In the previous essays, I explored the possibility that spacetime occupies an unfamiliar category, neither a traditional material medium nor merely an abstract mathematical description. One way such a category could arise is through emergence, a situation in which large-scale descriptions summarize deeper organization without directly revealing it. In a well-known discussion, Anderson (1972) argued that when many interacting components organize collectively, new large-scale behaviors can arise with their own stable laws. These descriptions remain reliable even though they do not reveal the underlying mechanisms. Some physicists have even suggested that spacetime itself may behave in this way, with Einstein’s equations emerging from deeper thermodynamic relationships (Jacobson 1995). Related approaches have also explored gravity as an emergent phenomenon arising from quantum or informational structure (Sakharov 1967; Verlinde 2011).

In such cases, the higher-level language remains accurate because underlying processes reliably produce the relationships that are precisely measured. If spacetime geometry belongs to this broader class of phenomena, then Einstein’s equations may represent a remarkably successful large-scale description rather than the final level of explanation. If spacetime geometry has emerged from an unseen organization, what characteristics would physics require that organization possess?

If spacetime curvature were emergent, the deeper organization responsible for it could not behave arbitrarily. The behavior of spacetime has already been measured with remarkable precision. Any underlying processes would therefore need to reproduce those same observable relationships. The known properties of spacetime already place strict constraints on whatever deeper structure might give rise to them.

Because any proposal for emergence must preserve its successes, general relativity itself becomes the guide for asking what deeper organization would be required. The theory already tells us how spacetime behaves: disturbances propagate, energy is conserved, and geometry evolves in response to changing conditions. If curvature were emergent, whatever produces it would therefore need to reproduce those same behaviors, matching the empirical success of general relativity.

Physics has encountered this situation before. When large-scale behavior emerges from deeper processes, observable properties constrain what lies beneath. Elasticity requires interactions that transmit stress (Landau and Lifshitz). Temperature requires microscopic motion that exchanges energy. Fluid behavior requires momentum transfer that sustains waves and vortices.

One requirement concerns the transmission of influence. General relativity shows that gravitational effects do not appear instantaneously but propagate across space at finite speed. Gravitational waves carry energy across vast regions of the universe before interacting with detectors on Earth (Abbott et al. 2016). Earlier observations of energy loss in binary pulsars provided indirect evidence for gravitational radiation propagating through space (Hulse and Taylor 1975). Emergent descriptions elsewhere in physics display similar behavior only when underlying interactions permit disturbances to travel through a system. Elastic materials transmit deformation through atomic forces, and fluids sustain waves through momentum exchange between molecules. If curvature represents a large-scale description of deeper processes, those processes must likewise sustain dependable transmission while preserving the cause-and-effect relationships observers measure.

Another requirement follows from conservation. Observations of gravitational radiation show that energy is transferred and redistributed with extraordinary precision (Abbott et al. 2016; Hulse and Taylor 1975). Conservation observed at macroscopic scales reflects reliable accounting at deeper levels. Thermodynamic laws endure because microscopic motion exchanges energy consistently across interacting systems. Any organization capable of producing spacetime curvature would therefore need the capacity to store, transfer, and redistribute energy in ways that preserve the conservation relationships observers measure.

A further requirement involves dynamical responsiveness. General relativity does not describe spacetime as a passive stage. Geometry evolves in response to matter and energy, and curvature in turn influences motion (Will 2014). This reciprocal relationship implies continual adjustment rather than static structure. In other areas of physics, such responsiveness arises only when underlying organization permits ongoing adaptation to changing conditions. If curvature were emergent, the deeper processes responsible for it would need to remain responsive across an enormous range of physical conditions, from weak gravitational fields to the violent environments surrounding compact objects.

Spacetime curvature remains coherent across extreme conditions, from interplanetary navigation and satellite timing to neutron stars and merging black holes (Will 2014). Emergent descriptions remain reliable only when the underlying organization preserves stability across such variation. Whatever produces curvature must therefore maintain coherence across many orders of magnitude.

These requirements apply not only locally but cosmologically. Universal expansion extends these requirements to the largest observable scales. Distances between galaxies evolve according to precise relationships linking energy density and curvature throughout cosmic history (Friedmann 1922; Planck 2018). If geometry summarizes deeper organization, that organization must itself evolve globally while maintaining local consistency. Expansion would then reflect evolving relationships within the underlying organization rather than motion into pre-existing emptiness.

One additional requirement follows from the symmetries already observed in nature. Experiments show that the laws of physics appear the same for observers moving at constant velocity, with no preferred direction or universal frame of rest detectable at accessible scales. This symmetry, known as local Lorentz invariance, has been tested with extraordinary precision in gravitational, atomic, and particle experiments (Will 2014). If spacetime curvature were emergent from deeper processes, those processes would therefore need to reproduce the same local symmetry. Any underlying organization would have to generate geometric behavior that appears locally identical to all observers while still permitting signals to propagate through it at finite speed.

These considerations emphasize general relativity’s durability. It succeeds because it captures stable relationships governing motion, energy, and causality across the observable universe. Emergence would suggest that those relationships arise from processes whose detailed structure remains hidden beneath the geometric description observers employ. Emergence therefore does not eliminate physical reality; it shifts the explanation to whatever organization produces the behavior geometry describes.

Without resolving Einstein’s question of whether spacetime belongs to an unfamiliar category (Essay #3), I have examined whether it could be emergent (Essay #4), and here identified the requirements such an underlying organization would need to satisfy. If curvature is emergent, its source must reproduce behaviors already observed throughout the universe: reliable transmission of influence, strict conservation, dynamical responsiveness to matter and energy, stability across extreme conditions, Lorentz invariance, and consistent evolution with cosmic expansion. Physics may not yet describe this organization directly, but observation has already placed strong constraints on what it could be.

I would like to hear your comments.

Robert J. Conover

References:

Anderson, P. W. (1972). More Is Different. Science, 177(4047), 393–396.

Abbott, B. P., et al. (LIGO Scientific Collaboration and Virgo Collaboration) (2016). Observation of Gravitational Waves from a Binary Black Hole Merger. Physical Review Letters, 116(6), 061102.

Friedmann, A. (1922). On the Curvature of Space. Zeitschrift für Physik, 10, 377–386.

Taylor, J. H., and Weisberg, J. M. (1982). A New Test of General Relativity: Gravitational Radiation and the Binary Pulsar PSR 1913+16. Astrophysical Journal, 253, 908–920.

Jacobson, T. (1995). Thermodynamics of Spacetime: The Einstein Equation of State. Physical Review Letters, 75(7), 1260–1263.

Landau, L. D., and Lifshitz, E. M. (1986). Theory of Elasticity (3rd ed.). Pergamon Press.

Planck Collaboration. (2018). Planck 2018 results. VI. Cosmological parameters. Astronomy & Astrophysics, 641, A6.

Sakharov, A. D. (1967). Vacuum quantum fluctuations in curved space and the theory of gravitation. Soviet Physics Doklady, 12, 1040–1041.

Verlinde, E. (2011). On the Origin of Gravity and the Laws of Newton. Journal of High Energy Physics, 2011(4), 29.

Will, C. M. (2014). The Confrontation between General Relativity and Experiment. Living Reviews in Relativity, 17, 4.