Johnathan Corgan wrote: > Brent Meeker wrote: > > >>>These questions may reduce to something like, "Is there a lower limit to >>>the amplitude of the SWE?" >>> >>>If measure is infinitely divisible, then is there any natural scale to >>>its absolute value? >> >>I think it is not and there is a lower limit below which cross terms in the >>density >>matrix must be strictly (not just FAPP) zero. The Planck scale provides a >>lower >>bound on fundamental physical values. So it makes sense to me that treating >>probability measures as a continuum is no more than a convenient >>approximation. But >>I have no idea how to make that precise and testable. > > > Having measure ultimately having a fixed lower limit would I think be > fatal to QTI. But, consider the following: > > At every successive moment our measure is decreasing, possibly by a very > large fraction, depending on how you count it. Every moment we branch > into only one of a huge number of possibilities. A "moment" here is on > the order a Planck time unit.
First, it may not be such a large factor. All nearby trajectories in configuration space constructively interfere to produce quasi-classical evolution in certain bases. So if we are essentially classical and I think we are (c.f. Tegmark's paper on the brain) then "we" are not decreasing in measure by MWI splitting on a Planckian or even millisecond time scale. The evolution of our world is mostly deterministic. Second, if there is a lower limit on the interference terms in the SE of the universe, then the density matrix gets diagonalized. Then the MWI goes away. QM is, as Omnes' says, a probabilistic theory and it predicts probabilities. Probabilities mean something happens and other things don't. So we don't risk vanishing. The fact that our probability seems to become vanishingly small is only a artifact of what we take as the domain of possibilities and it is no different than our improbability pre-QM. But undoubtedly there are mathematical difficulties with assuming a lower bound on probabilities. All our mathematics and theory has been built around continuous variables for the very good reason that it seems overwhelmingly difficult to do physics in discrete variables - just look at how messy numerical solution of partial differential equations is compared to the equations themselves. Brent Meeker --~--~---------~--~----~------------~-------~--~----~ You received this message because you are subscribed to the Google Groups "Everything List" group. To post to this group, send email to firstname.lastname@example.org To unsubscribe from this group, send email to [EMAIL PROTECTED] For more options, visit this group at http://groups.google.com/group/everything-list -~----------~----~----~----~------~----~------~--~---