On Sat, Jan 30, 2021 at 11:20 AM smitra <smi...@zonnet.nl> wrote: > On 30-01-2021 00:37, Bruce Kellett wrote: > > > > 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 > > > > This argument is wrong for two reasons. First, your definition of > irreversibility is wrong, it has nothing to do with the practical > impossibility to reverse the evolution of the state. Time evolution is > said to be reversible if two different initial state will evolve to two > different final state, which is true for unitary time evolution. >
You are making exactly the same mistake as was made earlier with Deutsch's definition of 'world'. You are using a technical definition that does not always relate to the usual meaning of the term. 'Reversible' means that the situation can be reversed. In this context, it means that coherence can be restored. If you want to mean something different, then you should use a different term, and your objection collapses. The second mistake that leads to the wrong conclusion that a pure state > evolves to a mixed state is that this requires entanglement with an > infinite number of physical degrees of freedom when, precisely due to > locality (finite c), only a finite number of degrees of freedom get > entangled at any given time. > This is technically incorrect. There is no requirement for an infinite number of degrees of freedom. Escape of just one IR photon to outer space is sufficient to destroy reversibility. Then, in order to reflect this irreversibility, the off-diagonal elements of the density matrix should be exactly zero (reducing the pure state to a mixture). Unitary evolution cannot give this, so unitary evolution, by itself, is unable to capture that whole reality about the physical state. What this shows is that the notion of a World is only approximate, and > therefore cannot play any role in defining what observation is, because > we obviously do observe things and that must then have a mathematically > exact formulation, not an approximate one, no matter how accurate that > approximation is. > The definition of 'world' in the context of QM is made exact precisely because of this irreversibility. Worlds are well-defined and distinct precisely because they can no longer interact or recohere. The laws of physics ensure this. A definition of observation should involve defining the algorithm that > defines the observer and the content of the observation in terms of the > relevant local physical degrees of freedom. Bullshit. You make arbitrary appeals to algorithms that do not exist. Besides, nothing that I have said is unique to the process of conscious observation. It is true for any interaction whatsoever in the quantum domain. There is no need to define a > "World" which is a meaningless concept, observer's are in principle only > aware of their own physical state. And that physical state is part of a unique world. The word 'world' is useful, and has clear operational content. That state can contain information > about the environment, but what matters is not the environment but the > computational state of the algorithm that defines the observer. Forget algorithms. We are talking about physics, here, not computationalism. This can be done rigorously in the MWI by invoking entanglement to get to > correlations between slightly different inputs and outputs of the > algorithm such that the spread in the inputs and outputs is below the > resolution the observer can detect. > So what? 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/CAFxXSLTFox5YzOQoz0C4RzFiUogx-LeOtSRTaKDK%3DQ3W%3Dtjr3A%40mail.gmail.com.
