wolram said:
...is
still some leeway for originality,...
Absolutely right! There is still plenty of room for totally new approaches to appear:
ones we (non-professional amateur watchers) have no way to anticipate.
You are asking me simply for my opinion, which carries no weight besides that of the onlooker. YES the problem is totally open (in my opinion).
Neither LQG nor string nor noncommutativegeometry nor dynamicaltriangulations is credible as a monopoly---they are all immature attempts or they have serious problems or both.
And I don't think anybody is close to real rigorous testability either.
Smolin has gone out on a limb and unequivocally predicted some variation in the speed of light with photon energy----to be detected by GLAST.
But Ashtekar and Rovelli have not followed him out on the limb. They have not signed off on the prediction. I do not understand this division of opinion.
If no variation of gammaray photon speed is detected by GLAST this will be a serious embarrassment for Smolin. (but not for Ashtekar and Rovelli)
I guess you could say that LQG
as Smolin understands it predicts this effect that GLAST is sensitive enough to detect if it is real and therefore LQG-as-Smolin-understands-it will be shot down or refuted or in serious trouble if the effect is not found.
Smolin's latest word on this came out just this month
http://arxiv.org/hep-th/0501091
Falsifiable predictions from semiclassical quantum gravity
Lee Smolin
9 pages
"Predictions are derived for the upcoming AUGER and GLAST experiments from a semiclassical approximation to quantum gravity. It is argued that to first order in the Planck length the effect of quantum gravity is to make the low energy effective spacetime metric energy dependent. The diffeomorphism invariance of the semiclassical theory forbids the appearance of a preferred frame of reference, consequently the local symmetry of this energy-dependent effective metric is a non-linear realization of the Lorentz transformations,
which renders the Planck energy observer independent. This gives a form of deformed or doubly special relativity (DSR), previously explored with Magueijo, called the rainbow metric. The argument is general, and applies in all dimensions with and without supersymmetry, and is, at least to leading order, universal for all matter couplings. The argument is illustrated in detail in a specific example in loop quantum gravity.
A consequence of DSR realized with an energy dependent effective metric is a helicity independent energy dependence in the speed of light to first order in the Planck length. However, thresholds for Tev photons and GZK protons are unchanged from special relativistic predictions. These predictions of quantum gravity are falsifiable by the upcoming AUGER and GLAST experiments."
I think Smolin is a risk-taker and that he has laid it on the line here.
he says that the Planck energy is
observer-independent just like the speed of light (if LQG is right) and
so just like the speed of light looks the same to all observers (which is bad enough, we all find this a bit weird)
now, in addition, there is this other physical quantity (an energy this time, not a speed) which looks the same to all observers. And the only way this can happen is by a slight bending of the rules of special relativity which he says will be detectable by GLAST.
