© 2026 Aqora Quantum S.A.S.

Terms Privacy Legal Notice

CRC Press eBooks

From Quantum to Classical

F. J. Duarte

Published Apr 10, 2026• 0 citations

Abstract

Born was convinced that the ‘indeterministic foundations’ of quantum mechanics were here to stay. He also left a calling, that has been largely ignored, to show that the ‘apparently deterministic’ laws of classical physics were derivable from the indeterminacy of quantum mechanics. Here, we attempt to answer the calling left to us by Born and we do so first by showing that the beautiful laws of classical optics are directly derivable from the N -slit quantum probability equation. Secondly, we use the quantum probability dependent intensity to arrive, via Heisenberg's uncertainty principle, first at Newton's second law and then to Newton's law of universal gravitational. What this shows is that there is an explicit cohesiveness in physics with quantum mechanics at the foundations. The only ‘price to pay’ is that the laws of classical physics become approximate rather than ‘exact.’ No more determinism. This is entirely consistent with the fields of experimental physics, quantum or classical, where no measurement is exact.

DOI: 10.1201/9781003649434-17

Related papers

From quantum interference to Newton’s second law

Francisco Duarte

An indeterministic version of Newton’s second law is derived from the formalism of N-slit quantum interference measurements. This result is an extension of the derivation of the approximate version of Planck’s quantum energy equation. Going from the quantum realm to the classical domain is achieved via the application of Heisenberg’s uncertainty principle. The stochastic version of Newton’s second law is then extended to provide a derivation of an approximate version of Newton’s law of universal gravitational. Our results are applied to formulate an expression for the derivative of the momentum operator.

•Feb 3, 2025•0 citations

From quantum interference to Newton’s second law

F.J. Duarte

An indeterministic version of Newton’s second law is derived from the formalism of N-slit quantum interference measurements. This result is an extension of the derivation of the approximate version of Planck’s quantum energy equation. Going from the quantum realm to the classical domain is achieved via the application of Heisenberg’s uncertainty principle. The stochastic version of Newton’s second law is then extended to provide a derivation of an approximate version of Newton’s law of universal gravitational. Our results are applied to formulate an expression for the derivative of the momentum operator.

•Feb 27, 2025•0 citations

From quantum interference to Newton’s second law

Francisco Duarte

An indeterministic version of Newton’s second law is derived from the formalism of N-slit quantum interference measurements. This result is an extension of the derivation of the approximate version of Planck’s quantum energy equation. Going from the quantum realm to the classical domain is achieved via the application of Heisenberg’s uncertainty principle. The stochastic version of Newton’s second law is then extended to provide a derivation of an approximate version of Newton’s law of universal gravitational. Our results are applied to formulate an expression for the derivative of the momentum operator.

•Jan 21, 2025•0 citations

From quantum interference to Newton’s second law

F.J. Duarte

An indeterministic version of Newton’s second law is derived from the formalism of N-slit quantum interference measurements. This result is an extension of the derivation of the approximate version of Planck’s quantum energy equation. Going from the quantum realm to the classical domain is achieved via the application of Heisenberg’s uncertainty principle. The stochastic version of Newton’s second law is then extended to provide a derivation of an approximate version of Newton’s law of universal gravitational. Our results are applied to formulate an expression for the derivative of the momentum operator.

•Jan 21, 2025•0 citations

From quantum interference to Newton’s second law

F.J. Duarte

An indeterministic version of Newton’s second law is derived from the formalism of N-slit quantum interference measurements. This result is an extension of the derivation of the approximate version of Planck’s quantum energy equation. Going from the quantum realm to the classical domain is achieved via the application of Heisenberg’s uncertainty principle. The stochastic version of Newton’s second law is then extended to provide a derivation of an approximate version of Newton’s law of universal gravitational. Our results are applied to formulate an expression for the derivative of the momentum operator.

