The measurement problem remains one of the main unsolved puzzles of quantum physics. Neighboring papers in the archive explore wave function collapse, quantum measurements, and entanglement, but they often stop at abstract models or special cases. This paper develops the Q-model of an objective field, which offers a concrete mechanism of collapse through amplitude amplification, and applies it for the first time to realistic Schrödinger cat states, including two-mode entangled states.
The authors model the system and the measuring device as single-mode fields, and the measurement of the x quadrature as parametric amplification of the amplitude x(t). To describe the dynamics they use coupled forward-backward stochastic differential equations, in which the amplitude x propagates backward in time from a future boundary condition, while p propagates forward from the initial one. The boundary conditions are derived from the Q-function and the Wigner function of the initial state. The equations are solved numerically for superpositions of squeezed and coherent states, including the two-mode case with an entangled measuring device.
It is shown that as the amplitude x(t) is amplified, branches form that correspond to different eigenvalues, and the Born rule is reproduced in the limit of large amplification. For a macroscopic measuring device, the outcome of the measurement is already fixed at the moment tm when the coupling to the device is complete, which is consistent with macroscopic realism. The postselected distributions of the amplitudes x and p, conditioned on the outcome of the measuring device, have variances that violate the uncertainty relation, which points to their hidden character. Wave function collapse is described as a two-stage process: amplification creates the branches, and then information about the additional variable p is lost, which leads to projection of the system state.
The work demonstrates that the Q-model of an objective field provides a concrete mechanism of collapse compatible with macroscopic realism, unlike approaches based only on decoherence. Unlike neighboring papers, which often stop at abstract superpositions, this one considers realistic Schrödinger cat states, including entangled two-mode states, which brings the model closer to experimental testing. This strengthens the case for hidden variables, which do not conflict with Bell's theorem thanks to weakened assumptions about locality.
The model can be extended to multimode systems and continuous measurements, and also tested in experiments with parametric amplification and Schrödinger cat states. It may be possible to study its connection to gravitational collapse and quantum cosmology, where the measurement problem is equally acute.
The results may influence the interpretation of quantum mechanics and the development of quantum technologies, where an understanding of collapse matters for error correction.
The next step could be an experimental test of the model's predictions on platforms with optical Schrödinger cats and superconducting qubits.
The paper directly links the measurement problem to the long-standing dispute about the completeness of quantum mechanics raised by Schrödinger and Einstein, and proposes a solution through hidden variables compatible with macroscopic realism.
Schrödinger's cat was proposed as a mockery of the Copenhagen interpretation, yet today cat states are created in laboratories with hundreds of photons.
The idea that reality is determined by measurement is played with in the film Interstellar, where quantum data are transmitted through a wormhole.