Earth's core older than surface ?

[killium]

Since there is no net gravity at the center of Earth and since gravity fields slows down time, is it correct to postulates that matter at the center of the Earth is older than matter near the surface ?

 

[GraemeH]

Since there is no net gravity at the center of Earth and since gravity fields slows down time, is it correct to postulates that matter at the center of the Earth is older than matter near the surface ?

Matter at the center of the Earth is at the lowest gravitational potential (at the bottom of the gravity well) but it still feels the gravitational force from the matter around it. So the vector sum will be zero but the gravitational potential field will still have a finite value, thus the clock runs slower as predicted by General Relativity. However, since the Earth's mass is relatively low, the time dilation effect will be of the order of nanoseconds. Also, the Earth's core is molten and undergoes convective mixing, so any time dilation effect on a given particle will occur only for a small amount of time.

To answer your question, yes, the postulate is theoretically reasonable but proving it by sampling the Earth's core is a completely different matter.