An Algorithmic Interpretation of Quantum Probability

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dc.contributor.advisorHattiangadi, Jagdish
dc.creatorRandall, Allan Frederick
dc.date.accessioned2014-07-15T19:33:42Z
dc.date.available2014-07-15T19:33:42Z
dc.date.copyright2014-01-31
dc.date.issued2014-07-09
dc.date.updated2014-07-09T16:39:48Z
dc.degree.disciplinePhilosophy
dc.degree.levelDoctoral
dc.degree.namePhD - Doctor of Philosophy
dc.description.abstractThe Everett (or relative-state, or many-worlds) interpretation of quantum mechanics has come under fire for inadequately dealing with the Born rule (the formula for calculating quantum probabilities). Numerous attempts have been made to derive this rule from the perspective of observers within the quantum wavefunction. These are not really analytic proofs, but are rather attempts to derive the Born rule as a synthetic a priori necessity, given the nature of human observers (a fact not fully appreciated even by all of those who have attempted such proofs). I show why existing attempts are unsuccessful or only partly successful, and postulate that Solomonoff's algorithmic approach to the interpretation of probability theory could clarify the problems with these approaches. The Sleeping Beauty probability puzzle is used as a springboard from which to deduce an objectivist, yet synthetic a priori framework for quantum probabilities, that properly frames the role of self-location and self-selection (anthropic) principles in probability theory. I call this framework "algorithmic synthetic unity" (or ASU). I offer no new formal proof of the Born rule, largely because I feel that existing proofs (particularly that of Gleason) are already adequate, and as close to being a formal proof as one should expect or want. Gleason's one unjustified assumption--known as noncontextuality--is, I will argue, completely benign when considered within the algorithmic framework that I propose. I will also argue that, to the extent the Born rule can be derived within ASU, there is no reason to suppose that we could not also derive all the other fundamental postulates of quantum theory, as well. There is nothing special here about the Born rule, and I suggest that a completely successful Born rule proof might only be possible once all the other postulates become part of the derivation. As a start towards this end, I show how we can already derive the essential content of the fundamental postulates of quantum mechanics, at least in outline, and especially if we allow some educated and well-motivated guesswork along the way. The result is some steps towards a coherent and consistent algorithmic interpretation of quantum mechanics.en_US
dc.identifier.urihttp://hdl.handle.net/10315/27640
dc.language.isoenen_US
dc.rightsAuthor owns copyright, except where explicitly noted. Please contact the author directly with licensing requests.
dc.subjectQuantum physicsen_US
dc.subjectPhilosophy of scienceen_US
dc.subjectMetaphysicsen_US
dc.subject.keywordsPossible worldsen_US
dc.subject.keywordsQuantum mechanicsen_US
dc.subject.keywordsQuantum foundationsen_US
dc.subject.keywordsQuantum probabilityen_US
dc.subject.keywordsInterpretation of quantum mechanicsen_US
dc.subject.keywordsProbabilityen_US
dc.subject.keywordsBorn ruleen_US
dc.subject.keywordsMany worldsen_US
dc.subject.keywordsEveretten_US
dc.subject.keywordsFrequentismen_US
dc.subject.keywordsBayesianismen_US
dc.subject.keywordsPropensityen_US
dc.subject.keywordsInterpretationen_US
dc.subject.keywordsGenerative interpretationen_US
dc.subject.keywordsSynthetic a priorien_US
dc.subject.keywordsAnthropic principleen_US
dc.subject.keywordsSelf-locationen_US
dc.subject.keywordsSelf-selectionen_US
dc.subject.keywordsSleeping Beautyen_US
dc.subject.keywordsAlgorithmic synthetic unityen_US
dc.subject.keywordsASUen_US
dc.subject.keywordsQuantum reconstructionen_US
dc.subject.keywordsGleasonen_US
dc.subject.keywordsFourier analysisen_US
dc.subject.keywordsData compressionen_US
dc.subject.keywordsAlgorithmic ontologyen_US
dc.subject.keywordsAlgorithmic probabilityen_US
dc.subject.keywordsSolomonoff probabilityen_US
dc.subject.keywordsKolmogorov complexityen_US
dc.subject.keywordsCosmic stabilityen_US
dc.subject.keywordsAbsolute idealismen_US
dc.subject.keywordsTranscendental idealismen_US
dc.subject.keywordsIdealismen_US
dc.subject.keywordsRealismen_US
dc.subject.keywordsMaterialismen_US
dc.subject.keywordsMetaphysicsen_US
dc.subject.keywordsOntologyen_US
dc.subject.keywordsEpistemologyen_US
dc.subject.keywordsLimit recursionen_US
dc.subject.keywordsLimiting recursionen_US
dc.subject.keywordsLambda calculusen_US
dc.subject.keywordsCombinatory calculusen_US
dc.subject.keywordsSK calculusen_US
dc.subject.keywordsAnalytical Engineen_US
dc.subject.keywordsMathematical Platonismen_US
dc.subject.keywordsMathematical constructivismen_US
dc.subject.keywordsRationalismen_US
dc.subject.keywordsComputational-ismen_US
dc.subject.keywordsMechanismen_US
dc.subject.keywordsStrong AIen_US
dc.subject.keywordsPhilosophy of minden_US
dc.subject.keywordsQuantum suicideen_US
dc.subject.keywordsQuantum miraclesen_US
dc.subject.keywordsImmortalityen_US
dc.subject.keywordsMathematical universeen_US
dc.titleAn Algorithmic Interpretation of Quantum Probabilityen_US
dc.typeElectronic Thesis or Dissertation

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