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Quantum Mechanics and the Arrow of Time

Richard Joseph Oldani

Published May 26, 2026• 0 citations
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Abstract

We reformulate matrix mechanics by incrementally heating a single hydrogen atom in order to derive the complete, diagonalized Hamiltonian matrix. The spectral lines and transition probabilities cannot be generated by reversing time thereby demonstrating asymmetry. Experimental evidence in support of the theoretical model is obtained from experiments performed with the simplest quantum system, an electron cyclotron. Wave mechanics is also reformulated by altering the original Schrödinger equation describing a time symmetric, conservative system to a system of two independent equations describing a time asymmetric, non-conservative system.

DOI
10.20944/preprints202601.2089.v4

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We reformulate matrix mechanics by incrementally heating a single hydrogen atom in order to derive the complete, diagonalized Hamiltonian matrix. The spectral lines and transition probabilities cannot be generated by reversing time thereby demonstrating asymmetry. Experimental evidence in support of the theoretical model is obtained from experiments performed with the simplest quantum system, an electron cyclotron. Wave mechanics is also reformulated by altering the original Schrödinger equation describing a time symmetric, conservative system to a system of two independent equations describing a time asymmetric, non-conservative system.
We reformulate matrix mechanics by incrementally heating a single hydrogen atom in order to derive the complete, diagonalized Hamiltonian matrix. The spectral lines and transition probabilities cannot be generated by reversing time thereby demonstrating asymmetry. Experimental evidence in support of the theoretical model is obtained from experiments performed with the simplest quantum system, an electron cyclotron. Wave mechanics is also reformulated by altering the original Schrödinger equation describing a time symmetric, conservative system to a system of two independent equations describing a time asymmetric, non-conservative system.
Matrix mechanics is not considered important for understanding quantum mechanics; however, it is the key to understanding time reversal asymmetry. We use a single, solitary atom to derive the diagonalized Hamiltonian matrix in continuous time and use it to visualize the irreversibility of time in a quantum system. Graphic evidence in support of the model is obtained from experiments performed with the simplest quantum system, an electron cyclotron. Theoretical arguments supporting time asymmetry in statistical mechanics that were presented by Feynman and Einstein are also cited. It is hypothesized that equations describing time reversal asymmetry must be derived in energy-time coordinates.
We show time reversal asymmetry in quantum mechanics by isolating a single, solitary hydrogen atom in a black body, deriving from it the diagonalized Hamiltonian matrix in continuous time, and using it to visualize the irreversibility of the emission and absorption of radiation. Graphic evidence in support of the model is obtained from experiments performed with the simplest quantum system, an electron cyclotron. The experimental evidence is used to obtain equations of motion to describe time asymmetry with respect to the energy-time conjugate variables in linear time which complement the time symmetric equations of motion in position-momentum coordinates given with respect to cyclical time. Theoretical arguments by Feynman and Einstein are shown to support time reversal asymmetry.
Matrix mechanics describes the spectral emissions of hydrogen gas, but quantum mechanics concerns the emission and absorption of radiation by a single atom. To obtain the spectral emissions of a single hydrogen atom we reformulate matrix mechanics by introducing thermal energy in infinitesimal increments and registering the spectral lines one by one until a complete spectrum is obtained. Wave mechanics is reformulated from a conservative to a non-conservative system by linking the output of matrix mechanics to the input of wave mechanics. To describe the gradual increase and decrease of energy by a quantum system we integrate between two specific endpoints, the atomic orbitals, and two specific times, the period τ, which are the conditions necessary for Hamilton’s principle. The Lagrangian method is shown to be superior for analyzing quantum theory because it describes quantum systems relativistically as evolutions in time.
Matrix mechanics describes the spectral emissions of hydrogen gas, but quantum mechanics concerns the emission and absorption of radiation by a single atom. To obtain the spectral emissions of a single hydrogen atom we introduce thermal energy in infinitesimal increments registering the spectral lines one by one until a complete spectrum is obtained. We describe the gradual increase of the internal quantum mechanical energy in a non-conservative system by integrating between two specific endpoints, the atomic orbitals, and two specific times, the period τ, which are the conditions necessary for Hamilton’s principle. Wave mechanics is shown to be limited to conservative systems. A complete quantum mechanics is formulated using energy-time conjugate variables as the time integral of a Lagrangian independently of Hamiltonian formulations that use position-momentum conjugate variables.
Matrix mechanics describes the spectral emissions of hydrogen gas, but quantum mechanics concerns the emission and absorption of radiation by a single atom. To obtain the spectral emissions of a single hydrogen atom we introduce thermal energy in infinitesimal increments registering the spectral lines one by one until a complete spectrum is obtained. We describe the gradual increase of the internal quantum mechanical energy by integrating between two specific endpoints, the atomic orbitals, and two specific times, the period τ, which are the conditions necessary for Hamilton’s principle. Continuous time is thereby introduced to quantum mechanics during energy absorption by means of a Lagrangian formulation using energy-time conjugate variables, independently of Hamiltonian formulations that use position-momentum conjugate variables.