Gravity from uncertainty

My latest paper 'Gravity from the uncertainty principle' has just been published :) by the journal Astrophysics & Space Science. The paper is here (try the 'look inside' option).

The idea is as follows and was inspired partly by a course I teach at Plymouth on the mathematics of GPS positioning. I treat the size of the orbit of an object as an uncertainty in the position of each of its Planck masses (the dx from Heisenberg's uncertainty principle: dx.dp = hbar). So as an orbit shrinks in size, the uncertainty in position decreases, so the uncertainty in momentum (dp) must increase to compensate and this means that the uncertainty in the force must increase. When I sum this effect for all the possible interactions between the Planck masses in the two objects, Newton's gravity law appears.

This derivation of classical gravity from a principle of quantum mechanics, which takes just one page of maths, is interesting given that gravity and quantum mechanics have been thought to be incompatible. This model also suggests that only whole Planck masses gravitate, so as a test I've suggested that space dust should mostly be less than a Planck mass since only the larger dust would be gravitationally captured by larger masses.