Incompatible observables in classical physics: A closer look at measurement in Hamiltonian mechanics

• URL: http://arxiv.org/abs/2104.02064v2
• Date: Thu, 06 Mar 2025 01:23:58 GMT
• Title: Incompatible observables in classical physics: A closer look at measurement in Hamiltonian mechanics
• Authors: David Theurel,
• Abstract summary: I examine measurement in classical Hamiltonian physics as a process involving the joint evolution of an object-system and a finite-temperature measuring apparatus.<n>Measuring an observable leaves all Poisson-commuting observables undisturbed but inevitably disturbs all non-Poisson-commuting observables.<n>I show that a classical version of Ozawa's model of quantum measurement, originally proposed as a means to violate the Heisenberg relation, does not violate the classical relation.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Quantum theory famously entails the existence of incompatible measurements; pairs of observables which cannot be simultaneously measured to arbitrary precision. Incompatibility is widely regarded to be a uniquely quantum phenomenon, linked to failure to commute of quantum operators. Even in the face of deep parallels between quantum commutators and classical Poisson brackets, no connection has been established between the Poisson algebra and any intrinsic limitations to classical measurement. Here I examine measurement in classical Hamiltonian physics as a process involving the joint evolution of an object-system and a finite-temperature measuring apparatus. Instead of the ideal measurement capable of extracting information without disturbing the system, I find a Heisenberg-like precision-disturbance relation: Measuring an observable leaves all Poisson-commuting observables undisturbed but inevitably disturbs all non-Poisson-commuting observables. In this relation the role of h-bar is played by an apparatus-specific quantity, q-bar. While not a universal constant, q-bar takes a finite positive value for any apparatus that can be built. I show that a classical version of Ozawa's model of quantum measurement, originally proposed as a means to violate the Heisenberg relation, does not violate the classical relation. Hence, incompatibility may prove to be a feature not only of quantum, but of classical physics too. This approach points the way to studying the Bayesian epistemology of classical physics, which was until now assumed to be trivial. It now seems possible that it is non-trivial and bears a resemblance to the quantum formalism. These findings may be of interest to researchers working on foundations of quantum mechanics, particularly for psi-epistemic interpretations. And there may be applications in the fields of precision measurement, nanoengineering and molecular machines.

