Algorithmic Randomness and Physical Typicality

• URL: http://arxiv.org/abs/2609.06268v1
• Date: Sat, 05 Sep 2026 21:28:42 GMT
• Title: Algorithmic Randomness and Physical Typicality
• Abstract summary: We consider how one might characterize physical typicality using ideas from the theory of algorithmic randomness.<n>We show how taking a physical state to be typical relative to a computable measure when it is Martin-Lf random allows one to formulate the distribution postulate in Bohmian mechanics.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Appeals to typicality are common in physics, but it is often unclear what it means for a physical state to be typical relative to a probability measure, and correspondingly unclear what a law that appeals to typicality asserts. Here we consider how one might characterize physical typicality using ideas from the theory of algorithmic randomness. As a concrete example, we show how taking a physical state to be typical relative to a computable measure when it is Martin-Löf random allows one to formulate the distribution postulate in Bohmian mechanics as a statistical constraining law of the theory. Using a toy model, we show how this constraint guarantees the standard Born statistics for computable experimental protocols. Algorithmic Bohmian mechanics (aBM) thus illustrates how algorithmic randomness may be used to provide precise content to a statistical law.

Related papers

• The Distribution Postulate in Algorithmic Bohmian Mechanics [0.0]
  We show how one might use the theory of algorithmic randomness to formulate the distribution postulate as an objective constraining law.<n>In return, algorithmic Bohmian mechanics guarantees the standard Born statistics for a collection of canonical quantum experiments in the limit.
  arXiv  Detail & Related papers  (2026-06-15T03:27:03Z)
• Non-additive measures for quantum probability? [0.0]
  It is well-established that quantum probability does not follow classical Kolmogorov probability calculus.<n>The proper extension of probability calculus may require the use of non-additive measures.
  arXiv  Detail & Related papers  (2025-07-15T21:05:28Z)
• Testing trajectory-based determinism via time probability distributions [41.99844472131922]
  We introduce a prescription for constructing an arrival-time probability distribution within generic trajectory-equipped theories.<n>We derive a conditional probability distribution that is unreachable by quantum mechanics.<n>Our results can be tested experimentally, thereby assessing the validity of trajectory-based determinism.
  arXiv  Detail & Related papers  (2024-04-15T11:36:38Z)
• A refinement of the argument of local realism versus quantum mechanics by algorithmic randomness [0.0]
  In quantum mechanics, the notion of probability plays a crucial role. In modern mathematics, probability theory means nothing other than measure theory. We present a refinement of the Born rule, called the principle of typicality, for specifying the property of results of measurements in an operational way.
  arXiv  Detail & Related papers  (2023-12-20T18:22:42Z)
• Depolarizing Reference Devices in Generalized Probabilistic Theories [0.0]
  QBism is an interpretation of quantum theory which views quantum mechanics as standard probability theory supplemented with a few extra normative constraints. We show that, given any reference measurement, a set of post-measurement reference states can always be chosen to give its probability rule very form. What stands out for the QBist project from this analysis is that it is not only the pure form of the rule that must be understood normatively, but the constants within it as well.
  arXiv  Detail & Related papers  (2023-12-20T06:22:55Z)
• Symbolic Recovery of Differential Equations: The Identifiability Problem [52.158782751264205]
  Symbolic recovery of differential equations is the ambitious attempt at automating the derivation of governing equations. We provide both necessary and sufficient conditions for a function to uniquely determine the corresponding differential equation. We then use our results to devise numerical algorithms aiming to determine whether a function solves a differential equation uniquely.
  arXiv  Detail & Related papers  (2022-10-15T17:32:49Z)
• Non-probabilistic typicality, with application to quantum mechanics [0.0]
  The first hypothesis is the existence of random phenomena/experiments whose events cannot generally be assigned a definite probability. The second hypothesis is that the evolution of a quantum particle can be considered as a typicalistic phenomenon.
  arXiv  Detail & Related papers  (2022-09-29T17:49:14Z)
• Nonparametric Conditional Local Independence Testing [69.31200003384122]
  Conditional local independence is an independence relation among continuous time processes. No nonparametric test of conditional local independence has been available. We propose such a nonparametric test based on double machine learning.
  arXiv  Detail & Related papers  (2022-03-25T10:31:02Z)
• Why we should interpret density matrices as moment matrices: the case of (in)distinguishable particles and the emergence of classical reality [69.62715388742298]
  We introduce a formulation of quantum theory (QT) as a general probabilistic theory but expressed via quasi-expectation operators (QEOs) We will show that QT for both distinguishable and indistinguishable particles can be formulated in this way. We will show that finitely exchangeable probabilities for a classical dice are as weird as QT.
  arXiv  Detail & Related papers  (2022-03-08T14:47:39Z)
• Causal Expectation-Maximisation [70.45873402967297]
  We show that causal inference is NP-hard even in models characterised by polytree-shaped graphs. We introduce the causal EM algorithm to reconstruct the uncertainty about the latent variables from data about categorical manifest variables. We argue that there appears to be an unnoticed limitation to the trending idea that counterfactual bounds can often be computed without knowledge of the structural equations.
  arXiv  Detail & Related papers  (2020-11-04T10:25:13Z)
• Contextuality scenarios arising from networks of stochastic processes [68.8204255655161]
  An empirical model is said contextual if its distributions cannot be obtained marginalizing a joint distribution over X. We present a different and classical source of contextual empirical models: the interaction among many processes. The statistical behavior of the network in the long run makes the empirical model generically contextual and even strongly contextual.
  arXiv  Detail & Related papers  (2020-06-22T16:57:52Z)
• Generalized Sliced Distances for Probability Distributions [47.543990188697734]
  We introduce a broad family of probability metrics, coined as Generalized Sliced Probability Metrics (GSPMs) GSPMs are rooted in the generalized Radon transform and come with a unique geometric interpretation. We consider GSPM-based gradient flows for generative modeling applications and show that under mild assumptions, the gradient flow converges to the global optimum.
  arXiv  Detail & Related papers  (2020-02-28T04:18:00Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.