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Pardon the long post...
M(A,B)\equiv Pr(A\cap \overline{B}\cup B\cap \overline{A})
will act as a metric with regard to the triangle inequality:
M(A,B) + M(B,C) \ge M(A,C)
This in essence is Bell's inequality. This inequality does not hold under QM...that is if you assert that these sets of outcomes correspond to quantum observables.
Note that you can take a given quantum theory and embed it within a much larger "conspiracy type" classical theory with the same outcomes. One is thereby failing to match up the classical observables with quantum observables. Such is the case in the Bohm pilot-wave type theories where in the wave-functions of the original quantum theory becomes a classical wave unobservable in practice but granting god-like powers observable in principle. However if you in turn "quantize" these again you get a whole new level of Bell inequalities and their violation.
The principle reason I object to these is that they also require non-local causation which in turn means future acting on past. How can we then say the system is in a given state if in the future some cause could revise history and change that state. The state-of-reality picture breaks down by itself without need of invoking QM.
Ultimately I think the order of causation necessarily dictates the time arrow and thus "backwards in time" casuation is both physically and semantically meaningless. The past is the class of phenomena which causally effected our current process of thinking and remembering.
Similarly nearness in space fundamentally is defined by the relative magnitude of causal effect. The sun warms my face more than Alpha Centauri, it is nearer. My fingers feel my keyboard while I have no sensation of yours. It is nearer. The only mystery is how phenomena shake down into events which can be parameterized in 3+1 dimensional space-time. IMNSHO That's what will reconcile quantum theory and Einstein's GR.
As I explained and speaking only for myself and not ThomasT, I see specifically EPR-Bell as evidence that we must abandon conventional classical reality. As bad as that may sound on first glance it is a proper step toward operationalism. It is not states of reality we see in the lab but phenomena, or as they used to say in the 60's-70's "happenings".
To be repetitive, I don't see any LR explanation possible due to the R issue not the L one. Call me a Local Actualist in contrast to your Local Realism. It is more than a preference. It is a position I've derived from my study of the foundations of QM and its logical structure. Classically probabilities are measures. Quantum mechanically they are squares of measures.
Let me also add that completeness changes meaning in the absence of the concept of state.
QM is quantum complete in a way that CM is not. You have a larger class of observables for a given distinct set of simultaneously distinguishable observable values.
I agree with your words though probably not your meaning. I assert Bell has nothing to do with locality per se. You seem to presume that Bell-EPR automatically imply Non-Locality which blinds you to seeing my point... that it has nothing to do with locality per se.
You need to carefully study the distinction between the lattice of logical propositions about a classical system's state (a lattice of sets with inclusion as the order relation) and the lattice of logical propositions about a quantum system's observables (a lattice of subspaces with sub-space inclusion as the order relation).
The fact that we get a continuum of observables and hence a continuum of distinct logical proposition for a quantum system which can has only a finite spectrum of distinct simultaneous observable values precludes any operationally meaningful "reality" description of that system. The basic laws of classical probability will be violated by the predicted quantum transition probabilities no matter how many hidden variables you introduce...
or you must incorporate a conspiracy theory wherein God knows exactly what future experiments we will make and tweaks and convolutes the initial hidden variables in such a way as to mimic quantum predictions. In either case reality is meaningless or inscrutable to us mere mortals. It should thus IMNSHO be excised from the theory all together.
What happens happens. If we can quantify rules about what happens that predict then we're ahead of the game. Test them empirically and you have science. Hypothesize about the deeper reality behind it and you have mysticism.
Contrary to what? Yes I mean realism in this sense. Specifically the modeling of the universe or that part of the universe affecting the outcome of an experiment as a set of points corresponding to states in some manifold or state set. This idea of "the state of the system" or "the state of the system and its environment" be that local or not is all that one needs in essence to derive Bell's inequality. Allow non-local causation if you like. Include any hidden variables you like. You still get outcomes of experiments caused by states of reality and modes of preparation of the system resulting in probability distributions over this set of states. The probability distributions will be positive specifically because in a reality picture negative probability is meaningless. The distributions will be additive over subsets because of the logic of classical reality. Therefore the probabilities for the set difference (XOR) for two sets of experimental outcomes ...RandallB said:What evidence do either of you use to come to these one of contrary conclusions?
[note: by ‘reality issues’ I assume you guys mean “Realism” as in the realism of a classical reality verses the possible reality of a multidimensional and/or “FTL” wave function or entanglement collapse.]
M(A,B)\equiv Pr(A\cap \overline{B}\cup B\cap \overline{A})
will act as a metric with regard to the triangle inequality:
M(A,B) + M(B,C) \ge M(A,C)
This in essence is Bell's inequality. This inequality does not hold under QM...that is if you assert that these sets of outcomes correspond to quantum observables.
Note that you can take a given quantum theory and embed it within a much larger "conspiracy type" classical theory with the same outcomes. One is thereby failing to match up the classical observables with quantum observables. Such is the case in the Bohm pilot-wave type theories where in the wave-functions of the original quantum theory becomes a classical wave unobservable in practice but granting god-like powers observable in principle. However if you in turn "quantize" these again you get a whole new level of Bell inequalities and their violation.
