Is space a projection?
As the golden light of the sun creeps across a room in the sleepy hours of the afternoon, you can see the shadows of objects across the room stretch and merge into strange shapes. Many times, the shadows even bear little resemblance to the original object. A three dimensional object, despite being rigid and possessing a defined shape can create a variety of projections onto a surface.
Of course, one can expand this idea of projections to higher dimensions. We can imagine a 4D cube projecting a 3D cube onto 3D space.
I wonder if our universe is nothing more than a projection from some higher dimensional space onto our own. If that were the case, we can imagine that certain geometric problems such as intersecting lines are just the result of projection and can solved by imagining a higher dimensional strucuture. While driving on the highway with my family, I noted that it would be much more efficient if the highway were higher dimensional. After all, a 2D highway wouldn’t have any bridges and while we have bridges, there could be hyper-bridges in other dimensions that take advantage of the extra axes of space. Highways in higher dimensions could be ultra-complex. However, it would also be more efficient as they would have more pathways for hyper-cars to use.
The highway example can also be used to describe more complex computers. In higher dimensions, more pathways can be created for particles to travel along. As such, more efficient computers could theoretically be constructed without any 3D limitations. Extra dimensions of space also means that there are more ways of arranging a group of particles in higher dimensions than in lower dimensions, indicating greater entropy. Perhaps this entropy, if detected, could indicate the presence of higher dimensions wrapped into tight hyperstructures known as Kalabi-Yau manifolds (predicted by string theory).
In fact, it has already been calculated that the internal entropy of such spaces produces the exact Bekenstein-Hawking Entropy equation that is used to describe black holes!
There are also theories that the universe caould be described as a hologram of sorts. This is derived from an attempt at unifying (at least partially) some aspects of quantum mechanics with general relativity. The theory is AdS/CFT correspondence and it states that in a space known as Anti-DeSitter Space (hence the AdS in the theory name) where there is an overall negative curvature of space, the laws of quantum mechanics on the boundary of the space (which is infinitely far away from the interior due to the asymptotic nature of the space) is equivalent to the laws of gravity in the bulk (interior). This theory relates to the Holographic Principle in which conditions on a 2D surface can determine 3D geometry inside the surface.
The nature of spacetime is elusive and remains to be fully understood. In fact, understanding the nature of spacetime is the battlefield of various different theories of quantum gravity such as string theory and loop quantum gravity (which I will write about in another post). This is the frontier of theoretical physics and represents one of the greatest eras of exploration into the mysterious quantum nature of spacetime.