Can we project a 4D world using 3D video technology?

Not in any coherent sense. We are not built to comprehend the fourth physical dimensional. Any kind of television that would be able to project a truly 3D image would only be able to play 3 dimensional "shadows" of 4 dimensional objects like the hyper cube shown above. The hyper cube itself is a 3D shadow of a spinning 4 dimensional cube. A good way to think of it is imagining you had a glass cube and you spun it around continuously along an axis. The 2D shadow of the 3d cube on a near by flat surface, looks like two connected squares passing "through" each other. The shadow of the cube has unequal sides and angles where as the cube has of course equal sides at 90 degree angles. Likewise this is why the 3D image of a spinning hyper cube is two connected cubes passing through each other. The hyper cube in 4D also has all equal sides at right angles but this is lost in the 3D projection.