# A Maxwell Universe – PART II — A. THE POINT-MASS PATH ## The ancients  Geometry is ancient. Long before physics existed as a discipline, geometric relationships were studied as ideal forms: perfect lines, circles, and ratios. By Euclid (~300 BCE), geometry had become an abstract deductive system, independent of the imperfections of the physical world. At the same time, Greek atomists such as Leucippus and Democritus proposed the opposite ontology: indivisible point-like atoms moving in void. From the start, Western thought carried two incompatible intuitions — reality as geometry, and reality as points. Debates about whether numbers or perfect forms “exist” continue even today. ## Plato  Plato held that geometric relations belong to a realm more real than the material world. In the *Republic* (510d–511a), he describes the objects of geometry as “eternal and unchanging,” while the visible world offers only “images and shadows of the true” (596a). In the *Timaeus*, he even assigns the Platonic solids as the elemental constituents of matter. Modern perceptual psychology echoes this: humans routinely impose geometric structure on ambiguous patterns, as documented by Gestalt research (Wagemans et al., *Annual Review of Psychology*, 2012). ## Descartes  Descartes preserved the ancient view of geometry as abstract but introduced a crucial tool: analytic geometry. Coordinates allowed curves to be represented symbolically. For example, a circle of radius $r$ in the $x$–$y$ plane can be written as $$ x^2 + y^2 = r^2 . $$ This unified algebra and geometry. Crucially, introducing $x$, $y$, and $r$ does **not** imply that the circle exists *in* a physical space. The coordinate system is only a convenient abstraction — a way to describe relationships without committing to a container in which they “live.” His physics rejected both vacuum and action at a distance. All influence had to be transmitted by contact. He imagined matter as a continuous medium structured by *vortices*. Space was not a background arena separate from matter; the two were identical: > “The extension in length, breadth, and depth which constitutes the nature of a > body is the same as that which constitutes the nature of space.” > — *Principles of Philosophy*, II, §10 Descartes thus offered a relational, medium-based ontology — an early form of field thinking. ### Descartes’ Vortices Long before Newton’s point-mass ontology hardened into the standard story, Descartes proposed a universe filled with continuous substance. There are no empty gaps, no distant action, no isolated particles. Everything moves because everything pushes on everything else. Motion cannot cross a void; it must propagate through a medium. That medium naturally forms *vortices*. A Cartesian vortex is not a swirling fluid inside space. It **is** the local organization of motion that *creates* the sense of space. Coherent regions of rotation sustain themselves through continuous contact interactions. Bodies are carried along by the circulating flow, not pushed by external forces. What later physics names “inertia” is, for Descartes, the natural persistence of motion in a rotating medium. Common misunderstandings obscure several essential points: 1. **The medium is universal.** Descartes does not place vortices *within* space; the vortices *generate* the relational structure that we interpret as space. 2. **Bodies are not separate from the medium.** A “body” is merely a denser or more organized region of the same continuous substance. 3. **There is no empty space.** The medium fills all that exists. Motion is always relational and always transmitted through contact. 4. **Gravity is not attraction.** Smaller bodies spiral inward because the surrounding circulation creates pressure gradients — not because of any mysterious force acting across emptiness. 5. **Geometry emerges from flow patterns.** Straight-line motion is simply the trajectory that best preserves the local structure of rotation. Descartes’ error was not conceptual but mathematical. Without the tools of wave theory and field dynamics, he could not quantify how vortices remain stable or how they propagate influence without losing coherence. --- ## Newton  Newton and Leibniz invented the mathematical language — calculus — that Descartes and earlier thinkers lacked. Newton also reshaped the ontology of physics: he removed the medium, restored action at a distance, and introduced absolute space and absolute time as a fixed, God-given stage. > “Absolute space, in its own nature, without relation to anything external, > remains always similar and immovable.” > — *Principia*, Scholium He treated bodies as mathematical points only for convenience: > Bodies may be “considered as points” when their size is irrelevant. > — *Principia*, Book I, Lemma I But the enormous success of celestial mechanics elevated this convenience into a foundational assumption. Matter became point-masses; gravity became an instantaneous force acting across empty space. Newton himself was uneasy with the metaphysics: > “That gravity should be innate, inherent, and essential to matter… is to me so > great an absurdity…” > — Letter to Bentley (1692) Yet no mechanism for transmission was available, and the equations worked. ### Why Newton Needed Absolute Space and Absolute Motion Newton’s mechanics could not function without a fixed background. This is not a philosophical preference but a mathematical requirement woven into the structure of his laws. Inertia, acceleration, straightness, and uniformity all depend on a reference that does not move. Without such a reference, Newton believed motion would be ambiguous, and the laws would lose their meaning. #### Inertia Demands a Non-Negotiable Baseline Newton’s First Law states: > A body perseveres in its state of rest, or of uniform motion in a straight > line... But “straight” relative to what? “Uniform” with respect to what clock? If motion is purely relative, then any object moving on a curve can always claim to be moving straight — by redefining the coordinate system. Newton recognized this directly. In the *Scholium* he warns that relative descriptions can always be reinterpreted: > *“If relative places are considered as absolute, the motions that result from > their translation will be the same, as if they had been real.”