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:quant-ph/0407096

The Emergence of Classical Dynamics in a Quantum World

Tanmoy Bhattacharya A, Salman Habib, Kurt A. Jacobs

Published Jul 14, 2004• 8 citations
arXivHTMLPDF

Abstract

Ever since the advent of quantum mechanics, it has been clear that the atoms composing matter do not obey Newton's laws. Instead, their behavior is described by the Schroedinger equation. Surprisingly though, until recently, no clear explanation was given for why everyday objects, which are merely collections of atoms, are observed to obey Newton's laws. It would seem that, if quantum mechanics explains all the properties of atoms accurately, they, too, should obey quantum mechanics. This reasoning led some scientists to believe in a distinct macroscopic, or ``big and complicated,'' world in which quantum mechanics fails and classical mechanics takes over, although there has never been experimental evidence for such a failure. Even those who insisted that Newtonian mechanics would somehow emerge from the underlying quantum mechanics as the system became increasingly macroscopic were hindered by the lack of adequate experimental and theoretical tools. In the last decade, however, this quantum-to-classical transition has become accessible to experimental study and quantitative description, and the resulting insights are the subject of this article.

DOI
10.48550/arxiv.quant-ph/0407096

Related papers

The Emergence of Quantum Theory

Peter Joshua Atkins, Julio de Paula, James Keeler

Toward the end of the nineteenth century, experimental evidence summarized in this Topic showed that classical mechanics, which was very successful at explaining the motion of everyday objects such as pendulums and projectiles, failed when it was applied to individual atoms, nuclei, and electrons. Quantum mechanics was devised to take its place and became the basis for a broader framework—quantum theory—for describing radiation and matter.

Oxford University Press eBooks•Dec 26, 2025•0 citations

The Physics of Quantum World of Particles

Varinderjit Kaur

The quantum world has always ignited human curiosity to unveil and speculate on the fascinating secrets of microscopic particles. This curiosity has opened a window to other branches of physics pushing the boundaries of classical understanding. After years of experimentation and analysis, scientists revealed that at microscopic dimensions, Newtonian mechanics failed not only quantitatively but even qualitatively and conceptually, clearing the way for new ideas. The nature of the difference between Newtonian mechanics and quantum mechanics is presented, with the core difference being the inherently probabilistic nature of quantum mechanics. This probabilistic foundation has led to revolutionary concepts like wave-particle duality and entanglement, fundamentally challenging classical ideas of causality and locality. The present article provides a well-focused and comprehensive overview of foundation ideas, concepts, and applications of quantum mechanics that make it principally different from Newtonian mechanics.

Journal of Advanced Research in Electronics Engineering and Technology•Dec 2, 2024•0 citations

Quantum feedback and the quantum–classical transition

Hideo Mabuchi

Exploring quantum reality? Twentieth-century physics bequeaths us an unruly enigma in the equivocal dichotomy between quantum and classical. Mesoscopic systems: which are they, or when? To some this distinction is but a matter of modeling convenience; to others, the partition bears ontological weight. Whichever one's stance, debates on this issue sharpen our introspection on “Why the quantum?” by demanding rigorous justification for choices of calculative consequence, intuitively made on every day in every field of physics. The limits seem clear. For few particles, left to their own devices, quantum mechanics runs rampant with its nonclassical phenomenology, viz. superposition, tunneling, and entanglement. But for the largish objects of our everyday experience, the sensory familiarity of classical mechanics holds sway: each object has its (singular) place, and every obstacle must be gone round or over. Strange, then, to ponder how big things are made from small! Somehow the assemblage of perceivable matter inevitably converts quantum constituents to classical collective, as if the ordering of the universe were ruled by atoms' aversion to the public embarrassment of quantum behavior writ large. It's a shame in a sense, for the senses slighted of paranormal experience, but superposition … what would it look like anyway?

