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

Progress in physics

The Quantum Space Phase Transitions for Particles and Force Fields

Ding-Yu Chung, Volodymyr Krasnoholovets

Published Jul 1, 2006• 3 citations
OpenAlex

Abstract

We introduce a phenomenological formalism in which the space structure is treated in terms of attachment space and detachment space. Attachment space attaches to an object, while detachment space detaches from the object. The combination of these spaces results in three quantum space phases: binary partition space, miscible space and binary lattice space. Binary lattice space consists of repetitive units of alternative attachment space and detachment space. In miscible space, attachment space is miscible to detachment space, and there is no separation between attachment space and detachment spaces. In binary partition space, detachment space and attachment space are in two separate continuous regions. The transition from wavefunction to the collapse of wavefuction under interference becomes the quantum space phase transition from binary lattice space to miscible space. At extremely conditions, the gauge boson force field undergoes a quantum space phase transition to a “hedge boson force field”, consisting of a “vacuum ” core surrounded by a hedge boson shell, like a bubble with boundary. 1 The origin of the space structure

Related papers

Energetic Thresholds for the Quantum–Classical Transition: The Absolute Medium Framework

SREEMAN BARUA

The quantum–classical divide remains one of the most persistent conceptual challenges in modern physics. Conventionally, this transition is explained through decoherence— the environment-induced loss of phase coherence via interaction with external degrees of freedom. While phenomenologically successful, decoherence theory does not provide a fundamental mechanical substrate for why quantum behavior emerges preferentially at small scales and vanishes systematically at large ones. It remains a statistical account rather than a mechanistic one. The Absolute Medium (AM) framework offers an alternative foundation by re-conceptualizing spacetime not as an abstract arena, but as a Universal Force Continuum— a baseline of potential energy that precedes and underlies physical matter. In this formulation, the vacuum is characterized not by emptiness but by structured tension, where the “graininess” emerges from equilibrium conditions within the continuum itself.This graininess is quantified by the Energetic Net, defined by the fundamental length scale Lfund ≈ 3.34 nm. This scale represents the characteristic spacing at which the continuum’s tension reaches local equilibrium, creating a natural lattice structure. The continuum is neither rigid nor fluid in conventional terms, but exists in a state of dynamic equilibrium where its tension field supports both wave-like propagation and particle-like anchoring. This intrinsic structural property of the vacuum introduces a natural scale separation that defines two distinct dynamical regimes:• Slippage (Quantum) Regime (d < Lfund, m < mcrit): Particles interact with the continuum through local tension fluctuations without engaging its equilibrium structure. Their motion is governed by stochastic variations in the continuum’s potential field, yielding emergent quantum behavior.• Bulk-Coupled (Classical) Regime (d ≥ Lfund, m ≥ mcrit): Objects span multiple equilibrium nodes of the continuum, engaging its fundamental structure. They must displace the continuum’s equilibrium configuration, triggering deterministic volumetric coupling that recovers classical mechanics. This proposal replaces abstract decoherence with a concrete mechanical transition rooted in the continuum properties of the vacuum. It offers a first-principles explanation for the emergence of both quantum and classical dynamics from a unified energetic continuum, with the transition governed by intrinsic properties of the medium rather than external interactions.

•Mar 25, 2026•0 citations

The Structure of a Quantum World*

Jill North

I argue that the fundamental space of a quantum mechanical world is the wavefunction's space. I argue for this using some very general principles that guide our inferences to the fundamental nature of a world, for any fundamental physical theory. I suggest that ordinary three-dimensional space exists in such a world, but is non-fundamental; it emerges from the fundamental space of the wavefunction.

