>> 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)?
>
> Why would it disappear?

The assumption is that if there are more than 3 spatial dimensions, we 
can only view and measure an infinitely "thin" 3D slice of a higher 
dimensional world. If mass is conserved in 4D (or higher) space then it 
should be possible (or even usual) for mass to change in a 3D slice.

I guess the assumption comes from the analogy with living in a 2D world 
where you can't see the 3rd dimension - objects that move in the 3rd 
dimension would appear to grow and shrink in your 2D world, leading you 
to formulate that mass is not always conserved in your world, it 
"disappears" off somewhere you can't measure or see.

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