The principle reason I object to these is that they also require non-local causation which in turn means future acting on past. How can we then say the system is in a given state if in the future some cause could revise history and change that state. The state-of-reality picture breaks down by itself without need of invoking QM.
Ultimately I think the order of causation necessarily dictates the time arrow and thus "backwards in time" casuation is both physically and semantically meaningless. The past is the class of phenomena which causally effected our current process of thinking and remembering.
Similarly nearness in space fundamentally is defined by the relative magnitude of causal effect. The sun warms my face more than Alpha Centauri, it is nearer. My fingers feel my keyboard while I have no sensation of yours. It is nearer. The only mystery is how phenomena shake down into events which can be parameterized in 3+1 dimensional space-time. IMNSHO That's what will reconcile quantum theory and Einstein's GR.
I can speak of locality without invoking classical realism. You are right about Einstein but we can translate his concept of local objective realty into one of locally causal phenomena...what I would call local actuality.Neither of you can use Bell or EPR-Bell as evidence as it is only able to address “Local” as understood by Einstein which requires both Locality AND Realism.
As I explained and speaking only for myself and not ThomasT, I see specifically EPR-Bell as evidence that we must abandon conventional classical reality. As bad as that may sound on first glance it is a proper step toward operationalism. It is not states of reality we see in the lab but phenomena, or as they used to say in the 60's-70's "happenings".
Again I qualify that I seen no non-local implications to either QM or EPR-Bell. It is simply a matter of classical being classical (wherein Bell's inequality applies) and quantum being quantum wherein it doesn't. Classical reality is fine for classical theory and wrong for quantum theory. No mysteries no worries.From what do you derive assurance that any solution that may come in the future claiming to be more complete than the Non-Locals (from QM to BM to Strings) should not be required to explain the non-local implications of EPR-Bell as if non-locality means nothing.
As a Local Realist like myself (the Einstein claim) I see that as the exact obligation of any LR explanation.
To be repetitive, I don't see any LR explanation possible due to the R issue not the L one. Call me a Local Actualist in contrast to your Local Realism. It is more than a preference. It is a position I've derived from my study of the foundations of QM and its logical structure. Classically probabilities are measures. Quantum mechanically they are squares of measures.
Let me also add that completeness changes meaning in the absence of the concept of state.
QM is quantum complete in a way that CM is not. You have a larger class of observables for a given distinct set of simultaneously distinguishable observable values.
I'm not clear about what you mean by "Non-Local solution currently in use". If by solution you mean interpretation then the majority of polled quantum theorists adopt the Copenhagen interpretation (which I've been explaining) wherein reality is dropped and locality may then be preserved. If on the other hand you mean by "solution" the actual theory with predictions which match empirical data, QM wins and it is a local causal theory. Pay attention to the meaning of "locality" it is rooted in the causal connection of events and no reference to the states of objects or reality is necessary. It is operationally meaningful in a way that "state of reality" is not.Until a detailed description in LR terms can match the measured EPR-Bell results the Non-Local solution currently in use must be considered at least viable if not most likely complete, regardless of what my or anyone’s personal preference might be.
Again I'm not sure to which "current explanation" you are referring. The current consensus denies what Bell "was originally looking for" and failed to find.And IMO any solution that wishes to discredit the current explanation of EPR-Bell results must do so using both locality and realism, in other words find the complete solution Bell himself was originally looking for that demonstrates a more complete hidden variable LR solution as possible.
Arguments trying to decide if we have a mis-perception in understanding nature because of nonlocality in nature verses nature not based on realism have nothing to do with Bell, as they only address which Non-Local approach is preferable.
I agree with your words though probably not your meaning. I assert Bell has nothing to do with locality per se. You seem to presume that Bell-EPR automatically imply Non-Locality which blinds you to seeing my point... that it has nothing to do with locality per se.
You need to carefully study the distinction between the lattice of logical propositions about a classical system's state (a lattice of sets with inclusion as the order relation) and the lattice of logical propositions about a quantum system's observables (a lattice of subspaces with sub-space inclusion as the order relation).
The fact that we get a continuum of observables and hence a continuum of distinct logical proposition for a quantum system which can has only a finite spectrum of distinct simultaneous observable values precludes any operationally meaningful "reality" description of that system. The basic laws of classical probability will be violated by the predicted quantum transition probabilities no matter how many hidden variables you introduce...
or you must incorporate a conspiracy theory wherein God knows exactly what future experiments we will make and tweaks and convolutes the initial hidden variables in such a way as to mimic quantum predictions. In either case reality is meaningless or inscrutable to us mere mortals. It should thus IMNSHO be excised from the theory all together.
What happens happens. If we can quantify rules about what happens that predict then we're ahead of the game. Test them empirically and you have science. Hypothesize about the deeper reality behind it and you have mysticism.
Mysticism (from the Greek μυστικός – mystikos- 'seeing with the eyes closed, an initiate of the Eleusinian Mysteries; μυστήρια – mysteria meaning "initiation"[1]) is the pursuit of achieving communion, identity with, or conscious awareness of ultimate reality, the Other, divinity, spiritual truth, or God through direct experience, intuition, or insight.--Wikipedia
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