Oxford University Press eBooks•Apr 8, 2013•121 citations

The Cosmic Digital Code and Quantum Mechanics

Ding-Yu Chung

This paper posits that the cosmic digital code as the law of all physical laws contains two mutually exclusive values: attachment space attaching to object and detachment space detaching from object. However, the cosmic physical system could not start with mutually exclusive attachment space and detachment space at the same time in the beginning. The way out of this impasse is that the complete cosmic system consists of both the cosmic physical system and the unphysical cosmic digital code. The unphysical cosmic digital code allows the coexistence of attachment space and detachment space at the same time. The cosmic digital code behaves as gene in organism, and the cosmic physical system behaves as organ. Under different conditions and times, different spaces in the cosmic digital code are activated to generate different spaces in the cosmic physical systems with different physical laws for different universes in the multivese. All universes start from the primitive multiverse, which only has attachment space attaching to 10D string without the four force fields. During the big bang in our universe, detachment space emerged to detach particle from its four force fields. Such detachment, however, cannot be completely and permanently detached, because particle still attaches to its force fields. The result is hybrid space, combining both attachment space and detachment space in coherent state, such as particle and its force fields. Hybrid space is the space for wavefunction whose probability density is proportional to attachment space, and inversely proportional to detachment space. The collapse of wavefunction in decoherent state is the separation of attachment space and detachment space in such way that attachment space attaches to particle, and detachment space separately detaches from all probability density.

arXiv:quant-ph/0204033•Apr 6, 2002•2 citations

The formation of the conceptual foundations of quantum field theory

Tian Yu Cao

Quantum field theory (QFT) can be analyzed in terms of its mathematical structure, its conceptual system for physical descriptions, or its basic ontology. The analysis can be done logically or historically. In this chapter, only the genesis of the conceptual foundations of QFT relevant to its basic ontology will be treated; no discussion of its mathematical structures or its epistemological underpinnings will be given. Some conceptual problems, such as those related to probability and measurement, will be discussed, but only because of their relevance to the basic ontology of QFT, rather than their intrinsic philosophical interest. Here, by basic ontology I mean the irreducible entities that QFT is invented to describe. The often mentioned candidates for the basic ontology of QFT, in fact of the physical world, are the discrete particle and the continuous field. Another possible candidate (the spacetime point) has also been suggested recently (Redhead, 1983). Since the aim of this chapter is to analyze the historical process in which the conceptual foundations of QFT were laid down, rather than the logical structure of QFT which philosophers of the present day treat, no discussion of the last possibility will be given. The content of this chapter involves the formation and interpretation, in a roughly chronological order, of the concepts of the wave function, quantization, quantization of the field, the vacuum, interactions between fields, and renormalization. The first two topics will be discussed in relation to the quantization of the field, with their role being taken as the starting point of the conceptual development of QFT.

Cambridge University Press eBooks•Feb 13, 1997•0 citations

Suppression of the quantum collapse in binary bosonic gases

Hidetsugu Sakaguchi, Boris A. Malomed

Attraction of the quantum particle to the center in three-dimensional space with potential $\ensuremath{-}{V}_{0}{r}^{\ensuremath{-}2}$ gives rise to the quantum collapse, i.e., nonexistence of the ground state (GS) when the attraction strength exceeds a critical value [${({V}_{0}^{(\mathrm{cr})})}_{1}=1/8$, in the present notation]. Recently, we have demonstrated that the quantum collapse is suppressed and the GS is restored if repulsive interactions between particles in the quantum gas are taken into account in the mean-field approximation. This setting can be realized in a gas of dipolar molecules attracted to the central charge, with dipole-dipole interactions taken into regard as well. Here we analyze this problem for a binary gas. GSs supported by the repulsive interactions are constructed in a numerical form, as well as by means of analytical approximations for both miscible and immiscible binary systems. In particular, the Thomas-Fermi approximation is relevant if ${V}_{0}$ is large enough. It is found that the GS of the miscible binary gas, both balanced and imbalanced, features a weak phase transition at another critical value, ${({V}_{0}^{(\mathrm{cr})})}_{2}=1/2\ensuremath{\equiv}4{({V}_{0}^{(\mathrm{cr})})}_{1}$. The transition is characterized by an analyticity-breaking change in the structure of the wave functions at small $r$. To illustrate the generic character of the present phenomenology, we also consider the binary system with attraction between the species (rather than repulsion) in the case when the central potential pulls a single component only.

arXiv:1310.5442•Physical Review A•Oct 28, 2013•16 citations

Induced interaction and crystallization of self-localized impurity fields in a Bose-Einstein condensate

