Classical and quantum physics represent two distinct theories; however, quantum physics is regarded as the more fundamental of the two. It is posited that classical mechanics should arise from quantum mechanics under certain limiting conditions. Nevertheless, this remains a challenging objective. In this work, we explore the potential for unifying the dynamics of classical and quantum physics. This discussion does not suggest that classical behavior emerges from quantum mechanics; rather, it demonstrates the exact equivalence between the dynamics of quantum observables and their classical counterparts. It is shown that the Heisenberg equations of motion can be cast in a form that is structurally equivalent to Newton's equations of motion, with $\hbar$ dropping out from the equations. In a generalized analysis, the Heisenberg equations are cast in a form that is identical to the classical Hamilton's equations of motion. This implies that both quantum and classical dynamics are governed by the same form of equations, with the Heisenberg operators substituting the classical observables.Classical and quantum physics represent two distinct theories; however, quantum physics is regarded as the more fundamental of the two. It is posited that classical mechanics should arise from quantum mechanics under certain limiting conditions. Nevertheless, this remains a challenging objective. In this work, we explore the potential for unifying the dynamics of classical and quantum physics. This discussion does not suggest that classical behavior emerges from quantum mechanics; rather, it demonstrates the exact equivalence between the dynamics of quantum observables and their classical counterparts. It is shown that the Heisenberg equations of motion can be cast in a form that is structurally equivalent to Newton's equations of motion, with $\hbar$ dropping out from the equations. In a generalized analysis, the Heisenberg equations are cast in a form that is identical to the classical Hamilton's equations of motion. This implies that both quantum and classical dynamics are governed by the same form of equations, with the Heisenberg operators substituting the classical observables.

quant-pharXiv:2601.10423Jan 16, 20260 citations

Measurement Quantization Unites Classical and Quantum Physics

Jody A. Geiger

Unifying quantum and classical physics has proved difficult as their postulates are conflicting. Using the notion of counts of the fundamental measures—length, mass, and time—a unifying description is resolved. A theoretical framework is presented in a set of postulates by which a conversion between expressions from quantum and classical physics can be made. Conversions of well-known expressions from different areas of physics (quantum physics, gravitation, optics and cosmology) exemplify the approach and mathematical procedures. The postulated integer counts of fundamental measures change our understanding of length, suggesting that our current understanding of reality is distorted.Unifying quantum and classical physics has proved difficult as their postulates are conflicting. Using the notion of counts of the fundamental measures—length, mass, and time—a unifying description is resolved. A theoretical framework is presented in a set of postulates by which a conversion between expressions from quantum and classical physics can be made. Conversions of well-known expressions from different areas of physics (quantum physics, gravitation, optics and cosmology) exemplify the approach and mathematical procedures. The postulated integer counts of fundamental measures change our understanding of length, suggesting that our current understanding of reality is distorted.

Journal of High Energy Physics Gravitation and CosmologyJan 1, 20187 citations

Classical and Quantum Physics

Marmo, G, David Martı́n de Diego, Lecanda, Miguel

Springer proceedings in physicsJan 1, 201918 citations

Both Classical & Quantum Information; Both Bit & Qubit: Both Physical & Transcendental Time

Vasil Dinev Penchev

Information can be considered as the most fundamental, philosophical, physical and mathematical concept originating from the totality by means of physical and mathematical transcendentalism (the counterpart of philosophical transcendentalism). Classical and quantum information, particularly by their units, bit and qubit, correspond and unify the finite and infinite. As classical information is relevant to finite series and sets, as quantum information, to infinite ones. A fundamental joint relativity of the finite and infinite, of the external and internal is to be investigated. The corresponding invariance is able to define physical action and its quantity only on the basis of information and especially: on the relativity of classical and quantum information. The concept of transcendental time, an epoché in relation to the direction of time arrow can be defined. Its correlate is that information invariant to the finite and infinite, therefore unifying both classical and quantum information.Information can be considered as the most fundamental, philosophical, physical and mathematical concept originating from the totality by means of physical and mathematical transcendentalism (the counterpart of philosophical transcendentalism). Classical and quantum information, particularly by their units, bit and qubit, correspond and unify the finite and infinite. As classical information is relevant to finite series and sets, as quantum information, to infinite ones. A fundamental joint relativity of the finite and infinite, of the external and internal is to be investigated. The corresponding invariance is able to define physical action and its quantity only on the basis of information and especially: on the relativity of classical and quantum information. The concept of transcendental time, an epoché in relation to the direction of time arrow can be defined. Its correlate is that information invariant to the finite and infinite, therefore unifying both classical and quantum information.

Jan 1, 20210 citations

Classical approach to quantum theory

Jack Cohn

International Journal of Theoretical PhysicsJan 1, 19832 citations

\hbar

dropping out from the equations. In a generalized analysis, the Heisenberg equations are cast in a form that is identical to the classical Hamilton's equations of motion. This implies that both quantum and classical dynamics are governed by the same form of equations, with the Heisenberg operators substituting the classical observables.