Space as Relation

Main text

Axis 1 — Distance before dimension

1.1 Space as a stage: genealogy of the container

The history of thinking about space is the history of how a symbolic fiction — the fiction of a previous container — acquired the status of ontological reality. This fiction is no accident in the history of ideas. It is a consequence of a deep inscriptional need. The symbolic regime requires a stage to organise its records. The question about the origin of this presupposition is, therefore, also a question about the way in which the inscriptional regime projects its own conditions onto what it describes.

Isaac Newton faced a practical and philosophical problem at the same time. The Principia Mathematica needed a basis for the universality of the laws of motion. Kepler had described the orbits of the planets; Galileo had described the fall of bodies; Huygens had described pendulum movement. How was it possible for the same law of acceleration to operate in such diverse contexts — an apple falling on a farm in Woolsthorpe, the Moon orbiting the Earth, Mars gliding around the Sun — if there was no single, immutable frame of reference that gave universal meaning to the terms "horizontal", "vertical", "rest", "motion"? Newton responded by postulating absolute space: an independent, immutable, infinite, homogeneous reality, prior to any material body. Newtonian space was not a metaphor for the stage. It was an effective stage, with positive ontological properties. In a 1693 letter, Newton wrote that space was "sensorium Dei" — the organ through which God perceived all things. The inscriptional need — the requirement for a fixed reference for mathematical laws to be valid — was transmuted into a metaphysical thesis: space is an entity prior to matter. The gain was immense: two centuries of modern science, technology, navigation and astronomy were founded on this presupposition. The ontological cost, however, was equally immense. Reality gained a fundamental duplicity. There was not just matter in motion; there was matter in motion within space. Space acquired the status of an entity, a thing among things, even if non-material. And distance — that material conformity that two bodies can sustain when separated — became the reading of a neutral interval, the property of an indifferent container.

Gottfried Leibniz saw the problem and rejected the solution. In an epistolary debate with Samuel Clarke, a Newtonian defender, Leibniz argued that attributing reality to space independent of matter violates the Principle of Sufficient Reason. If space were a substantial entity, it would be conceivable that the universe would occupy a different "position" in space — a universe shifted a few trillion kilometers to the west, with all of its internal constitution preserved. Nothing within the universe would change; the entire body configuration would remain identical. However, why would the universe be in that position and not another? The Newtonian answer — "because God put it there" — broke the Principle. For Leibniz, space was not an independent entity, it was ordo coexistentiae, the order of how things coexist. Space is a system of relationships. Two bodies are close not because they exist in an interval of space that unites them; They are close because their material relationship constitutes what we call proximity. Extraordinary gain: Leibniz eliminated ontological duplicity, refused that reality contained very subtle and undetectable entities such as absolute space. However, the cost was as profound as the gain. If space is a relationship, what sustains the relationship? Leibniz responded with the doctrine of pre-established harmony: monads do not interact causally; there is a prior harmony that makes changes in one monad correspond to changes in others. The mechanism of the relationship remained obscure, metaphysical, suspended in divine intention. The relationship was real, but the reality of the relationship lacked a physical mechanism.

Immanuel Kant displaced the entire question. He did not ask "is space an entity or a relationship?" — asked "who is there space for?" Space is not a property of things in themselves, nor a system of relations between things in themselves; It is an a priori form of human sensibility. The subject does not know the space itself; He knows it as a structure through which he organises sensory multiplicity. Euclidean geometry, therefore, is not true about cosmic space; it is invariant to transcendental subjectivity. Gain: Kant resolved the tension between mathematical necessity (Euclidean geometry must be true, under penalty of incoherence) and contingency of the empirical world (the world could have been different). The answer: the need is transcendental, not cosmic. However, the cost quickly emerged. In the 19th century, mathematicians such as Carl Friedrich Gauss, János Bolyai, Nikolai Lobachevsky and Bernhard Riemann demonstrated that non-Euclidean geometries — where Euclid's axioms did not apply — are logically coherent. If Euclidean geometry were really an a priori form of human sensibility, how could the human intellect conceive other geometries? The Kantian response entered into crisis. The thesis that Euclidean space is transcendentally necessary collapsed before the history of mathematics itself. Bernhard Riemann took the issue to a more radical generalisation: the geometry of a space can be determined intrinsically, without reference to any surrounding space. The curvature does not depend on how the space is immersed in an upper container; can be calculated from the internal relationships between its points. Gauss even tried to empirically measure whether physical space was Euclidean, taking measurements of triangles formed by mountains in Lower Saxony — if space were Euclidean, the sum of the angles should be exactly 180 degrees. The measurements were inconclusive, however the gesture was revealing: geometry became an empirical question, not a necessary truth. If geometry was contingent — whether it could be Euclidean or not — then the structure of space was not a fixed transcendental condition. It could change. It could depend on the subject.

Hermann Minkowski, in 1908, unified space and time into a single metric structure. The interval between two events — the separation not only in space, but also in time — is no longer absolute. Two observers in relative motion would measure different spatial and temporal intervals, although the combined interval would remain invariant. The decomposition into space and time is relative to the state of motion. The absolute separation between space and time, intact from Parmenides to Kant, dissolved.

Albert Einstein dissolved the structure of the debate. It did not answer the question "is space an entity, relationship or form of subjectivity?" because he showed that the question is based on a false presupposition: that there is something called the "nature of space" that exists prior to the description of matter. General Relativity establishes that space-time is not the stage where matter acts. It is a dynamic field whose geometry is determined by the local mass-energy distribution. Mass-energy curves space-time; the curvature of space-time determines the geodesics along which mass-energy moves. There is mutual co-determination without logical precedence. The "where" is not an independent property of matter; it is a consequence of the material configuration. The conceptual revolution was complete: the field equations — Gμν = 8πTμν — establish this relationship so that the curvature tensor (left side) is proportional to the energy-momentum tensor (right side). There is no linear causality — matter-energy and curvature are two aspects of a single phenomenon. A body in free fall follows a geodesic, straight path in curved geometry. What appears to be "attraction" is convergence of geodesics. The genealogy ends here: Newton needed an absolute foundation for the invariance of the laws to make sense; Leibniz refuted the existence of such a foundation, but remained metaphysical; Kant relocated necessity to subjectivity, but the history of geometry contradicted his thesis; Einstein showed that there is no legitimate question about the "nature of space" separable from the question about how matter reorganises itself. The container reveals itself to be a retroactive illusion of the inscription regime, not a property of the real.

1.2 Distance as a material relationship

Saying that "distance is relationship" is not a trivial or merely linguistic statement. It means more than "distance depends causally on things" or "distance is instrumental, constructed by measurement." It means that distance constitutes the interval in an ontologically primary way. The effective separation between two material configurations is not inert void filled and measured to a greater extent. It is itself a mode of material difference, a mode of relationship that sustains itself as such. Distance is primary in relation to dimension. The geometric dimension — the structure of multiple organised directions, the x, y, z axes, the metric tensor — arises when a multiplicity of distances can be coordinated in a regular system. When the separations between multiple pairs of points acquire a standard, reciprocal proportionality, they allow uniform calculation and transition between different directions. However, distance as such — the pure relationship of separation — logically precedes this regime of geometric regulation. When only two sites differ, there is already distance between them. There is no dimension — there are no coordinates, there are no axes. Just separation. The dimension emerges later, when a system of multiple distances is organised, when order, direction, proportionality are introduced.

Three questions immediately arise and demand an answer. First: what is dimensionless distance? It is not "distance before any measurement" — which would be trivially unknowable. It is distance as a real condition that makes any measurement possible. Two material configurations that differ sustain their difference — neither collapses into the other, neither becomes indistinguishable from the other. This non-absorption is distance. There is no "empty gap" between them that lacks properties; there is the persistence of difference as a relationship. Direction, magnitude, axes — these are ways in which the inscriptional regime captures this persistence. They are real at the level of the concrete (the measured, the quantified), however they do not constitute the distance at the level of the real. A temperature gradient between two regions has distance (the regions differ and maintain the difference) before any thermometer introduces scale. The scale makes the difference legible; it does not create it.

