On Mon, May 9, 2022 at 12:47 PM Brent Meeker <[email protected]> wrote:
> On 5/8/2022 5:39 PM, Bruce Kellett wrote: > > On Mon, May 9, 2022 at 10:32 AM Brent Meeker <[email protected]> > wrote: > >> On 5/8/2022 5:25 PM, Bruce Kellett wrote: >> >> On Mon, May 9, 2022 at 10:17 AM Brent Meeker <[email protected]> >> 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 [email protected]. To view this discussion on the web visit https://groups.google.com/d/msgid/everything-list/CAFxXSLQmhv_PUROcK6_daPqQf%2BjPbrzqLkisf7sgnm7EjRWPHw%40mail.gmail.com.
