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

Experimental Noise, Idealizations and the Classical-Quantum Relation

Gebhard von Oppen

Published Jun 3, 2010• 0 citations
Publisher

Abstract

Classical dynamics and the classical concept of space-time reality is based on the assumption that the objects of physics can be observed continuously. The discrete structure of matter (atoms) and fields (quanta), however, implies that the process of observation is quantized. In this paper we discuss the consequences of this paradigm change from continuity to discreteness and from determinism to chance. By taking into account the quantized structure of observation, we are led to the conclusion that the classical concept of reality has to be replaced by a quantum concept of observability. It implies that quantum dynamics is not a generalization of classical dynamics. Rather, the two theories apply to complementary idealizations of nature representing opposite extremes on a scale of observability. They are related by correspondence rules. Both theories disregard experimental noise. Statistical and thermal noise provide the experimental foundation for statistical physics.

DOI
10.17877/de290r-115

Related papers

Space-Time in Quantum Theory

H. Capellmann

Abstract Quantum Theory, similar to Relativity Theory, requires a new concept of space-time, imposed by a universal constant. While velocity of lightcnot being infinite calls for a redefinition of space-time on large and cosmological scales, quantization of action in terms of a finite, i.e. non vanishing, universal constanthrequires a redefinition of space-time on very small scales. Most importantly, the classical notion of “time”, as one common continuous time variable and nature evolving continuously “in time”, has to be replaced by an infinite manifold of transition rates for discontinuous quantum transitions. The fundamental laws of quantum physics, commutation relations and quantum equations of motion, resulted from Max Born’s recognition of the basic principle of quantum physics:To each change in nature corresponds an integer number of quanta of action. Action variables may only change by integer values ofh, requiring all other physical quantities to change by discrete steps, “quantum jumps”. The mathematical implementation of this principle led to commutation relations and quantum equations of motion. The notion of “point” in space-time looses its physical significance; quantum uncertainties of time, position, just as any other physical quantity, are necessary consequences of quantization of action.

arXiv:2006.00503•Foundations of Physics•Apr 1, 2021•15 citations

Conceptual Difficulties of Standard Quantum Mechanics and the Role of Noise in Overcoming Them

G. C. Ghirardi

We briefly review the difficulties of the standard version of quantum mechanics in accounting for all kinds of physical processes (in particular both the micro and the macroscopic ones) and we argue that to overcome such difficulties one has to give up the superposition principle, i.e., to break the linear nature of the theory. We then show that the simple introduction of terms violating the linearity of the deterministic evolution of the standard theory has physically unacceptable consequences. Taking this into account we are led to modify the quantum dynamics by adding to Schrödinger’s equation, besides nonlinear terms, a coupling with an appropriate noise. We show that, with such a move, one can work out a theory which is internally consistent and it allows to account, in a quite simple and physically appealing way, for natural processes including the measurements and the classical behavior of macroscopic bodies. On the basis of our analysis, we are led to conclude that the consideration of the noise represents a crucial element for understanding the laws of nature.

Fluctuation and Noise Letters•Aug 4, 2016•2 citations

Preface

Xavier Oriols

This paper is an introduction to the eleven works of the special issue on Quantum and Classical Frontiers of Noise. The weather, and its butterfly effect, is the typical example that explain why many natural phenomena are, in fact, not predictable with certainty. Noise in classical or quantum phenomena, understood as the difference between the empirical output of an experiment and its statistical prediction, is a measure of such uncertainty. One of the great contributions of noise appeared in 1905 when Einstein showed how the noisy (Brownian) motion of a dust particle seen in a microscope provided uncontroversial evidences on the existence of the (unseen) atoms. The aim of this special issue is to provoke discussions on how noise can help us to better understand (the reality behind) classical and quantum theories, and the frontier between them.

arXiv:1612.03430•Fluctuation and Noise Letters•Sep 1, 2016•1 citation

Are Biology and Medicine Only Physics? Building Bridges Between Conventional and Complementary Medicine

