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January 17, 20260 citationsOpen Access

The Born Rule as Constraint Measure: Dissolving the Probability Problem in Quantum Mechanics

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RIRyuhei ISHIBASHI

Key Points

  • The aim is to dissolve the probability problem in quantum mechanics by reinterpreting the Born rule.
  • Analyzing the Born rule as a measure on constraint-satisfying configurations
  • Utilizing concepts from causal eliminativism
  • Exploring geometry of Hilbert space in relation to measurement outcomes
  • Reinterpretation of the Born rule eliminates the need for causal explanations of probability
  • Gleason's theorem is framed as identifying a unique measure rather than deriving probabilistic outcomes
  • Probabilistic causation is deemed non-existent, resolving the associated puzzle

Abstract

The Born rulethe prescription that measurement probabilities equal the squared mod- ulus of wave function amplitudeshas resisted satisfactory explanation for nearly a century. We argue that this diculty stems from a hidden assumption: that probability names a causal concept requiring causal explanation. Drawing on causal eliminativism, we reinterpret the Born rule not as describing the probabilistic eects of measurement, but as specifying a measure on the space of constraint-satisfying congurations. From this perspective, Glea- son's theorem does not derive probability from quantum mechanics; rather, it identies |ψ|2 as the unique coherent measure compatible with Hilbert space geometry. The question Why does measurement cause probabilistic outcomes? dissolves: there is no causation, hence no probabilistic causation, hence no puzzle. What remains is a geometric fact about constraint structure

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Cite This Study

Ryuhei ISHIBASHI (2026) studied this question.

synapsesocial.com/papers/696b26b2d2a12237a934a01ahttps://doi.org/10.5281/zenodo.18256778
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