Gravitational fields change the flow of time measured by clocks and by any process that tracks time. General relativity describes this as gravitational time dilation: clocks deeper in a gravity well run more slowly relative to observers farther away. Radioactive decay is a stochastic quantum process whose probability evolves with an object's proper time, the time experienced locally by the decaying nucleus. Consequently, the number of decay events observed per unit coordinate time depends on gravitational potential through its effect on proper time. Locally measured decay rates do not change for local observers, but a distant observer will record slowed decay from sources deep in a gravitational well.
Physical mechanism
The theoretical link is straightforward in relativistic quantum theory. Decay laws are written in terms of proper time, so an unstable nucleus with decay constant lambda will follow an exponential survival probability proportional to e^{-lambda times proper time}. In a gravitational potential where proper time accumulates more slowly, the same nucleus will have experienced less proper time after a given interval of coordinate time, and therefore will have a higher survival probability when viewed from a distant frame. This is not a change in nuclear physics constants but a relativity of elapsed time. Experimental demonstrations of time affecting decay include cosmic-ray muon lifetime studies by David H. Frisch and J. H. Smith, Massachusetts Institute of Technology, which showed longer apparent lifetimes for fast-moving muons, illustrating that decay responds to the relevant time parameter.
Observational evidence and consequences
Direct laboratory measurements of gravitational effects on clocks and frequency are well established. Robert V. Pound and Glen A. Rebka Jr., Harvard University, measured gravitational redshift of gamma rays consistent with time dilation, and atomic clock comparisons in airborne experiments by J. C. Hafele and R. E. Keating, US Naval Observatory, confirmed combined special and general relativistic timing shifts. Those results validate the expectation that decay rates, when referenced to distant coordinate time, will be affected by gravitational potential. Practically on Earth the magnitude is extremely small and radiometric dating, nuclear medicine, and waste management remain effectively unchanged in ordinary environments. Astrophysically, however, radioactive isotopes near neutron stars or black holes would appear to decay more slowly to distant telescopes, altering light curves and nucleosynthesis signatures. This has consequences for interpreting observations, for models of heavy-element production in extreme environments, and for how different cultures and territories value astronomical observations that rely on decay-dependent signals.