H. P. Dürr

In classical physics, the world is considered as a matter-based reality, the arrangement of whose parts in time is uniquely determined by certain dynamic laws. By contrast, modern quantum physics reveals that matter is not composed of matter, but reality is merely potentiality. The world has a holistic structure, which is based on fundamental relations and not material objects, admitting more open, indeterministic developments. In this more flexible causal framework, inanimate and animate matter are not to be considered as fundamentally different but as different order structures of the same immaterial entity. In a stable configuration, effectively all the uncertainties are statistically averaged out, thus the unique and deterministic behavior of ordinary inanimate matter is exhibited; whereas in the case of statically unstable but dynamically stable configurations, the “lively” features of the underlying quantum structure have a chance to surface to the mesocopic level and to be connected with what we observe as the phenomenon of life. This supposition can be more explicitly treated and clarified by identifying the electric dipole moment of biomolecules as the ordering parameter of the corresponding macroquantum system. This has important consequences for biology and medicine. In particular, it suggests the existence of a quantum-based “software,” essential perhaps for the logistics of biological processes, which are hidden behind the matter/energy-based “hardware” that alone is considered in the conventional approach. In medicine it opens an opportunity to build bridges between conventional medicine based essentially on the classical paradigm, and the various forms of complementary medicine, which have strong affinities with the new features of the modern holistic worldview.

Bulletin of Science Technology & Society•Oct 1, 2002•5 citations

Dynamics of observed reality: abridged version of classical and quantum mechanics. Technical report

Ahteshamul Haque, Thomas F. George

This paper is concerned with a unified description of classical and quantum physics. A different way of thinking about the quantum world is expounded, which already has led to significant results in statistical mechanics and holds future promise for quantum mechanics. An explanation is provided for the original motivation in quantum theory, the formalisms that have evolved from it, and their differences with the classical theories. The conceptual difficulty that permeates our view of the microscopic world is spelled out and a remedy thereof suggested.

