Q: If gravity affects time, do radioactive materials get shorter half-lives on large planets and stars? (via Quora)
A: No. As far as the radioactive material itself is concerned, its half-life is the same as always. All objects within the same frame of reference experience the same time effects.
The half-life would only appear to be changed for someone observing from a different place within the gravitational frame.
And, when viewed from a different frame, higher gravity slows time; it doesn’t speed it up. So, when somehow viewed from afar, the half-life would be longer, not shorter.
But the effect of this stretching-out of time — time dilation — is, like other relativistic effects, tiny for human-scale masses and speeds.
Even with Earth-sized masses, it’s not much: Over the 4.5 billion years the Earth has existed, the material towards the center of the core has aged only about 2.5 years less than material at the surface.
That’s something like a minuscule 0.000000005555555555555556 % difference — way, way below the level of human perception; and having no meaningful effect the in everyday world.
Although it’s a tiny amount, it can and has been measured repeatedly and conclusively. For example, ultra-precise lab clocks can detect time dilation effects over as little as one meter’s height difference, here in Earth’s normal surface gravity.
See Gravitational time dilation.
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