In this essay series I have been exploring Einstein’s puzzle of spacetime as a physical category (see essay #3). One possibility considered was that spacetime may emerge from some deeper, pre-geometric substrate rather than existing as a substance in its own right. If such a condition existed, observation suggests it was expanding, and that continued expansion could naturally give rise to circulating motion. The previous essay considered whether circulating motion in such an environment could reorganize into hierarchies of vortices. Here I consider how those vortices may have further evolved.

Expansion steadily reduces density, altering the conditions under which motion can remain coherently organized. In any expanding system, a declining density changes how effectively different regions remain dynamically coupled. As density and coherence decline, conservation laws require motion to reorganize rather than disappear. This general principle underlies both classical continuum physics and modern cosmology (Peebles 1993; Weinberg 2008). In this view, vortices that once extended across large regions may have begun concentrating into smaller domains in order to preserve angular momentum.

Several pathways might, in principle, produce such concentration in the early universe. One possibility is gradual gravitational accumulation, in which matter slowly gathers into increasingly dense regions. Another is the amplification of random density fluctuations, where small irregularities grow over time as gravity strengthens their contrast with the surrounding environment. Both ideas play central roles in standard cosmological models. Yet the unexpectedly early appearance of supermassive black holes (SMBHs) raises questions about whether gradual accumulation alone could operate quickly enough. A third possibility is that circulation already present in the system reorganized into more concentrated forms, allowing existing motion to condense into smaller and faster structures without waiting for matter to assemble slowly over time.

Experiments with rotating systems show that when density or cohesion declines, large vortices can lose their coupling to the surrounding environment. When this occurs, the circulation does not disappear. Conservation of angular momentum requires the remaining motion to become concentrated within a smaller region, producing a faster and more tightly organized vortex (Greenspan 1968; Tritton 1988).

Processes resembling this pattern appear in many physical environments. Shu (1987), for example, describes how rotating gas clouds collapse into dense stellar cores while conserving angular momentum. Lynden-Bell and Pringle (1974) showed how accretion disks redistribute angular momentum outward while material spirals inward toward compact centers, a mechanism later extended by Balbus and Hawley (1998) through magnetohydrodynamic turbulence. Even laboratory vortices undergo transitions in which broad circulation reorganizes into narrower and faster structures when the original configuration becomes unstable (Greenspan 1968; Tritton 1988). Together, these examples suggest that concentrated rotation can emerge naturally when large rotating systems lose coherence.

As a vortex contracts, its rotational speed naturally increases. This faster motion generates stronger internal stresses, much as a spinning ice skater experiences greater forces while pulling in her arms. Studies of rotating fluids show that increasing shear can create strong pressure gradients and structural strain within the flow (Kundu and Cohen 2008; Landau and Lifshitz 1987). Analyses of rotating astrophysical systems similarly show that when rotational energy and internal stresses exceed stability limits, large structures can reorganize into smaller and denser configurations (Chandrasekhar 1969).

If similar reorganizations occurred repeatedly in the expanding early universe, the result could have been a hierarchy of increasingly compact vortices. Each stage of collapse would concentrate circulation further while leaving behind a denser and more stable remnant. Residual motion outside these compact structures would remain within the larger environment, where it could continue influencing subsequent evolution. In many physical systems, such repeated reorganizations arise naturally when conservation laws operate in environments whose density and coherence are steadily changing (Greenspan 1968; Chandrasekhar 1961).

At sufficiently high rotation and compaction, the universe already provides an example of such extreme concentration, we know of as black holes. Observations from the James Webb Space Telescope have revealed massive black holes and unexpectedly mature galaxies already present during the universe’s first few hundred million years (Greene et al. 2024). Explaining how such enormous concentrations formed so early remains one of the open questions in modern cosmology.

If circulating motion was already present during the earliest stages of cosmic evolution, and if repeated losses of coherence caused that motion to reorganize into smaller and faster vortices, then the unusually early appearance of supermassive black holes may not be as mysterious as it first appears.

Such processes would raise another intriguing possibility. The structure we describe mathematically as spacetime may not be only a passive geometric stage. It might instead reflect a deeper physical organization capable of sustaining motion, concentration, and reorganization long before galaxies formed. In his 1920 Leiden lecture, Einstein suggested that space may possess physical qualities even though it should not be regarded as a conventional material medium (Einstein 1920). Could this be the kind of unfamiliar physical category he had in mind?

I invite your comments.

Robert J. Conover

References:

Balbus, S. A., and J. F. Hawley. 1998. “Instability, Turbulence, and Enhanced Transport in Accretion Disks.” Reviews of Modern Physics 70: 1–53. https://doi.org/10.1103/RevModPhys.70.1. arXiv: astro-ph/9707123.

Chandrasekhar, S. 1961. Hydrodynamic and Hydromagnetic Stability. Oxford: Clarendon Press.

Chandrasekhar, S. 1969. Ellipsoidal Figures of Equilibrium. New Haven, CT: Yale University Press.

Einstein, A. 1920. “Ether and the Theory of Relativity.” Address delivered at the University of Leiden, May 5, 1920. Reprinted in Sidelights on Relativity. London: Methuen and Co., 1922.

Greene, J. E., et al. 2024. “Intermediate-Mass Black Holes and Early Black Hole Growth with JWST.” Annual Review of Astronomy and Astrophysics. https://doi.org/10.1146/annurev-astro-052920-015826.

Greenspan, H. P. 1968. The Theory of Rotating Fluids. Cambridge: Cambridge University Press.

Kundu, P. K., and I. M. Cohen. 2008. Fluid Mechanics. 4th ed. Amsterdam: Elsevier Academic Press.

Landau, L. D., and E. M. Lifshitz. 1987. Fluid Mechanics. 2nd ed. Oxford: Pergamon Press.

Lynden-Bell, D., and J. E. Pringle. 1974. “The Evolution of Viscous Discs and the Origin of the Nebular Variables.” Monthly Notices of the Royal Astronomical Society 168: 603–637. https://doi.org/10.1093/mnras/168.3.603.

Peebles, P. J. E. 1993. Principles of Physical Cosmology. Princeton, NJ: Princeton University Press.

Shu, F. H. 1987. “Star Formation in Molecular Clouds: Observation and Theory.” Annual Review of Astronomy and Astrophysics 25: 23–81. https://doi.org/10.1146/annurev.aa.25.090187.000323.

Tritton, D. J. 1988. Physical Fluid Dynamics. 2nd ed. Oxford: Clarendon Press.

Weinberg, S. 2008. Cosmology. Oxford: Oxford University Press.