Second: why is the dimension not equally primary? Because dimension is a coordination structure — it requires a system of multiple articulated distances. An isolated distance has no direction (direction requires at least two non-parallel distances). An isolated distance has no magnitude (magnitude requires units, which is a ratio between distances). The dimension is the coordination regime; distance is what is coordinated. It is not about temporal priority (distance first, then dimension) — it is about logical priority. Every dimensional table presupposes the distances it organises; no distance presupposes the dimensional frame that captures it.

Third: how does this position differ from classical metaphysical relationism — the thesis that there are "relations without relata"? The classic problem arises when relations are conceived as logically secondary to the terms they connect: if the terms disappear, the relation should disappear too. However, the thesis here is not "relations without relata." The reports themselves are configurations of relationships. A material configuration is not a substance that later enters into a spatial relationship — it is already a pattern of material differences, already relational from the beginning. Distance is not a relationship between pre-given atoms; it is the mode of difference by which configurations sustain their distinction. There is no level at which non-relational "things" are reached that relationships would connect. The co-determination between matter-energy and geometry expresses precisely this: there is no matter prior to space nor space prior to matter — there are material differences that are sustained as a relationship.

It is important to distinguish this position from another with which it could be confused: the Cartesian identification of matter with extension. For Descartes, to be material is to be extended — extension is the essence of matter, what matter is in itself. The position of this chapter retains inseparability (matter and space do not separate); However, it reverses the direction of determination. In Descartes, extension is primary and determines what matter can be — matter is res extenso, a substance whose nature is to be extended. Here, material differences are primary and determine what space can be — space is a relational unfolding of differences, not an attribute of a substance. The divergence has three faces: the Cartesian extension is homogeneous (each part of the res extenso has the same nature), the relational distance is heterogeneous (each region has its own metric); extension is continuous and infinitely divisible as a property of substance, distance is possibly discrete on a fundamental scale; extension is essence (defines what matter is), distance is relationship (defines how differences are sustained). Confusion between the two positions would eliminate what the thesis founds again: that space is not a property of matter, but a way of articulating material differences — a way that changes as the differences are reconfigured.

A second demarcation is necessary, this time with the phenomenological tradition. Heidegger, in Being and Time (1927), also rejected space as a container. His analysis of Räumlichkeit — spatiality — shows that space is not a neutral given in which the subject finds himself: it is constituted by the way in which Dasein orients itself, approaches, organises proximity and distance depending on its practical projects. Heideggerian distance is not geometric interval — it is Ent-fernung, "detachment", active suppression of distance by practical involvement. The gain is real and must be retained: spatiality is not a prior frame, it is constituted. However, the divergence is equally profound and has three faces. First: Heideggerian spatiality is constitutively dependent on Dasein — without a projecting being, there is no space. In the pre-symbolic regime, there is no Dasein, there is no project, there is no practical guidance; there are material differences that sustain relationships independently of any entity that lives or understands them. Second: Räumlichkeit is always already significant — space is articulated according to a totality of references (the hammer refers to the nail, which refers to the work). In the real material prior to inscription, there is no significance, there is no remission — there are constraints, gradients, conformities. Third: Heidegger never extended the analysis to cosmology. The attempt to do so would produce a contradiction: either the cosmic space prior to life is "inauthentic" (a category that only makes sense for a Dasein), or it is not space at all — which would deny the material reality of 13.8 billion years of subjectless spatial differences. The thesis of this chapter retains the criticism of the container; however, it bases spatiality on material differences — not on the ways of being of a understanding entity. Space as a material relationship is prior to and independent of any Räumlichkeit.

The already established terminological discipline applies here with precision: the geometric dimension belongs to the symbolic regime, to theory — it is an operator of the inscriptional level. Distance belongs to the material relationship, to the real — it is a mode of difference prior to any regime of representation. This distinction is not a mere conceptual artifice. It is an operative separation between what can be captured in inscription and what all inscription presupposes. Distance is what the inscription makes legible — but it is not inscription. It is the real that forces the inscription to be distance, to have extension, to offer a captureable interval. When it is stated "the distance between A and B is 5 meters," three ontological levels overlap and are distinguished without confusing. At the level of the real — prior to any inscription — there is a material difference that remains as an effective separation. Two configurations that differ maintain this difference; there is no collapse into indifference; there is no absorption of one into the other. It is pure material relationship, conformity that does not cease, tension that cannot be resolved. It is not captureable in an image or concept — it is what every image and every concept presupposes. It is inaccessible to inscription not because it is transcendent or mysterious, but because it is a condition of access: without real distance, without material difference that is sustained, no inscription would be possible. At the concrete level — the real made legible, inscriptionable — this material difference is translated into a sign that the inscription regime can establish. The established metric, the standardized unit (the meter), the proportionality that makes the separation quantifiable, transmissible from one observer to another, storable in an instrument. The concrete is always symbolic — it rests on convention, on a shared inscriptional regime. However, it is symbolic that refers to the real; It is capture that brings the real aspect to legibility. At the level of theory — pure symbolic reorganisation — the legible captures (the measurement, the number, the unit) are recoded into conceptual structure. Traditional Euclidean geometry, the Hilbert spaces of quantum mechanics, the metric tensor of General Relativity, the abstract tangent space of differential topology. Each level is ontologically necessary; none can be reduced to the previous or the next. The real without concrete remained mute. Concrete without real would be empty symbolic capture, baseless language games. A theory without concrete would be pure speculation. General Relativity described the concrete — the observables, the metrics, the measurement processes — with hitherto unprecedented precision. He showed that metrics — the way of measuring distances, calculating angles, determining a straight line — is not universal. There is no single way of measuring that is valid throughout the universe. The metric depends on the local distribution of energy and mass. In a region close to a massive star, the metric tensor is different than in a region in empty intergalactic space. Each region of space-time has its own local geometry, its own way of spatial articulation. There is no scale or geometric pattern that forces uniformity, that crosses the entire universe. However, this does not mean that the distance disappears or becomes illusory. It means precisely the opposite: distance becomes radicalised as the essence of reality. Distance is always local, always relational, always determined by the material configurations that constitute it. Without matter, without energy, there is no distance — there is emptiness. And emptiness is not space; it is the absence of a relationship. Loop quantum gravity — a research program that seeks to unify General Relativity with quantum mechanics, still without experimental confirmation — advances a conjecture with significant ontological consequences: spatial continuity would be an approximation. In the regime of extreme densities and energies, the structure of spacetime could be discrete — network of elementary relations, not continuous manifold. If this conjecture were confirmed, distance would be radicalised as a pure relationship: not measured in an underlying continuity, but connectivity between nodes of a combinatorial structure. What seemed to need space to exist — distance, separation — would be what defines space in the first place. The conjecture remains open. What does not remain open is the conceptual progression that motivates it: from Newton to Einstein, each revision eliminated a layer of substantiality from space. Distance, in any of these pictures, is not "property" or "entity" or "form" — it is material difference, a relationship that persists, that is sustained, that articulates the multiple without reducing it to indifference.

