This is part of a series on the origin of spacetime and the early universe. See Essay #11 for a summary of the first ten essays.

In Essay #10 I examined how large rotating regions of the hypothesized pre-geometric substrate could plausibly collapse into a series of compact cores, eventually producing supermassive black holes (SMBHs). The earliest SMBHs and the elementary particles around us seemingly belong to completely different categories of nature. One spans millions or billions of solar masses, while the other exists at scales billions of billions of times smaller. Yet if both ultimately emerged from the same evolving universe, some continuous physical process must connect those extremes. This essay explores one possible bridge between them.

Essay #10 suggested SMBHs resulted from the collapse and reorganization of large cosmic vortices. According to experimental and theoretical studies of rotating systems, vortices show that circulation can survive major structural transitions (Greenspan 1968). When a large rotating region contracts and becomes concentrated into a compact core, the broader organized motion that existed before the collapse can persist in altered form. Similar behavior appears in astrophysical systems, where studies of rotating accretion disks show that angular momentum can be redistributed rather than destroyed as matter reorganizes around compact centers (Lynden-Bell and Pringle 1974).

Studies of rotating systems likewise show that circulation can become increasingly concentrated within a vortex, allowing coherent rotating structures to persist primarily through their own internal organization (Chandrasekhar 1961; Batchelor 1967; Donnelly 1991). These studies are presented as analogies rather than literal descriptions of the hypothesized Substrate, but they demonstrate that organized rotation can evolve toward compact, long-lived structures whose persistence depends increasingly on the stability of their internal circulation. If comparable behavior occurred in the early universe, the smallest surviving micro-vortices would represent the natural culmination of the cascade rather than an entirely new class of objects.

When circulation reorganizes into smaller structures, the rotation within those structures typically intensifies. Conservation of angular momentum implies that as the radius of a rotating system decreases, its rotation rate must increase. Similar behavior appears in many rotating systems, from laboratory vortices to contracting astrophysical disks, where shrinking rotating regions spin faster and concentrate motion into denser cores (Batchelor 1967; Chandrasekhar 1961).

If a comparable process occurred during the continued expansion of the young universe, each successive generation would have formed within an expanding environment that became progressively less capable of supporting organized rotation. As density continued to decline, progressively smaller vortices would receive less support from their surroundings, making further subdivision increasingly difficult. Eventually the cascade would reach a point where still smaller coherent vortices could no longer be sustained. From that stage onward, only the most compact and internally stable micro-vortices would remain.

Each generation in this sequence would not simply be a smaller version of the one before it. As circulation became confined within progressively smaller regions, conservation of angular momentum would cause each new vortex to spin more rapidly than the last. The vortices would become smaller, their rotation increasingly concentrated within their own boundaries, and their dependence on the surrounding environment would gradually diminish. Over time, the environment would naturally favor compact vortices capable of sustaining their organized motion largely through their own internal dynamics.

Studies of rotating systems likewise show that as external support weakens, circulation increasingly becomes concentrated within the vortex itself, allowing coherent rotating structures to persist primarily through their own internal organization (Chandrasekhar 1961; Batchelor 1967; Donnelly 1991). These studies are offered as analogies rather than literal descriptions of the hypothesized Substrate, but they suggest a broader principle: there are practical limits to how far organized motion can continue subdividing. Beyond that point, only the most stable rotating structures remain.

If a comparable process occurred during the continued expansion of the young universe, each successive generation would have formed within an environment that became progressively less capable of supporting organized rotation. The cascade would therefore not continue indefinitely. Instead, it would gradually approach a point where further subdivision was no longer possible, leaving only the most compact and internally organized vortices as the final survivors of the cascade.

Those surviving micro-vortices would represent a fundamentally new class of stable structures. Rather than appearing suddenly as entirely new objects, they could be understood as the final surviving members of an evolutionary sequence that began with the largest rotating structures in the young universe. If this possibility proves physically plausible, then the apparent divide between cosmology and particle physics becomes considerably smaller. The next question is whether such surviving micro-vortices could possess the stability and physical properties required of the elementary particles observed today.

I look forward to your comments.

Robert J. Conover

References:

Batchelor, G. K. (1967). An Introduction to Fluid Dynamics. Cambridge University Press.

Bond, J. R., Kofman, L., & Pogosyan, D. (1996). How filaments of galaxies are woven into the cosmic web. Nature, 380, 603–606.

Chandrasekhar, S. (1961). Hydrodynamic and Hydromagnetic Stability. Oxford University Press.

Donnelly, R. J. (1991). Quantized Vortices in Helium II. Cambridge University Press.

Frisch, U. (1995). Turbulence: The Legacy of A. N. Kolmogorov. Cambridge University Press.

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

Kolmogorov, A. N. (1941). The local structure of turbulence in incompressible viscous fluid for very large Reynolds numbers. Doklady Akademii Nauk SSSR, 30, 301–305.

Libeskind, N. I., et al. (2018). Tracing the cosmic web. Monthly Notices of the Royal Astronomical Society, 473(1), 1195–1217.

Lynden-Bell, D., & Pringle, J. E. (1974). The evolution of viscous discs and the origin of the nebular variables. Monthly Notices of the Royal Astronomical Society, 168, 603–637.

Springel, V., et al. (2005). Simulations of the formation, evolution and clustering of galaxies and quasars. Nature, 435, 629–636.