•Aug 1, 1988•0 citations

L'imaginaire et l'intuition dans les sciences

Roger Balian

Abstract. Quantum physics against intuition. Since Galileo, deeper understanding of physical reality often contradicts everyday’s intuition. This trend has become dramatic a century ago, rendering modern physics abstruse to the laymen. The scientist can exert his intuition and his imagination within an elaborate mathematical language, but it is impossible to translate his ideas faithfully into ordinary language; this difficulty may be one of the causes of the present tarnish of the image of science. A first shock was brought in by relativity, which revolutionized our conceptions of space and time, but quantum physics presents even more counter-intuitive features. One has been led to represent physical quantities pertaining to a system, such as the position or the velocity of a particle, no longer by ordinary numbers but by “observables”, mathematical objects which belong to a non-commutative algebra. Namely, the product of two such observables is not a unique new observable but may depend on their order: the products AB and BA may differ.The values that a physical quantity can take constitute a set of ordinary numbers, the eigenvalues a( n) of the observable A. This set may be discrete as a consequence of the algebra. The discreteness of the eigenvalues of the energy of an atom explains the spectrum of its radiation. Any component of the intrinsic angular momentum of an electron can take only two opposite values, baffling our geometric intuition.If two observables commute (i.e., AB = BA), they are compatible: both may take well-defined values chosen among the eigenvalues. If they do not commute (i.e., AB ≠ BA), which occurs for the position and velocity of a particle, for the electric and magnetic field, or for the components of an angular momentum, they are incompatible: their values cannot be measured nor even specified simultaneously. Each of them presents statistical fluctuations which must be larger than some lower bound (Heisenberg’s inequality). The state of a system, prepared under some definite conditions, should be identified as the set of expectation values of all observables.Thus, quantum physics, our most fundamental description of nature, is a theory involving irreducible probabilities and unavoidable uncertainties. Its predictions do not refer to a single system, but to a statistical ensemble, and the observer cannot be completely disregarded. Moreover it may involve aspects which are apparently contradictory (Bohr’s complementarity). An electron, an atom or a molecule may behave in limiting cases either as a particle or as a wave; under intermediate conditions, it behaves as both, but each of the descriptions is blurred with probabilities. As a wave, it can interfere with itself. Likewise, an electromagnetic field has the double nature of a set of photons and of a wave. At the macroscopic scale, relative fluctuations are small, so that determinism emerges.Quantum probabilities differ from standard ones. In particular, quantum correlations involving four observables pair wise violate Bell’s inequalities, so that microscopic quantities are intrinsically indeterminate and depend on the observation process.The GHZ paradox, due to Greenberger, Horne and Zeilinger, exemplifies the most troublesome conceptual feature of quantum physics. Indeed, it baffles not only intuition, but also current logics. It deals with a physical system made of three correlated particles. Various observables, A1, A2, A3, B1, B2 and B3 ≡ B1 B2, which we do not specify here, can be measured on such a composite system. Each of them may take discrete values a1 , a2, a3, b1, b2 equal either to +1 or to –1. Since the three observables A1 B1, A2 B2 and A3 B3 are compatible, they can be simultaneously controlled. Consider then a statistical ensemble of systems, all prepared identically in such a way that A1 B1 = A2 B2 = A3 B3 = +1. If we measure A1 and B1, we shall find either a1 = b1 = +1 or a1 = b1 = –1, that is always a1 = b1; likewise for a2 = b2 = ±1 and a3 = b1 b2 = ±1. We are tempted to infer that a simultaneous determination of the values a1, a2 and a3 of A1, A2 and A3 (which are compatible) should verify a3 = a1 a2, that is, a1 a2 a3 = 1. However both theory and experiment provide in all cases a1 a2 a3 = –1. In fact the four statements a1 = b1, a2 = b2, a3 = b1 b2 and a1 a2 a3 = –1 which seem contradictory are separately “true”, in the sense that each one can be verified experimentally; but such experiments cannot be performed on a single system. We are not allowed to make a logical reasoning based on a simultaneous consideration of the values of B1 and A2 because these observables do not commute. No calculation, no experiment can simultaneously provide values for the numbers b1 and a2. Hence, we cannot regard as true together the statements a1 = b1 and a2 = b2, although they can be checked by separate experiments. Each one is true, but their union is meaningless.Thus, if theory does not allow us to imagine thought experiments in which several statements on a system might simultaneously be checked, we cannot draw conclusions by putting such statements together. We are led to regard the “truth” of a quantum statement as contextual. The values of physical quantities are not attached only to the system in itself, but also refer to the context in which their relations may be verified. Quantum mechanics does not deal with objects per se, but with what we know and what we can infer about them. It does not provide a direct image of the reality of the object since it involves its observation. Although it is a perfect tool for letting us make statistical predictions, and although it appears as our most basic theory owing to its precision and generality, it violates our daily intuition, our elementary mathematical intuition and our feelings about reality. Its probabilities and even its logics obey rather shocking new rules.