1.3 When the distance stops being neutral

General Relativity provided concrete and dramatically visible examples of the radical non-neutrality of distance. The presence of matter-energy not only occupies space in a pre-existing container — it transforms the very structure of how separations are measured, how paths are defined, how proximity and distance are related. A concentrated mass, such as that of a star or especially a black hole, radically modifies the local geometry. Spacetime close to the mass is more curved than far from it. This is not a side effect, a superficial disturbance of an underlying immutable geometry. It is a structural transformation of geometry itself — there is no geometry "before" the matter-energy that is transformed. Geometry is a reading of material distribution. Light, which in Newtonian mechanics would travel in a straight line in empty space (and the straight line was straight because space was Euclidean), follows geodesics of curved space-time. A geodesic is the line of shortest distance between two points in a given geometry — the generalisation of the concept of a straight line to curved spaces. If the geometry changes — if the metric tensor varies from point to point — then the geodesics change too. There is a single geodesic between point A and point B in Euclidean space (the straight line). However, in curved space, there are multiple possible "straight lines", multiple geodesics if the geometry varies in other directions. Arthur Stanley Eddington (1882-1944), a renowned British astronomer, organised expeditions in 1919 to measure the apparent position of stars near the solar limb during a total solar eclipse on May 29. If Einstein's theory was correct, if space-time near the Sun was radically curved by its immense mass, then light from distant stars, when passing close to the Sun, would be deflected by the curvature. The stars would appear to be in different positions than they do when the Sun is out of the way — displaced in the sky. Eddington observed precisely this deviation. He found that starlight was deflected by about 1.75 arc seconds — a value that coincided with Einstein's prediction. The confirmation was celebrated worldwide as a victory for relativity. It was, above all, dramatic confirmation that the distance light travels is not independent of the nearby mass distribution. The solar presence, its enormous material concentration, transformed space — it did not simply "occupy" it, but it transformed the very metric through which distances are defined and measured. Gravitational lensing has made this phenomenon even more dramatically visible. When light from a distant galaxy passes close to a concentrated mass — a massive galaxy, a cluster of galaxies, especially a black hole — the curvature of space-time around that mass bends multiple rays of light. The pattern is not simple refraction; is true geometric deformation. The distant galaxy is seen not in a single point in the sky, but in multiple points — the multiple images correspond to the multiple paths that light can take around the gravitational lens. It is as if there are multiple "ways to go straight" — multiple geodesics — depending on the trajectory the photon chooses. Each path is "shortest" — follows geodesics of curved spacetime — however in radically curved space, "shortest" is not unique. It does not converge to a single endpoint. The same distant galaxy, a singular reality, appears in several different locations in the observational sky. This is not an optical illusion. It reflects the multiplicity of the geometric structure: there are multiple ways of standing in relation across the same distance, and this is a consequence of curvature. Gravitational redshift offers yet another profound manifestation. Robert Pound and Glen Rebka, in 1959, carried out an experiment in the laboratory with a 22 meter high tower at Harvard. They emitted gamma radiation (photons of enormous frequency) from the bottom of the tower and measured the frequency when they reached the top — a very small height. They found that the frequency changed. The radiation emitted from the bottom of a gravity well was redder (lower frequency) when it reached the top. It wasn't because the photon "lost energy" in a classical way. It was because the spacetime metric at the bottom of the tower was different from that at the top — the curvature due to the presence of the massive Earth was slightly different at different altitudes. Therefore, what was meant by "frequency" — the number of oscillations per unit of time — was encoded differently in two places. As if the energetic distance between emission and reception had modified the very meaning of frequency, time, measurement. The global positioning system (GPS) depends entirely on this radical non-neutrality of distance. The satellites that transmit signals to terrestrial receivers move in an orbit 20 thousand kilometers high, close to a gigantic gravitational mass — the Earth — and moving at approximately 4 kilometers per second. General Relativity and Special Relativity simultaneously change the rate of time on satellites compared to the Earth's surface. Time runs faster on satellites (weaker gravitational field, higher altitude); however, it moves more slowly relative to the ground (higher speed also disturbs the metric). The two effects compete; The net result is that time on satellites passes about 38 microseconds faster per day than on the surface. Without relativistic corrections — without taking into account that the metric is different in orbit and on the surface, that time passes at different speeds depending on local geometry — the position calculation would diverge by several meters per day. The system would become useless for accurate navigation. Each relativistic correction made daily on hundreds of GPS satellites is an operational admission that distance is not neutral, that metrics change with material configuration, that space is a consequence, not a foundation. Cosmological distance offers yet another level of complexity and reveals new aspects of this non-neutrality. When astronomers measure the distance to a distant galaxy, there is no single number that definitively answers the question "how far away is it?" We talk about comoving distance — the separation that the two objects would have if the universe were "frozen" in its current expansion. We talk about luminous distance — deduced from redshift (the change in frequency caused by the expansion of the universe) under the assumption of a certain cosmological history. We talk about angular distance — simply the angle subtended by the galaxy in the sky, translated into distance units only through a cosmological model. Each definition translates a different relational form, a way in which matter-energy articulates through separation. None are "true" in an absolute sense; all are instruments for articulating the real through distinct inscriptional regimes. None are superfluous — each measures a different aspect of the relationship that constitutes the cosmic interval. Quantum nonlocality offers constraints of a radically different kind. When two particles are entangled — prepared in a joint quantum state — measurement results on one particle instantly correlate with those on the other, regardless of spatial separation — a correlation that is not explainable by hidden local variables. This was indicated theoretically in the critique of Einstein, Podolsky and Rosen (1935) and confirmed experimentally through tests of Bell inequalities initiated by John Bell (1964) and carried out by Alain Aspect and others (1982 onwards). Classical spatial separation — two objects in different positions — does not exhaust the way in which reality is articulated in entangled states. This does not violate Relativity — no usable information is transmitted faster than light. However, it reveals that spatial separation is not an absolute barrier to certain modes of quantum correlation. Distance, again, is no longer neutral — it admits correlation regimes that do not respect classical locality. Separation does not completely isolate. Distance is a mode of articulation that admits multiple relationship regimes — some local, others not — without non-locality implying causality at a distance. (Note: non-locality refutes local determinism; its ontological interpretation remains open — it depends on the interpretative framework of quantum mechanics that is adopted. The passage from "non-local correlation" to "the real itself is non-local" would be a philosophical interpretation, not a direct reading of the experimental data.)

1.4 If distance is relationship, what maintains relationships?

Distance is a primary material relationship — sustained separation between differences that remain distinguishable. The geometric dimension is a later legibility regime. Every example examined — curvature, bending of light, gravitational redshift, cosmological distance, quantum correlations — confirms that distance is not neutral: it depends on the material configuration, changes with it, is inseparable from it. The container fell; In its place was a network of material relationships that are sustained locally.

However, relationships without cohesion would dissolve. If distance is sustained separation, something has to sustain the separation. Differences that were not maintained by any constraint would disperse into homogeneity — uniform gas without persistent configurations. Thermodynamics precisely describes this tendency: in an isolated system, entropy increases to a maximum, differences in temperature, pressure and density attenuate, and the system converges to thermal equilibrium — a state where no spontaneous reorganisation is possible. If the universe were just dispersion without cohesion, the result would be accelerated heat death: maximum homogeneity without persistent structures. That galaxies, stars, clusters and filaments of the cosmic web exist — configurations that persist for billions of years against the entropic trend — requires a cohesion operator that sustains differences as differences. The question is precise: what produces cohesion between separate material configurations? What keeps differences as differences, separations as separations, intervals as intervals?

Tradition responded: gravity — force of attraction between bodies. The word "attraction" presupposes what it is intended to explain: bodies separated in a previous space that "attract" each other through that space. If space is a relationship, gravity cannot be a force that crosses it from outside. Cohesion must be relational — internal to the very structure that sustains the distances. Gravity does not operate in space; it is of space — it is the way material relations constrain each other.

Distance does not separate points in a space; sustains the differences of which space is a consequence.

Axis 2 — Gravity as relational cohesion

2.1 From strength to bond: genealogy of gravity

The question that emerges from the dissolution of the container — if space is not a prior stage and distance is a primary material relationship — finds an answer in a second layer: what maintains these relationships? What sustains cohesion between differences? The history of gravity is the history of this question taking progressively more radical forms.

Aristotle conceived gravity as an intrinsic property of the essence of each substance. The earth element, by nature, tends towards the centre of the cosmos; the water follows him; the air rises; the fire heads towards the periphery. It is not an interaction between bodies — it is a manifestation of telos in which each substance seeks its own place. The fall of a stone is an expression of its essence, and the Aristotelian universe is an ontological hierarchy where gravity functions as the realisation of this structure. The gain is evident: explanatory coherence within a cosmos ordered by constitutive principles. Within this scheme, each gravitational phenomenon is intelligible — the stone falls because the earth tends toward the centre, the smoke rises because the fire tends toward the periphery. However, the cost is profound: teleology is lodged as a foundation. Gravity does not just describe processes — authorizes them, guides them toward constitutive ends. The cosmos is a theater of essences in realisation, and the fall is the final act of an ontological drama. The question "why does the stone fall?" receives an answer that is, ultimately, circular: fall because its nature is to fall. The essence explains the process that the essence already presupposes.