Cambridge University Press eBooks•Apr 22, 2004•1 citation

Quantum Mechanics

Teunis C. Dorlas

At the beginning of the twentieth century, it became clear that microscopic particles do not obey Newton's laws of classical mechanics. The idea of light quanta was at odds with the established wisdom that light is a wave phenomenon, of course, but no other explanation of the photoelectric effect seemed possible. The next step in the development of quantum mechanics was taken by Niels Bohr, who introduced postulates about the discreteness of the energy of the bound electrons in an atom similar to the discreteness of the energy of light quanta. Modern quantum mechanics was founded by Werner Heisenberg, Max Born, Erwin Schroedinger, Paul Adrian Maurice Dirac, Wolfgang Pauli, Enrico Fermi, and others. In quantum mechanics, it is in general fundamentally impossible to determine the exact outcome of an experiment; one can only determine the probability of any given outcome.

CRC Press eBooks•Mar 2, 2021•0 citations

Mathematical Results in Quantum Mechanics

J. Dittrich, Pavel Exner, Miloš Tater

At the age of almost three quarters of a century, quantum mechanics is by all accounts a mature theory. There were times when it seemed that it had borne its best fruit already and would give way to investigation of deeper levels of matter. Today this sounds like rash thinking. Modern experimental techniques have led to discoveries of numerous new quantum effects in solid state, optics and elsewhere. Quantum mechanics is thus gradually becoming a basis for many branches of applied physics, in this way entering our everyday life. While the dynamic laws of quantum mechanics are well known, a proper theoretical understanding requires methods which would allow us to de­ rive the abundance of observed quantum effects from the first principles. In many cases the rich structure hidden in the Schr6dinger equation can be revealed only using sophisticated tools. This constitutes a motivation to investigate rigorous methods which yield mathematically well-founded properties of quantum systems.

Birkhäuser Basel eBooks•Jan 1, 1999•22 citations

Quantum violation of macroscopic realism and the transition to classical physics

Johannes Kofler

The descriptions of the quantum realm and the macroscopic classical world differ significantly not only in their mathematical formulations but also in their foundational concepts and philosophical consequences. When and how physical systems stop to behave quantum mechanically and begin to behave classically is still heavily debated in the physics community and subject to theoretical and experimental research. This dissertation puts forward an approach to the quantum-to-classical transition fully within quantum theory and conceptually different from already existing models: It neither needs to refer to the uncontrollable environment of a system (decoherence) nor to change the quantum laws itself (collapse models), but puts the stress on the limits of observability of quantum phenomena due to the imprecision of our measurement apparatuses. For a certain class of time evolutions it is this mere restriction to coarse-grained measurements which is sufficient to see the natural emergence of macroscopic realism and even the classical Newtonian laws out of the full quantum formalism. But there also exist "non-classical" Hamiltonians for which a classical spatiotemporal description of the system's time evolution remains impossible even under fuzzy measurements or decoherence. It is argued that such Hamiltonians are unlikely to be spontaneously realized in nature because of their high complexity. The last part addresses the question of the origin of quantum randomness and proposes a link with mathematical undecidability.

