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 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. 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]. 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