Arrow of Time

The “arrow of time” problem addresses the origin of macroscopic irreversibility from microscopically time-reversible dynamical laws.  The dynamical equations of physics are time reversal symmetric.  Ensembles of physical systems select configurations that prefer an increase in entropy, or a preferred “arrow of time.” Nevertheless, the time symmetry of dynamical equations also implies that if we repeat an experiment sufficiently many times, we should be able to record statistically rare events where the state of the system reverts to its initial conditions. The resolution to the paradoxical situation emerges from the statistics of these experimental realizations: realizations with a backward arrow of time in which the system returns to its initial conditions are exponentially less likely to occur compared to their forward counterparts. 

Understanding the arrow of time is of fundamental interest in both science and philosophy. Experimentally probing such questions in quantum theory requires systems with near-perfect isolation from the environment and systems that exhibit long coherence times. Ultracold atoms and in particular Bose-Einstein condensed atoms are uniquely suited to this task. We have experimentally demonstrated a striking parallel between the statistical irreversibility of wavefunction collapse and the arrow of time problem in the weak measurement of the quantum spin of a spinor Bose-Einstein condensate. Our observations include statistically rare events where the arrow of time is inferred backward.  Nevertheless, we find evidence for absolute irreversibility and a strictly positive average arrow of time for the measurement process which in turn is captured by a fluctuation theorem. Moreover, we demonstrate absolute irreversibility for measurements performed on our quantum many-body entangled wavefunction with significant implications for studying quantum many-body dynamics and quantum thermodynamics. 

In a and c in the figure above, the probability distributions for particular values of the arrow of time, Q, are shown for two different initial spin distributions. A negative Q indicates a backward arrow of time. The insets display the experimentally measured probability distributions of the atoms, pF(r) , from which Q is calculated. b shows the irreversibility of wavefunction collapse for different measurement strengths, σ, when half the atoms are initialized in each spin state. d also shows macroscopic irreversibility, but this time for constant measurement strength and different initial atom distributions, z. The red dashed lines in b and d are theory predictions given by the integral fluctuation theorem for the arrow of time for weak spin measurements.