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

Physics

Discovering Bohr’s Yin-Yang Diagram in Quantum Tunneling Dynamics

Ciann-Dong Yang

Published Jul 18, 2024• 2 citations
Publisher

Abstract

On 17 October 1947, Niels Bohr was made a knight of the Order of the Elephant by the King of Denmark in view of his outstanding achievements and contributions to science. Bohr designed his own coat of arms that featured a pattern of Yin and Yang (Tai Chi symbol) to symbolize the wave-particle complementarity. However, Bohr’s Yin-Yang diagram (YYD) was neither drawn based on the principles of quantum mechanics, nor did it originate from the traditional Taoist YYD. Scientists still have doubts about the legitimacy of using YYD as the icon of the wave-particle complementarity, because the YYD belonging to quantum mechanics itself is unknown so far. This article reports the YYDs existing in quantum mechanics and justifies the role of YYD in the wave-particle duality by showing that any system, whether classical or quantum, has an ideal YYD as long as it satisfies Bohr’s principle of complementarity (BPC). The deviation of a deformed YYD from the ideal YYD indicates the extent to which a real system satisfies BPC. This article constructs the quantum YYD by the complex quantum trajectory of a particle tunneling via a step barrier, which displays the continuous transition between the wave behavior and the particle behavior. It appears that the YYD designed by Bohr in his coat of arms resembles the YYD generated by tunneling motion, not only in appearance but also in the governing equation.

DOI
10.3390/physics6030059

Related papers

Constellations of Complementarity: Niels Bohr’s Transreading of Chinese Classics

Huiwn Helen Zhang

This article explores the physicist Niels Bohr’s cosmopolitan vision through the lens of his foundational complementarity principle. Bohr’s coat of arms—combining a Latin motto with the yin-yang symbol—stands as a visual manifesto of his lifelong quest to reconcile opposites. Archival research and textual analysis illuminate how Bohr transformed Chinese classics into epistemological allegories, reviving ancient ideas to bridge science and humanities. Tracing a thread from Bohr’s retelling of a Song‑dynasty tale to illustrate quantum mechanics, through his fusion of Schiller’s Confucius poems with Kierkegaard’s philosophy, to his 1937 dialogue in China on Zhuangzi’s “Joy of the Fish” and Princeton’s “identical twins” parables, this article weaves cross‑cultural encounters into constellations of complementarity. At the heart of these constellations lies my most surprising discovery: Bohr’s spectator‑actor analogy which he attributed to Laozi—sprang from the Danish recreation of the Daodejing, not the Chinese original. Unfolding this discovery maps out a multilayered migration of ideas through a practice I term “transreading.” In an era of disciplinary fragmentation, this article reveals an intellectual history in which science and humanities co‑create meaning. Bohr’s vision affirms a timely truth: the future of knowledge depends on the courage and imagination to transread across cultures and worlds.

•May 1, 2026•0 citations

PRINCIPLE OF YIN-YANG COMPLEMENTARITY IN AEROSPACE SCIENCES

Virgil Stanciu, Cristina PAVEL

This paper is a transdisciplinary field that combines, harmoniously, the principle of complementarity introduced by the great physicist Niels Bohr in quantum mechanics and the ancient Chinese philosophy, whose essence is "Diagram of the Supreme Ultimate". The allegations are supported by religious, quantum and geometry arguments. Defined concepts of di-mension, coordinate system and specific concepts as: perpendicular in geometry, orthogonal in mathematical analysis, correct in law and ortho in religion. It is shown, further, classification for principle of complementarity, by the two manifestations, harmonic and non-harmonic. As applications, we use the known areas of fluid mechanics, hydro and aerodynamics. Based on the concepts of source, vortex and parallel motion through dyadic and triadic combinations, arriving, finally at a scientific explanation of the philosophical concept of Yin and Yang, underlying Chinese philosophy.

•May 1, 2014•0 citations

Bohr, Quantum Physics and theLaozi

Keekok Lee

This contribution argues that Bohr's notion of complementarity can be traced back to the Laozi which he would have read. In Chinese philosophy, polar contrasts such as yin and yang are not regarded as mutually exclusive; they are co-present, existing as a harmonious Whole. Such a conception of metaphysics and logic stood Bohr in good stead for characterising quantum phenomena which are at once both wave and particle. His notion of complementarity bears witness to the possibility of communication and understanding between two different philosophical approaches and scientific traditions—this account adds to Lloyd's concept of semantic stretch.

