Interesting post from Sara Reardon in Symmetry (A joint Fermilab/SLAC publication):
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In 2008, Fermilab particle astrophysicist Craig Hogan made waves with a mind-boggling proposition: The 3D universe in which we appear to live is no more than a hologram. Now he is building the most precise clock of all time to directly measure whether our reality is an illusion.
The idea that spacetime may not be entirely smooth — like a digital image that becomes increasingly pixelated as you zoom in – had been previously proposed by Stephen Hawking and others. Possible evidence for this model appeared last year in the unaccountable “noise” plaguing the GEO600 experiment in Germany, which searches for gravitational waves from black holes. To Hogan, the jitteriness suggested that the experiment had stumbled upon the lower limit of the spacetime pixels’ resolution.
Black hole physics, in which space and time become compressed, provides a basis for math showing that the third dimension may not exist at all.