In 2005 the anniversary of Einstein's miracle year there was much talk of "new Einstien"s and why there have been no new ones. Carlo Rovelli published a very good book on the subject. String theory and M theory were as hot as the surface of the sun. In a heated exchange on Wikipedia I made the acquaintance of Lubos Motl. There was much excitement 4 years ago. So what happened? Why no accepted theory of quantum gravity?
- String theory, planck scale strings interacting with M-branes in 11 dimensional space. That's just one out of a number of string theories.
- Loop Quantum Gravity where area is an operator and space-time is a spin foam at the Planck scale...
- My very own theory where path length (s) as well as area are quantum operators, and space is the 4d lattice of the symmetry group, lie algebra, and lie group f(4) at the Planck scale.
The problem with quantum gravity, in any and all theories that have a chance of being correct, is that they take strongest effect at length scales we may never be able to probe with any earthly accelerator. To test any of them directly is virtually physically impossible.
However take heart. There is some hope that astronomical observations may shed light on the subject. For in each of the above theories it is just possible that at the highest energies the speed of light varies. High energy gamma ray burst may unveil a tiny variance between their emissions, and the ordinary light we have studied. If so this would be a big pointer in the right direction. The basic idea is that in a quantum space time the path a photon would take from one point to another would not be continuous. It would evolve in a series of quantum leaps from one point to another to another. The effect of the discreteness of space-time would be amplified when the wavelength of the light becomes comparable to the Planck length.
To see this consider my little theory. In it there is an operator S which gives the possible null path's for a ray of light or any particle. (Page 26) The eigenvalues of this operator are what makes space time quantized in my theory. If a gamma ray had high enough energy there is a better chance that it would not select the shortest path at each step in it's long journey to our telescopes and hence it would arrive more slowly than light which has traveled here more quickly.
That said I could not claim such a result as support for my theory exclusively, the same would be true of LQG and a non-perturbative background independent string theory as well.
The current status of quantum gravity is that we are in a holding pattern. Until we get new data there is nothing new to say.
That said I have noticed a trend, of which I am now a part, to shift gears to quantum cosmology and the application of theories of quantum gravity to the early evolution of the universe. That is where serious theoretical quantum gravity research has gone, for now.
I can offer you the explanation from my EQUAL PARTITION OF THE VACUUM., that combines three familiar concepts of science into a model of virtual particles, vacuum energy, and zero point oscillators.
For example you could claim that an isolated particle of less than one plank mass has its energy equally partitioned between gravitational mass, and electromagnetic energy. If true then the particle would produce no gravitational field and no curvature of space, until subjected to the induction of a different gravitating mass. So the whole argument sort of makes sense.
Nothing like that has been reported experimentally, but we haven't done much testing on isolated particles in flat space.
If this is a major feature of physical science, then it should be observable by astronomy for low density clouds of gas or fine dust.
On the hand with similar reasoning if the isolated particle was subjected to more of an electromagnetic field than a gravitational field, then by induction it would add to the total electromagnetic field tending to curve space backward and accelerate the separation of galaxies.
It is possible to conceive of a universe with a lot of isolated particles, that sometimes accelerates and other times decelerates, depending on the induced polarization of the isolated particles.
Some sort of observable proof would be needed for that.