Australasian Philosophical Review•Jul 3, 2017•4 citations

Niels Bohr’s Complementarity and Quantum Tunneling

Slobodan Perović

Niels Bohr’s complementarity principle is a tenuous synthesis of seemingly discrepant theoretical approaches (the wave mechanical approach, and that of Heisenberg and early Bohr) based on a comprehensive analysis of relevant experimental results. Yet the role of complementarity, and the experimentalist-minded approach behind it, were not confined to a provisional best-available synthesis of well-established experimental results alone. They were also pivotal in discovering and explaining the phenomenon of quantum tunneling in its various forms. The core principles of Bohr’s method and the ensuing complementarity account of quantum phenomena remain highly relevant guidelines in the current controversial debate and in experimental work on quantum tunneling times.

•Nov 11, 2017•2 citations

Yin-Yang Dynamics: The Evolution Mechanism of Physical Systems and the Reconstruction of Causality

Zhang Pan

Standard physics confronts three deep fractures between macroscopic thermodynamics, microscopic quantum mechanics, and cosmology: the origin of the irreversibility of the arrow of time, causal inversion in quantum measurement, and dynamical singularities where pure-state physical systems cannot maintain self-sustaining evolution. This paper proposes “Yin-Yang Dynamics,” defining it as the underlying non-linear mechanism driving the evolution of all physical systems. Abandoning the traditional approach of treating Yin and Yang as static attributes or philosophical metaphors, the article establishes the ontological status of “Yin and Yang as the fundamental architecture of system dynamics.” On this basis, it constructs the “Yin-Yang non-commutative algebra” and the “Yin-Yang state transition matrix,” deducing the critical phase transition equations for system evolution. The study demonstrates that time is not an external container, but a lawful sequential structure generated by the mutual rooting and waxing/waning of Yin and Yang; traditional linear causality is reconstructed within the Yin-Yang topology as closed-loop “mutual-root causality.” This mechanism not only exhibits high isomorphism in microscopic quantum delayed-choice experiments and macroscopic dissipative structures, but also mathematically reconstructs the laws of causality and the arrow of time. This paper provides a rigorous and derivable non-Western ontological approach for constructing a unified dynamics beyond reductionism.

•Oct 30, 2026•0 citations

On the Quantum Footpath

David D. Nolte

This chapter shows how the concept of the trajectory of a quantum particle almost vanished in the battle between Werner Heisenberg’s matrix mechanics and Erwin Schrödinger’s wave mechanics. It took Niels Bohr and his complementarity principle of wave-particle duality to cede back some reality to quantum trajectories. However, Schrödinger and Einstein were not convinced and conceived of quantum entanglement to refute the growing acceptance of the Copenhagen Interpretation of quantum physics. Schrödinger’s cat was meant to be an absurdity, but ironically it has become a central paradigm of practical quantum computers. Quantum trajectories took on new meaning when Richard Feynman constructed quantum theory based on the principle of least action, inventing his famous Feynman Diagrams to help explain quantum electrodynamics.

