On Sun, Oct 18, 2020, 8:47 PM Bruce Kellett <[email protected]> wrote:
> 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. > I agree that black hole density is the largest possible mass for a given volume. However, I disagree with that characterization of the Bekenstein bound. The Bekenstein bound isn't about what volume a black hole of given mass will have; that was known well before Bekenstein. 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. > You must be thinking of something else. That maximum is reached when the mass forms a black hole of the given > radius. > True, but this isn't what the Bekenstein bound is. > 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. Jason > 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 > <https://groups.google.com/d/msgid/everything-list/CAFxXSLTx9q3HH7gppJkNTRhgA_1bSJ591rFYS4kirK4oZxrPxg%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%2BBCJUgFKW_OB2g0f%3DvuRH%2BhLu%2BErg1coHdS77EAY4y4x9vhoQ%40mail.gmail.com.
