A microscopic model of wave-function dephasing and decoherence in the double-slit experiment

Area of Science:

• Quantum Mechanics
• Foundations of Physics
• Quantum Measurement Theory

Background:

• Quantum measurement is typically described as a process outside standard quantum mechanics, involving dephasing, decoherence, and wave-function collapse.
• Existing approaches like consistent histories and environmental decoherence offer insights but have limitations in fully explaining the measurement process.
• Wave-function collapse is often considered an irreversible process inherent to macroscopic measurement apparata, not solely due to thermal environmental interactions.

Purpose of the Study:

• To investigate the dynamics of quantum state evolution during measurement using a novel approach based on the Schrödinger equation with a time-dependent Hamiltonian.
• To provide an exact, unitary solution for the time-evolved state without Markovian approximations, offering a more complete description of decoherence.
• To explore the implications of this model for fundamental quantum measurement problems, including the Wigner's friend and Mott experiments.

Main Methods:

• Utilized the Schrödinger equation with a time-dependent Hamiltonian that accurately reflects microscopic interactions during measurement.
• Solved the time-evolution of the quantum system exactly, maintaining unitarity throughout the calculation and avoiding Markovian approximations.
• Analyzed the short-time and long-time behavior of the collapsing wave-function, connecting Fermi's golden rule to exponential decay.

Main Results:

• Demonstrated that wave-function collapse is a temporary state; the wave-function can explicitly 'un-collapse' if the measurement apparatus is sufficiently small.
• For macroscopic systems, dephasing rapidly leads to decoherence, with collapse reversal timescales potentially exceeding the age of the universe.
• Showed that the short-time behavior of a collapsing system follows the Fermi's golden rule (quadratic-in-time) rather than exponential decay, while long-term behavior remains exponential.

Conclusions:

• The study provides a unified mathematical formulation connecting short-term Fermi's golden rule behavior to long-term exponential wave-function collapse.
• Reversed the notion that collapse is solely an irreversible process, showing its temporary nature, especially for smaller measurement systems.
• The findings have significant implications for interpreting quantum measurement paradoxes like Wigner's friend, suggesting macroscopic measurement apparatuses ensure consistent outcomes regardless of observer consciousness.