Oxford University Press eBooks•Aug 22, 2018•0 citations
On 17 October 1947, Niels Bohr was made a knight of the Order of the Elephant by the King of Denmark in view of his outstanding achievements and contributions to science. Bohr designed his own coat of arms that featured a pattern of Yin and Yang (Tai Chi symbol) to symbolize the wave-particle complementarity. However, Bohr’s Yin-Yang diagram (YYD) was neither drawn based on the principles of quantum mechanics, nor did it originate from the traditional Taoist YYD. Scientists still have doubts about the legitimacy of using YYD as the icon of the wave-particle complementarity, because the YYD belonging to quantum mechanics itself is unknown so far. This article reports the YYDs existing in quantum mechanics and justifies the role of YYD in the wave-particle duality by showing that any system, whether classical or quantum, has an ideal YYD as long as it satisfies Bohr’s principle of complementarity (BPC). The deviation of a deformed YYD from the ideal YYD indicates the extent to which a real system satisfies BPC. This article constructs the quantum YYD by the complex quantum trajectory of a particle tunneling via a step barrier, which displays the continuous transition between the wave behavior and the particle behavior. It appears that the YYD designed by Bohr in his coat of arms resembles the YYD generated by tunneling motion, not only in appearance but also in the governing equation.
This article explores the physicist Niels Bohr’s cosmopolitan vision through the lens of his foundational complementarity principle. Bohr’s coat of arms—combining a Latin motto with the yin-yang symbol—stands as a visual manifesto of his lifelong quest to reconcile opposites. Archival research and textual analysis illuminate how Bohr transformed Chinese classics into epistemological allegories, reviving ancient ideas to bridge science and humanities. Tracing a thread from Bohr’s retelling of a Song‑dynasty tale to illustrate quantum mechanics, through his fusion of Schiller’s Confucius poems with Kierkegaard’s philosophy, to his 1937 dialogue in China on Zhuangzi’s “Joy of the Fish” and Princeton’s “identical twins” parables, this article weaves cross‑cultural encounters into constellations of complementarity. At the heart of these constellations lies my most surprising discovery: Bohr’s spectator‑actor analogy which he attributed to Laozi—sprang from the Danish recreation of the Daodejing, not the Chinese original. Unfolding this discovery maps out a multilayered migration of ideas through a practice I term “transreading.” In an era of disciplinary fragmentation, this article reveals an intellectual history in which science and humanities co‑create meaning. Bohr’s vision affirms a timely truth: the future of knowledge depends on the courage and imagination to transread across cultures and worlds.
This paper is a transdisciplinary field that combines, harmoniously, the principle of complementarity introduced by the great physicist Niels Bohr in quantum mechanics and the ancient Chinese philosophy, whose essence is "Diagram of the Supreme Ultimate". The allegations are supported by religious, quantum and geometry arguments. Defined concepts of di-mension, coordinate system and specific concepts as: perpendicular in geometry, orthogonal in mathematical analysis, correct in law and ortho in religion. It is shown, further, classification for principle of complementarity, by the two manifestations, harmonic and non-harmonic. As applications, we use the known areas of fluid mechanics, hydro and aerodynamics. Based on the concepts of source, vortex and parallel motion through dyadic and triadic combinations, arriving, finally at a scientific explanation of the philosophical concept of Yin and Yang, underlying Chinese philosophy.
This contribution argues that Bohr's notion of complementarity can be traced back to the Laozi which he would have read. In Chinese philosophy, polar contrasts such as yin and yang are not regarded as mutually exclusive; they are co-present, existing as a harmonious Whole. Such a conception of metaphysics and logic stood Bohr in good stead for characterising quantum phenomena which are at once both wave and particle. His notion of complementarity bears witness to the possibility of communication and understanding between two different philosophical approaches and scientific traditions—this account adds to Lloyd's concept of semantic stretch.
Niels Bohr’s complementarity principle is a tenuous synthesis of seemingly discrepant theoretical approaches (the wave mechanical approach, and that of Heisenberg and early Bohr) based on a comprehensive analysis of relevant experimental results. Yet the role of complementarity, and the experimentalist-minded approach behind it, were not confined to a provisional best-available synthesis of well-established experimental results alone. They were also pivotal in discovering and explaining the phenomenon of quantum tunneling in its various forms. The core principles of Bohr’s method and the ensuing complementarity account of quantum phenomena remain highly relevant guidelines in the current controversial debate and in experimental work on quantum tunneling times.
Standard physics confronts three deep fractures between macroscopic thermodynamics, microscopic quantum mechanics, and cosmology: the origin of the irreversibility of the arrow of time, causal inversion in quantum measurement, and dynamical singularities where pure-state physical systems cannot maintain self-sustaining evolution. This paper proposes “Yin-Yang Dynamics,” defining it as the underlying non-linear mechanism driving the evolution of all physical systems. Abandoning the traditional approach of treating Yin and Yang as static attributes or philosophical metaphors, the article establishes the ontological status of “Yin and Yang as the fundamental architecture of system dynamics.” On this basis, it constructs the “Yin-Yang non-commutative algebra” and the “Yin-Yang state transition matrix,” deducing the critical phase transition equations for system evolution. The study demonstrates that time is not an external container, but a lawful sequential structure generated by the mutual rooting and waxing/waning of Yin and Yang; traditional linear causality is reconstructed within the Yin-Yang topology as closed-loop “mutual-root causality.” This mechanism not only exhibits high isomorphism in microscopic quantum delayed-choice experiments and macroscopic dissipative structures, but also mathematically reconstructs the laws of causality and the arrow of time. This paper provides a rigorous and derivable non-Western ontological approach for constructing a unified dynamics beyond reductionism.
This chapter shows how the concept of the trajectory of a quantum particle almost vanished in the battle between Werner Heisenberg’s matrix mechanics and Erwin Schrödinger’s wave mechanics. It took Niels Bohr and his complementarity principle of wave-particle duality to cede back some reality to quantum trajectories. However, Schrödinger and Einstein were not convinced and conceived of quantum entanglement to refute the growing acceptance of the Copenhagen Interpretation of quantum physics. Schrödinger’s cat was meant to be an absurdity, but ironically it has become a central paradigm of practical quantum computers. Quantum trajectories took on new meaning when Richard Feynman constructed quantum theory based on the principle of least action, inventing his famous Feynman Diagrams to help explain quantum electrodynamics.