Newton radically displaced this understanding. Gravity became not an essential property, but a quantifiable interaction: F = Gmm'/r². A universal law that works indifferently for any mass, in any context, without appeal to substantial natures or ontological places. The teleological essence has been eliminated. However, Newton introduced an ambiguity that he himself recognised: he called gravity "attraction" — a word that carried an anthropomorphic residue, a suggestion that bodies sought each other out. In his correspondence with Bentley between 1692 and 1693, Newton insisted that it would be "absurd" to conceive of bodies attracting each other through a vacuum without material mediation — without something operating between them that was not just a mathematical formula. The law worked with extraordinary precision, making it possible to predict eclipses, calculate orbits, and determine the masses of celestial bodies. The gain was immense: quantitative universality, predictive accuracy, unification of terrestrial and celestial phenomena under the same law. However, the mathematical structure carried a disturbing metaphysical consequence: action at a distance operated instantaneously. The Newtonian equation did not contain a time parameter between the separation of two bodies and the transmission of gravitational force between them. This meant that gravity propagated infinitely quickly — immediate connection at any distance in the universe, without the mediation of an intermediate material process. Newton recognised the difficulty; did not offer a solution. The question remained open: how did the attraction operate? Of what nature was the bond? The language of force remained — and with it, the ambiguity between a successful mathematical formula and the physical mechanism that explained it.

Ernst Mach transformed Leibniz's metaphysical critique into an operative physical program. In Die Mechanik (1883), he attacked absolute space through its most decisive consequence: inertia. Newton justified inertia by absolute space — bodies resist acceleration because they exist against an immobile background. Mach reversed it: the inertia of a body is determined by the distribution of all matter in the universe. Newton's famous bucket is solved without resorting to an invisible entity — the concavity of the water results from the rotation relative to distant stars, not from confrontation with transcendent space. Double win: eliminates the container as a cause; transforms inertia into a relational property — not intrinsic resistance of the body, but an effect of the relationship with the rest of cosmic matter. Einstein explicitly recognised it as a decisive inspiration and gave the name "Mach's principle" to this thesis. But Mach remained an empiricist — distant matter determines local inertia as an observable fact, not as a constitutive co-determination. No mechanism, no dynamic geometry. Absolute space has been eliminated; nothing replaced it as a structure. This structure would be the curvature of space-time.

The path to this dissolution was not deductive but perceptual. In 1907, Einstein had a seemingly simple insight: a body in free fall experiences no weight. In a falling elevator, objects float freely — the effect of gravity disappears. This seemed like a secondary detail, but Einstein saw something structural in it. If gravity disappears under free fall, then it is not an intrinsic property of the world — it is the effect of relative acceleration. An observer in free fall is inertial; an observer on the Earth's surface is accelerated upward, away from free fall. The gravitational "force" that holds bodies on the surface is not attraction — it is the Earth pushing against the acceleration. Einstein called this insight "the happiest thought of my life" because he saw in it the dissolution of a false problem. Gravity and inertia were no longer separate phenomena — they became facets of the same phenomenon seen from different frames of reference. If inertia is a kinematic property — the pattern of trajectories in space-time — and gravity is indistinguishable from inertia, then gravity is also geometry. There is no "gravitational force" as a separate entity; there is curvature of space-time that determines the trajectories.

Einstein eliminated the ambiguity by eliminating the very idea of "force." Matter-energy creates curvature in space-time; curvature dictates the paths that matter-energy takes. The field equations — Gμν = 8πTμν — establish this relationship: the curvature tensor (left side) is proportional to the energy-momentum tensor (right side). There is no linear causality — matter-energy and curvature are two aspects of a single phenomenon. A body in free fall follows a geodesic, straight path in curved geometry. What appears to be "attraction" is the convergence of geodesics — lines that approach each other not because they are "looking for" each other, but because the underlying geometry brings them together. The conceptual revolution simultaneously eliminated Aristotle's teleological residue (the fall does not realise essence — it is a trajectory determined by geometry) and Newton's internal tension (there is no "force" operating at a distance — there is local co-determination between matter and geometry). However, General Relativity brought a new tension, yet to be completely resolved: the formulation allows solutions where there is geometry without any matter-energy present — Minkowski's empty and flat space-time satisfies Einstein's equations where there is no body generating curvature. This means that Mach's principle — that geometry should be entirely determined by the distribution of matter in the universe — is not formally fulfilled in Einstein's theory. Metrics can exist independently of matter. The tension remains open: is the underlying geometry an intrinsic structure, or a residue of mathematical formalism that does not correspond to anything in reality?

John Wheeler expressed the synthesis precisely: "Matter tells space how to curve; space tells matter how to move." Codetermination without logical precedence. His geometrodynamics went further: he proposed that matter and space are not separate entities that interrelate, but rather internal differentiations of a single system — space-time as a fundamental material reality. Gravity becomes an immanent reconfiguration of a relational structure that is, simultaneously, geometry and matter. Wheeler further suggested that at the smallest scale — the Planck scale, approximately 10⁻³⁵ meters — the geometry of spacetime itself would not be smooth or continuous. Quantum fluctuations would be so violent at that scale that the topology would constantly change, with geometry forming and dissolving in rapid succession. This concept of "quantum foam" suggested that space-time continuity is only a valid approximation at larger scales — the fundamental reality would be a fluctuating network of topological relations where the distinction between space and time would become even more radical and less definable.

The genealogy traces the trajectory of the concept: from essential property to quantifiable force to constitutive relationship to dynamic geometry. Each shift eliminates assumptions about agency or teleology. What remains is pure relational operation — material conformity where matter-energy and geometry are reciprocally linked in a constitutive indivisibility. However, a question remains that none of these formulations directly answer: what type of causality operates when no intention governs, when no essence guides, when no purpose authorizes?

2.2 Gravity as cohesion without subject

Gravity operates as a bond that intends nothing. It coheres without intention, organises without purpose, differentiates without purpose. Exactly because no intention governs it, it remains open — capable of producing any configuration that material relations allow, within the given concrete universe.

What kind of causality is this? It is not efficient causality in the classical sense — there is no agent that produces the effect. Gravity does not "make" matter move; matter follows geodesics determined by the geometry that it itself configures. It is not final causation — there is no purpose that the operation accomplishes. The cosmic web is not the destination of gravity; it is a contingent consequence of particular fluctuations. It is not formal causality in the sense of a pattern imposed from outside — the form that emerges (galaxy, cluster, void) does not pre-exist the operation that produces it. What operates is constitutive co-determination: each matter-energy configuration constrains and is constrained by all others, with none being "the cause." The curvature of space-time at a point is a function of the distribution of matter-energy throughout its surroundings; the movement of matter-energy is a function of curvature throughout the region. Neither term precedes the other; Both mutually determine each other in a regime where the distinction between cause and effect loses its operational meaning.

The closest philosophical category is immanent causality — the cause does not transcend the effect, it does not operate on it from outside, however it is the system itself that configures itself. The position of this chapter retains immanence: gravity is not an external force that applies to matter, it is a relational property of the matter-energy-geometry system. However, immanent causality in its strongest historical form presupposes necessity — the effect follows from the cause with geometric necessity.

The proximity to Spinoza is maximum here — and the divergence equally decisive. In Ethics (1677), Spinoza founded immanent causality as a principle: the substance is the cause of itself (cause sui), it is not produced by anything external, it expresses itself in its ways without the cause transcending the effect. Deus sive Natura — God, that is, Nature — is the totality that produces itself. Gravity, as an immanent co-determination where matter-energy and geometry are mutually configured, seems to confirm Spinoza: no external agent, no transcendence, the system is its own cause. Three divergences prevent assimilation. First: in Spinoza, immanence is necessary — each mode follows from the nature of the substance with geometric necessity (more geometrico); nothing is contingent, contingency is just ignorance of causes. In gravitational co-determination, contingency is constitutive — the primordial fluctuations that generated the cosmic web do not necessarily follow from any principle; the cosmological constant is not deducible; the discrepancy of 10¹²⁰ between the predicted and observed value of the vacuum energy is a sign of irreducibility, not of transient ignorance. Second: Spinoza postulates a single substance — ultimate, indivisible reality, with infinite attributes. The thesis of this chapter does not operate with substance: the gravitational field is not a substance that expresses itself, it is a network of relationships without a non-relational substrate. The "reports" are configurations of relationships; there is no final layer that supports them. Where Spinoza needs substance to guarantee the unity of immanence, this position supports immanence through relational circularity — relations that sustain relations. Third: the Spinozist attributes (extension and thought) are parallel and irreducible — each one expresses the same substance under a different aspect. The real/concrete/theory tripartition is not parallelism: the real is not an aspect of the same thing as the concrete; the concrete is an operation of legibility on the real, and theory is the symbolic reorganisation of the concrete. There is asymmetric dependence (the concrete presupposes the real, the real does not presuppose the concrete), no parallel expression of common substance. What is retained from Spinoza is pure immanence — the refusal of any cause external to the system. What is refused is necessity, substance and parallelism. Gravity is immanent without being necessary, relational without being substantial, differentiated without being parallel.

