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: On 5/8/2022 3:42 PM, Bruce Kellett wrote:On Mon, May 9, 2022 at 6:37 AM smitra <[email protected]> wrote: On 08-05-2022 05:58, Bruce Kellett wrote: > It is when you take the SE to imply that all possible outcomes exist > on each trial. That gives all outcomes equal status. All outcomes can exist without these being equally likely. One can make models based on more branches for certain outcomes, but these are just models that may not be correct. Such models are certainly inconsistent with the SE. So if your concern is that the SE does not contain provision for a collapse, then you should doubt other theories that violate the SE. You can't have it both ways: you can't reject collapse models because they violate the SE and then embrace other models that also violate the SE. Either the SE is universally correct, or it is not. What matters is that such models can be formulated in a mathematically consistent way, which demonstrates that there is n o contradiction. The physical plausibility of such models is another issue. This has been discussed. To allow for real number probabilities, the number of branches on each split must be infinite.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.
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