The last six essays explored the puzzle left to us by Albert Einstein regarding spacetime. In General Relativity, spacetime is described mathematically as geometry, yet that geometry behaves as though it possesses physical properties. Spacetime therefore appears to belong to what Einstein once called an “unfamiliar category”, something neither ordinary matter nor mere abstraction.
In the previous essays, I explored how physicists have responded to this issue and identified the capacities any such deeper level would plausibly need to sustain: conservation and dynamical continuity, as required in relativistic field descriptions (Wald, 1984), along with the ability for relational structure to appear geometric at large scales, as explored in approaches to quantum gravity (Rovelli, 2004). No clear solution resolved Einstein’s puzzle. But Einstein insisted that something must underlie the success of relativity (Einstein, 1920). Special relativity works because reality possesses structure. The open question is what that structure might be.
We have lived with the puzzle for the past hundred years and could easily leave the matter there. Yet scientific inquiry rarely rests with acknowledged tension. When observation repeatedly suggests that description may conceal deeper organization, physics has often advanced by cautiously asking what must exist and then examining whether that possibility remains consistent with what is already known. Atoms were inferred long before they were directly observed. Neutrinos were proposed decades before detectors confirmed them (Pauli, 1930). In each case, reasoning preceded confirmation. A world-wide search is currently underway to find the particle that gives existence to dark matter.
Scientific progress does not advance by leaving issues unresolved. When observation repeatedly points beyond description, physics has historically taken the next step: when observation exposes limits in existing descriptions, it develops new theoretical frameworks or hypotheses to restore explanatory coherence (Kuhn, 1962; Lakatos, 1970). Such hypotheses are not arbitrary. They are constrained by what is already known: they must remain consistent with observation and typically preserve established conservation principles (Noether, 1918), while maintaining internal mathematical coherence as emphasized in physical theory (Feynman et al., 1963). If spacetime geometry belongs to what Einstein called an unfamiliar category, then the appropriate response is to ask what kind of physical condition could support geometry’s reliability without simply redefining geometry in new terms.
If we follow that method here, a disciplined possibility begins to take shape. Whatever underlies spacetime geometry would plausibly need to possess dynamical continuity, support the transport of conserved quantities, and permit structured interactions such as stress and propagation, while still appearing geometric at large scales. This line of reasoning aligns with approaches in quantum gravity that treat spacetime as emergent rather than fundamental (Oriti, 2014; Butterfield & Isham, 2001). In other words, it would resemble neither classical substance nor pure mathematics, but something physically real whose large-scale behavior is most efficiently described through geometry. For the sake of discussion, we may refer to this provisional possibility as a pre-geometric condition, not as a replacement for spacetime, but as a deeper level whose large-scale behavior appears geometric to observers.
If such a pre-geometric condition exists, it would not sit alongside the universe as an additional ingredient. In the earliest epoch, it would have constituted the universe itself. What we now describe as matter, radiation, and spacetime geometry would represent later expressions of that more fundamental condition. For that reason, when we examine the observable characteristics of the early universe, concentration, motion, conservation, we are simultaneously examining the constraints that would have governed the pre-geometric condition at that stage.
If that is so, then the characteristics of the early universe become directly relevant. In its earliest stage, the universe would have expressed the pre-geometric condition in its most concentrated form. Whatever constraints governed the early cosmos therefore also governed that underlying level. Observation already tells us several important things about those conditions.
Concentration and Expansion
Multiple independent lines of evidence show that the universe is expanding. Looking backward, expansion implies that the observable contents of the universe occupied a more compact, higher-density state in the past (Peebles, 1993; Weinberg, 2008). If a deeper, pre-geometric condition underlies spacetime, it would plausibly have existed in an extremely concentrated state at the universe’s beginning, evolving alongside the density changes that characterize cosmic history.
Motion & Conservation
Expansion and density loss involves change on cosmic scales and change implies activity. Looking backward reveals a universe already evolving. Even the earliest observable epoch reflected in the cosmic microwave background shows matter and radiation interacting. The early universe was not at rest but in motion.
Across well-tested domains of physics, motion unfolds under conservation laws. Energy does not vanish as systems evolve, momentum does not disappear during interaction, and angular momentum is redistributed rather than destroyed. These principles arise from the symmetry structure of physical laws and serve as foundational constraints on physical dynamics (Noether, 1918; Goldstein et al., 2002).
