err, so by initially assuming that something under the influence of a potential has a mass M, and calculating the Hamiltonian comes up with a proportionality constant of sqrt(M) means that the potential energy of the system is proportional to the sqrt of the mass of the bound object, all things being equal, not that the equivalence principle is broken.

okay typos above aside i just read their paper. it's good work.

they solved a few well known, relatively simple quantum mechanics problems, in college (from the griffiths intro to quantum mechanics book) these problems are usually solved by talking about an electron in an electric potential.

these fine scientists solved a simple quantum mechanics problem not using an electric potential, but using a gravitational potential. the solution ends up resulting in two dimensionless constants that define the particulars of the solution that are measurable. in solving the equation of a they kept separate the inertial mass and the gravitational mass, and the two measurable constants are expressed in such a way in the setup that they are considering such that by measuring these two constants the inertial mass and gravitational mass may both be solved for (two equations, two unknowns).

they are proposing that this is a way of investigating experimentally the distinction if any between these two quantities.

also the appendix was really complicated and it was very hard to follow