arXiv:0812.0238•Dec 1, 2008•5 citations
Ever since the advent of quantum mechanics, it has been clear that the atoms composing matter do not obey Newton's laws. Instead, their behavior is described by the Schroedinger equation. Surprisingly though, until recently, no clear explanation was given for why everyday objects, which are merely collections of atoms, are observed to obey Newton's laws. It would seem that, if quantum mechanics explains all the properties of atoms accurately, they, too, should obey quantum mechanics. This reasoning led some scientists to believe in a distinct macroscopic, or ``big and complicated,'' world in which quantum mechanics fails and classical mechanics takes over, although there has never been experimental evidence for such a failure. Even those who insisted that Newtonian mechanics would somehow emerge from the underlying quantum mechanics as the system became increasingly macroscopic were hindered by the lack of adequate experimental and theoretical tools. In the last decade, however, this quantum-to-classical transition has become accessible to experimental study and quantitative description, and the resulting insights are the subject of this article.
The quantum world has always ignited human curiosity to unveil and speculate on the fascinating secrets of microscopic particles. This curiosity has opened a window to other branches of physics pushing the boundaries of classical understanding. After years of experimentation and analysis, scientists revealed that at microscopic dimensions, Newtonian mechanics failed not only quantitatively but even qualitatively and conceptually, clearing the way for new ideas. The nature of the difference between Newtonian mechanics and quantum mechanics is presented, with the core difference being the inherently probabilistic nature of quantum mechanics. This probabilistic foundation has led to revolutionary concepts like wave-particle duality and entanglement, fundamentally challenging classical ideas of causality and locality. The present article provides a well-focused and comprehensive overview of foundation ideas, concepts, and applications of quantum mechanics that make it principally different from Newtonian mechanics.
Exploring quantum reality? Twentieth-century physics bequeaths us an unruly enigma in the equivocal dichotomy between quantum and classical. Mesoscopic systems: which are they, or when? To some this distinction is but a matter of modeling convenience; to others, the partition bears ontological weight. Whichever one's stance, debates on this issue sharpen our introspection on “Why the quantum?” by demanding rigorous justification for choices of calculative consequence, intuitively made on every day in every field of physics. The limits seem clear. For few particles, left to their own devices, quantum mechanics runs rampant with its nonclassical phenomenology, viz. superposition, tunneling, and entanglement. But for the largish objects of our everyday experience, the sensory familiarity of classical mechanics holds sway: each object has its (singular) place, and every obstacle must be gone round or over. Strange, then, to ponder how big things are made from small! Somehow the assemblage of perceivable matter inevitably converts quantum constituents to classical collective, as if the ordering of the universe were ruled by atoms' aversion to the public embarrassment of quantum behavior writ large. It's a shame in a sense, for the senses slighted of paranormal experience, but superposition … what would it look like anyway?
At the beginning of the twentieth century, it became clear that microscopic particles do not obey Newton's laws of classical mechanics. The idea of light quanta was at odds with the established wisdom that light is a wave phenomenon, of course, but no other explanation of the photoelectric effect seemed possible. The next step in the development of quantum mechanics was taken by Niels Bohr, who introduced postulates about the discreteness of the energy of the bound electrons in an atom similar to the discreteness of the energy of light quanta. Modern quantum mechanics was founded by Werner Heisenberg, Max Born, Erwin Schroedinger, Paul Adrian Maurice Dirac, Wolfgang Pauli, Enrico Fermi, and others. In quantum mechanics, it is in general fundamentally impossible to determine the exact outcome of an experiment; one can only determine the probability of any given outcome.
At the age of almost three quarters of a century, quantum mechanics is by all accounts a mature theory. There were times when it seemed that it had borne its best fruit already and would give way to investigation of deeper levels of matter. Today this sounds like rash thinking. Modern experimental techniques have led to discoveries of numerous new quantum effects in solid state, optics and elsewhere. Quantum mechanics is thus gradually becoming a basis for many branches of applied physics, in this way entering our everyday life. While the dynamic laws of quantum mechanics are well known, a proper theoretical understanding requires methods which would allow us to de­ rive the abundance of observed quantum effects from the first principles. In many cases the rich structure hidden in the Schr6dinger equation can be revealed only using sophisticated tools. This constitutes a motivation to investigate rigorous methods which yield mathematically well-founded properties of quantum systems.
The descriptions of the quantum realm and the macroscopic classical world differ significantly not only in their mathematical formulations but also in their foundational concepts and philosophical consequences. When and how physical systems stop to behave quantum mechanically and begin to behave classically is still heavily debated in the physics community and subject to theoretical and experimental research. This dissertation puts forward an approach to the quantum-to-classical transition fully within quantum theory and conceptually different from already existing models: It neither needs to refer to the uncontrollable environment of a system (decoherence) nor to change the quantum laws itself (collapse models), but puts the stress on the limits of observability of quantum phenomena due to the imprecision of our measurement apparatuses. For a certain class of time evolutions it is this mere restriction to coarse-grained measurements which is sufficient to see the natural emergence of macroscopic realism and even the classical Newtonian laws out of the full quantum formalism. But there also exist "non-classical" Hamiltonians for which a classical spatiotemporal description of the system's time evolution remains impossible even under fuzzy measurements or decoherence. It is argued that such Hamiltonians are unlikely to be spontaneously realized in nature because of their high complexity. The last part addresses the question of the origin of quantum randomness and proposes a link with mathematical undecidability.