The primordial universe demonstrates this precisely. The cosmic microwave background reveals infinitesimal density fluctuations (~10⁻⁵) — oscillations of the primordial quantum field stretched to cosmological scales during inflation. When the expansion slowed, these fluctuations persisted as regions of slightly higher and slightly lower density. Gravity operated as an amplifier, however the amplification process was not instantaneous — it was graded, contingent at each stage. The microscopic fluctuations went through distinct epochs of differential amplification. For the first three hundred thousand years, radiation dominated cosmic dynamics; Ordinary matter and radiation were densely coupled. When the universe cooled to ~3000 kelvin, recombination occurred — electrons and protons joined together into neutral atoms, and the radiation decoupled from the matter. This transition allowed gravity to operate on matter without continued interference from radiative pressure. The fluctuations persisted, now able to grow without the resistance that had compressed them.

There followed the cosmic dark ages — millions of years where matter emitted no detectable electromagnetic radiation. Gravity continued to operate: denser regions curved space-time more, forcing surrounding matter to converge, reinforcing concentration, increasing curvature. Blind positive feedback, without observer, without purpose. When the first stars formed, some 100 to 200 million years after the Big Bang, the cosmic web had already emerged in its essential lines — filaments of matter that diverged between gigantic voids. Proto-spiral and proto-elliptical galaxies formed by coalescence of smaller structures. At every scale, from clumps of dark matter to clusters of galaxies, the pattern was identical: gravity as co-determination that amplifies contingency, no guidance, no destiny.

Before recombination, matter and radiation coupled as a unified fluid — plasma in which radiation pressure prevented gravitational collapse. This plasma oscillated under compression and re-expansion: when gravity contracted a region, radiation pressure counterattacked, sending matter back out. The result was pressure waves propagated through the primordial cosmic structure — baryonic acoustic oscillations that produced durable conformity in the configuration of subsequent matter. When recombination released the radiation (~380,000 years after it began), these oscillations froze: the pattern that existed at the time light and matter uncoupled was permanently incorporated into the distribution of galaxies we observe today. The effect is a characteristic scale (~490 million light-years in current space) that permeates the cosmic structure — a material ruler produced in reality by the co-determination between radiation and gravity during the plasma era. This pattern is readable in the observational data as a peak in the galaxy correlation function. The decisive point is not that the peak is "ordered"; is that co-determination between material constraints produced structured conformity without prior necessity. Scale comes from physical constants — which is why it is universal — yet the concrete spatial distribution of this scale in the real universe is contingent. Different initial conditions (different amplitudes in the primordial quantum fluctuations) would have frozen oscillations of the same characteristic scale at different positions in space. The type of structure is determined by the constraints; what particular structure there is is not.

Slightly different initial fluctuations would have produced different morphology. The current distribution of matter is contingent in the strong sense: accomplished, but not necessary. It is the product of material co-determination, not of a geometric law prior to matter.

Dark matter radicalises the argument and reveals the nature of this relational causality. Approximately 85% of all matter in the universe does not emit electromagnetic radiation — it is inferred exclusively from its gravitational effects. In the 1970s, Vera Rubin and Kent Ford observed that the speeds of stars orbiting galaxies remained abnormally high in the peripheral regions — they should slow down with distance from the centre, as predicted by models based only on visible matter, but they did not slow down. Flat galactic rotation curves indicated the presence of non-luminous matter, concentrated in halos around galaxies, exerting gravitational constraints otherwise undetectable. Later observations of gravitational lensing — bending light from distant galaxies by the bending created by massive clusters — provided independent verification.

Even more decisive: dark matter halos function as gravitational scaffolds. Cosmological simulations show that without sufficient dark matter, primordial fluctuations amplified by gravity do not produce observable structure — galaxies, clusters and superclusters do not emerge with the density and dimensions attested. Dark matter halos stabilise the growth of structure, create wells of gravitational potential where ordinary matter accumulates, and condition the formation of galaxies. The co-determination between matter-energy and geometry operates independently of electromagnetic visibility. Dark matter is a real material difference — an operation that constrains geometry, produces curvature configurations, guides the cohesion of ordinary matter — without being a concrete difference in the electromagnetic regime in which current instruments operate.

The real/concrete distinction finds precise empirical anchoring here: the relational real systematically exceeds what the regime of electromagnetic legibility can capture. The curvature that dark matter produces exists whether there are observers or not, or whether there are instruments to infer it or not. Its reality does not depend on readability. It exists as a constitutive material operation — a relationship that constrains, propagates, transforms. The material universe is more than what the inscriptional regime can describe.

2.3 Provisional stabilisation, not permanence

Gravitational cohesion does not eternalize configurations. It organises them temporarily, keeps them differentiated, however, always under a finite horizon of transformation. Provisional stabilisation as an ontological regime is a direct consequence of immanence without teleology.

Stars exemplify the fundamental pattern. A star is a dynamic balance between thermal pressure generated by nuclear reactions in the core and gravitational contraction that surrounds it. It is not inert rest — it is continuous confrontation: outward pressure contains inward gravity. As long as nuclear fuel persists, this balance remains. The star is a transitory form that lasts millions or billions of years — a duration that seems permanent on a human scale, but is a finite interval on a cosmic scale. The Sun, with its hydrogen reserves, has sustained the balance for around 4.6 billion years and will sustain it for approximately another 5 billion. When nuclear fuel runs out, thermal pressure decreases. Gravitational contraction resumes predominance. What follows depends on mass: medium-mass stars like the Sun transform into white dwarfs, where electronic degeneracy pressure — a consequence of the Pauli exclusion principle — replaces nuclear thermal pressure as the support mechanism; more massive stars collapse into neutron stars, where matter is compressed to nuclear densities; above approximately twenty solar masses, not even the neutron pressure can resist — a black hole is formed, a region where the curvature of space-time prevents any escape trajectory. Each destination is a new stabilisation with its own temporal limits. The stellar form is not a permanent essence — it is a provisional configuration sustained by specific material constraints that have a finite duration.

Galaxies amplify this pattern on a much larger scale. The Milky Way is not a fixed structure. It results from previous mergers with smaller galaxies — a process that is reconstructed based on the distribution of ages and metallicities of stellar populations. Its spiral shape is a dynamic pattern, not a morphological essence: sustained by differential rotation and the distribution of matter (including the dark matter halo), it reorganises itself when external disturbances alter the balance. The predicted collision with the Andromeda galaxy, in approximately 4.5 billion years, will produce a merger of two systems into a single galaxy of entirely different morphology — probably ellipsoidal. The spirals will be disturbed, the stellar trajectories will be completely reorganised, and a new configuration will emerge. The galaxy we observe now is a dynamic pattern supported by gravitational balances that will reorganise when the next merger imposes new constraints. Galactic stability is provisional like stellar stability — it differs only in temporal scale.

The scale increases even further when considering galaxy clusters — systems containing hundreds or thousands of galaxies, all bound together gravitationally. The Virgo cluster, the Perseus cluster, the Coma cluster — these structures span regions millions of light years away. Within them there is not only the space between galaxies, but also intergalactic gas heated to temperatures of tens of millions of degrees, visible through X-ray observations. This hot intergalactic gas represents more mass than all the matter present in the cluster's visible galaxies — most of the cluster's baryonic mass exists outside the galaxies, distributed as high-energy plasma. However, even clusters are not final structures. Collisions between clusters rearrange their configurations. The Bullet Cluster documents two structures in the process of colliding: the intergalactic gas from both has been slowed by friction, heated, and comes together in a single central region; however, the galaxies, less dense and less affected by friction, continue on separation trajectories. The dark matter in each cluster, detected only gravitationally, also separates from the visible gas. What seemed like a coherent configuration disintegrates and reorganises itself. Even on the scale of millions of light years, no configuration remains inviolate.

