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Radiometric dating relies on accurate knowledge of the half-lives of radioactive elements. Skeptics have argued that since many elements' half-lives are too long for anyone to have observed them, we can't know what they were in the distant past.

There are various counterarguments based on terrestrial evidence, like agreement between elements in the same sample, and corroboration from varves, tree rings, and ice layers.

Another counterargument I've seen is by looking at supernova, we get a window "back in time" to when their light began its long journey to us, and that much of this light was generated by radioactive decay, confirming that decay rates were the same then as now.

I don't quite follow this explanation, and would like some help. Distant starlight doesn't give us a rock sample in which to analyze proportions of parent and daughter elements. Does it still somehow give evidence of specific radioactive decay rates? If so, how?

I know next to nothing about astronomy, so please explain this to me like I'm a child.

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When an unstable atom decays, it releases energy. At an earlier time, there are more unstable atoms, so the released energy is larger. At different times, there are different atoms left, so the energy released is different. You can measure the decay rate by following the time-series of this energy.

$$ E(t) = E_0 \exp[-\lambda t]$$

where $E$ is the energy, $t$ is time, $E_0$ is energy at $t=0$, $\lambda$ is the decay constant. This is a very simple picture. In reality, it will be a bit more complicated because of other effects causing the deviation of the observed energy, such as scattering.

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  • $\begingroup$ This leaves a lot unanswered for me. By looking at a glow of a specific brightness, how would you know that it was caused by a the decay of a specific amount of a specific element, or by radioactive decay at all? $\endgroup$ – Nathan Long Jan 13 at 23:05
  • $\begingroup$ Because other power sources would have the light curve behave differently. For example, fallback accretion onto a blackhole would be $\propto t^{-5/3}$, or $\propto t^{-2}$ for a magnetar spindown engine, etc. $\endgroup$ – Kornpob Bhirombhakdi Jan 14 at 1:34
  • $\begingroup$ I had to Google "light curve". :) Wikipedia says it's a graph of light intensity over time. Assuming you somehow could prove that some light from a supernova was being generated by decay of element X, wouldn't you have to measure the light for a very long time in order to draw that curve? $\endgroup$ – Nathan Long Jan 14 at 16:08
  • $\begingroup$ Define long ??? $\endgroup$ – Kornpob Bhirombhakdi Jan 14 at 16:48

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