It's telling you snipped all my examples of encoding more information by using extra volume to get more combinations of positions.
Do you not have an answer for the 1 kg in 2 meters vs. 2 kg in 1 meter? Jason On Monday, October 19, 2020, Bruce Kellett <[email protected]> wrote: > On Tue, Oct 20, 2020 at 12:02 PM Jason Resch <[email protected]> wrote: > >> On Monday, October 19, 2020, Bruce Kellett <[email protected]> wrote: >> >>> >>> but the entropy at the bound increases only if the mass is also >>> increased. >>> >>> When you say "at the bound" you are talking about black holes, which is >> the point of maximum mass and maximum entropy for a given volume. >> > > > When you are far from the limit, as in most physical situations, the > entropy bound is largely irrelevant. That is why I keep talking about black > holes. It is only in that case, when the bound is saturated, that it is of > any physical relevance. Most of your examples refer to physical situations > that are far from saturating the bound. So in those case, talking about the > bound is otiose. > > > <snip> > > It's a generally accepted in computer science that a turing machine >>>> allowed to use infinite space could store infinite information, even with >>>> fixed total mass/energy. >>>> >>>> You do not have massless tapes on which to store your infinite >>> information. So this would appear to be nonsensical. A Turing machine in a >>> physical object, and it is subject to the laws of physics. >>> >> >> The tape can be empty space, while the information can be represented by >> placement of one particle in a definite location within that infinite space. >> > > > That does not make physical sense. How do you control the placement of > your particle? How do you read its position? How do you know that it hasn't > moved in the interim? Unless you have some physical way of fixing it in > place, it conveys no useful information. Hence the need for a tape -- and > you do not have access to massless tapes! > > > <snip> > > That specifies the volume within which the energy is enclosed. But >>> increasing the volume does not, of itself, increase the entropy. The >>> maximum entropy for a fixed mass-energy is fixed by the surface area of a >>> black hole of radius R = 2M. >>> >>> >> That's false. The maximum entropy is NOT fixed unless both the >> mass-energy AND the volume are fixed. >> > > What do you think R = 2M does? > > If the bound were as you say, determined solely by mass-energy, then R >> would not appear in the equation as it does. >> > > > At the limit, R is fixed by the mass. > > > > Putting a black hole in a bigger volume does not increase the entropy of >>> that black hole. Specifying coordinates for the constituents of the BH is >>> either irrelevant, or requires additional mass. >>> >> >> See my grid example. No additional mass is needed for the black hole to >> occupy a certain position in the grid. If the grid has is 10^10^100 cells, >> then the location of the hole provides at least 10^100 bits of information. >> This is more information/entropy than in even a galactic mass black hole. >> > > See my discussion of the infinite tape. Similar considerations apply here. > If you want to increase the entropy beyond what is given by the black hole, > you have to increase the mass in the larger volume. Placing the BH > arbitrarily in space does not increase the information, because it > cannot encode any information unless its location is fixed in some physical > manner. > > Bruce > > > The upshot of all of this is that the expansion of space in a >>> cosmology does not increase the maximum possible entropy. The maximum >>> entropy is set by the amount of mass-energy in the cosmology, and that does >>> not increase with the expansion. >>> >> -- > 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/CAFxXSLSnXJpUo-dn2yfeS85FwY2oOvwkc-_J% > 2BGQ7YCG6t15HcQ%40mail.gmail.com > <https://groups.google.com/d/msgid/everything-list/CAFxXSLSnXJpUo-dn2yfeS85FwY2oOvwkc-_J%2BGQ7YCG6t15HcQ%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%2BBCJUjmCWoKNAAD1CorW8OAv7_S1RpZJudkcxL5_dvHyf9GWQ%40mail.gmail.com.
