Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

arXiv:0904.4406

Quantum wave packets in space and time and an improved criterion for classical behavior

C. L. Herzenberg

Published Apr 28, 2009• 0 citations
arXivHTMLPDF

Abstract

An improved criterion for distinguishing conditions in which classical or quantum behavior occurs is developed by comparing classical and quantum mechanical measures of size while incorporating spatial and temporal restrictions on wave packet formation associated with limitations on spatial extent and duration.
DOI
10.48550/arxiv.0904.4406

Related papers

Localization of quantum objects in an expanding universe and cosmologically induced classicality

C. L. Herzenberg

Independent studies by different authors have proposed that classicality may be induced in quantum objects by cosmological constraints presented by an expanding universe of finite extent in space-time. Cosmological effects on a quantum system can be explored in one approach by considering an object at rest in space with a universal Hubble expansion taking place away from it, and developing a Schroedinger type governing differential equation incorporating an intrinsic expansion speed. Wave function solutions to this governing equation exhibit pronounced central localization. The extent of concentration of probability depends on mass; objects with small masses tend to behave in a delocalized manner as ordinary quantum objects do in a static space, while quantum objects with large masses are concentrated into much smaller regions. To develop a criterion for classicality, we consider that if the size of the localized region of concentrated probability density is larger than the size of the corresponding extended object, then quantum behavior could be expected; whereas if the region of high probability density for the location of the center of mass is smaller than the size of the object, the object would behave in a more classical manner. The resultant size threshold for classicality accords with results of other studies examining these issues based on uncertainty relations and wave packets. This size threshold is informative for the case of compact extended objects and, as the constraint applies to the center of mass of the system, does not lead to inconsistencies for quantum correlations between distant entangled quantum objects. While local decoherence may lead to classicality under a variety of conditions, cosmologically induced classicality would appear to cause fundamental limitations on quantum behavior in our universe.

arXiv:1011.5418•Nov 22, 2010•0 citations

Principles of an Objective Quantum Theory of Wave Packets

A. Jabs

•Jul 2, 2020•1 citation

Phase-space description of photon emission

D. V. Karlovets, A. A. Shchepkin, A. D. Chaikovskaia +4 more

Interactions between charged particles and light occur in real space and time, yet quantum field theory usually describes them in momentum space. Whereas this approach is well suited for calculating emission probabilities and cross sections, it is insensitive to spatial and temporal phenomena such as, for instance, radiation formation, quantum coherence, and wave packet spreading. These effects are becoming increasingly important for experiments involving electrons, photons, atoms, and ions, particularly with the advent of attosecond spectroscopy and metrology. Here, we propose a general method for describing the emission of photons in phase space via a Wigner function. Several effects for Cherenkov radiation are predicted, absent in classical realm or in quantum theory in momentum space, such as a finite spreading time of the photon, finite duration of the flash and a quantum shift of the photon arrival time. The photon spreading time turns out to be negative near the Cherenkov angle, the flash duration is defined by the electron packet size, and the temporal shift can be both positive and negative. The characteristic time scales of these effects lie in the atto- and femtosecond ranges, thereby illustrating atomic origins of these macroscopic phenomena. The near-field distribution of the photon field resembles the electron packet shape, thus making ``snapshots'' of the emitter wave function. Our approach can easily be generalized to the other types of radiation and extended to scattering, decay, and annihilation processes, bringing tomographic methods of quantum optics to particle physics.

quant-pharXiv:2512.21783•Dec 29, 2025

DYNAMICS OF THE INTERACTION BETWEEN CLASSICAL AND QUANTUM SYSTEMS AND THE REDUCTION OF THE WAVE PACKET

C. Marcio Do Amaral, S. Joffily

•Jan 1, 1985•0 citations

Time Evolution of Wave Packets in Quantum Chaotic Systems —A Manifestation of Quantum Chaos

Junqing Li, Fang Liu, Luo Yi-Xiao +1 more

International Conference on Nuclear Reaction and Beyond•Dec 1, 2000•0 citations

On the Equivalence of Spatial and Temporal Localization Boundary-Regime Behavior and the Destabilization of Classical Spacetime Structure

