Actually, I think Hawking was saying that even with the same relative motion (or non-motion), there are relativistic effects of living on a mountatin top versus living at sea level. True, any motion relative to non-motion, such as walking up a mountain, will have some effect.

But I think Hawking was saying that there is increased gravity at sea level, relative to a mountain top and increased gravity will cause time near it to progress more slowly relative to time with less gravity, in the same manner that increased velocity causes time to progress more slowly for the moving observer than for the motionless one.


As to the rest of this discussion, it's interesting, but I'm sorry it's just a bit too above me.