On 18 Sep, 22:20, "Stephen P. King" <[email protected]> wrote: > Hi Peter and Friends, > > -----Original Message----- > From: [email protected] > > [mailto:[email protected]] On Behalf Of 1Z > Sent: Friday, September 17, 2010 8:16 AM > To: Everything List > Subject: Re: A superposition in QM is just due to a choice of basis? > > On 28 Aug, 20:29, "Stephen P. King" <[email protected]> wrote: > > Hi Bret, > > > Could you elaborate on this point and/or point me to a > > good discussion of it? From what I have studied so far there is no > > solution to the measurement problem so far in terms of an explanation > > of the way that the choice is made in each successive event, world or > > whatever. Even decoherence does not help things from what I can tell, > > but this business that "What's a superposition in one basis is still > > an eigenfunction in some basis." is new to me. > > It is a much overlooked point. It pretty completely disposes of the version > of MWI that says the objectively decomposes into N classical universes. > I believe the relativity of superposition is best handled by the relational > interpretation > > http://en.wikipedia.org/wiki/Relational_quantum_mechanics > *** > > I would like to quote from this web article reference by 1Z and > make a comment: > > "Observer-dependence of state > According to O, at t2, the system S is in a determinate state, namely spin > up. And, if quantum mechanics is complete, then so is his description. But, > for O', S is not uniquely determinate, but is rather entangled with the > state of O — note that his description of the situation at t2 is not > factorisable no matter what basis chosen. But, if quantum mechanics is > complete, then the description that O' gives is also complete. > Thus the standard mathematical formulation of quantum mechanics allows > different observers to give different accounts of the same sequence of > events. There are many ways to overcome this perceived difficulty. It could > be described as an epistemic limitation — observers with a full knowledge of > the system, we might say, could give a complete and equivalent description > of the state of affairs, but that obtaining this knowledge is impossible in > practice. But whom? What makes O's description better than that of O', or > vice versa? Alternatively, we could claim that quantum mechanics is not a > complete theory, and that by adding more structure we could arrive at a > universal description — the much vilified, and some would even say > discredited, hidden variables approach. Yet another option is to give a > preferred status to a particular observer or type of observer, and assign > the epithet of correctness to their description alone. This has the > disadvantage of being ad hoc, since there are no clearly defined or > physically intuitive criteria by which this super-observer ("who can observe > all possible sets of observations by all observers over the entire > universe"[8]) ought to be chosen. > RQM, however, takes the point illustrated by this problem at face value. > Instead of trying to modify quantum mechanics to make it fit with prior > assumptions that we might have about the world, Rovelli says that we should > modify our view of the world to conform to what amounts to our best physical > theory of motion.[9] Just as forsaking the notion of absolute simultaneity > helped clear up the problems associated with the interpretation of the > Lorentz transformations, so many of the conundra associated with quantum > mechanics dissolve, provided that the state of a system is assumed to be > observer-dependent — like simultaneity in Special Relativity. This insight > follows logically from the two main hypotheses which inform this > interpretation: > Hypothesis 1: the equivalence of systems. There is no a priori distinction > that should be drawn between quantum and macroscopic systems. All systems > are, fundamentally, quantum systems. > Hypothesis 2: the completeness of quantum mechanics. There are no hidden > variables or other factors which may be appropriately added to quantum > mechanics, in light of current experimental evidence. > Thus, if a state is to be observer-dependent, then a description of a system > would follow the form "system S is in state x with reference to observer O" > or similar constructions, much like in relativity theory. In RQM it is > meaningless to refer to the absolute, observer-independent state of any > system." > > It is this notion that "it is meaningless to refer to the absolute, > observer independent state of any system" what has deep implications when > applied to the Universe itself. In effect, it argues that there is no such > thing as a "view from nowhere" ala Nagle IF and only IF we are thinking that > that a state can have any sort of property definiteness associated to it as > an independent entity. This seems to undermine the traditional idea of an > objective universe existing with a definite set of properties
without supporting the traditional alternative that it is all in the mind > absent the > notion of interactions of systems with each other. OTOH, we could take this > as a positive and propose that definiteness emerges from interactions > between subsets of the Universe. definiteness as far as they are concerned > This is where I believe the notion that > there is a plurality of Minds obtains in a coherent fashion. > > On this list we have been discussing any ideas that run from > metaphysical postulates, such as Arithmetic realism, etc. We need to be > sure that our thinking is consistent with the implications of ideas such as > this one discussed here. The line of questions that I have been making > relates to whether or not it is consistent to consider the notion of > interaction without some explanation or allowance for a notion of change as > a fundamental primitive. > I have tried to argue, with very limited success, that we need to > rethink the idea that we can have entities, such as numbers or strings of > integers, that can have particular properties and be differentiated with > respect to each other and completely neglect how this is the case. > Basically, this point that Carlo Rovelli is trying to make argues against > Platonism in the sense that the Ideals cannot be considered to have > properties that obtain from their mere existence. We cannot just do a Box > Diamond p statement and establish that p exists with some set of properties > and not some complementary set of properties. We need to be more specific; > that Box Diamond p specifies some predicate only has some sort of > definiteness if and only if there is some sort of specified of that > sentence. > > Onward! > > Stephen P. King -- You received this message because you are subscribed to the Google Groups "Everything List" group. To post to this group, send email to [email protected]. To unsubscribe from this group, send email to [email protected]. For more options, visit this group at http://groups.google.com/group/everything-list?hl=en.