If the early universe was concentrated, expanding, and in motion, then that motion would have been governed by conservation. Motion under conservation does not remain shapeless. Across many physical systems, one especially durable way motion reorganizes itself is through angular momentum.
When motion unfolds under conservation laws, it does not remain shapeless. Some motions fade quickly. Others reorganize into more durable forms. Across many physical systems, one conserved quantity repeatedly proves especially effective at sustaining organized behavior: angular momentum.
From rotating galaxies and accretion disks to atmospheric systems and laboratory fluids, circulation commonly emerges when matter or energy redistributes under conservation constraints (Binney & Tremaine, 2008; Pringle, 1981; Pedlosky, 1987). Even when large-scale rotation is not obvious at the outset, small imbalances can grow through instabilities, gradually organizing irregular motion into coherent circulation. Such behavior is widely observed across both astrophysical and terrestrial systems.
Angular momentum has practical advantages. Rotation allows motion to persist without requiring continual outward translation. It confines activity within a bounded region. For this reason, rotational patterns often endure where other forms of motion dissipate.
None of this implies that the early universe must have been globally rotating. Observations remain consistent with large-scale isotropy. But isotropy does not exclude localized circulation within a dynamically evolving system. Conservation does not require stillness; it governs how motion organizes.
If the earliest observable universe was concentrated, expanding, and active, then whatever internal motion existed within this pre-geometric condition would have unfolded under these same constraints. Under such circumstances, organized circulation would not be an arbitrary addition, but a physically plausible and commonly observed response to motion governed by conservation laws (Landau & Lifshitz, 1987; Frisch, 1995).
Under such conditions, motion would not simply disperse. Conservation ensures that motion must reorganize as the environment changes.
Conclusion
Nothing in this argument replaces geometry or diminishes its success. Geometry continues to describe how the universe behaves.
If spacetime’s reliability reflects a deeper level of organization, then that organization did not arise late in cosmic history. It would have been present from the beginning, existing in the same highly compact, expanding, internally active state that characterized the early universe and governed by conservation from the outset.
I don’t yet see a downside to hypothesizing a pre-geometric condition as the structure from which spacetime may have emerged. It will be interesting to contemplate how exactly physics will determine the direction that condition evolves.
I invite your comments.
Robert J. Conover
References:
Butterfield & C. J. Isham (Eds.), Physics meets philosophy at the Planck scale: Contemporary theories in quantum gravity. Cambridge University Press.
Callender and N. Huggett (Eds.), Physics Meets Philosophy at the Planck Scale. Cambridge University Press.
Binney, J., and Tremaine, S. (2008). Galactic Dynamics (2nd ed.). Princeton University Press.
Einstein, A. (1920). Relativity: The Special and the General Theory. Henry Holt and Company.
Feynman, R. P., Leighton, R. B., and Sands, M. (1963). The Feynman Lectures on Physics, Vol. I. Addison-Wesley.
Frisch, U. (1995). Turbulence: The Legacy of A. N. Kolmogorov. Cambridge University Press.
Goldstein, H., Poole, C., and Safko, J. (2002). Classical Mechanics (3rd ed.). Addison-Wesley.
Kuhn, T. S. (1962). The Structure of Scientific Revolutions. University of Chicago Press.
Lakatos, I. (1970). Falsification and the methodology of scientific research programmes. In I. Lakatos and A. Musgrave (Eds.), Criticism and the Growth of Knowledge. Cambridge University Press
Landau, L. D., and Lifshitz, E. M. (1987). Fluid Mechanics (2nd ed.). Pergamon Press.
Noether, E. (1918). Invariante Variationsprobleme. Nachrichten von der Gesellschaft der Wissenschaften zu Göttingen, 235–257.
Oriti, D. (Ed.). (2014). Approaches to Quantum Gravity: Toward a New Understanding of Space, Time and Matter. Cambridge University Press.
Pauli, W. (1930). Letter proposing the neutrino hypothesis. (Published in collected scientific correspondence).
Pedlosky, J. (1987). Geophysical Fluid Dynamics (2nd ed.). Springer.
Peebles, P. J. E. (1993). Principles of Physical Cosmology. Princeton University Press.
Pringle, J. E. (1981). Accretion discs in astrophysics. Annual Review of Astronomy and Astrophysics, 19, 137–162
Rovelli, C. (2004). Quantum Gravity. Cambridge University Press.
Weinberg, S. (2008). Cosmology. Oxford University Press.