Would an object appear to be standing still in 3D space if it was moving only along a 4D space vector?

Say we have small object, a digital wristwatch for example that is lying flat on a table, not moving along any of the 3D space vectors relative to us (X, Y, Z axes.) To us that watch is stationary.

Now, what would happen to our little wristwatch from our 3D perspective if it suddenly started accelerating, moving or rotating along a 4D vector? (W axis.)

Would we notice this movement or would the watch still be lying peacefully on the table as if nothing is happening? Would it still display the right time?