Barry Kieran Radcliffe

This paper began with a thought experiment exploring whether sufficiently accelerated temporal localization produces behavior structurally analogous to the quantum-regime phenomena observed under extreme spatial localization. Modern microscopy already demonstrates that progressively compressed spatial distinguishability destabilizes classical localization and produces wave-like, probabilistic, and nonlocal behavior associated with quantum mechanics. This paper asks whether equivalent destabilization would emerge if distinguishability were compressed temporally rather than spatially. The paper proposes that under sufficiently compressed temporal localization, stable classical persistence would progressively fail in ways structurally analogous to quantum-regime spatial localization. Galaxies, stars, and large-scale cosmic structures would no longer appear as persistent classical objects, but as evolving relational density patterns whose distinguishability becomes increasingly unstable across compressed observational intervals. The central argument is that quantum behavior does not arise from microscopic scale alone, but from sufficient localization of distinguishable structure within spacetime. At extreme localization, both spatial and temporal distinguishability progressively fail and converge toward the same quantum boundary condition. The only difference is whether distinguishability is compressed spatially or temporally from within spacetime. Accordingly, spatial localization and temporal localization become structurally equivalent under sufficient compression. At the boundary, the distinction between space and time ceases to retain independent physical meaning.

•May 13, 2026•0 citations
Independent studies by different authors have proposed that classicality may be induced in quantum objects by cosmological constraints presented by an expanding universe of finite extent in space-time. Cosmological effects on a quantum system can be explored in one approach by considering an object at rest in space with a universal Hubble expansion taking place away from it, and developing a Schroedinger type governing differential equation incorporating an intrinsic expansion speed. Wave function solutions to this governing equation exhibit pronounced central localization. The extent of concentration of probability depends on mass; objects with small masses tend to behave in a delocalized manner as ordinary quantum objects do in a static space, while quantum objects with large masses are concentrated into much smaller regions. To develop a criterion for classicality, we consider that if the size of the localized region of concentrated probability density is larger than the size of the corresponding extended object, then quantum behavior could be expected; whereas if the region of high probability density for the location of the center of mass is smaller than the size of the object, the object would behave in a more classical manner. The resultant size threshold for classicality accords with results of other studies examining these issues based on uncertainty relations and wave packets. This size threshold is informative for the case of compact extended objects and, as the constraint applies to the center of mass of the system, does not lead to inconsistencies for quantum correlations between distant entangled quantum objects. While local decoherence may lead to classicality under a variety of conditions, cosmologically induced classicality would appear to cause fundamental limitations on quantum behavior in our universe.
Interactions between charged particles and light occur in real space and time, yet quantum field theory usually describes them in momentum space. Whereas this approach is well suited for calculating emission probabilities and cross sections, it is insensitive to spatial and temporal phenomena such as, for instance, radiation formation, quantum coherence, and wave packet spreading. These effects are becoming increasingly important for experiments involving electrons, photons, atoms, and ions, particularly with the advent of attosecond spectroscopy and metrology. Here, we propose a general method for describing the emission of photons in phase space via a Wigner function. Several effects for Cherenkov radiation are predicted, absent in classical realm or in quantum theory in momentum space, such as a finite spreading time of the photon, finite duration of the flash and a quantum shift of the photon arrival time. The photon spreading time turns out to be negative near the Cherenkov angle, the flash duration is defined by the electron packet size, and the temporal shift can be both positive and negative. The characteristic time scales of these effects lie in the atto- and femtosecond ranges, thereby illustrating atomic origins of these macroscopic phenomena. The near-field distribution of the photon field resembles the electron packet shape, thus making ``snapshots'' of the emitter wave function. Our approach can easily be generalized to the other types of radiation and extended to scattering, decay, and annihilation processes, bringing tomographic methods of quantum optics to particle physics.
This paper began with a thought experiment exploring whether sufficiently accelerated temporal localization produces behavior structurally analogous to the quantum-regime phenomena observed under extreme spatial localization. Modern microscopy already demonstrates that progressively compressed spatial distinguishability destabilizes classical localization and produces wave-like, probabilistic, and nonlocal behavior associated with quantum mechanics. This paper asks whether equivalent destabilization would emerge if distinguishability were compressed temporally rather than spatially. The paper proposes that under sufficiently compressed temporal localization, stable classical persistence would progressively fail in ways structurally analogous to quantum-regime spatial localization. Galaxies, stars, and large-scale cosmic structures would no longer appear as persistent classical objects, but as evolving relational density patterns whose distinguishability becomes increasingly unstable across compressed observational intervals. The central argument is that quantum behavior does not arise from microscopic scale alone, but from sufficient localization of distinguishable structure within spacetime. At extreme localization, both spatial and temporal distinguishability progressively fail and converge toward the same quantum boundary condition. The only difference is whether distinguishability is compressed spatially or temporally from within spacetime. Accordingly, spatial localization and temporal localization become structurally equivalent under sufficient compression. At the boundary, the distinction between space and time ceases to retain independent physical meaning.