On Sat, Jan 30, 2021 at 1:41 AM Bruno Marchal <marc...@ulb.ac.be> wrote:
> On 28 Jan 2021, at 06:58, Bruce Kellett <bhkellet...@gmail.com> wrote: > > > This is certainly a problem for Deutsch's interpretation of 'world'. > Because there are an infinite number of equivalent sets of basis vectors > available for every Hilbert space, it makes little sense to claim that an > observer is uncertain as to which basis he is in. He could choose any basis > whatsoever. But if he wants his choice to make sense in his lived life, he > would be wise to choose the basis that is singled out by decoherence as > stable against environmental degradation. In other words, he has to rely on > decoherence to solve the basis problem. Deutsch has no way of resolving the > preferred basis problem in his approach since, to him, all bases correspond > to equivalent 'worlds’. > > > That is why it is preferable to abandon the idea of “world” (an idea which > BTW belongs more to metaphysics than physics) and use the “relative state”, > or the “history” notions instead. > > Decoherence is irreversible from inside the multiverse for the same reason > that statistical physics is reversible, in Everett. The whole “universe” > remains “in principle” reversible, bit not from inside, unless amnesia and > ultra-sophisiticated technology (which doubtfully could ever exist). > It is difficult to give any sensible meaning to a statement like this. The idea behind the universality of unitary evolution in Everettian QM is that the initially pure state always remains pure. In an interaction with decoherence, the off-diagonal elements of the density matrix remain finite, albeit arbitrarily small. This means that there always remains a non-zero probability that the state will recohere. But this picture is, in fact, wrong. As has been pointed out, the irreversibility introduced by decoherence is actually an 'in principle' irreversibility, induced by the laws of physics, such as the speed of light being an upper limit on possible speeds, and the laws of thermodynamics limiting local decreases in entropy. Once decoherence entangles the results of any interaction with the wider thermal environment, it is not possible to avoid the loss of information to outer space via the emission of IR photons. This process is in principle irreversible, because these photons can never be captured and returned. What is more, decoherence is general and will always result in entanglement with the wider thermal environment. And this entanglement will generally happen very quickly -- in fractions of a second. So the loss of thermal photons is essentially instantaneous. Given this, the probability that the initial state will eventually recohere is exactly zero. If the density matrix is to reflect this physical reality, then the off-diagonal elements will have to be set to precisely zero, the pure state has to reduce to a mixture. This cannot happen by unitary evolution, true, so unitary evolution itself cannot reflect the whole of physical reality. The limit as the off-diagonal elements of the density matrix become small via decoherence, and approach zero, is a singular limit -- the progression from infinitesimal to zero is not continuous. The Schrodinger equation cannot capture this singular limit so it cannot capture the whole of the physical reality. The "collapse postulate" has a sound physical basis! Decoherence does, indeed, lead the initially pure state to become mixed. That is physically unavoidable. Claiming that the coherence is not lost to the "whole universe" is just an empty rhetorical flourish, with no operational content. 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/CAFxXSLRoXkdg3t3oJgrSr501q%3Dh_R5%3DRk2b%2B0DmuD2%3DN6W1neQ%40mail.gmail.com.
