Quantum gravity can be understood by considering the logical consqquences of a single unifying postulate or principle of nature. I call it the postulate of quantized space time.
First some observations.
The Gravitational force seems to pervade the entire universe. However gravity is the weakest of all the forces in the entire universe. To get a easily measurable force of gravity there needs to be a planetary or larger mass nearby. So any theory of quantum gravity must require a large amount of mass to create a small effect in space time. Gravity also seems to be an exclusively attractive force. It also has only monopole and quadrupole moments. The lowest radiative gravitational moment is the quadrupole moment.
There is no way to distinguish between a mass and bound energy state. Mass is energy in a bound state. Only concentrated in these bound states called mass have we actually observed the gravitational field of an object. Free energy seems to react to gravitational fields but does not possess a gravitational field of it's own. Furthermore the bound states of energy are quantized into discrete steps.
The Planck length seems to be the smallest possible interval of length in space. Consider the Schwarzchild radius of a black hole with mass equal to the Planck Mass.
The standard formula is
I will set all constants but G equal to one. The Planck units are defined as follows.
The Planck length
Mass and time can be expressed in terms of the Planck length.
With these units in mind the Schwarzchild radius of a black hole with mass equal to one Planck mass.
Now suppose we compute the Invariant interval between two points separated by one Planck unit in 3-space and time.
Is this just a coincidence of geometry and physics? Or is more going on here. Those observations are my basis for stating the following postulate.
Mass-energy alters the local space-time interval in increments that are integer multiples of the Planck length.
On my personal website I go into great detail of proving that even such a quantized manifold can still be differentiable in a certain sense. Thus preserving the calculus we all know and love. I define differential tensor operators on that space and run through which ones commute and which do not.
I have the following interesting results to report.
I have a fully quantum mechanical formula for the Schwarzschild radius of any mass of energetic field.
I have a tensor operator which based on computation of the non gravitational (flat space) stress energy predicts the possible curved space-time intervals and hence give a value of gravitational action due to those non-gravitational fields.
In the coming days I will publish a follow up paper related to thermodynamics of black holes, and other opaque surfaces.