Gravity-Related Wave Function Collapse

Abstract

The gravity-related model of spontaneous wave function collapse, a longtime hypothesis, damps the massive Schrödinger Cat states in quantum theory. We extend the hypothesis and assume that spontaneous wave function collapses are responsible for the emergence of Newton interaction. Superfluid helium would then show significant and testable gravitational anomalies.

Appendix: Newton Oscillator

Take a homogeneous ball of mass density $\rho$, bore a narrow diagonal hole through it, and gently place a probe somewhere into the hole (Fig. 1). The probe oscillates harmonically at frequency

$$\begin{aligned} \omega _G=\sqrt{4\pi G\rho /3}, \end{aligned}$$

where $G$ is the Newton constant. It is remarkable that the frequency is the function of density $\rho$ only, it does not depend separately on the size and the mass of the ball. In typical condensed matter the density $\rho$ is a few times 1 g/cm$^3$, the frequency of the Newton oscillator is $\omega _G \sim 10^{-3}$/s, the period is as long as cca 1 h.

Formally, we can consider the Newton oscillator inside a homogeneous ball of nuclear density $\rho ^\mathrm {nucl}\sim 10^{12}$ g/cm$^3$. The oscillator frequency

$$\begin{aligned} \omega _G^\mathrm {nucl}=\sqrt{4\pi G\rho ^\mathrm {nucl}/3} \end{aligned}$$

becomes of the order of $10^{3}$/s, the period is as small as cca 1 ms.

Fig. 1

Schematic view of a homogeneous ball of density $\rho$, with an infinite narrow diagonal hole where the probe is oscillating at frequency $\omega _G=\sqrt{4\pi G\rho /3}$ under the directional force of the Newton field of the ball