Above this scale rises the cosmic web, gigantic filaments of galaxies separated by immense voids of hundreds of millions of light years. These filaments were formed by gravitational collapse from density fluctuations in the early universe, grew by continued accretion, yet remain in continuous reconfiguration. No filament is topologically fixed — galaxies migrate, mergers continue, structure changes. There is no final pattern, nor convergence to permanent morphology.

Black holes represent the extreme of this dynamic — a configuration where gravity reaches its maximum conceivable intensity, where the curvature of space-time is so radical that the very notion of "escape" disappears. However, even the most extreme gravitational bond has a finite duration. Near the event horizon, the gradient between the extreme gravitational field and the surrounding vacuum generates radiation emission — Hawking radiation. The mechanism, described by Stephen Hawking in 1974, results from quantum effects near the boundary of the black hole: the extreme gravitational field generates conditions for energy from the field itself to be converted into radiation that propagates outwards. The black hole continually loses energy. A black hole of stellar mass — about ten solar masses — completely evaporates in approximately 10⁶⁷ years. A supermassive black hole in the galactic core — millions or billions of solar masses — persists much longer, but the time frame remains finite. The most extreme gravitational cohesion conceivable ends up giving way. The most radical stabilisation that the universe allows is, even so, provisional.

The ontological consequence is decisive. Gravity does not eternalize the configurations it organises. It allows differentiation without elimination — without gravitational cohesion, the universe would be a homogeneous gas in perpetual dispersion, with no distinct forms that persist. Gravity amplifies differences and keeps them differentiated. However, cohesion is always provisional. This is an anti-teleological consequence: gravity does not "lead to" final structures, it does not accomplish cosmic purpose, it does not lead to increasing complexity or progressive integration. The narrative of "cosmic evolution" — from primordial simplicity to contemporary galactic structure — is a retroactive projection of the symbolic regime onto the material. The real material contains the capacity for differentiation — to remain differentiated; gravity amplifies this differentiation, maintains it against the thermodynamic tendency towards homogeneity. But amplification is not guidance. Gravitational cohesion does not authorize any preferential direction in reality. That structure emerges from quantum fluctuations is contingency, not destiny. That this structure persists for a billion years is a property of specific material constraints, not a realisation of essence. That it reorganises itself in collisions, that it transforms into new equilibria, that even the most extreme gravitational bond finally dissolves — all this reveals material immanence as a regime where nothing is self-founded, where all stability is provisional, where no configuration holds ontological privilege that allows it to escape transformation.

2.4 If gravity is relational cohesion, space is tense

Gravity is not a force that crosses previous space. It is the very constitutive relationship between matter-energy and geometry — immanent, contingent, provisional cohesion. If so, space-time is not a neutral void awaiting content. It is a structure under permanent tension.

Curvature is tension — sustained deformation of geometry by the presence of matter-energy. Matter-geometry co-determination is tension — relational circularity without rest. The quantum vacuum with its fluctuations is tension — minimum energy that never reaches zero, permanent oscillation of the field. Accelerated cosmic expansion is tension — spacetime does not just warp locally; it expands globally under the effect of intrinsic energy that the theory does not yet accommodate.

What follows is the transition from operator (gravity as cohesion) to ontology (space as tense body). If cohesion is relational and not substantial, if it is provisional and not permanent, if it is contingent and not necessary, then the space that this cohesion constitutes cannot be an inert stage — it is a dynamic, energetic, responsive body. The distinction is precise and must be fixed: constitutive tension is not episodic instability. A star that collapses into a supernova experiences episodic instability — an event localized in time that transforms one configuration into another. The constitutive tension of space-time is of another nature: it is the permanent condition of every configuration, including those that seem stable. Even intergalactic space, apparently empty and calm, is a field under tension — quantum vacuum fluctuations operate continuously, cosmic expansion expands distances, dark energy exerts negative pressure. There is no relaxed state of space-time, there is no configuration in which tension ceases. Tension is a constitutive condition, not an episodic disturbance. It is what space is made of.

Gravity does not travel through space; it is the tension that space is made of.

Axis 3 — Space as a tense body

3.1 Space as a dynamic field

The genealogy of the container has fallen: space is not a stage prior to matter, nor a system of relationships between closed substances, nor an a priori form of sensibility. It is constitutive co-determination between matter-energy and geometry. Gravity showed how this co-determination operates as relational cohesion — amplification of differences, provisional stabilisation, bond without subject. The only question left is: what kind of reality is this space-time that curves, that vibrates, that responds? If it is not a container, what is it?

The answer from contemporary physics is precise: it is field. Space-time is neither substance nor void — it is a dynamic field with measurable physical properties. The quantum vacuum is a state of minimum energy, not zero energy. Energy fluctuations persist continually in this state — not as disturbances on an inert background, but as a constitutive property of the field itself. The Casimir effect (Casimir 1948, experimentally confirmed by Lamoreaux 1997) offers quantitative demonstration: between two very close parallel conducting plates, certain oscillation frequencies are suppressed by geometric confinement, and the energy difference between the inside and outside produces a measurable pressure gradient. The field exerts force. The "emptiness" resists, compensates, operates. The classic opposition of being/non-being — matter versus emptiness, plenitude versus absence — dissolves as a false dichotomy. Space is not where nothing exists; it is a relational regime where energy is minimal but never zero, where the organisation is continuous and where no region is genuinely inert.

A philosophical consequence of this fact remains generally implicit and must be made explicit: if space-time is a dynamic field with variable local curvature, then space is constitutively heterogeneous. It is not the same everywhere, it is not indifferent to the distribution of matter-energy, it does not offer a uniform environment in which things are arranged. The curvature varies from point to point. Vacuum energy, although minimal, has properties that depend on local boundary conditions — the Casimir effect demonstrates this: the energy between the plates differs from the energy outside them. This constitutive heterogeneity has profound philosophical implications. The tradition from Newton to Kant treated space as fundamentally homogeneous — the same in all directions, in all places, at all times. Bergson took this identification to the extreme: he defined space as a homogeneous medium par excellence, quantitative, opposed to qualitative duration. In this reading, space is impoverishment — domain of the repeatable, the measurable, the undifferentiated. General Relativity dissolves this identification. Spacetime is not homogeneous at all; It is a field where the geometry changes with the matter-energy, where the metric is local, where no region is identical to another in the gravitational regime. This means that space is already qualitative — not in the sense that it has subjective qualities, but in the sense that it carries constitutive differences that cannot be reduced to quantitative variations on a neutral background. The opposition between space (quantitative, homogeneous) and time (qualitative, heterogeneous), which structured much of post-Kantian philosophy, is a false dichotomy produced by Newtonian assumptions that Einstein made untenable.

From here comes the conceptual foundation of "tense body" — the central category of this axis. "Body" does not mean substance. It means that the field has physical properties (energy, pressure, responsiveness) that make it more than a passive background. It is not a scenario where things happen; is a constitutive participant in what happens. "Tense" means that every state is maintained by opposing constraints — there is no relaxed state, no equilibrium without countervailing forces. The vacuum is "tense" in this precise sense: its minimum energy is not zero, its oscillations are not disturbances but a constitutive property. The distinction between "tense body" and "field" in the strictly physical sense is ontological: field is a mathematical operator that assigns values to points in a space; tense body is a category that states that the field is the real — not a description of the real, but the real itself as a configuration of material differences in tension. The distinction between "tense body" and substance is equally sharp: substance has intrinsic properties independent of relations; the tense body has no properties outside of the relations that constitute it — everything about it is relational, responsive, co-determined.

Whitehead's process philosophy offers the closest conceptual proximity to this position — and therefore requires rigorous demarcation. In Process and Reality (1929), Whitehead rejected substance as a fundamental category and replaced it with actual entities — process events that are constituted by mutual prehension. Each current entity "seizes" the others, inherits from them, and constitutes itself from the relational field. The extensive continuum — the means of extension that enables the connection between events — is not a Newtonian container: it is an abstract condition of extension, updated differently by each event. Reality is process, not substance; it is relational, not isolated; It is dynamic, not static. The gain is threefold and must be retained: (a) the refusal of substance as a category of the real, (b) mutual immanence — each event is constituted from the others, without transcendence, (c) the inseparability between process and extension — the "where" is not previously given, it emerges with the event. These three aspects converge with the tense body thesis: dynamic, relational field, without fixed substrate.

