>> Why would they move in the other dimensions, if they are only moved in
>> our three or four?
>> What force would move them?
>
> Why would they *not* move in the other dimensions? Why would all forces
> just happen to be perpendicular to those dimension?

If there was ever any component of any force not wholly constrained 
within our 3D "view" then surely this could be used to accelerate a mass 
along one of these other dimensions which we would see as mass 
disappearing (apart from any 4D GR stuff)?

Or, our idea of "mass" is somehow not telling us the whole story (dark 
matter?).

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