My last essay discussed the puzzle Einstein encountered when he recognized that the geometry of spacetime appeared to possess physical qualities. Geometry is normally understood as a way of organizing relationships between objects. In general relativity, however, spacetime geometry bends light, governs motion, participates in energy exchange, and transmits gravitational waves. A framework that influences events so directly begins to look like more than mathematics alone.
According to Einstein’s 1920 lecture, this places spacetime in an unfamiliar category between a material medium and abstract geometry. Other physicists explored similar questions from different directions, but despite decades of investigation, those approaches produced no broad consensus.
If spacetime is neither a traditional substance nor simply an abstract mathematical description, what could lie between substance and geometry?
Physics has encountered similar challenges before, particularly when familiar categories proved inadequate to describe collective behavior. In many complex systems, the behavior we observe at large scales does not reveal the detailed processes occurring underneath. Elasticity describes how a solid bends without referring to the individual atoms inside it. Temperature summarizes the motion of countless molecules without tracking any one of them directly.
Physicists describe this recurring behavior as emergence, a situation in which stable large-scale patterns arise from many interacting parts working together. The laws governing the individual components remain valid, but new and often simpler rules appear at larger scales. Familiar quantities such as temperature or elasticity summarize collective behavior without requiring scientists to track individual constituents. These kinds of large-scale descriptions provide accurate and practical ways of understanding organized systems (Anderson 1972).
Fluid and condensed-matter systems provide particularly vivid examples of emergence. In rotating fluids, vortices can form, persist, and be measured as coherent structures without requiring scientists to track the individual molecules that make up the fluid. Atmospheric storms, whirlpools, and superfluid vortices can travel, interact, and exchange energy as if they were independent objects. Yet nothing new has been added to the system. A vortex is a stable pattern of circulating motion within an existing medium, such as water in a whirlpool or air in a storm. Its persistence arises from conservation laws and the collective behavior of the surrounding fluid rather than from the presence of a separate object (Greenspan 1968).
In each of these cases, geometry emerges as a practical language describing how disturbances move through an organized system. Paths lengthen or shorten according to local conditions, signals propagate at characteristic speeds, and stable structures follow trajectories determined by collective response. Observers embedded within such systems would naturally describe these behaviors geometrically, even if the underlying organization were hidden from view. In general relativity, curvature performs a remarkably similar role: it determines how light travels, how clocks run, and which events can influence one another. Geometry would remain real and measurable, while its origin might lie in processes operating beneath the level at which geometry itself becomes visible. In certain condensed-matter systems, researchers have shown that disturbances moving through an organized medium can behave mathematically as if they were traveling through curved spacetime, even though the underlying system consists only of interacting particles (Volovik 2003).
None of these ideas diminish the extraordinary success of general relativity. Geometry would continue to describe what observers measure, even if deeper processes ultimately give rise to those relationships. Several researchers have explored this possibility directly, proposing that gravitational behavior might emerge from deeper physical processes rather than existing as a fundamental interaction in its own right (Sakharov 1967; Jacobson 1995). Geometry, therefore, may describe how a deeper organization behaves when viewed at large scales. Just as elasticity does not replace atoms but summarizes their collective motion, spacetime curvature might summarize relationships emerging from processes not yet fully understood.
Spacetime may belong to an unfamiliar category after all. One that is not a classical substance, but something whose large-scale behavior appears geometric because that is the most efficient way to describe it. Physics has previously encountered category shifts. Heat was once treated as a fluid called caloric until molecular motion provided a deeper explanation. Magnetism appeared mysterious until understood as organized charge and spin. Each transition required recognizing that familiar descriptions were effective approximations rather than ultimate explanations.
What deeper structure might lie between substance and geometry is not yet known. But physics has repeatedly shown that familiar descriptions sometimes turn out to summarize deeper processes rather than reveal them directly. Could Einstein’s “unfamiliar category” reflect something similar, a geometry emerging as the large-scale expression of a deeper physical organization? If so, spacetime curvature may be recording relationships whose underlying structure has not yet come into view.
I look forward to your comments.
Robert J. Conover
References:
Anderson, P. W. (1972). More is Different. Science 177, 393–396.
Greenspan, H. P. (1968). The Theory of Rotating Fluids. Cambridge University Press, Cambridge.
Sakharov, A. D. (1967). Vacuum quantum fluctuations in curved space and the theory of gravitation. Soviet Physics Doklady, 12, 1040–1041.
Jacobson, T. (1995). Thermodynamics of spacetime: The Einstein equation of state. Physical Review Letters, 75, 1260–1263.
Volovik, G. E. (2003). The Universe in a Helium Droplet. Oxford: Oxford University Press. (International Series of Monographs on Physics, Vol. 117).