I think that the biggest news in a while in quantum mechanics is newly forming ability of experimenters to do quantum experiments with gravity. A fine example of an experiment already done is Phase Shift in an Atom Interferometer due to Spacetime Curvature across its Wave Function by Asenbaum et al. They conclude:

Therefore, the phase shift of this interferometer is not determined by the local acceleration along a single populated trajectory, demonstrating that the atomic wavefunction is a nonlocal probe of the spacetime manifold [34].

Thus they have experimentally shown that wave functions feel gravity pretty much where they ‘are’ in real space ( try not to think of configuration space at this point! ). No one really doubted this would happen. Still, it leads one to wonder what about the other side – the backreaction – to this. Do the atoms in the Asenbaum experiment source gravity in the same way they detect it? It would seem obvious that they should, but no one has done an experiment to verify this (see later in this article).

A proposal in the opposite spirit to the above results is given by Kafri, Taylor, and Milburn (KTM) in A classical channel model for gravitational decoherence. KTM posits a way for the gravity to be sourced as follows:

That is, the gravitational centre of mass coordinate,x_{i}, of each particle is continuously measured and a classical stochastic measurement record, J_{k}(t), carrying this information acts reciprocally as a classical control force on the other mass.

In other words in the KTM model, the source and detection channels for a particle are both as in semi-classical gravity. The expectation value of the particle’s is the mass location for both source and detection.

You can sense that the Asenbaum experiment shows KTM does not work – the experiment shows that atom, which is in a dual humped wave function with a separation of *centimeters* cannot be seeing only the average field – the wave function senses the curvature. The paper by Altamirano, Corona-Ugalde, Mann, and Zych Gravity is not a Pairwise Local Classical Channel , confirm these feelings about KTM – like theories. They don’t work.

Here we show that single-atom interference experiments achieving large spatial superpositions can rule out a framework where the Newtonian gravitational inter-action is fundamentally classical in the information-theoretic sense: it cannot convey entanglement. Specifically, in this framework gravity acts pairwise between massive particles as classical channels, which effectively induce approximately Newtonian forces between the masses.

So gravity is not truly semi-classical. No surprise to me, or to the quantum gravity workers (LQG, String Theory, etc). What many/most quantum gravity people like to think, however, is that KTM or similar (Diosi – Penrose), Rosenfeld like semi-classical gravity basically exhaust the spectrum of classical gravity theories.

### The BMV Experimental Proposals

The papers describing the BMV experiments by Bose et al., Marletto and Vedral, and Christodoulou and Rovelli.

These proposed experiments are in some ways similar to the Asenbaum experiment described above, but instead of atoms, small particles like micro diamonds are prepared in position-dependent superpositions, and instead of a huge mass of lead, two diamonds are dropped near each other, so they can feel the gravitational effect of the other also in a position superposition diamond. The promise of these experiments is tremendous – if successful they might show that gravity is quantized: Christodoulou and Rovell state

...detecting the [BMV] effect counts as evidence that the gravitational field can be in a superposition of two macroscopically distinct classical fields and since the gravitational field is the geometry of spacetime (measured by rods and clocks), the BMV effect counts as evidence that quantum superposition of different spacetime geometries is possible, can be achieved..

A problem I see in these BMV papers is that they all use the predictions of semi-classical theories (not KTM but semiclassical as a source only) as a classical test case, without much thought to the predictions of other ‘classical’ theories of gravity. The possibilities are many and the experimental consequences are not simple.

### Bohmian Trajectories and General Relativity

There have been some papers over the years touting the usefulness of the Bohmian trajectory viewpoint as a better approximation to classical field – quantum system interaction. Usually, the case for using Bohmian trajectories is one of computational or conceptual efficiency, but as Ward Struve in Semi-classical approximations based on Bohmian mechanics puts it:

Finally, although we regard the Bohmian semi-classical approximation for quantum gravity as an approximation to some deeper quantum theory for gravity, one could also entertain the possibility that it is a fundamental theory on its own. At least, there is presumably as yet no experimental evidence against it.

#### The BMV experiment with Bohmian trajectories

The interpretation of the BMV experiment if one assumes Bohmian trajectories are ‘real’ results in the following conclusions:

- Each run of the experiment has particles in any one of 4 configurations, – the trajectories.
- There is no superposition of gravitational fields – each run has a different gravitational field configuration.
- The resulting experimental statistics show entanglement – even though gravity is classical throughout.

The last point is the most surprising. We look at why an experimenter will see entanglement with Bohmian trajectories.

At the heart of the argument is the fact that while these Bohmian trajectories look very classical, they are actually quantum – more clearly *sub*quantum aspects of (Bohm/de Broglie) quantum theory. So we have a situation where we can get behaviour very similar – ( i.e. showing entanglement ) to quantum gravity for the BMV experiment by using classical gravity coupled to Bohmian trajectories, where there is a superposition of gravitational fields – but only in the boring classical histories of the experiment viewpoint. Since the experimenter has only histories to look at, showing that the gravitational field was in a superposition requires more than merely observing some level of entanglement in the BMV experiment.