Energy as a Primitive Ontology for the Physical World

We reanalyze from a modern perspective the bold idea of G. Helm, W. Ostwald, P. Duhem and others that energy is the fundamental entity composing the physical world. We start from a broad perspective reminding the search for a fundamental ``substance’’ (perhaps better referred to as ous'\i a, the original Greek word) from the pre-Socratics to the important debate between Ostwald and Boltzmann about the energy vs. atoms at the end of the 19th century. While atoms were eventually accepted (even by Ostwald himself), the emergence of Quantum Mechanics and Relativity were crucial to suggest that the dismissal of energy in favor of atoms was perhaps premature, and should be revisited. We discuss how the so-called primitive ontology programme can be implemented with energy as the fundamental entity, and why fields (and their quanta, particles) should rather be considered as non-fundamental. We sketch some of the difficulties introduced by the attempt to include gravitation in the general scheme.

💡 Research Summary

The paper revisits the long‑standing proposal that energy, rather than particles or fields, is the fundamental constituent of the physical world. Beginning with a historical survey, the authors trace the search for a basic “substance” (the Greek ousía) from the Pre‑Socratics through the 19th‑century debate between Wilhelm Ostwald, who championed an energy‑centric view, and Ludwig Boltzmann, who defended atomism. Although Ostwald eventually conceded to the atomic paradigm, the authors argue that the advent of quantum mechanics and relativity rendered the dismissal of energy premature.

Quantum mechanics introduced energy quantisation, wave‑particle duality, and the central role of the Hamiltonian, suggesting that energy is not merely a derived quantity but a primary dynamical variable. Relativity, via the equivalence of mass and energy (E = mc²), further blurred the distinction between “matter” and “energy”, indicating that what we call particles are specific excitations of an underlying energy distribution.

Against this backdrop, the authors adopt the primitive ontology (PO) programme, which insists that any physical theory must specify a clear, observer‑independent ontology of the world’s basic entities. Traditionally, PO has been instantiated by point particles (in Bohmian mechanics) or by field configurations (in GRW‑type collapse models). The paper proposes to replace these with an energy‑density field defined on space‑time. In this picture, particles and fields become emergent, higher‑level descriptions of patterns in the underlying energy flow. The wave function is reinterpreted as a tool for calculating the evolution of the energy density rather than as a fundamental ontic object. This shift promises to alleviate the measurement problem and to provide a more unified account of quantum and classical regimes.

The authors acknowledge several formidable challenges. First, the locality of energy is problematic in general relativity, where the stress‑energy tensor is covariantly conserved but its components are coordinate‑dependent, making it difficult to assign a unique energy density to a region of curved space‑time. To address this, they sketch a novel geometric framework in which energy density and flux are treated as a non‑conservative, irreversible flow on a fiber bundle over space‑time, thereby decoupling the notion of energy from the traditional pseudo‑tensor constructions.

Second, thermodynamic irreversibility and entropy raise questions for a PO based on a conserved quantity. The authors argue that entropy increase can be understood as the manifestation of an intrinsic asymmetry in the energy flow, allowing a non‑conservative primitive ontology without contradicting the overall conservation laws of the theory.

Third, incorporating gravitation remains an open problem. The paper suggests that an energy‑centric PO may dovetail with approaches to quantum gravity such as loop quantum gravity or spin‑network models, where the fundamental excitations are essentially quanta of geometric energy. However, a fully consistent mathematical formulation that simultaneously quantises energy and reproduces the dynamical geometry of general relativity is still lacking.

In the concluding section, the authors emphasize that re‑establishing energy as the primitive ontology could provide a fresh metaphysical foundation for physics, one that naturally integrates quantum mechanics, special and general relativity, and possibly quantum gravity. They stress that while the proposal is conceptually attractive, substantial technical work is required to resolve issues of energy localisation, irreversibility, and the quantum‑gravitational interface before the programme can be considered a viable alternative to the prevailing particle‑field ontology.