Abstract
I impose the Newtonian criteria of inertial frames on the c.o.m.trajectories of massive objects undergoing spontaneous collapse of their wave function. The corresponding modification of the so far used stochastic Schrödinger equation eliminates the Brownian motion of the c.o.m., and restores the exact inertial motion for free masses. For the collapse of Schrödinger cat states the Born rule is satisfied invariably. The proposed machinery comes from the radical assumption that, in the vicinity of the spontaneously localized mass, the stochastic fluctuations of the c.o.m.—inevitable in the collapse process—would drag the physical inertial frame with themselves. The perspective of a general theory is presented where the spontaneous-collapse-caused breakdown of local energy-momentum conservation could be remedied by altering the metric, resulting in collapse-induced curvature of the space-time. My assumption of frame-drag by quantized masses is independent of the general relativistic frame-drag by classical masses.
Highlights
Spontaneous collapse (SC) theories, reviewed in [1,2], propose that emergence of classical data in quantum systems is spontaneous and universal, and does not require quantum measurements, nor decohering effects of the occasional environment
|ψi = α|ψ1 i + β|ψ2 i with macroscopically different |ψ1 i, |ψ2 i were somehow prepared, it should quickly be collapsed through a random process either to |ψ1 i or to |ψ2 i with the probabilities |α|2 and | β|2 according to the Born-rule
Available SC theories fulfill the above requirements at a cost of additional noise: the dynamics of |ψi are charged by a diffusive motion in the Hilbert space which is a mandatory consequence of the SC mechanisms
Summary
Spontaneous collapse (SC) theories, reviewed in [1,2], propose that emergence of classical data in quantum systems is spontaneous and universal, and does not require quantum measurements, nor decohering effects of the occasional environment. Merits of SC theories are objectivity, universality, and dynamic equations of how classical data emerge from quantum systems. Available SC theories fulfill the above requirements at a cost of additional noise: the dynamics of |ψi are charged by a diffusive motion in the Hilbert space which is a mandatory consequence of the SC mechanisms. This means the non-conservation of momenta and energy but even an eternal increase of the latter.
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