Optomechanical test of the Schrödinger-Newton equation

[marcus]

Bee Hossenfelder called attention to an interesting paper in this post:
A newly proposed table-top experiment might be able to demonstrate that gravity is quantized
http://backreaction.blogspot.com/2015/10/a-newly-proposed-table-top-experiment.html

Here's the paper:
http://arxiv.org/abs/1510.01696
Optomechanical test of the Schrödinger-Newton equation
André Großardt, James Bateman, Hendrik Ulbricht, Angelo Bassi
(Submitted on 6 Oct 2015)
The Schrödinger-Newton equation has been proposed as an experimentally testable alternative to quantum gravity, accessible at low energies. It contains self-gravitational terms, which slightly modify the quantum dynamics. Here we show that it distorts the spectrum of a harmonic system. Based on this effect, we propose an optomechanical experiment with a trapped microdisc to test the Schrödinger-Newton equation, and we show that it can be realized with existing technology.
13 pages, 4 figures, 1 table, 1 page of supplemental material

====comment====
If I understand correctly, the Schrö-Newt equation would hold if gravity were FUNDAMENTALLY semiclassical. And therefore NOT needing to be quantized. Quantum matter would produce a kind of classical probability distribution of gravitational forces--in the non relativistic limit. So if this equation can be experimentally REFUTED this would indicate that gravity is not fundamentally semiclassical and that a quantum theory of gravity is definitely required.

 

[marcus]

It builds on analysis made in a companion paper by the same authors, posted earlier:
http://arxiv.org/abs/1510.01262
Effects of Newtonian gravitational self-interaction in harmonically trapped quantum systems
André Großardt, James Bateman, Hendrik Ulbricht, Angelo Bassi
(Submitted on 5 Oct 2015)
The Schrödinger-Newton equation has gained attention in the recent past as a nonlinear modification of the Schrödinger equation due to a gravitational self-interaction. Such a modification is expected from a fundamentally semi-classical theory of gravity, and can therefore be considered a test case for the necessity of the quantisation of the gravitational field. Here we provide a thorough study of the effects of the Schrödinger-Newton equation for a micron-sized sphere trapped in a harmonic oscillator potential. We discuss both the effect on the energy eigenstates and the dynamical behaviour of squeezed states, covering the experimentally relevant parameter regimes.
22 pages, 14 figures

Bee's comment:
==quote==
In the new paper now, the researchers propose a different method. They consider a tiny charged disk of osmium with a mass of about a nano-gram, held by electromagnetic fields in a trap. The particle is cooled down to some hundred mK which brings it into the lowest possible energy state. Above this ground-level there are now discrete energy levels for the disk, much like the electron orbits around the atomic nucleus, except that the level spacing is tiny. The important point is that the exact energy values of these levels depend on the gravitational self-interaction of the whole object. Measure the spacing of the energy levels precisely enough, and you can figure out whether the gravitational field was quantized or not.
[See Bee's Figure 1]
For this calculation they use the Schrödinger-Newton equation, which is the non-relativistic limit of semi-classical gravity incorporated in quantum mechanics. In an accompanying paper they have worked out the description of multi-particle systems in this framework, and demonstrated how the system approximately decomposes into a center-of-mass variable and the motions relative to the center of mass. They then calculate how the density distribution is affected by the gravitational field caused by its own probability distribution, and finally the energy levels of the system.
...
...
Suppose they make this measurement and they do, as expected, not find the additional shift of energy levels that should exist if gravity was unquantized. This would not, strictly speaking, demonstrate that perturbatively quantized gravity is correct, but merely that the Schrödinger-Newton equation is incorrect. However, since these are the only two alternatives I am aware of, it would in practice be the first experimental confirmation that gravity is indeed quantized.
==endquote==

 

[MTd2]

I think this would violate HUP. Considering the gravitational waves emitted, you'd be able to detect the particles going both ways, but that would be a classical sign.