No there is no quantum gravity in this experiment, the gravitational field of the Earth is a purely classical, external field. So the results could be computed with the same mathematics as of Schrödinger theory for the hydrogen atom, all one needs is to replace the Coulomb potential of the proton by the Newtonian gravitational potential of the Earth (and, of course, something else to describe the other, non-gravitational parts of the experimental device).

Dear Ilja,

yes, there is no direct detection of gravitons, but this experiment has principal meaning for quantum physics and unification of fundamental physical interactions, because it is the first demonstration that gravitation acts as other fields (not as geometry). In the paper Nesvizhevsky et al., Nature, Volume 415, Issue 6869, pp. 297-299 (2002), Quantum states of neutrons in the Earth's gravitational field ( http://adsabs.harvard.edu/abs/2002Natur.415..297N ) they presented results of an experiment for free fall of ultra-cold neutrons, where quantum states of falling neutrons were measured, exactly as quantum states of an electron in the Coulomb field. So they demonstrate that the nature of gravity force is the same as in other fundamental forces, i.e. exchange of virtual particles, including virtual gravitons.

What is more, in the paper Nesvizhevsky & Protasov, “Constrains on non-Newtonian gravity from the experiment on neutron quantum states in the Earth's gravitational field”, Class.Quant.Grav. 21 (2004) 4557-4566 ( http://arxiv.org/abs/hep-ph/0401179 ) they put very strong restriction on the prediction of modern multidimensional theories about deflection of the gravity force from the Newtonian law at small scales – they found pure Newtonian behavior up to sizes about 10^(-9) m.

So this is the first experiments having the quantum meaning of the weak gravitational interaction.

Without doubt, it is the closest thing to a quantum gravity experiment we have. And I like it if it allows to reject some of the superstringy nonsense.

The question if it demonstrates "that the nature of gravity force is the same as in other fundamental forces" interests me. I would like it (I prefer theories which do not make such differences and don't like the spacetime interpretation), but I doubt if such an experiment allows to solve such interpretational questions.

Of course this one experiment cannot proof the validity of the field gravity approach.

For distinguish between geometrical and field gravity approaches one needs to perform crucial experiments/observations which first, should be formulated and second, should be realized.

For detailed discussion of such possibilities see

the book http://link.springer.com/book/10.1007/978-94-007-2379-5/page/1

and papers http://arxiv.org/abs/0809.2323 and http://arxiv.org/abs/0809.2328

Before looking at the equations of your papers in detail, just a few questions. I have some understanding of Logunov's RTG with massive graviton. There is, of course, also the earlier version which can be defined as the RTG limit m_g->0. The notion "field-theoretic approach to gravity" can, of course, be applied to this m_g->0 limit of RTG. Is there a difference between your field-theoretic approach and this?

Yes, I know well the works by Logunov et al. group and had many discussions with them at several conferences.

They call their approach as RTG (relativistic gravity theory) and also as a field approach to gravitation, where they introduce Minkowski space for gravity and effective Riemann space for matter. Actually they postulate the “Principle of Geometrization” which is equivalent to the geometrical approach of general relativity plus an additional restrictions on the metric tensor.

Hey also modified Einstein’s equations by addition the rest-mass term in the field equations.

By the way there is another “field gravity approach” by Babak & Grischuk

( http://arxiv.org/abs/gr-qc/0209006 ) where they construct a generalization of general relativity

on the case of massive gravitons with two spins – spin2 and spin0. Obviously if their theory in the limit of zero gravitons masses identical with geometrical GR, then they do not construct a field gravity theory. Actually they also postulate the “geometrization principle”.

These “geometrical-field” theories assumes that the sum of n_ik + h_ik = g_ik where n_ik – is the metric of the Minkowski space (non-tensor in curved space) and h_ik is an additional quantities (non-tensor) so the sum is the tensor of the Riemann space – its metric tensor.

Within the consistent field approach which is based only on Minkowski space the sum of two tensors of Minkowski space is again the tensor of Minkowski space. This difference changes radically the theoretical model of gravitational interaction.