If one estimates as an example the ratio between the electric and the gravitational force between two electrons one finds 
Where mpl is the so-called Planck-mass and related to the gravitational constant as 1/mpl2 = G. That is, the gravitational interaction in this case is by roughly 43 orders of magnitude smaller than the electric one. The reason for this is that the mass-scale associated with gravity, the Planck-mass, is much much larger than the typical particle masses. Nobody knows why that is, this is also called the 'Hierarchy problem'. On the other hand, macroscopically seen the Planck-mass isn't a large mass at all. In fact, it is a scale that is perfectly handy for experiments. In grams, the Planck-mass is roughly 22 micrograms.
Last year, I came across a paper by Dr. Raymond Chiao who proposes an experiment to exploit this fact
- New directions for gravity-wave physics via "Millikan oil drops"
Authors: Raymond Y. Chiao
Naturally, I was very interested and looked into the topic. Since there were many details I didn't understand, I have been in email contact with the author for some while. Three months ago, there was a newer, and more extended version on the arxiv: gr-qc/0702100, which caused me to again contact Dr. Chiao. In the following I would like to share my concerns about the effect explained in these works.
The proposal is to use objects of about Planck-mass that only carry a total electric charge of order one. For these objects, the electric and gravitational force would then be of roughly the same strength. The concrete scenario which Chiao describes uses something called 'Millikan Oil Drops'. I admit that I don't understand all the features of these drops, but essentially these are cooled and super-fluid helium drops coated with electrons. Their superconductivity is claimed to be an important part of the experimental setup.
These drops, so the claim, would be strongly coupled to gravitational radiation, and could amplify it such that it becomes detectable . Essentially you can envision a pair of drops acting like an antenna. Excited through a periodic electromagnetic field, they would emit both electromagnetic and gravitational radiation. It is argued that gravitational radiation has to be as strong as the electric radiation, because the droplets are designed such that they are equally strong subject to both forces: "This is a strong hint that mesoscopic-scale quantum effects can lead to non-negligible couplings between gravity and electromagnetism that can be observed in the laboratory."
The first obvious objection that springs into my mind is, yes, both forces act equally. But equally weak. There is no way the process of simply cooling matter can affect the gravitational force, unless one introduces some kind of modification of gravity. But Chiao claims this is an effect of purely classical general relativity, and there is no modification necessary. I was looking for a derivation of the gravitational wave emission. There is none, in neither work. All that one can find is the electromagnetic case, and then the repeated argument that the gravitational case is identical. In such a way, Chiao derives the drops are reflecting gravitational waves: "Hence it follows that nearly perfect reflection of gravity waves should occur from a superconductor at temperatures well below its transition temperature."
This argument can very easily be defeated. The electric charge of the drop is confined to the surface (they are 'coated'). The mass of the objects is equally distributed throughout the drop. Thus, the source terms for both, electromagnetic and gravitational field are not equal. The argument that both can be treated by applying a symmetry principle just does not apply. Though in a linear approximation of gravity both are essentially described by a wave-equation, both have different initial values. The paper says: "From the Maxwell-like equations [...], and the boundary conditions that follow from them, it follows that there should exist an analogous reflection of a gravitational plane wave from a planar vacuum-superconductor [...]". The boundary conditions hardly ever follow from the equations.
I also totally don't understand why one could possibly expect superconductivity to enhance classical gravitational effects. The argument relies on a postulated symmetry between gravitational and electromagnetic behavior. Even if one believes it, this symmetry would be based on the low temperature and the amazing properties of the droplets. Yet, the gravitational field of the droplets doesn't change with the temperature. How then can such an experiment possibly change the behavior for gravitational waves? I do understand that the electromagnetic properties change, but I find it extremely implausible to conclude from that that the gravitational field is also affected .
Since the effect can not be caused by the electric properties of the electrons, it had to be caused by their motion. It could then only be the masses of the electrons that cause the gravitational radiation to be strong. But this is more than implausible. The whole setup takes place in the linear regime of gravity. The total mass of all of the electrons is many orders of magnitude lower than the total mass of the droplets. A contribution to the gravitational field that is several orders of magnitude smaller can in the linear regime not result in a radiation that is several orders of magnitude larger (than that of the object without the electrons).
There has been some experimental evidence that superconducting materials might display unusual gravitational effects. I am somewhat sceptical about that, but it might be possible. Who knows? That is, the proposed experiment might be worthwhile to do. However, whether or not there is such an effect, I have very strong doubts about the explanation offered in Dr. Chiao's papers.
Aside: I would have liked to share here part of my email communication with Dr. Chiao to make sure I did not misinterpret his explanations, but he didn't agree on that .
Footnote 1: The speed of light and Planck's constant are equal to one, so are maybe occurring factors of some pi or 137 or so.
Footnote 2: One should note here that gravitational radiation has never been directly detected. Indirect detection through radiative loss in binary systems was awarded with the Nobel Prize in 1993.
Footnote 3: Strictly spoken, the gravitational field of course is affected if the electromagnetic field changes since the electromagnetic field strength also is a source to the field equations. However, compared to the mass of the objects this is a negligible effect. It neither affect the conclusion, nor is it claimed by Chiao to be responsible for the effect.
Footnote 4: That might be partly due to him offering to add my name to the acknowledgements, and me replying I'd rather not be mentioned there.
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