On Sun, Aug 11, 2019 at 6:54 AM smitra <[email protected]> wrote: > On 10-08-2019 10:20, Bruce Kellett wrote: > > On Sat, Aug 10, 2019 at 6:16 PM smitra <[email protected]> wrote: > > > >> On 10-08-2019 09:49, Bruce Kellett wrote: > >>> > >>> But when you cannot reach, or ignore, some of this larger number > >> of > >>> degrees of freedom, you end up with a mixed state. That is how > >>> decoherence reduces the pure state to a mixture on measurement -- > >>> there are always degrees of freedom that are not recoverable -- > >> those > >>> infamous IR photons, for example. The brain does not take all > >> this > >>> entanglement with the environment into account, so it is a > >> classical > >>> object. > >>> > >> > >> And that step of tracing out the environmental degrees of freedom > >> is > >> where we make a mathematical approximation in order to be able to > >> do > >> practical calculations. But as you have said in this thread, the > >> mathematics we use to describe a system is not necessarily a good > >> physical representation of the system. It's not up to the brain to > >> decide to not take entanglement into account. > > > > No, the brain has no choice. It simply cannot take these environmental > > dof into account. So on its own reckoning, it is a classical object. > > It cannot be "classical" in the way we conventionally define it, as > that's a concept that cannot exist in the known universe.
That will be news to my table and chairs..... > What we want > to do is extract an object out of an entangled state in a physically > correct way, instead of a way that yields negligible errors when > computing expectation values of generic macroscopic observables, but is > physically incorrect. > OK. What we want is to extract the observed classical universe from a quantum substrate. Simply denying that this is possible is not an option. If FAPP is the best that can be achieved, so be it. There is no point hankering after unobtainable perfection. Progress might be possible, but simply denying that the classical world exists is silly. >> We may describe the brain > >> as a classical object, but that doesn't make it so. > > > > Tell me one practical way in which this makes a difference. > > There is no practical difference between a collapse interpretation and > the MWI, neither is there a practical difference between a theory that > says that all planets that are beyond the cosmological horizon are made > out of green cheese and the standard astrophysical models There is, actually. That would be to deny the cosmological hypothesis that the universe is uniform and isotropic on the large scale. Denying that would have local consequences. > .I do think that sticking to the relevant physics one can learn a great > deal more than by invoking irrelevant models. E.g. in thermodynamics we > ignore the correlations between the molecules that makes the physical > state a specially prepared state w.r.t. inverse time evolution. So, > ignoring the correlations and pretending that everything is random is > good enough if we focus on being able to predict measurement outcomes, > but the fact that the state isn't just any random state follows from the > fact that entropy would go down under time reversal while it would > increase if the state were truly random. > That depends on whether you think of time reversal as "running the film backwards", or as reversing the sign of t in your equations. So, the well known paradoxes in statistical physics go away when we take > into account the way we've oversimplified the physics. In the case of QM > exactly the same thing happens when using the density matrix formalism > and tracing out the environment. You lose the information needed to > describe the inverse time evolution correctly. But unlike ion > statistical physics, that's not the topic under discussion. The ignored > correlations between the degrees of freedom in the brain and the > environment do however solve a lot of other paradoxes invoked by people > who argue that AI can never generate consciousness. > > > Let's consider a robot with an electronic brain that runs a well defined > algorithm. Then there exists a notion about what algorithm the brain is > running, and we may call this a classical description of the electronic > brain. We include in the algorithm the exact computational state. The > exact description of the physical state involves all the entanglements > of all the atoms in the electronic brain and all the other local degrees > of freedom in the environment. If we then extract the computational > state represented as a bitstring out of this state, then the exact > physical state can be written as: > > |psi> = |b1>|e1> + |b2>|e2> + |b3>|e3> > > where the |bj> are normalized computational states and the |ej> are the > unnormalized "environmental" state that include everything except the > computational state. But you set up the problem with a well-defined algorithm, so there can be only one computational state. > Then <ej|ej> is the probability for the system to > be in the state |bj>|ej>. So, it also includes the state of the atoms in > the brain given whatever computational state the brain is in. Now > suppose that the robot is conscious, then what it will know/feel about > itself and its local environment will be contained in the bistring > describing its computational state, but the mapping from computational > states to awareness cannot be one to one. Why not? There is only one computational state for the well-defined algorithm at any particular moment -- so only one "awareness". > Whatever we are aware of, > won't precisely specify the exact computational state defined by what > all the neurons are doing at some time. This means that there exists a > large number of different |bj>'s that generate the exact same awareness > for the robot. > The conclusion does not follow. > Suppose that the robot is subjectively aware that it prepared the spin > of an electron to be polarized in the positive in the x-direction and > knows that I measured the spin then before I let the robot know the > result of the measurement, the robot will find itself in the state: > > |psi> = |up> + |down>] > Not if the robot knows that you measure in the x-direction. Otherwise, it is just classical ignorance. > where > > |up> = sum over states where |ej> contains Saibal finding spin up of > |bj>|ej>, > > |down> = sum over states where |ej> contains Saibal finding spin down of > |bj>|ej>. > > The robot will thus be in a superposition of two classes of worlds where > the result of the spin measurement is different. > This conclusion does not follow. Since there is only one computational state consistent with the algorithm, if the robot does no know the result of your y-direction measurement, there is nothing in its brain or computational state corresponding to your result. So it is in the same computational state as previously (or the temporal development of that). When it learns your result, or becomes entangled in some way with your result, it then enters the single computational state representing inclusion of knowledge of your result. You are looking at the "relative state" of your result from the wrong direction. 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