Related papers

• Observation of Quantum Darwinism and the Origin of Classicality with Superconducting Circuits [9.09683951826704]
  How can we rationalize everyday classical observations from an inherently quantum world? Quantum Darwinism offers a compelling framework to explain this emergence of classicality. We observe the highly structured branching quantum states that support classicality and the saturation of quantum mutual information.
  arXiv  Detail & Related papers  (2025-04-01T13:33:32Z)
• Quantum-like cognition and decision making in the light of quantum measurement theory [0.0]
  We characterize the class of quantum measurements that matches the applications of quantum theory to cognition. We highlight the role of it noncommutativity of the state update maps generated by measurement back action'' We speculate that distinguishing quantum-like properties of the cognitive effects are the expressions of the latter, or possibly both.
  arXiv  Detail & Related papers  (2025-03-07T18:30:44Z)
• Bohmian Mechanics fails to compute multi-time correlations [0.0]
  Bohmian mechanics is a realistic, non-local theory of classical particle trajectories. We set up a spatial version of the GHZ system with qubits realised as positional observables.
  arXiv  Detail & Related papers  (2025-02-20T11:03:38Z)
• Operationally classical simulation of quantum states [41.94295877935867]
  A classical state-preparation device cannot generate superpositions and hence its emitted states must commute. We show that no such simulation exists, thereby certifying quantum coherence. Our approach is a possible avenue to understand how and to what extent quantum states defy generic models based on classical devices.
  arXiv  Detail & Related papers  (2025-02-03T15:25:03Z)
• Compatibility of Quantum Measurements and the Emergence of Classical Objectivity [0.0]
  We consider the KDQ distributions describing arbitrary collections of measurements on disjoint components of some generic multipartite system. We show that the system dynamics ensures that these distributions are classical if and only if the Hamiltonian supports Quantum Darwinism.
  arXiv  Detail & Related papers  (2024-11-16T19:01:30Z)
• Quantum Simulation of Nonlinear Dynamical Systems Using Repeated Measurement [42.896772730859645]
  We present a quantum algorithm based on repeated measurement to solve initial-value problems for nonlinear ordinary differential equations. We apply this approach to the classic logistic and Lorenz systems in both integrable and chaotic regimes.
  arXiv  Detail & Related papers  (2024-10-04T18:06:12Z)
• Efficiency of Dynamical Decoupling for (Almost) Any Spin-Boson Model [44.99833362998488]
  We analytically study the dynamical decoupling of a two-level system coupled with a structured bosonic environment. We find sufficient conditions under which dynamical decoupling works for such systems. Our bounds reproduce the correct scaling in various relevant system parameters.
  arXiv  Detail & Related papers  (2024-09-24T04:58:28Z)
• The Hidden Ontological Variable in Quantum Harmonic Oscillators [0.0]
  The standard quantum mechanical harmonic oscillator has an exact, dual relationship with a completely classical system. One finds that, where the classical system always obeys the rule "probability in = probability out", the same probabilities are quantum probabilities in the quantum system.
  arXiv  Detail & Related papers  (2024-07-25T16:05:18Z)
• Is the Born rule a result of measurement noise? [0.0]
  The Born rule asserts the distribution of eigenstates observed in unbiased quantum measurements, but the reason it holds remains elusive. This manuscript discusses how the Born rule might be explained by Schrodinger equation dynamics.
  arXiv  Detail & Related papers  (2024-07-03T14:20:11Z)
• Teaching ideal quantum measurement, from dynamics to interpretation [0.0]
  Ideal measurements are analyzed as processes of interaction between the tested system S and an apparatus A. Conservation laws are shown to entail two independent relaxation mechanisms. Born's rule then arises from the conservation law for the tested observable.
  arXiv  Detail & Related papers  (2024-05-29T22:36:06Z)
• Beable-guided measurement theory [0.0]
  We investigate the genesis of the quantum randomness in the de Broglie's theory in more details. We show that the strong fluctuations of beable parameters arise randomising the system in accordance with the uncertainty relation.
  arXiv  Detail & Related papers  (2024-04-15T17:01:22Z)
• Evolution of many-body systems under ancilla quantum measurements [58.720142291102135]
  We study the concept of implementing quantum measurements by coupling a many-body lattice system to an ancillary degree of freedom. We find evidence of a disentangling-entangling measurement-induced transition as was previously observed in more abstract models.
  arXiv  Detail & Related papers  (2023-03-13T13:06:40Z)
• Quantum measurements and equilibration: the emergence of objective reality via entropy maximisation [0.0]
  We formalise the hypothesis that quantum measurements are driven by the natural tendency of closed systems to maximize entropy. We lay the groundwork for self-contained models of quantum measurement, proposing improvements to our simple scheme.
  arXiv  Detail & Related papers  (2023-02-22T10:06:17Z)
• Quantum Instability [30.674987397533997]
  We show how a time-independent, finite-dimensional quantum system can give rise to a linear instability corresponding to that in the classical system. An unstable quantum system has a richer spectrum and a much longer recurrence time than a stable quantum system.
  arXiv  Detail & Related papers  (2022-08-05T19:53:46Z)
• Probing finite-temperature observables in quantum simulators of spin systems with short-time dynamics [62.997667081978825]
  We show how finite-temperature observables can be obtained with an algorithm motivated from the Jarzynski equality. We show that a finite temperature phase transition in the long-range transverse field Ising model can be characterized in trapped ion quantum simulators.
  arXiv  Detail & Related papers  (2022-06-03T18:00:02Z)
• Measurement of a quantum system with a classical apparatus using ensembles on configuration space [0.48733623015338234]
  We use the approach of ensembles on configurations space to give a detailed account of a classical apparatus measuring the position of a quantum particle. We show that the probability of the pointer of the classical apparatus is left in a state that corresponds to the probability of the quantum particle. Since this formalism incorporates uncertainties and finite measurement precision, it is well suited for metrological applications.
  arXiv  Detail & Related papers  (2022-05-19T15:48:12Z)
• Finite resolution ancilla-assisted measurements of quantum work distributions [77.34726150561087]
  We consider an ancilla-assisted protocol measuring the work done on a quantum system driven by a time-dependent Hamiltonian. We consider system Hamiltonians which both commute and do not commute at different times, finding corrections to fluctuation relations like the Jarzynski equality and the Crooks relation.
  arXiv  Detail & Related papers  (2021-11-30T15:08:25Z)
• Gentle Measurement as a Principle of Quantum Theory [9.137554315375919]
  We propose the gentle measurement principle (GMP) as one of the principles at the foundation of quantum mechanics. We show, within the framework of general probabilistic theories, that GMP imposes strong restrictions on the law of physics.
  arXiv  Detail & Related papers  (2021-03-28T11:59:49Z)
• Evolution of a Non-Hermitian Quantum Single-Molecule Junction at Constant Temperature [62.997667081978825]
  We present a theory for describing non-Hermitian quantum systems embedded in constant-temperature environments. We find that the combined action of probability losses and thermal fluctuations assists quantum transport through the molecular junction.
  arXiv  Detail & Related papers  (2021-01-21T14:33:34Z)
• A non-relativistic theory of quantum mechanics with local modulus symmetry [8.415967794907697]
  We have constructed a non-relativistic theory of quantum mechanics based on local modulus symmetry. A new real and positive function called the quantum metric function is attached to the complex conjugate of the wave function. In an expanding universe, these theoretical features produce new effects that deviate from predictions of conventional quantum mechanics and Newtonian gravity.
  arXiv  Detail & Related papers  (2020-08-18T05:36:11Z)
• Entropic Uncertainty Relations and the Quantum-to-Classical transition [77.34726150561087]
  We aim to shed some light on the quantum-to-classical transition as seen through the analysis of uncertainty relations. We employ entropic uncertainty relations to show that it is only by the inclusion of imprecision in our model of macroscopic measurements that we can prepare a system with two simultaneously well-defined quantities.
  arXiv  Detail & Related papers  (2020-03-04T14:01:17Z)
• Non-destructively probing the thermodynamics of quantum systems with qumodes [0.6144680854063939]
  In quantum systems there is often a destruction of the system itself due to the means of measurement. One approach to circumventing this is the use of ancillary probes that couple to the system under investigation. We highlight means by which continuous variable quantum modes (qumodes) can be employed to probe the thermodynamics of quantum systems in and out of equilibrium.
  arXiv  Detail & Related papers  (2017-07-13T17:57:11Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.