Time asymmetry and quantum equations of motion

Joan A. Vaccaro

An asymmetry exists between time and space in the sense that physical systems inevitably evolve over time, whereas there is no corresponding ubiquitous translation over space. The asymmetry, which is presumed to be elemental , is represented by equations of motion and conservation laws that operate differently over time and space. If, however, the asymmetry was found to be due to deeper causes, this conventional view of time evolution would need reworking. Here we show, using a sum-over-paths formalism, that a violation of time reversal (T) symmetry might be such a cause. If T symmetry is obeyed, then the formalism treats time and space symmetrically such that states of matter are localized both in space and in time. In this case, equations of motion and conservation laws are undefined or inapplicable. However, if T symmetry is violated, then the same sum over paths formalism yields states that are localized in space and distributed without bound over time, creating an asymmetry between time and space. Moreover, the states satisfy an equation of motion (the Schrödinger equation) and conservation laws apply. This suggests that the time–space asymmetry is not elemental as currently presumed, and that T violation may have a deep connection with time evolution.

H. D. Zeh

Arno Böhm, Manuel Gadella, M. Mithaiwala

Richard Joseph Oldani

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.

B. Renaud, R. M. Whitley, Carlos R. Stroud

A Heisenberg picture QED treatment is presented of the resonance fluorescence of a two-level atom. It is shown that the equations of motion for first-order correlation functions have an asymmetry with respect to the two time arguments. This asymmetry arises in a correct and careful evaluation of the unequal-time commutator between free-field and atomic operators. General solutions of these equations are found without going to the stationary limit.

Arno Böhm