The calculation follows from the discovery of a geometry whose form explicitly derives from the axioms underpinning QM and GR theories: Current functional theories impose these axioms on top of an existing (differential Cartesian) geometry (which comes with its own set of assumptions built in)
The properties of this geometry (if the new theory is on the right track) require that some quite precisely known CODATA 2010 physical constants must be related to G in a previously (as far as I am aware) unsuspected way.
By revisiting the dimensional analysis of these CODATA values (which engineers are well trained to do) a simple grouping was found that neatly expressed this proposed relationship. When calculated, the error bars straddled a rather curious number to better than 0.01% accuracy. Coincidence? - maybe - it has happened before. My only defence is the result proceeded from the logical requirements of the calculation and not vice versa.
By proposing this curious number was exactly correct, and noting that the error in its calculation was dominated by the uncertainty in G, a value of G could be calculated from the other CODATA 2010 values in the group that was more precise than current accepted empirical results: This is the value quoted in the question.
Thank you yes I have seen these values - I based my calculations on values/uncertainties in physical constants from http://physics.nist.gov/cuu/Constants/ (CODATA 2010.) Unfortunately the empirical disagreement between the more recent accurate empirical measurements of G does not help resolve this issue - (hence my question)
As regards the prediction in my question, it sits a touch higher than the upper limit of ref 3 in the article you posted. The "curious number" I refer to above remains just that. It is the dimensionless group from which it is was calculated that follows from the new theory - the answer was supposed to be a small integer, rather than the simple rational fraction (to within 0.01%) that this curious number turned out to be. Not accurate enough to be proof of anything, but intriguing enough to be worth following up - particularly given the simplicity of the dimensionless group concerned.
@Joachim; The fact that G has even been measured to current accuracy is a truly remarkable and largely underrated achievement. In my opinion speculating about whether G is changing or directional is pointless compared to making efforts to progress the technologies involved to measure it better (or differently) Given the money being poured into projects like LHC, why is the humble G being left out given its lack of current accuracy compared to other constants? For example the two most accurate methods in the prior article you posted disagree with each other. Not much can be concluded from two points that disagree, but what if we get say 15 groups repeating these experiments around the world? 15 data points would maybe make some sense of what is the same and what is different.
When it can be measured better a lot of this other pondering about artifacts and external effects will either go away or show clear trends. There seems to be a curious lack of interest in G - mostly I suspect because the physics world has split into QM practitioners and GR practitioners and G is really only relevant when the two fields interact; Thus it has great relevance to the unification problem; perhaps most physicists have just given up on this. Or am I wrong? Who uses G on a day to day basis in their work? Anyone out there willing to put their hand up?
Andrew, If they (LHC) used G in their QM work, there would be no work. No specialist is going to raise their hand to that. You would have an industry (supported by we know who, in turn, supported by we know who, given personhood and bailed out time and again by we know who, by that time uninformed, hoodwinked taxpaying voters) collapse, rather than a convenient 'wave collapse,' throwing darts, or perpetual tail-chasing. Still, throughout history, while rendering unto Caesar, single advancements have shifted such paradigms, while we know who continues to capitalize, some for the common good and hopefully not just for themselves, as today, leading to recent uprisings, we know who however lamely try to quash.