Quantum Mechanics and the Arrow of Time

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.