Problems with the Newton-Schr\"odinger Equations

Understand

We examine the origin of the Newton-Schr\"odinger equations (NSEs) that play an important role in alternative quantum theories (AQT), macroscopic quantum mechanics and gravity-induced decoherence.

• We show that NSEs for individual particles do not follow from general relativity (GR) plus quantum field theory (QFT).
• Contrary to what is commonly assumed, the NSEs are not the weak-field (WF), non-relativistic (NR) limit of the semi-classical Einstein equation (SCE) (this nomenclature is preferred over the `M\/oller-Rosenfeld equation') based on GR+QFT.
• The wave-function in the NSEs makes sense only as that for a mean field describing a system of $N$ particles as $N \rightarrow \infty$, not that of a single or finite many particles.