* In other words: **relative-only frameworks erase the distinction between straight and curved motion**, making inertia undefinable. Thus Newton introduces: > *“Absolute space… remains always similar and immovable.”* Not because space must be an entity, but because the mathematics of inertia cannot survive without a stable baseline. #### True Motion vs. Apparent Motion Newton repeatedly insists that we must distinguish real motion from apparent motion: > *“The true motions can be distinguished from apparent ones by their causes and > effects.”* A rotating bucket gives one of the clearest causes and effects: the concave surface of the water appears when the water rotates relative to something external, even when it is not rotating relative to the bucket. For Newton, this shows: - rotation is not relative, - acceleration is not relative, - inertia is not relative. Acceleration must be measured against a fixed background — *absolute space* — because forces depend on acceleration, and therefore so must the laws. #### Acceleration Requires a Fixed Frame Newton’s core law is: $$ \mathbf{F} = m\mathbf{a} = m\frac{d^2\mathbf{x}}{dt^2}. $$ Acceleration is the **second derivative** of position. But second derivatives are not invariant under arbitrary motions of the coordinate system. If the coordinate grid accelerates, the same object can appear to accelerate or not accelerate depending on the observer. For Newton, this was intolerable. If acceleration is relative, then: - forces become relative, - momentum becomes relative, - the entire structure collapses. Thus, acceleration must be defined with respect to something that does *not* accelerate — absolute space. #### Numbers Do Not Settle Without a Fixed Stage Newton understood that velocity and acceleration must have unique values for his conservation laws and planetary dynamics to work. If motion is defined only relationally: - velocity has no unique value, - momentum is undefined, - planetary orbits cannot be predicted consistently. In correspondence with Bentley (1692), Newton explains: > *“The orbital motions cannot be explained without assuming a certain fixed > frame.”* In short: **The numbers themselves require a fixed reference.** Without absolute space, there is no unique measure of velocity, no stable time parameter, and no definition of straightness — and thus no mechanics. #### Why Newton Felt Forced Into This Position Newton was not happy with action at a distance, and he was not happy with absolute space. He repeatedly calls instantaneous attraction *“an absurdity.”* He disliked making space into a “thing.” But he had no mechanism for transmitting forces, and no mathematical tools for emergent geometry. His equations demanded: - a fixed background, - an immutable standard of rest, - non-relative acceleration. He had no choice but to introduce absolute space as the container in which all dynamics occur. This was not metaphysics. It was structural. ### From Newton to Maxwell and Beyond The irony is that Newton introduced absolute space to maintain the consistency of his equations, while Maxwell later produced equations whose consistency *forbids* such a background. Maxwell’s waves require a medium in early interpretations, but the failure to detect that medium led to the opposite extreme — Einstein’s relational spacetime. Both Newton and Einstein tried to preserve the form of their equations; neither had access to a deeper causal substrate. In a Maxwell-Universe ontology, neither absolute space nor curved spacetime is fundamental. They are reconstructions — attempts to impose order on causal flow. Newton needed absolute space to make inertia meaningful. Maxwell reveals why inertia might arise without it. ### Mach and the Relational Critique Newton used the rotating bucket to argue for absolute rotation: the concave surface of the water, he said, reveals rotation relative to absolute space, not relative to the bucket. Ernst Mach disagreed. For Mach, the concavity arises because the water is rotating relative to the *mass distribution of the entire universe*. If the distant stars were somehow fixed to the bucket, or if the whole universe rotated in perfect synchrony with the water, the surface would remain flat. This view treats inertia not as a property defined by a container space, but as a response to all other mass in the cosmos. Rotation is relational: it is determined by the motion of the water relative to everything else. Mach never supplied a mechanism; he only exposed the logical weakness in Newton’s argument: the bucket experiment does not uniquely identify absolute space as the cause. It only shows that the water responds to something *outside* the bucket—but whether that “something” is space itself or the rest of the universe remains undecidable within Newton’s framework. It is also worth remembering what Newton and Mach did **not** know: electromagnetism, field momentum, and boundary-induced shear effects had not yet been discovered. Superconductivity and frictionless interfaces were unimaginable. The possibility that the bucket–water interaction depends on microscopic coupling or on momentum transfer mediated by fields lay centuries beyond their reach. Both thinkers worked without