Two-Particle Asynchronous Quantum Correlation: Wavefunction Collapse Acting as a Beamsplitter

Abstract

A two-body quantum correlation is calculated for a particle reflecting from a moving mirror. Correlated interference results when the incident and reflected particle substates and their associated mirror substates overlap. Using the Copenhagen interpretation of measurement, an asynchronous joint probability density (PDF), which is a function both of the different positions and different times at which the particle and mirror are measured, is derived assuming that no interaction occurs between each measurement. Measurement of the particle first, in the correlated interference region, results in a splitting of the mirror substate into ones which have and have not reflected the particle. An analog of the interference from the Doppler effect for only measurements of the particle (a marginal PDF), in this two-body system, is shown to be a consequence of the asynchronous measurement. The simplification obtained for a microscopic particle reflecting from a mesoscopic or macroscopic mirror is used to illustrate asynchronous correlation interferometry. In this case, the small displacement between these mirror states can yield negligible environmental decoherence times. In addition, interference of these mirror states does not vanish in the limit of large mirror mass due to the small momentum exchange in reflecting a microscopic particle.

Collective behavior in quantum interference: an alternative superposition principle

“…The assumed hard-sphere interaction for weak s-wave scattering in the Born approximation is represented in the Hamiltonian by delta function potentials. Justification of the following results is found in the appendix with related calculations found in the literature [22,23].…”

“…If, on the other hand, the momentum exchanged in the interaction is sufficient to spatially separate the scatterer substates of having and not having reflected the particle then all interference vanishes, even though the system remains in a superposition state (such an example is found in a particle scattering from a mirror [22]). This elimination of interference occurs in both SQI and CQI.…”

“…Some of the calculational details that are outlined below are given elsewhere for related systems [22,23]. The initial separable three-body scatterer state is…”

Planck scale displacement of a connected mirror pair: an energy measurement in a gravitational field

“…Related many-body calculations of a particle reflecting from a mirror [16], a particle interacting with rigid mirrors arranged in a Fabry-Perot configuration [17], and of two particles reflecting from a mirror [18] are found in the literature. If only the particle is measured (the results are then predicted by a marginal distribution) and the coherence length of the C.M.…”

Quantum correlation interferometry in reflection: Application to the quantum–classical transition, decoherence, and indirect measurement

“…The mirrors, beamsplitters, and even the particles then become integral parts of the interferometers and therefore are all treated as quantum objects. A simple example is of one non-local particle reflecting from a static mirror, both of which are initially uncorrelated, generating two-body correlated "standing wave" interference between both the particle and mirror [14]. This interference is a consequence of the system being in a superposition of both having and not having reflected the particle.…”