particular volume. That maximum is reached when the mass forms a black hole of the given radius. 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. 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/CAFxXSLTx9q3HH7gppJkNTRhgA_1bSJ591rFYS4kirK4oZxrPxg%40mail.gmail.com.
