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I am under the impression that there must be a duality between physical theories and statistical models that have no reference to physical theories. For instance, given an apparatus, a researcher can begin to collect data and form statistical models for expected results given preparations. I believe this is called operationalism, or perhaps instrumentalism. Suppose you have a successful physical theory and also an instrumental statistical model that predicts experiments, what is the relationship (precisely speaking) that relates the two? What are the main references that attempt to address this? There has been considerable work on this subject in quantum mechanics. What about classical mechanics?

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  • $\begingroup$ Quantum theory originally related to a physical models and Einstein after looking at Planck's ideas came closest to pointing that out with the photoelectric effect. Quantum theories or predictions CAN be derived with REAL and physical photon models. Photons are classical mechanics and the relation between quantum mechanics can be found in in many things including frequency, speed, direction, energy, coherence, distance and maybe intensity, or polarization etc. $\endgroup$ – Bill Alsept Jan 11 '18 at 16:45
  • $\begingroup$ The "duality between physical theories and statistical models that have no reference to physical theories" is the duality between "having a clue about what is going on" and "having no idea why this works". $\endgroup$ – Stéphane Rollandin Jan 11 '18 at 17:01
  • $\begingroup$ @StéphaneRollandin Exactly! Not only does the statistical model not have a clue as to what’s going on but doesn’t even seem to be concerned or interested about what’s really physically happening. $\endgroup$ – Bill Alsept Jan 11 '18 at 18:33
  • $\begingroup$ Isn't this the same question you asked 6 years ago? viz. Causality and operationalism: from sets and functions to monads $\endgroup$ – sammy gerbil Jan 11 '18 at 20:20

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