Sergio Rica, David C K Roberts

We model the behavior of $N$ classical impurity fields immersed in a larger Bose-Einstein condensate by $N+1$ coupled nonlinear Schr\"odinger equations in one, two, and three space dimensions. We discuss the stability of the uniform miscible system and show the importance of surface tension for self-localization of the impurity fields. We derive analytically the attractive tail of the impurity-impurity interaction due to mediation by the underlying condensate. Assuming all impurity fields interact with the same strength, we explore numerically the resulting phase diagram, which contains four phases: (I) all fields are miscible; (II) the impurity fields are miscible with each other but phase separate from the condensate as a single bubble; (III) the localized impurity fields stay miscible with the condensate, but not with each other; and (IV) the impurity fields phase separate from the condensate and each other, forming a crystalline structure within a bubble. Thus, we show that a crystal can be constructed solely from superfluid components. Finally, we argue that the crystalline phases maintain their superfluid behavior, i.e., they possess a nonclassical rotational inertia, which---combined with lattice order---is a characteristic of supersolidity.

arXiv:0904.1569•Physical Review A•Jul 16, 2009•6 citations
We introduce a phenomenological formalism in which the space structure is treated in terms of attachment space and detachment space. Attachment space attaches to an object, while detachment space detaches from the object. The combination of these spaces results in three quantum space phases: binary partition space, miscible space and binary lattice space. Binary lattice space consists of repetitive units of alternative attachment space and detachment space. In miscible space, attachment space is miscible to detachment space, and there is no separation between attachment space and detachment spaces. In binary partition space, detachment space and attachment space are in two separate continuous regions. The transition from wavefunction to the collapse of wavefuction under interference becomes the quantum space phase transition from binary lattice space to miscible space. At extremely conditions, the gauge boson force field undergoes a quantum space phase transition to a “hedge boson force field”, consisting of a “vacuum ” core surrounded by a hedge boson shell, like a bubble with boundary. 1 The origin of the space structure
The quantum–classical divide remains one of the most persistent conceptual challenges in modern physics. Conventionally, this transition is explained through decoherence— the environment-induced loss of phase coherence via interaction with external degrees of freedom. While phenomenologically successful, decoherence theory does not provide a fundamental mechanical substrate for why quantum behavior emerges preferentially at small scales and vanishes systematically at large ones. It remains a statistical account rather than a mechanistic one. The Absolute Medium (AM) framework offers an alternative foundation by re-conceptualizing spacetime not as an abstract arena, but as a Universal Force Continuum— a baseline of potential energy that precedes and underlies physical matter. In this formulation, the vacuum is characterized not by emptiness but by structured tension, where the “graininess” emerges from equilibrium conditions within the continuum itself.This graininess is quantified by the Energetic Net, defined by the fundamental length scale Lfund ≈ 3.34 nm. This scale represents the characteristic spacing at which the continuum’s tension reaches local equilibrium, creating a natural lattice structure. The continuum is neither rigid nor fluid in conventional terms, but exists in a state of dynamic equilibrium where its tension field supports both wave-like propagation and particle-like anchoring. This intrinsic structural property of the vacuum introduces a natural scale separation that defines two distinct dynamical regimes:• Slippage (Quantum) Regime (d < Lfund, m < mcrit): Particles interact with the continuum through local tension fluctuations without engaging its equilibrium structure. Their motion is governed by stochastic variations in the continuum’s potential field, yielding emergent quantum behavior.• Bulk-Coupled (Classical) Regime (d ≥ Lfund, m ≥ mcrit): Objects span multiple equilibrium nodes of the continuum, engaging its fundamental structure. They must displace the continuum’s equilibrium configuration, triggering deterministic volumetric coupling that recovers classical mechanics. This proposal replaces abstract decoherence with a concrete mechanical transition rooted in the continuum properties of the vacuum. It offers a first-principles explanation for the emergence of both quantum and classical dynamics from a unified energetic continuum, with the transition governed by intrinsic properties of the medium rather than external interactions.
