Abstract
Wavefunction collapse models modify Schrödinger’s equation so that it describes the collapse of a superposition of macroscopically distinguishable states as a dynamical process. This provides a basis for the resolution of the quantum measurement problem. An additional generic consequence of the collapse mechanism is that it causes particles to exhibit a tiny random diffusive motion. Here it is shown that for the continuous spontaneous localization (CSL) model—one of the most well developed collapse models—the diffusions of two sufficiently nearby particles are positively correlated. An experimental test of this effect is proposed in which random displacements of pairs of free nanoparticles are measured after they have been simultaneously released from nearby traps. The experiment must be carried out at sufficiently low temperature and pressure in order for the collapse effects to dominate over the ambient environmental noise. It is argued that these constraints can be satisfied by current technologies for a large region of the viable parameter space of the CSL model. The effect disappears as the separation between particles exceeds the CSL length scale. The test therefore provides a means of bounding this length scale.
Highlights
Wavefunction collapse models modify Schrödinger’s equation so that it describes the collapse of a superposition of macroscopically distinguishable states as a dynamical process
Dynamical wavefunction collapse models[1,2] provide a unified description of quantum dynamics encompassing both unitary evolution and state reduction
The most prominent collapse model is the continuous spontaneous localization (CSL) model[3,4] in which a superposition of quasi-localized matter states will collapse at a rate which increases with the mass of the object
Summary
With density operator ρt and free Hamiltonian H. The two-particle density matrix is represented in coordinate space as ρt (x1, y1, x 2, y 2) = x1, x 2 ρt|y1, y 2〉. Note that by setting D = 0 (standard quantum mechanics) in Eqs (16 and 17) we find σX2 = σξ2/2 This reflects the fact that the two particles are behaving independently and their distributions are uncorrelated. To observe the effect we must distinguish σX2 and σξ2/2 We can estimate these variances by repeatedly measuring the displacements of two particles simultaneously dropped from nearby traps (see Fig. 1). Taking the mass of the particles to be 109 amu such that ħ2t2/4m2σ4 ≪ 1 , this results in the following constraint on n: n Shown is the region of parameter space currently ruled out by diffraction experiments involving particles of mass 105 amu[16].
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
