- #1
BohmianRealist
Gold Member
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When conversing informally about QM, there is often wonder about the apparently acausal nature of processes that we may call "quantum leaps" between physical states. It is often said that the purely mathematical foundations of QM give no reason for such wonderment, i.e., that the math, in itself, simply forces this state of affairs upon us, and that all interpretive questions are just the legacy of the all-too-human tendency to ask overly philosophical questions concerning the ultimate nature of our shared experience that we call "reality".
Before I dive into the topic at hand, I want to thank the members of this forum who took the time to distill the vast area of human knowledge called quantum mechanics into 7 Basic Rules.
In terms of those rules, everything seems to be remain comfortably within the mental framework that we may call "classical logic" for the first four of them, and for the first sentence of the fifth. Rule #4 speaks of an operator "with real spectrum" acting on the Hilbert space. All thinking is situated entirely within the domain of mathematics up to here, at which point the physically significant notion of "measurement" is introduced (in rule #5) by speaking of the resulting values of the application of the operator. But only the case of a supposed "discrete spectrum" is considered, and the two remaining rules follow from this case.
The obvious question that is begged is, "What about the case of a continuous spectrum?" But an even deeper mystery is the conceptual leap that is necessary in thinking that there is some sense whereby something like a "spectrum" can even exist without being placed wholly within the realm of things that are characterized by the quality of continuity. Taking this tack, we may replace the word "spectrum" with the phrase "continuous range of values", and then wind up with the second sentence of rule #5 saying, "In the case of a discrete continuous range of values...".
The mind halts here. It doesn't simply "wonder" at the mystery of a new kind of science: it just cannot continue this train of thought, because the kind of thoughtful consideration that we call "logic" has terminated. And given that all sciences are merely particular applications of logic, what possibilities are left when thinking about how to proceed in the development of the "inner workings" of foundational (or non-interpretive) QM?
Before I dive into the topic at hand, I want to thank the members of this forum who took the time to distill the vast area of human knowledge called quantum mechanics into 7 Basic Rules.
In terms of those rules, everything seems to be remain comfortably within the mental framework that we may call "classical logic" for the first four of them, and for the first sentence of the fifth. Rule #4 speaks of an operator "with real spectrum" acting on the Hilbert space. All thinking is situated entirely within the domain of mathematics up to here, at which point the physically significant notion of "measurement" is introduced (in rule #5) by speaking of the resulting values of the application of the operator. But only the case of a supposed "discrete spectrum" is considered, and the two remaining rules follow from this case.
The obvious question that is begged is, "What about the case of a continuous spectrum?" But an even deeper mystery is the conceptual leap that is necessary in thinking that there is some sense whereby something like a "spectrum" can even exist without being placed wholly within the realm of things that are characterized by the quality of continuity. Taking this tack, we may replace the word "spectrum" with the phrase "continuous range of values", and then wind up with the second sentence of rule #5 saying, "In the case of a discrete continuous range of values...".
The mind halts here. It doesn't simply "wonder" at the mystery of a new kind of science: it just cannot continue this train of thought, because the kind of thoughtful consideration that we call "logic" has terminated. And given that all sciences are merely particular applications of logic, what possibilities are left when thinking about how to proceed in the development of the "inner workings" of foundational (or non-interpretive) QM?