The divergences are equally threefold and structural. First: Whiteheadian prehension is proto-experiential. Whitehead refuses the bifurcation of nature between "things that experience" and "things that do not experience" — every current entity has some form of feeling, however rudimentary. It is pan-experientialism: there is no inert matter, all reality has an experiential interior. Now, in the pre-symbolic territory, the notion of experience — even if proto-experience, even if "feeling" in the Whiteheadian technical sense — projects onto the material real a category that presupposes receptivity, selectivity, integration. Material differences that are sustained as tension do not "grasp" anything, do not "feel" anything — they operate as reciprocal constraints with no experiential interior. The tense body is dynamic without being experiential. Second: Whitehead's eternal objects — forms of definity, patterns that current entities "enter" — reintroduce Platonic residue. Although Whitehead insists that eternal objects do not exist outside of their ingress into events, their existence as a repertoire of pure possibilities is structurally analogous to Forms. The thesis of this chapter does not operate with possible forms that enter: the form is the remainder of the material operation, not the pattern that configures it. No repertoire of possibilities pre-exists the tensions that produce configuration. Third: the Whiteheadian God — in his primordial nature — is the principle of novelty, that which orders eternal objects and provides relevant possibilities for each event. Even though Whitehead rejects the classical theistic God, the function is teleological: there is guidance in the availability of possibilities, a preference for the intensity of experience. Gravitational co-determination has no principle of novelty — there is no instance that makes possibilities available or that guides any type of intensity. Contingency is radical: what emerges is what material constraints allow, without prior selection. What remains from Whitehead is relational processuality and the refusal of substance. What is rejected is experience as a universal category, possible forms as a repertoire, and any principle of novelty or orientation.

3.2 Dynamism, energy, responsiveness

The dissolution of the being/non-being dichotomy does not exhaust the characterization of space as a tense body. It remains to describe how this body manifests itself: not as an inert substance to be determined by external content, but as dynamic, energetic, responsive. These are not properties added to the space as separable attributes; they are modes of operation that define what it means to be a relational body in a regime of material immanence.

The first aspect emerges from the most elementary observation: the geometry of space is not fixed. When Hubble established in 1929 that distant galaxies move away from each other, and when Lemaître before him had deduced the same conclusion from Einstein's equations, the finding was not simply that objects move within preexisting, immobile space. It was that the very distances between them — the metric that relates them — transform. Space expands. There is no movement through a stable container; there is a reconfiguration of the relational field that constitutes the very measure of separation. For decades, this reality was understood as expansion that mutual gravitational attraction should progressively stop. But in 1998, observations of Type Ia supernovae revealed that the expansion does not slow down — it speeds up. Divergence between galaxies does not dampen under mutual attraction; intensifies. Riess, Perlmutter and Schmidt consolidated the data: there is a cosmic repulsive energy, operating at a global level, which counteracts the aggregating effect of gravity. Empty space — the quantum vacuum — has an intrinsic energy density, what cosmologists call the cosmological constant Λ, which functions as repulsive gravity. Space is not a neutral theater of external dynamics; it is itself dynamic, a centre of dynamics, an active participant in the reorganisation of the relationships that constitute it.

This dynamicity is revealed with particular clarity in extreme gravitational events. When two black holes orbit each other and come closer together beyond a certain point, the curvature of space-time near each becomes so pronounced that gravitational waves — perturbations in the geometry itself — radiate outward at the speed of light. It is not a wave of something transported through a previous medium; It is space itself that vibrates, oscillates, transmits energy through the deformation of itself. The detection of the first gravitational wave in September 2015, by LIGO, recorded the merger of two black holes that combined sixty-five solar masses. After the merger, the geometry stabilised into a single black hole with approximately sixty-two solar masses. Three solar masses had been converted into radiant energy — energy that traveled through space in the form of metric oscillation, propagated deformation. The detectors measured distortions of order 10⁻¹⁸ meters in the four-kilometer-long arms. The magnitude is minimal by human perception; however, it reveals an absolutely central aspect: space is neither rigid nor inert. It actively participates in the dynamics that occur in it — or rather, that occur as a reconfiguration of it. In August 2017, the merger of two neutron stars was detected simultaneously using gravitational waves (GW170817) and direct electromagnetic radiation — visible light, gamma rays, wavelengths across a wide range of the spectrum. Confirmation of the same source through two distinct propagation regimes validated the structural thesis: dynamic space-time and radiant matter operate in a single material regime. Space is not just a setting where matter radiates; It is an active participant in each event, a physical support for the undulation, a propagator of the energy that is constitutive of it.

Complementing this dynamism verifiable on a cosmic scale, there is the energeticity of the vacuum on a microscopic scale. Quantum mechanics establishes that the minimum energy state of a system — what is called the ground state or quantum vacuum — is not absolute zero. There is always a residual energy, a permanent vibration of the field. The vacuum is not ontological silence; it is constrained oscillation within statistical limits. This reality manifests itself particularly clearly in the Casimir effect, theoretically predicted by Casimir in 1948 and experimentally confirmed by Lamoreaux in 1997. When two parallel metallic plates are positioned very close to each other — micrometers apart — certain modes of oscillation of the quantum field between them become confined, that is, suppressed by the geometry of the confinement. Outside the plates, in open space, all modes oscillate freely. The difference in energy density creates a gradient: there is more energy outside than inside the confinement. This gradient produces a measurable force that brings the plates closer together. The vacuum, that which intuitively appears to be non-being or absolute emptiness, exerts pressure, offers resistance, behaves like a body endowed with mechanical properties. The "nothing" that constitutes empty space is not indifferent; opera. The cosmological constant — intrinsic energy of empty space — reveals this energetics on a global scale. The discrepancy between the value predicted by quantum field theory and the observed remains open (~10¹²⁰) — the largest numerical discrepancy in the history of physics. This gap between calculated and observed is not a defect to be resolved in the existing theoretical framework. It is a sign that the relationship between the descriptive levels (quantum field theory and cosmological observation) is not deductive. The vacuum has energy; its magnitude escapes the current theoretical framework.

The discrepancy of 10¹²⁰ is not a technical defect capable of being resolved within the existing framework — it is a revelation that the real material exceeds any isolated legibility regime. Quantum field theory adds up all the contributions of quantum fields to calculate the energy density of the vacuum, obtaining an astronomically large value. Cosmological observation measures, through accelerated expansion, a tiny but non-zero magnitude. Between these two numbers — one theoretical, the other empirical — a chasm opens up that no approximation can bridge. It is not a question of measurement precision or calculation refinement. It is a divergence between two regimes of description that operate on the same real without achieving deductive convergence. In the lexicon of tripartition: theory (QFT) and the concrete (cosmological observation) extract irreconcilable results from the same material reality. This does not signal a failure of physics — it signals that the real is vaster than any unified description available. The quantum vacuum demonstrates that space as a tense body persists as a material difference that no isolated legibility can totalize. The permanent gap between calculated and observed is a sign of the opening of the real, not a gap in knowledge.

However, characterizing the space only as dynamic and energetic would still be insufficient to capture its tense body condition. Responsiveness distinguishes a body that simply varies from one that actually responds. A passive container, in the classical conception, would be indifferent to its contents: the box would remain a box whether it was empty or full. Responsiveness, by contrast, designates the constitutive co-determination between space and that which operates in it. In this regime, there is no entity that acts on another from the outside in; there is reciprocity where each term shapes the other continually.

This reciprocity lies at the heart of General Relativity. The curvature of space-time at a point is a direct function of the local distribution of mass and energy. Conversely and simultaneously, the trajectory that a particle follows — and therefore the movement, the dynamics of any body — is determined by the local curvature of space-time. The classical notion of inertia — the tendency of a body to maintain its state of rest or uniform movement — is no longer an intrinsic property of the body. It is reformulated as an expression of a geometric principle: a body in free fall follows the most direct geodesic in curved space-time. When a massive star collapses and its density increases without limit in the classical approximation, the nearby space-time responds in a qualitative and not merely quantitative way: an event horizon is formed, a boundary beyond which there is no possible regression. It is not that matter falls and then space reacts; is that matter in its fall and space in its curvature reach a regime where the distinction between "the matter here" and "the space there" ceases to be operational. Gravitational lensing confirms this responsiveness: light does not move "in" space; it moves "with" space, its trajectory is a reading of the geometry that surrounds it.

