Plate Tectonics

If the Earth has been slowly cooling over its history, presumably this means that the crust must be getting thicker too, right? How would that effect plate tectonics? Would the continental plates be thinner in the past than they are today? What about mountain building (from plates colliding) – if the plates are thinner in the past would mountains be smaller (because there is less material) or taller (because the plates move faster and there is less material to lift at the collision point)? Would the plates move faster in the past, since they were thinner (and lighter)? Would the thinner crust allow more volcanic activity to reach the surface, adding more material and slowly thickening the plates until they reach a thickness that would be constant between different geological times?

Or has internal radioactivity in deep in the Earth allowed the surface of the planet to be roughly constant over geological time? Over time, the amount of radioactive materials in the Earth (keeping it warmer) should decrease, which should lead to the same cooling effects, although over a longer period of time than if there were no radioactive materials in the Earth.

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