DOH!! You missed your own answer!!
The atom is indeed mostly empty space, but it's surrounded by a "shell" of electrons orbiting quite quickly, thereby giving the impression of a solid shell and stopping photons of light, hence everyday objects appear solid......
Now, if you could stop the electrons from orbiting the nucleus, you would have the key to invisibility, as photons of light would no longer be blocked by the electron shell!!!
This answer is complete speculation, and some would say complete bollocks, but I had fun writing it!!