•Dec 1, 2025•0 citations

From quantum interference to Newton’s second law

F.J. Duarte

An indeterministic version of Newton’s second law is derived from the formalism of N-slit quantum interference measurements. This result is an extension of the derivation of the approximate version of Planck’s quantum energy equation. Going from the quantum realm to the classical domain is achieved via the application of Heisenberg’s uncertainty principle. The stochastic version of Newton’s second law is then extended to provide a derivation of an approximate version of Newton’s law of universal gravitational. Our results are applied to formulate an expression for the derivative of the momentum operator.

•Jan 16, 2026•0 citations

Born was convinced that the ‘indeterministic foundations’ of quantum mechanics were here to stay. He also left a calling, that has been largely ignored, to show that the ‘apparently deterministic’ laws of classical physics were derivable from the indeterminacy of quantum mechanics. Here, we attempt to answer the calling left to us by Born and we do so first by showing that the beautiful laws of classical optics are directly derivable from the N -slit quantum probability equation. Secondly, we use the quantum probability dependent intensity to arrive, via Heisenberg's uncertainty principle, first at Newton's second law and then to Newton's law of universal gravitational. What this shows is that there is an explicit cohesiveness in physics with quantum mechanics at the foundations. The only ‘price to pay’ is that the laws of classical physics become approximate rather than ‘exact.’ No more determinism. This is entirely consistent with the fields of experimental physics, quantum or classical, where no measurement is exact.

An indeterministic version of Newton’s second law is derived from the formalism of N-slit quantum interference measurements. This result is an extension of the derivation of the approximate version of Planck’s quantum energy equation. Going from the quantum realm to the classical domain is achieved via the application of Heisenberg’s uncertainty principle. The stochastic version of Newton’s second law is then extended to provide a derivation of an approximate version of Newton’s law of universal gravitational. Our results are applied to formulate an expression for the derivative of the momentum operator.

An indeterministic version of Newton’s second law is derived from the formalism of N-slit quantum interference measurements. This result is an extension of the derivation of the approximate version of Planck’s quantum energy equation. Going from the quantum realm to the classical domain is achieved via the application of Heisenberg’s uncertainty principle. The stochastic version of Newton’s second law is then extended to provide a derivation of an approximate version of Newton’s law of universal gravitational. Our results are applied to formulate an expression for the derivative of the momentum operator.

An indeterministic version of Newton’s second law is derived from the formalism of N-slit quantum interference measurements. This result is an extension of the derivation of the approximate version of Planck’s quantum energy equation. Going from the quantum realm to the classical domain is achieved via the application of Heisenberg’s uncertainty principle. The stochastic version of Newton’s second law is then extended to provide a derivation of an approximate version of Newton’s law of universal gravitational. Our results are applied to formulate an expression for the derivative of the momentum operator.

An indeterministic version of Newton’s second law is derived from the formalism of N-slit quantum interference measurements. This result is an extension of the derivation of the approximate version of Planck’s quantum energy equation. Going from the quantum realm to the classical domain is achieved via the application of Heisenberg’s uncertainty principle. The stochastic version of Newton’s second law is then extended to provide a derivation of an approximate version of Newton’s law of universal gravitational. Our results are applied to formulate an expression for the derivative of the momentum operator.

An indeterministic version of Newton’s second law is derived from the formalism of N-slit quantum interference measurements. This result is an extension of the derivation of the approximate version of Planck’s quantum energy equation. Going from the quantum realm to the classical domain is achieved via the application of Heisenberg’s uncertainty principle. The stochastic version of Newton’s second law is then extended to provide a derivation of an approximate version of Newton’s law of universal gravitational. Our results are applied to formulate an expression for the derivative of the momentum operator.

An indeterministic version of Newton’s second law is derived from the formalism of N-slit quantum interference measurements. This result is an extension of the derivation of the approximate version of Planck’s quantum energy equation. Going from the quantum realm to the classical domain is achieved via the application of Heisenberg’s uncertainty principle. The stochastic version of Newton’s second law is then extended to provide a derivation of an approximate version of Newton’s law of universal gravitational. Our results are applied to formulate an expression for the derivative of the momentum operator.