arXiv subjects

Peter Caradonna

Publications and source records attributed to Peter Caradonna.

9 recordsLinked to original sources

arXiv2026

Interpersonally Comparable Utility

We develop a theory of measurement scales for utility functions, based on a generalization of the notion of numeraire commodity. Every sufficiently well-behaved utility is denominated in some scale of this form, and conversely, the choice of a compatible scale unit uniquely identifies utilities up to an additive constant. We define a profile of utilities to be interpersonally comparable precisely when they are denominated in a common measurement unit. We study when profiles of comparable utilities exist, as well as how a planner ought to aggregate them, and provide applications to social choice and welfare economics.

econ.TH↗

arXiv2026

Roadmap Towards Quantum Entanglement Positron Emission Tomography (QE-PET)

Annihilation photons are quantum entangled in their polarization, a property that is not accessible in state-of-the-art clinical Positron Emission Tomography (PET). This roadmap describes the current status of research in the emerging field of quantum entanglement applications involving these photons for medical diagnosis. It outlines the underlying physics phenomena and the development of detector systems that can serve as a foundation for future Quantum Entanglement PET (QE-PET) scanners. These scanners will be capable of utilizing the entanglement between annihilation photons by measuring their Compton scattering on electrons. This roadmap comprises up-to-date experimental results on the study of quantum entanglement and the decoherence of annihilation photons, alongside the current theoretical understanding of these phenomena. The methods and detector technologies described herein are being developed (i) in order to enhance standard PET imaging by suppressing random coincidences in the reconstruction of annihilation site density distributions, (ii) in order to establish the degree of quantum entanglement as a diagnostic biomarker for tissue pathology and oxygenation, and (iii) in order to elaborate a method for pH imaging. Whether entanglement-based imaging and pH mapping can be successfully translated into clinical practice remains an open question and a subject of exciting ongoing research. This roadmap serves as an invitation to the scientific community to join this burgeoning field.

physics.med-ph↗

arXiv2026

Identification in Stochastic Choice

We characterize the identified sets of a wide range of stochastic choice models, including random utility, various models of boundedly-rational behavior, and dynamic discrete choice. In each of these settings, we show two distributions over choice rules are observationally equivalent if and only if they can be obtained from one another via a finite sequence of simple swapping transforms. We leverage this to obtain complete descriptions of both the defining inequalities and extreme points of these identified sets. In cases where choice frequencies vary smoothly with some parameters, we provide a novel global-inverse result for practically testing identification.

econ.TH↗

arXiv2024

Revealed Invariant Preference

We consider the problem of rationalizing choice data by a preference satisfying an arbitrary collection of invariance axioms. Examples of such axioms include quasilinearity, homotheticity, independence-type axioms for mixture spaces, constant relative/absolute risk and ambiguity aversion axioms, stationarity for dated rewards or consumption streams, separability, and many others. We provide necessary and sufficient conditions for invariant rationalizability via a novel approach which relies on tools from the theoretical computer science literature on automated theorem proving. We also establish a generalization of the Dushnik-Miller theorem, which we use to give a complete description of the out-of-sample predictions generated by the data under any such collection of axioms.

econ.TH↗

arXiv2024

Kinematic analysis of multiple Compton scattering in quantum-entangled two-photon systems

The Stokes-Mueller method is used to analyze the scattering of entangled photon pairs in a two-photon system. This study examines the scenario where one of the photons, part of a pair of maximally entangled annihilation photons, undergoes intermediate Compton scattering before both photons are detected using Compton polarimeters. The method also accounts for potential quantum-decoherence effects resulting from Compton scattering. The analysis investigates the scattering behavior in both parallel and perpendicular planes, identifying variations in the modulation factor that affect azimuthal correlations. These variations include increases, decreases, sign changes, or disappearances at certain intermediate scattering angles. This work aims to provide theoretical results that support the testing and verification of predictions made by quantum field theory.

hep-th↗

arXiv2023

A Note on Invariant Extensions of Preorders

We consider the problem of extending an acyclic binary relation that is invariant under a given family of transformations into an invariant preference. We show that when a family of transformations is commutative, every acyclic invariant binary relation extends. We find that, in general, the set of extensions agree on the ranking of many pairs that (i) are unranked by the original relation, and (ii) cannot be ranked by invariance or transitivity considerations alone. We interpret these additional implications as the out-of-sample predictions generated by invariance, and study their structure.

econ.TH↗

arXiv2020

Amplification of polarization correlations in Compton scattering of hard X-ray Bell states

The theoretical cross section for Compton scattering of maximally entangled Bell photons has yet to be rigorously confirmed by experiments. Test cases of Bell states for use in Compton scattering experiments can now be expanded given reports of creating all 4 Bell states in the hard X-ray regime by the process of spontaneous parametric down-conversion. We outline an experiment and apply a matrix method to parameterize Compton scattering theory using the phase matching angles. When the azimuths of two hypothetical photon counters are recorded at angles of 0 degrees and 90 degrees, and the ratio of their counting rates determined, azimuthal ratios are expected to be 600 times larger compared to 511 keV Bell photons.

quant-ph↗

arXiv2019

Probing entanglement in Compton interactions

This theoretical research aims to examine areas of the Compton cross section of entangled annihilation photons for the purpose of testing for possible break down of theory, which could have consequences for predicted optimal capabilities of Compton PET systems.We provide maps of the cross section for entangled annihilation photons for experimental verification.We introduce a strategy to derive cross sections in a relatively straight forward manner for the Compton scattering of a hypothetical separable, mixed and entangled states. To understand the effect that entanglement has on the cross section for annihilation photons, we derive the cross section so that it is expressed in terms of the cross section of a hypothetical separable state and of a hypothetical forbidden maximally entangled state.We find lobe-like structures in the cross section which are regions where entanglement has the greatest effect.We also find that mixed states do not reproduce the cross section for annihilation photons, contrary to a recent investigation which reported otherwise.We review the motivation and method of the most precise Compton scattering experiment for annihilation photons, in order to resolve conflicting reports regarding the extent to which the cross section itself has been experimentally verified.

physics.optics↗

arXiv2015

An atomic hydrogen beam to test ASACUSA's apparatus for antihydrogen spectroscopy

The ASACUSA collaboration aims to measure the ground state hyperfine splitting (GS-HFS) of antihydrogen, the antimatter pendant to atomic hydrogen. Comparisons of the corresponding transitions in those two systems will provide sensitive tests of the CPT symmetry, the combination of the three discrete symmetries charge conjugation, parity, and time reversal. For offline tests of the GS-HFS spectroscopy apparatus we constructed a source of cold polarised atomic hydrogen. In these proceedings we report the successful observation of the hyperfine structure transitions of atomic hydrogen with our apparatus in the earth's magnetic field.

physics.atom-ph↗