On Fri, Jul 2, 2021 at 4:02 AM smitra <smi...@zonnet.nl> wrote: > On 01-07-2021 02:04, Bruce Kellett wrote: > > > > Worlds have to be carefully defined. According to decoherence theory > > (which is also a consequence of the linearity of the Schrodinger > > equation), decohered worlds are truly separate and do not recombine. > > Non-decohered elements of a superposition do not constitute separate > > worlds. > > > This definition only works when you replace the real physical world by > an approximation obtained by taking an appropriate infinite scaling > limit that allows decoherence to involve an infinite number of degrees > of freedom.
This is not true. You can have decoherence with the involvement of only a very small number of environmental degrees of freedom. The buckyball experiments show precisely this -- it only takes the escape of one or two IR photons of an appropriate wavelength to cause complete decoherence and the destruction of interference. You can do this by e.g. letting hbar tend to zero. While we > as macroscopic observers are in some sense close to this limit, the > world we actually live in only has a finite number of physical degrees > of freedom in a finite volume. And locality implies that in a finite > time after some experiment, only a finite volume can be physically > affected by the experiments, therefore the decoherence is in reality > nothing more than an entanglement with a finite number of environmental > degrees of freedom. > The important point to notice is that decoherence always involves the escape of IR photons at the speed of light. These are never recoverable, so the laws of physics ensure that the decoherence is, in general, irreversible. You have to take extreme care in very controlled settings to have things reversible. And if they are reversible, there can be no permanent environmental record of the result of the experiment, so one could reasonably say that no measurement has been made. The exact physical state of the system plus environment therefore does > not become a mixed state. The fact that one cannot demonstrate that the > state after measuring a superposition is still a superposition using an > interference experiment does not mean that it isn't a superposition. The > observer itself has become entangled with the measured system, which is > the real reason why the observer cannot even in principle detect the > superposition. No. The real reason is that decoherence, and the recording of a result, is irreversible. The practical obstacle that the massive entanglement > involves an astronomically large number of degrees of freedom is of > course also true, but this cannot be physically relevant. > Of course the irreversibility, even without involving a large number of degrees of freedom, is physically relevant. Whereas, the presumed persistence of the superposition in the mythical "universal wave function" is, indeed, physically irrelevant. So, if you measure the z-component of a spin polarized in the > x-direction and I'm not aware of the measurement result, then my mind > will not have been entangled with the measurement result (you can also > put me outside your light cone for argument's sake). That does not always work -- consider entanglement and Bell pairs. Locality is not always true. The spin entangled > with you and a large but finite number of degrees of freedom will > therefore be in a superposition. The fact that hidden variables don't > exist means that it cannot be the case that you have made a definite > observation that I'm unaware of. Of course that can be the case. It is the formation of a permanent record in the environment that is relevant to the existence of the measurement, whether you are aware of the result or not. You can be entangled with the spin-up state without being aware of it. But obviously if I ask what you've > measured I'll always get an answer that I can verify to be correct. So, > the only way out of this problem is to assume that these suppositions > after measurements exist as different worlds where different > experimental outcomes have been found. > That conclusion does not follow. > > > > Not really. You can accept the Schrodinger equation as fundamental > > without agreeing to MWI. The fact that you can't derive the Born rule > > from the Schrodinger equation in a non-circular fashion is quite > > telling. It means that the Schrodinger equation is more naturally seen > > as a way of calculating the time evolution of probabilities. QM is a > > probabilistic theory, so its fundamental laws give probabilities. And > > probabilities are not worlds. > > > > Bruce > > Probabilities only become rigorously defined after an infinite number of > measurements and cannot therefore be invoked to define real physical > quantities. I do not accept the frequentist definition of probability as the limit of an infinite number of trials. If probability is a primitive (as in the propensity interpretation), then frequencies can be used to estimate probabilities, but they do not serve to define them. The frequentist notion of probability is so problematic that it is not really accepted by anyone any more. Bruce The Born rule can at best only be an effective physical > quantity, like e.g. thermodynamic quantities like temperature and > entropy. They can only be rigorously defined for idealized systems where > strictly speaking unphysical mathematical limits must be taken. > > Saibal > -- 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/CAFxXSLR8J7oTYe5ns-NKMd1MJKB%3D%3D6y18UcpWNLU14G6UH4g_A%40mail.gmail.com.
