Spontaneous Wave Function Collapse with Frame Dragging and Induced Gravity

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., 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.

Gravitational decoherence

“…with E DP (t) = Tr[ρ(t) Ĥ] where ρ(t) satisfies the Diósi-Penrose dynamics. From this relation, one can easily evaluate the different implications of the cut-off proposed, respectively, by Diósi [137] and Ghirardi et al [119]. In the former case, R 0 = 10 −15 m, one gets a rate for the energy increase of order 10 −4 K s −1 for a proton, which means a thermal catastrophe!…”

“…Diósi [123][124][125][126] postulated (75) and assumed that the spatial correlator of the noise is proportional to the Newtonian gravitational potential [137,138]:…”

Have underground radiation measurements refuted the Orch OR theory?

“…A final variant worth mentioning is the fascinating recent suggestion of Diósi [13] in which energy conservation is recovered by postulating that collapse has a "frame-dragging" effect on the background spacetime. The upshot, then, is that there seem to be many variants of OR and Orch OR left open, with much work to do to render them precise enough for experimental tests.…”

Schrödinger–Newton Equation with Spontaneous Wave Function Collapse

“…Note the important complex factors (1 + i) and (1 − i) compared to the small-∆x approximation (11) of the G-SSE model. The ancestor of this equation is Equation (11) in [4]. It eliminated both momentum and coordinate diffusion by construction.…”

“…Our SSNE partially realizes the concept of ref. [4], where the diffusion effects of a stereotypical collapse equation (our Equation (11) below) were completely eliminated by imposing frame drag. Additionally, a related vision of induced gravity was put forward.…”