• DOI:10.1023/B:IJTP.0000005969.92111.b5
• Corpus ID: 8493433

Quantum Trajectories, State Diffusion, and Time-Asymmetric Eventum Mechanics

@article{Belavkin2003QuantumTS,
  title={Quantum Trajectories, State Diffusion, and Time-Asymmetric Eventum Mechanics},
  author={Viacheslav P. Belavkin},
  journal={International Journal of Theoretical Physics},
  year={2003},
  volume={42},
  pages={2461-2485}
}

• V. Belavkin
• Published 1 October 2003
• Physics
• International Journal of Theoretical Physics

We show that the quantum stochastic Langevin model for continuous in time measurements provides an exact formulation of the von Neumann uncertainty error-disturbance principle. Moreover, as it was shown in the 1980s, this Markov model induces all stochastic linear and nonlinear equations of the phenomenological informational dynamics such as quantum state diffusion and spontaneous localization by a simple quantum filtering method. Here we prove that the quantum Langevin equation is equivalent to a Dirac-type boundary-value problem for the second quantized input “offer waves from future” in one extra dimension, and to a reduction of the algebra of the consistent histories of past events to an Abelian subalgebra for the “trajectories of the output particles.” This result supports the wave-particle duality in the form of the thesis of Eventum Mechanics that everything in the future is constituted by quantized waves, everything in the past by trajectories of the recorded particles. We demonstrate how this time arrow can be derived from the principle of quantum causality for nondemolition continuous in time measurements.