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These methods are largely independent of each other, based on separate observations and arguments, yet all point to a history much longer than 10,000 years.
Radioactive Dating There are basically two different kinds of radioactive dating methods.
Think of air bubbles frozen in an ice cube--the air is prevented from escaping by the solid ice, but will escape when the cube melts because the energy of the system is lower without the bubbles.
(Further separation could occur during solidification, due to different crystallizations of the parent and daughter isotopes.) This means that the information about how much decay took place prior to melting is lost.
According to relativity, time itself can be slowed down.
Everything that experiences time can therefore be given a longer effective lifetime if time is dilated. Traveling at a speed close to the speed of light causes time to slow down significantly, relative to the stationary observer.