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Interpretation of the Born Rule in QTIP Cosmology

Seungyoung Choi

Published Apr 19, 2026• 0 citations
Publisher

Abstract

This paper shows that the Born Rule, which is the principle of probability determination in modern quantum theory, is derived from the structure of QTIP cosmology. This interpretation is based on the reinterpretation of the conventional Feynman path integral through the information processing and representation structure of QTIP cosmology.

DOI
10.5281/zenodo.19651561

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This paper shows that the Born Rule, which is the principle of probability determination in modern quantum theory, is derived from the structure of QTIP cosmology. This interpretation is based on the reinterpretation of the conventional Feynman path integral through the information processing and representation structure of QTIP cosmology.
This paper interprets the Feynman path integral, which is a fundamental concept of modern quantum theory, from the perspective of QTIP cosmology. In this interpretation, the conventional Feynman path integral is redefined through the information processing and representation structure of QTIP cosmology, and through this, it is shown that the corresponding path integral can be interpreted as an equation representing the path structure resulting from Tick (T4)-based state transition and the real -domain expression of absolute information proposed in QTIP cosmology.
This paper proposes a mathematical approach for applying a single Hilbert space (HS) in QTIP Cosmology. Based on the mathematical structure of composite systems in quantum mechanics (QM) and quantum information theory (QIT), it examines the correspondence of superposition, normalization and the Born Rule, entanglement, subsystem measurement statistics, and generalization to N-particle systems. Rather than constructing a new composite Hilbert space through tensor products of independent Hilbert spaces, QTIP Cosmology proposes defining a relational subset HS within a single Hilbert space based on the boundary conditions among QIF_Is. This approach does not exclude the mathematical structures of QM/QIT, but proposes an alternative framework for applying them within a single Hilbert space.
Born's rule is the recipe for calculating probabilities from quantum mechanical amplitudes. There is no generally accepted derivation of Born's rule from first principles. In this paper, it is motivated from assumptions that link the ontological content of a proper physical model to the epistemic conditions of the experimental context. More precisely, it is assumed that all knowable distinctions should correspond to distinctions in a proper model. This principle of "ontological completeness" means, for example, that the probabilistic treatment of the double slit experiment with and without path information should differ. Further, it is assumed that the model should rely only on knowable ontological elements, and that failure to fulfill this principle of "ontological minimalism" gives rise to wrong predictions. Consequently, probabilities should be assigned only to observable experimental outcomes. Also, the method to calculate such probabilities should not rely on the existence of a precise path of the observed object if this path is not knowable. A similar principle was promoted by Born, even though he did not apply it to probability. Another crucial assumption is that the proper rule to calculate probabilities should be generally valid. It should be applicable in all experimental contexts, regardless the setup that determines which attributes of the studied object are observed, together with the probability to observe each of the associated attribute values. There is no need to refer to the Hilbert space structure of quantum mechanics in the present treatment. Rather, some elements of this structure emerge from the analysis.
An alternative formulation of quantum mechanics is proposed based on a principle that can be considered a generalization of the Born rule. The principle is composed of a mathematical expression and an associated interpretation, and establishes a correlation between the positions of a particle at two different times. Under reasonable conditions for the wave function, this correlation implies that the particles follow quasiclassical trajectories. It is also shown that the Born rule is equivalent to a particular case of the evolved principle. These features allow the principle to provide a unified explanation of the results of the statistical experiments and of the quasiclassical macroscopic evolution. There is a strong analogy between the quantum principle and a probabilistic principle which is necessary to derive empirical predictions from the mathematical formalism of probability theory. This principle is referred to by some authors as Cournot's principle, while other authors use the equivalent notion of typicality. In this paper probability theory and quantum mechanics are formulated in such a way as to explicitly include the two principles and to emphasize the very similar conceptual structure of the two theories.
Page has recently argued that the Born rule does not suffice for computing all probabilities in quantum cosmology. He further asserts that the Born rule's failure gives rise to the cosmological measure problem. Here I contend that Page's result stems from his use of an overly restrictive definition of the Born rule. In particular, I demonstrate that all of the probabilities he wishes to compute follow from the Born rule when generalized measurements are permitted. I also register two comments on Page's theoretical setting, relating respectively to Hilbert space dimensionality and permutation symmetry. These considerations lead me to conclude that the claimed insufficiency of the Born rule is by no means specific to the cosmological context.
Abstract Logical inference leads to one of the major interpretations of probability theory called logical interpretation, in which the probability is seen as a measure of the plausibility of a logical statement under incomplete information. Assuming that our usual inference procedure is working rationally for every set of logical propositions represented in terms of commuting projectors on a given Hilbert space, we extend the logical interpretation to quantum mechanics and derive the Born rule. Our result implies that, from epistemological viewpoints, we can regard quantum mechanics as a natural extension of classical probability theory.