Pulse propagation in a hyperlattice.

The classical dynamics and pulse propagation are presented for a series of latticelike structures whose spatial dimensionality ranges from one to four: four representing a hyperlattice. The lattices are connected 1‐D wave bearing systems of varying lengths and can illuminate some aspects of higher dimension structures. Short pulses are launched at an arbitrary point, reverberate throughout the entire structure, and detected at another point. Some aspects of increasing dimensionality are illustrated with particular emphasis on the transition from three to four spatial dimensions. In a hypothetical 4‐D world where only three are observable, the classical conservation laws and causality do not hold. The lack of causality is illustrated at each step in dimensionality by showing the “unexpected” pulse returns from the next higher dimension.