What would the universe be like if it had four spatial dimensions instead of three? Experimentalists are starting to explore the physics of higher dimensions with the help of recently developed tricks that synthetically mimic an extra fourth dimension in platforms such as ultracold atoms, photonics, acoustics, and even classical electric circuits. Although any such trick necessarily has limitations, as the fourth spatial dimension is always artificial, those approaches have proven that they can simulate some four-dimensional effects in controlled experimental systems.
But what is a fourth spatial dimension? In nonrelativistic physics, in which space and time are distinct, a spatial dimension is simply a direction along which objects can move both forward and backward (unlike time, which always flows from past to future). The number of relevant spatial dimensions in a system is defined by the directions along which spatial motion can take place or, alternatively, the number of spatial coordinates—for example, (x, y, z)—that must be specified to define where an object is at a particular moment in time.
The number of spatial dimensions can be reduced by constraining a system. For example, threading a bead onto a long, straight wire limits the bead to move in only one spatial dimension: either forward or backward along the wire. A single coordinate gives the bead’s position along the wire at any given moment.
What would happen, then, with an increase in the number of spatial dimensions to four or more? Theoretical physicists can simply extend familiar physical equations to an enlarged set of spatial coordinates—for example, (x, y, z, w). Often that extension leads to no new phenomena. But in certain fields of physics, new effects are predicted to emerge, such as so-called topological insulators, which are the primary source of inspiration for efforts to simulate 4D physics experimentally. This article delves into what 4D physics is and how experimental tricks to mimic 4D space work
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