Time in an alternate world

[Davideo]

How, if at all, would our perception of time change if the earth was shaped like a crumpled-up ball of paper?

[iNow]

How large of a difference in gravitational potential would there be between the peaks and troughs of the crumples, and how does that compare to the topology of Earth?

[Davideo]

The same as normal Earth, same as you would compare a mountain to a valley. Essentially the same conditions we live under, but with a different landscape. What most intrigues me is the idea of a piece sticking out, a kind of land peninsula in space. Would one side be hours ahead of the other? I understand that this is highly unlikely, but let's pretend it happened.

 

Crumple up a piece of paper and you can see why I ask, the nooks and crannies provide for an interesting (although hypothetical) environment.

[iNow]

I see. The answer to your question is, yes... There would be a relative difference between the peak and the valley, but it's no where near as large as you imply. It's more on the order of a nanosecond than anything even closely resembling long periods like hours. In much the same way, we experience slight time dilation when flying on an airplane (see Hefele-Keating experiment), but it's so small as to be disregardable.