Hermann eBooks•Dec 9, 2009•0 citations
Classical dynamics and the classical concept of space-time reality is based on the assumption that the objects of physics can be observed continuously. The discrete structure of matter (atoms) and fields (quanta), however, implies that the process of observation is quantized. In this paper we discuss the consequences of this paradigm change from continuity to discreteness and from determinism to chance. By taking into account the quantized structure of observation, we are led to the conclusion that the classical concept of reality has to be replaced by a quantum concept of observability. It implies that quantum dynamics is not a generalization of classical dynamics. Rather, the two theories apply to complementary idealizations of nature representing opposite extremes on a scale of observability. They are related by correspondence rules. Both theories disregard experimental noise. Statistical and thermal noise provide the experimental foundation for statistical physics.
Abstract Quantum Theory, similar to Relativity Theory, requires a new concept of space-time, imposed by a universal constant. While velocity of lightcnot being infinite calls for a redefinition of space-time on large and cosmological scales, quantization of action in terms of a finite, i.e. non vanishing, universal constanthrequires a redefinition of space-time on very small scales. Most importantly, the classical notion of “time”, as one common continuous time variable and nature evolving continuously “in time”, has to be replaced by an infinite manifold of transition rates for discontinuous quantum transitions. The fundamental laws of quantum physics, commutation relations and quantum equations of motion, resulted from Max Born’s recognition of the basic principle of quantum physics:To each change in nature corresponds an integer number of quanta of action. Action variables may only change by integer values ofh, requiring all other physical quantities to change by discrete steps, “quantum jumps”. The mathematical implementation of this principle led to commutation relations and quantum equations of motion. The notion of “point” in space-time looses its physical significance; quantum uncertainties of time, position, just as any other physical quantity, are necessary consequences of quantization of action.
We briefly review the difficulties of the standard version of quantum mechanics in accounting for all kinds of physical processes (in particular both the micro and the macroscopic ones) and we argue that to overcome such difficulties one has to give up the superposition principle, i.e., to break the linear nature of the theory. We then show that the simple introduction of terms violating the linearity of the deterministic evolution of the standard theory has physically unacceptable consequences. Taking this into account we are led to modify the quantum dynamics by adding to Schrödinger’s equation, besides nonlinear terms, a coupling with an appropriate noise. We show that, with such a move, one can work out a theory which is internally consistent and it allows to account, in a quite simple and physically appealing way, for natural processes including the measurements and the classical behavior of macroscopic bodies. On the basis of our analysis, we are led to conclude that the consideration of the noise represents a crucial element for understanding the laws of nature.
This paper is an introduction to the eleven works of the special issue on Quantum and Classical Frontiers of Noise. The weather, and its butterfly effect, is the typical example that explain why many natural phenomena are, in fact, not predictable with certainty. Noise in classical or quantum phenomena, understood as the difference between the empirical output of an experiment and its statistical prediction, is a measure of such uncertainty. One of the great contributions of noise appeared in 1905 when Einstein showed how the noisy (Brownian) motion of a dust particle seen in a microscope provided uncontroversial evidences on the existence of the (unseen) atoms. The aim of this special issue is to provoke discussions on how noise can help us to better understand (the reality behind) classical and quantum theories, and the frontier between them.
In classical physics, the world is considered as a matter-based reality, the arrangement of whose parts in time is uniquely determined by certain dynamic laws. By contrast, modern quantum physics reveals that matter is not composed of matter, but reality is merely potentiality. The world has a holistic structure, which is based on fundamental relations and not material objects, admitting more open, indeterministic developments. In this more flexible causal framework, inanimate and animate matter are not to be considered as fundamentally different but as different order structures of the same immaterial entity. In a stable configuration, effectively all the uncertainties are statistically averaged out, thus the unique and deterministic behavior of ordinary inanimate matter is exhibited; whereas in the case of statically unstable but dynamically stable configurations, the “lively” features of the underlying quantum structure have a chance to surface to the mesocopic level and to be connected with what we observe as the phenomenon of life. This supposition can be more explicitly treated and clarified by identifying the electric dipole moment of biomolecules as the ordering parameter of the corresponding macroquantum system. This has important consequences for biology and medicine. In particular, it suggests the existence of a quantum-based “software,” essential perhaps for the logistics of biological processes, which are hidden behind the matter/energy-based “hardware” that alone is considered in the conventional approach. In medicine it opens an opportunity to build bridges between conventional medicine based essentially on the classical paradigm, and the various forms of complementary medicine, which have strong affinities with the new features of the modern holistic worldview.
