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This is an interesting reference, but it seems to me that the measurements are controversial enough that they are certainly not, at this point, at the stage where they force any re-think of nuclear and solar physics as currently understood. The paper in question is Power spectrum analyses of nuclear decay rates. D. Javorsek II et al., Astropart. Phys. ...


No, a weak decay doesn't imply a change of $S$. For example, the decay of the neutron – the basic part of the beta-decay – has $S=0$ both in the initial and final state. So the first proposition is false and only the second one is true.


In QM most stuff boils down to particles. For example, electromagnetism is mediated by photons and EM radiation is literally just beams of photons. We should then have a couple of obvious candidates for strange and new kinds of radiation. The strong force is mediated by gluons and there are 8 types of gluons. At a larger scale (like with atomic nuclei) ...

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