This paper posits that the cosmic digital code as the law of all physical laws contains two mutually exclusive values: attachment space attaching to object and detachment space detaching from object. However, the cosmic physical system could not start with mutually exclusive attachment space and detachment space at the same time in the beginning. The way out of this impasse is that the complete cosmic system consists of both the cosmic physical system and the unphysical cosmic digital code. The unphysical cosmic digital code allows the coexistence of attachment space and detachment space at the same time. The cosmic digital code behaves as gene in organism, and the cosmic physical system behaves as organ. Under different conditions and times, different spaces in the cosmic digital code are activated to generate different spaces in the cosmic physical systems with different physical laws for different universes in the multivese. All universes start from the primitive multiverse, which only has attachment space attaching to 10D string without the four force fields. During the big bang in our universe, detachment space emerged to detach particle from its four force fields. Such detachment, however, cannot be completely and permanently detached, because particle still attaches to its force fields. The result is hybrid space, combining both attachment space and detachment space in coherent state, such as particle and its force fields. Hybrid space is the space for wavefunction whose probability density is proportional to attachment space, and inversely proportional to detachment space. The collapse of wavefunction in decoherent state is the separation of attachment space and detachment space in such way that attachment space attaches to particle, and detachment space separately detaches from all probability density.
Quantum field theory (QFT) can be analyzed in terms of its mathematical structure, its conceptual system for physical descriptions, or its basic ontology. The analysis can be done logically or historically. In this chapter, only the genesis of the conceptual foundations of QFT relevant to its basic ontology will be treated; no discussion of its mathematical structures or its epistemological underpinnings will be given. Some conceptual problems, such as those related to probability and measurement, will be discussed, but only because of their relevance to the basic ontology of QFT, rather than their intrinsic philosophical interest. Here, by basic ontology I mean the irreducible entities that QFT is invented to describe. The often mentioned candidates for the basic ontology of QFT, in fact of the physical world, are the discrete particle and the continuous field. Another possible candidate (the spacetime point) has also been suggested recently (Redhead, 1983). Since the aim of this chapter is to analyze the historical process in which the conceptual foundations of QFT were laid down, rather than the logical structure of QFT which philosophers of the present day treat, no discussion of the last possibility will be given. The content of this chapter involves the formation and interpretation, in a roughly chronological order, of the concepts of the wave function, quantization, quantization of the field, the vacuum, interactions between fields, and renormalization. The first two topics will be discussed in relation to the quantization of the field, with their role being taken as the starting point of the conceptual development of QFT.
Attraction of the quantum particle to the center in three-dimensional space with potential $\ensuremath{-}{V}_{0}{r}^{\ensuremath{-}2}$ gives rise to the quantum collapse, i.e., nonexistence of the ground state (GS) when the attraction strength exceeds a critical value [(V0(cr))1=1/8{({V}_{0}^{(\mathrm{cr})})}_{1}=1/8(V0(cr)​)1​=1/8, in the present notation]. Recently, we have demonstrated that the quantum collapse is suppressed and the GS is restored if repulsive interactions between particles in the quantum gas are taken into account in the mean-field approximation. This setting can be realized in a gas of dipolar molecules attracted to the central charge, with dipole-dipole interactions taken into regard as well. Here we analyze this problem for a binary gas. GSs supported by the repulsive interactions are constructed in a numerical form, as well as by means of analytical approximations for both miscible and immiscible binary systems. In particular, the Thomas-Fermi approximation is relevant if V0{V}_{0}V0​ is large enough. It is found that the GS of the miscible binary gas, both balanced and imbalanced, features a weak phase transition at another critical value, ${({V}_{0}^{(\mathrm{cr})})}_{2}=1/2\ensuremath{\equiv}4{({V}_{0}^{(\mathrm{cr})})}_{1}$. The transition is characterized by an analyticity-breaking change in the structure of the wave functions at small rrr. To illustrate the generic character of the present phenomenology, we also consider the binary system with attraction between the species (rather than repulsion) in the case when the central potential pulls a single component only.
We model the behavior of NNN classical impurity fields immersed in a larger Bose-Einstein condensate by N+1N+1N+1 coupled nonlinear Schr\"odinger equations in one, two, and three space dimensions. We discuss the stability of the uniform miscible system and show the importance of surface tension for self-localization of the impurity fields. We derive analytically the attractive tail of the impurity-impurity interaction due to mediation by the underlying condensate. Assuming all impurity fields interact with the same strength, we explore numerically the resulting phase diagram, which contains four phases: (I) all fields are miscible; (II) the impurity fields are miscible with each other but phase separate from the condensate as a single bubble; (III) the localized impurity fields stay miscible with the condensate, but not with each other; and (IV) the impurity fields phase separate from the condensate and each other, forming a crystalline structure within a bubble. Thus, we show that a crystal can be constructed solely from superfluid components. Finally, we argue that the crystalline phases maintain their superfluid behavior, i.e., they possess a nonclassical rotational inertia, which---combined with lattice order---is a characteristic of supersolidity.