This paper is concerned with a unified description of classical and quantum physics. A different way of thinking about the quantum world is expounded, which already has led to significant results in statistical mechanics and holds future promise for quantum mechanics. An explanation is provided for the original motivation in quantum theory, the formalisms that have evolved from it, and their differences with the classical theories. The conceptual difficulty that permeates our view of the microscopic world is spelled out and a remedy thereof suggested.
Abstract. Quantum physics against intuition. Since Galileo, deeper understanding of physical reality often contradicts everyday’s intuition. This trend has become dramatic a century ago, rendering modern physics abstruse to the laymen. The scientist can exert his intuition and his imagination within an elaborate mathematical language, but it is impossible to translate his ideas faithfully into ordinary language; this difficulty may be one of the causes of the present tarnish of the image of science. A first shock was brought in by relativity, which revolutionized our conceptions of space and time, but quantum physics presents even more counter-intuitive features. One has been led to represent physical quantities pertaining to a system, such as the position or the velocity of a particle, no longer by ordinary numbers but by “observables”, mathematical objects which belong to a non-commutative algebra. Namely, the product of two such observables is not a unique new observable but may depend on their order: the products AB and BA may differ.The values that a physical quantity can take constitute a set of ordinary numbers, the eigenvalues a( n) of the observable A. This set may be discrete as a consequence of the algebra. The discreteness of the eigenvalues of the energy of an atom explains the spectrum of its radiation. Any component of the intrinsic angular momentum of an electron can take only two opposite values, baffling our geometric intuition.If two observables commute (i.e., AB = BA), they are compatible: both may take well-defined values chosen among the eigenvalues. If they do not commute (i.e., AB ≠ BA), which occurs for the position and velocity of a particle, for the electric and magnetic field, or for the components of an angular momentum, they are incompatible: their values cannot be measured nor even specified simultaneously. Each of them presents statistical fluctuations which must be larger than some lower bound (Heisenberg’s inequality). The state of a system, prepared under some definite conditions, should be identified as the set of expectation values of all observables.Thus, quantum physics, our most fundamental description of nature, is a theory involving irreducible probabilities and unavoidable uncertainties. Its predictions do not refer to a single system, but to a statistical ensemble, and the observer cannot be completely disregarded. Moreover it may involve aspects which are apparently contradictory (Bohr’s complementarity). An electron, an atom or a molecule may behave in limiting cases either as a particle or as a wave; under intermediate conditions, it behaves as both, but each of the descriptions is blurred with probabilities. As a wave, it can interfere with itself. Likewise, an electromagnetic field has the double nature of a set of photons and of a wave. At the macroscopic scale, relative fluctuations are small, so that determinism emerges.Quantum probabilities differ from standard ones. In particular, quantum correlations involving four observables pair wise violate Bell’s inequalities, so that microscopic quantities are intrinsically indeterminate and depend on the observation process.The GHZ paradox, due to Greenberger, Horne and Zeilinger, exemplifies the most troublesome conceptual feature of quantum physics. Indeed, it baffles not only intuition, but also current logics. It deals with a physical system made of three correlated particles. Various observables, A1, A2, A3, B1, B2 and B3 ≡ B1 B2, which we do not specify here, can be measured on such a composite system. Each of them may take discrete values a1 , a2, a3, b1, b2 equal either to +1 or to –1. Since the three observables A1 B1, A2 B2 and A3 B3 are compatible, they can be simultaneously controlled. Consider then a statistical ensemble of systems, all prepared identically in such a way that A1 B1 = A2 B2 = A3 B3 = +1. If we measure A1 and B1, we shall find either a1 = b1 = +1 or a1 = b1 = –1, that is always a1 = b1; likewise for a2 = b2 = ±1 and a3 = b1 b2 = ±1. We are tempted to infer that a simultaneous determination of the values a1, a2 and a3 of A1, A2 and A3 (which are compatible) should verify a3 = a1 a2, that is, a1 a2 a3 = 1. However both theory and experiment provide in all cases a1 a2 a3 = –1. In fact the four statements a1 = b1, a2 = b2, a3 = b1 b2 and a1 a2 a3 = –1 which seem contradictory are separately “true”, in the sense that each one can be verified experimentally; but such experiments cannot be performed on a single system. We are not allowed to make a logical reasoning based on a simultaneous consideration of the values of B1 and A2 because these observables do not commute. No calculation, no experiment can simultaneously provide values for the numbers b1 and a2. Hence, we cannot regard as true together the statements a1 = b1 and a2 = b2, although they can be checked by separate experiments. Each one is true, but their union is meaningless.Thus, if theory does not allow us to imagine thought experiments in which several statements on a system might simultaneously be checked, we cannot draw conclusions by putting such statements together. We are led to regard the “truth” of a quantum statement as contextual. The values of physical quantities are not attached only to the system in itself, but also refer to the context in which their relations may be verified. Quantum mechanics does not deal with objects per se, but with what we know and what we can infer about them. It does not provide a direct image of the reality of the object since it involves its observation. Although it is a perfect tool for letting us make statistical predictions, and although it appears as our most basic theory owing to its precision and generality, it violates our daily intuition, our elementary mathematical intuition and our feelings about reality. Its probabilities and even its logics obey rather shocking new rules.