Responsiveness is also revealed in rotational regimes. A rotating mass — a planet, a neutron star, a black hole — does not just bend spacetime under its effect; drags space-time itself in its rotation. This phenomenon, called frame-dragging, was predicted by Lense and Thirring in 1918 and confirmed with high precision by the Gravity Probe B mission in 2011. Gyroscopes in near-Earth orbit measured the precession angle induced by Earth's rotation: space does not remain static when matter rotates; he himself is dragged, moves in a spiral, actively participates in the rotating dynamism. Responsiveness is not just static metric deformation (bending by mass), it is also dynamic participation in continuous reorganisation. Space responds not only to differences in mass and energy; it responds to orientation, angular momentum, rhythms of transformation.

What brings together dynamism, energy and responsiveness in a single characterization — tense body — is the fact that none of them are accessory or episodic. These are not properties that space "has" when certain conditions activate them. They are constitutive, permanent modes of operation that define what it means for space to be. Geometry is not immobile until matter arrives and disturbs it; geometry continually changes because the matter-energy that constitutes it never ceases to reorganise itself. The vacuum is not inert waiting to be activated; it vibrates permanently, it contains intrinsic energy that acts gravitationally on a cosmological scale. Space does not just respond when asked; it is in continuous response to the material regimes that inhabit it.

It is important, however, to remain rigorous about the status of this data. The observations of Riess, Perlmutter and Schmidt, the gravitational waves detected by LIGO, the Casimir effect — these are material conformities stabilised by the legibility regime. Instruments record light patterns, differences in strength, redshift spectra. Theory — Einstein's equations, Hubble's law — reorganises these conformities into a coherent structure. However, the material relationship that both levels reach without exhausting is the real thing: the dynamicity, the energeticity, the responsiveness of space-time as such, independent of any regime that describes them.

3.3 Voltage vs. instability

A critical distinction separates tension from instability, although they are often confused. Tension is constitutive and continuous — a permanent regime of difference and response that traverses every material configuration. Instability is episodic and localized — transition from one stress regime to another, where previous compensation ceases to be in effect.

Consider the shape of a star. The star remains in a transient configuration because there is dynamic equilibrium: the internal pressure of the plasma compensates for the gravitational contraction. This balance is permanent tension — two opposing forces in continual compensation. The form is not fixed; it is the effect of this tension. When nuclear fuel runs out, internal pressure drops. Compensation ceases to operate. Instability sets in: the star collapses or expands, depending on its mass. This reorganisation is a consequence of a change in tensions, not negation of them — the new regime (white dwarf, neutron star, black hole) is reconfigured tension, not absence of tension.

The quantum vacuum exemplifies tension without instability: it is a state of minimum energy where energy fluctuations persist as a constitutive property of the field. There is no episodic disturbance; there is a continuous oscillation regime. Instability occurs when enough energy is concentrated in a confined space and the equilibrium structure breaks down, triggering the transition to a new regime.

The ontological consequence is decisive. If the universe is a field of tension, stability is not the absence of change — it is the ability to maintain contrary relationships in permanent dynamic compensation. The star is stable not because it is still, but because it maintains balance between opposing forces. The quantum vacuum is stable not despite continuous fluctuations, but through them. There is no absolute rest. There are only dynamically sustained stress regimes. Every form, every matter-energy configuration is transient equilibrium — stable within certain limits, unstable when those limits are exceeded.

The consequence reformulates the concept of stability throughout cosmology. Classical stability — absolute rest, absence of change, permanence — is symbolic fiction of the same kind as the container and the beginning. No cosmological system rests in an absolute sense; all observable stability is active maintenance of dynamic compensations. This affects all scales of real operation. The proton, stable for 13.8 billion years, is sustained by the continuous compensation between the strong interaction and the electromagnetic repulsion of its constituent quarks — a balance that grand unification suggests could yield on immense time scales, on the order of 10³⁴ years. The observable universe itself is metastable: the Higgs field, which gives particles mass, may not inhabit its true energetic minimum; a quantum phase transition could rearrange the structure of the vacuum. Apparent stability — the regularity that allows cosmological processes on a scale of billions of years — is always a particular case of constitutive metastability. Where there was a dichotomy between stability and instability, there is now continuity: every configuration of the material universe is a transitory balance that the real sustains while the conditions of compensation are maintained.

This is where the divergence with Bergson becomes unavoidable. In Essay on the Immediate Data of Consciousness (1889) and in Matter and Memory (1896), Bergson defined space as a homogeneous medium — domain of the quantitative, the repeatable, the measurable, opposed to pure duration where quality, heterogeneity and interpenetration are constitutive. For Bergson, the error of science is to "spatialize" time — projecting the undifferentiated categories of space onto lived duration. Space is impoverishment: what remains when quality, internal difference, novelty are removed. The duration is the real; space is abstraction. The Bergsonian gain is real and must be retained: the criticism of the confusion between intensive magnitude (qualitative, indivisible) and extensive magnitude (quantitative, measurable) remains valid as an epistemological warning — measuring is not understanding, quantifying is not exhausting. The denunciation of the "spatialization of time" illuminates real defects in mechanistic thinking that reduces becoming to a trajectory in the space of phases. However, the Bergsonian thesis about space rests on assumptions that General Relativity has rendered untenable, and the divergence is threefold. First: space is not homogeneous. The curvature of space-time varies with the local distribution of matter-energy; the vacuum energy depends on the boundary conditions (the Casimir effect proves this); no region is geometrically identical to another in the gravitational regime. The homogeneity that Bergson attributes to space is a property of Newtonian space — which Einstein dissolved. Bergson was writing before General Relativity (1915) and, in the debate with Einstein in Paris (1922), insisted that the multiplicity of relativistic times was apparent, not real — a position that the scientific community rejected and that proved empirically wrong. Second: relational space is qualitative — not in the sense that it has subjective qualities, but in the sense that it carries constitutive differences irreducible to variation on a neutral background. The local metric, the curvature, the vacuum energy — these are properties of space-time that differ from region to region, that do not repeat uniformly, that constitute real heterogeneity. The Bergsonian opposition between (quantitative) space and (qualitative) duration dissolves when space itself is heterogeneous and irreducible to a uniform medium. Third: the opposition space/duration as abstraction/real reproduces a dichotomy that constitutive co-determination makes obsolete. If matter-energy and geometry co-determine each other, space is not an abstraction derived from reality — it is a constitutive aspect of reality. Relational distance is not an impoverishment of duration; It is a mode of material difference as constitutive as temporality. The choice between "time is real" and "space is abstraction" is false: both are modes of material difference, both are constitutive, neither is derived from the other. What remains from Bergson is the vigilance against the reduction of the qualitative to the quantitative. What is rejected is the thesis that space is by nature homogeneous, quantitative and abstract — a thesis that 21st century physics. XX refuted and that the relational ontology dissolves.

3.4 Space as a relationship: consequence

The container fell. What remained in its place is not conceptual emptiness — it is positive determination: space is a tense body, a dynamic field where matter-energy and geometry co-determine each other without precedence. Distance is a primary material relationship, prior to the geometric dimension that organises it. Gravity is relational cohesion that amplifies differences, temporarily stabilises, binds without a subject. Vacuum is a state of minimum energy with constitutive properties, not absence.

Each of these determinations reshapes what it means to "exist in relationship." Space does not precede matter as a condition of its arrangement — it emerges from it as a mode of its articulation. It is not a scenario that awaits completion; It is always the name of what material differences can sustain. The consequence is that no configuration exists outside of tension — and no tension is permanent. The forms that relational space allows are transitional balances between material constraints, not essences placed in a neutral dimension. If space is a constitutive relationship, then what persists in it does not persist through inertia — it persists as long as the tensions that sustain it remain maintained. The way it is configured, the time for which it is maintained, the way it is reconfigured when constraints change — all of this is a consequence of the specific material relations that operate, not of the properties of a container that would house them. If space is relationship and tension, then all form is transitory — and the question that arises is not "why does form change?" yet "how can form persist if all that sustains it is tension?" The answer leads to the following: form is neither a fixed essence nor an ephemeral accident — it is a dynamic balance between constraints that are temporarily maintained. The transience of form is a direct consequence of space as a tense body.

Space is not where nothing is; it is the tense body of all that is.