On Mon, May 9, 2022 at 12:47 PM Brent Meeker <meekerbr...@gmail.com> wrote:
> On 5/8/2022 5:39 PM, Bruce Kellett wrote: > > On Mon, May 9, 2022 at 10:32 AM Brent Meeker <meekerbr...@gmail.com> > wrote: > >> On 5/8/2022 5:25 PM, Bruce Kellett wrote: >> >> On Mon, May 9, 2022 at 10:17 AM Brent Meeker <meekerbr...@gmail.com> >> wrote: >> >>> >>> I don't think that's a problem. The number of information bits within a >>> Hubble sphere is something like the area in Planck units, which already >>> implies the continuum is a just a convenient approximation. If the area is >>> N then something order 1/N would be the smallest non-zero probability. >>> Also there would be a cutoff for the off-diagonal terms of the density >>> matrix. Once all the off-diagonal terms are zero then it's like a mixed >>> matrix and one could say that one of the diagonal terms has "happened". >>> >> >> As I have pointed out before, a finite number of branches does not work >> because after a certain finite number of splits, one would run out of >> branches to partition in anything like the way appropriate for the related >> probabilities. One cannot go adding more branches at that stage without >> rendering the whole concept meaningless. Keeping things finite has its >> attractions, but it does not work in this case. >> >> >> I think it depends on how you count splits. If the number of dof within >> a Hubble volume is finite, then the number of splits doesn't grow >> exponentially. They get cut off when their probability becomes too small. >> > > You are back to your notion of a smallest possible probability. That also > runs into problems if you run a long sequence of events where one outcome > has a very small probability on each trial. Try tossing a coin N times. The > probability of a sequence of N heads is 1/N. What happens when this gets > smaller than the smallest allowed probability? Is the next toss somehow > forbidden to give head again? You are making the whole notion of > probability problematic. > > > Yes, I can see a concern. But my back-of-the envelope estimate is that > the Hubble volume has the information content of ~10^96 bits. So it would > very hard experimentally to flip enough coins to test that limit. However > it would imply that you couldn't create a pseudo-random number generator > that could produce random numbers with that many bits. That would raise > the question of how would you tell? The sequence of numbers of a good > pseudo-random number generator look random until you test high order > correlations. > I don't think that the limited number of bits of information in the Hubble volume is much of a concern. I suspect that if the number of branches is finite, and there is a limit to how small a probability can be, then everything must be discrete -- space and time along with everything else. Or else you get a Zeno effect with radioactive decay. For a long-lived isotope, the probability of decay in a small time interval can be made as small as you want by taking a small enough time interval. Whether this is measurable is not really the issue. If there is a lower limit on probability, then decays are probably impossible without discrete time and space as well. 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 everything-list+unsubscr...@googlegroups.com. To view this discussion on the web visit https://groups.google.com/d/msgid/everything-list/CAFxXSLQmhv_PUROcK6_daPqQf%2BjPbrzqLkisf7sgnm7EjRWPHw%40mail.gmail.com.
