Attention Mylo.X:
From the article:
According to established theories, the decay of a specific radioactive material is a constant. This idea is used to determine what radiation doses to give to cancer patients, as well as to calculate the age of samples using carbon-14.
This is a prime example of why you should take what you read in a pop-sci article with a large grain of salt. No one
ever said that the rate of nuclear decay is constant. If that were the case you could use C-14 decay to determine the age of a substance going back millions of years instead of 58k to 62k years. The rate of decay is a probability statistic, not a constant. No one can state when, or even if, an unstable nucleus will decay. All that can be stated is the statistcal chance that it will decay during a certain time frame. Like any other statistic it has error bars indicated in the result.
Does the physics of stellar fusion somehow affect the rate? It's possible. Does that effect change the overall efficacy of, in my example, C-14 dating? Probably not. The error bars are already rather wide enough such that the affect is likely to be lost as noise in most cases. If it was a really significant effect we would have detected it during the past 115+ years of nuclear decay physics research (the Curie's announced the discovery of radium in 1898).
If what the article suggests is true is it important? Absolutely! Physics, as is science in general, is an endeavour based on building blocks. It advances one step at a time - with the occassional huge break through discovery that seems to by-pass several steps.
Special Relativity was one such "giant step". Yet SR, at its core, is nothing more than a re-statement of Newtonian relativity with an adjustment to the physical and mathematical meaning of mass. Einstein's famous equation E = mc^2 is an enhanced version of Newton's Ek = 1/2 mc^2. It is more generally true than Newton's equation but we still use Newton's equation for most purposes. Newton's equation is "incorrect" but the error is so small in most cases that it is undetectable. (In science-speak, Newton's equation is a limiting case of the domain of SR. It is good up to some limit and thereafter the error becomes too large to ignore.)