concepts that would later reshape our understanding of the mechanisms by which systems can exchange motion. ### Why Michelson–Morley Was Not the Decisive Blow The familiar story that Michelson and Morley “disproved the ether” is a later simplification. In 1887 the null result was surprising, but it was not regarded as fatal to the ether concept. First, a null result does not show that the ether does not exist; it shows only that the tested model of the ether was incomplete. Physicists of the time took the outcome as evidence that the theory needed revision, not rejection. Second, the response was immediate. FitzGerald and Lorentz introduced length contraction, and Lorentz developed a full dynamical framework in which the null result was expected. Lorentz Ether Theory absorbed the anomaly and remained empirically viable. At this stage, the experiment did not distinguish between an ether and no ether at all. Third, Maxwell’s equations were unaffected. They require a constant propagation speed, not a material substrate. The null result confirmed the constancy of the speed of light, which was compatible with both ether-based interpretations and early hints of relativity. Nothing in the data forced one reading over the other. Fourth, the ether carried enormous conceptual inertia. For centuries, waves had always been understood as motions of a medium. Space had long been treated as a container. One experiment could not overturn such a framework. The null result was important, but it merely constrained ether models rather than eliminating them. The real difficulties accumulated later. Ether theories multiplied, each introducing new assumptions to save the framework; none satisfied all observations. Meanwhile Maxwell’s equations proved self-sufficient, and Einstein’s reformulation showed that Lorentz symmetry does not require a preferred frame. Only then did the ether lose its role—not because one experiment refuted it, but because the overall conceptual structure that supported it eventually failed. ## Michelson–Morley and Relativity  By the late 19th century, ether theories were strained. The Michelson–Morley experiment added another tension point, but contrary to popular retellings, it did not eliminate the ether; it merely forced another revision.  The experiment failed to detect any motion relative to the ether. Lorentz did not abandon the framework; he strengthened it. To reconcile the null result with a stationary ether, he proposed that moving bodies physically contract along the direction of motion and that their internal clocks slow down. These were dynamical effects—real physical deformations of matter—introduced to preserve the ether as an undetectable reference frame.  Einstein took a different step. In 1905 he kept Lorentz’s mathematical transformations but reinterpreted them: not as distortions of matter within an ether, but as kinematic symmetries of all physical laws. The speed of light became invariant because the equations of physics require it, not because waves move through a hidden medium. Special Relativity removed the mechanical ether. General Relativity then replaced absolute space with a structured background: spacetime itself. In his 1920 Leiden lecture Einstein writes: > “According to the general theory of relativity, space is endowed with > physical qualities; in this sense, therefore, there exists an ether.”  Einstein ultimately hoped for a pure-field description of matter—geons, Einstein–Rosen bridges, and unified field theories—but these attempts never overcame the deeply rooted point-mass ontology inherited from Newton. ## Part II.B — Fragmentation The point-mass framework, extended by successive patches rather than replaced, produced a physics divided against itself. Each major theory preserved a different fragment of the original intuition. ### Classical Mechanics  Classical mechanics kept Newton’s ontology intact: point-masses with definite positions evolving in absolute space and time under continuous forces. Successful for everyday scales, it fails for atoms, radiation, and high velocities. ### Relativity  Relativity retained point-masses but discarded absolute space and absolute time. Space and time became geometric; gravity became curvature. The equations are smooth and deterministic. The ontology is local and continuous. Relativity cannot account for discrete jumps, probabilistic outcomes, or collapse-like behavior. ### Quantum Theory  Quantum theory abandoned definite positions but kept discreteness. A particle is point-like when detected and wave-like when not. Schrödinger sought a continuous field ontology, but Born reintroduced point behavior via the probability rule. Two incompatible rules govern the same entity: continuous evolution and abrupt collapse. ### Quantum Field Theory  Quantum Field Theory merges relativity with quantum amplitudes but restores particles through quantized excitations of fields — treated as point-like for interactions. Self-energy divergences follow; renormalization removes infinities without explaining their meaning. Feynman famously remarked that renormalization “sweeps infinity under the rug” and that point particles make no physical sense, even though the calculations work. ### The resulting split - Classical mechanics: continuous trajectories, absolute background. - Relativity: smooth deterministic fields, geometric background, localized particles. - Quantum mechanics: probabilistic discreteness, no trajectories, collapse. - QFT: continuous fields with point-like excitations and divergent self-energies. Each branch preserves a different part of the Newtonian inheritance: localization, continuity, determinism, or discreteness. None of them can be true together in the same ontology. The patches succeeded; the ontology did not.