The "Holographic Universe" is wrong.

Projection is lossy.  The "Holographic Universe" is wrong.

That's really all I need to say. You can project to lower dimensions from higher because you are removing information.  You can't go the other direction without making stuff up.

Projecting from a lower dimension is like upscaling a video. You need to "fill in the gaps" of the information  you deleted when you encoded it.

Optical illusions exist because information is lost when an image is projected onto our eyes. Our brain makes stuff up to fill in the gaps. 

Even if projecting a 3d hologram ( star wars like ) from a 2d emitter, you have to borrow from the time dimension to restore the 3rd dimension. Meaning your 2d pixel needs to emit information that will create a light at one 3d location and "then" emit more information that will create light at another location further back or closer up.  Or it needs to emit information  that will cause light to emit at two or more temporal points in time along its journey. 

You are still going from 3d to 3d. It's just that you are going from 2d space + 1 time (partition) to 3d space. And then that's just for one frame. So you've basically divided your time dimension into two dimensions by putting your depth data into the sub frame intervals, and then your animation into the intervals greater than one frame. 

Again you've borrowed a partition of your time dimension to encode a 3rd space dimension so that you can "upscale' From 2d to 3d.