Relationism, as applied to general relativity, holds that space and time have no independent existence apart from the physical objects and events that populate them. On this view, spatiotemporal structure is constituted by relations among material things and processes - not by a self-subsisting container or field that would persist even if the universe were emptied of all matter. Relationists argue that Einstein's general theory of relativity either supports this position or is most naturally interpreted in its light. The view is held by a significant minority of philosophers of physics and by a smaller number of working physicists, and stands in direct opposition to substantivalism, which treats spacetime as a genuine entity in its own right.
Relationists trace their lineage to Gottfried Wilhelm Leibniz, who argued against Newton's absolute space on the grounds that spatial facts must ultimately reduce to facts about distances and orientations among bodies. If two universes differed only in where all matter was located within an otherwise empty absolute space - shifted five feet to the left, say - there would be no observable, physical, or even conceptual difference between them. Leibniz held that positing such a difference violates the principle of sufficient reason and the identity of indiscernibles. Relationists argue that general relativity vindicates this intuition in a deep way: the theory's general covariance means that diffeomorphic models - those related by smooth coordinate transformations - represent the same physical state of affairs, precisely because there is no additional structure over and above the relational facts.
A central pillar of relationist interpretations is Mach's Principle, the thesis that inertia is not a property of matter relative to absolute space but arises from the distribution and motion of all other matter in the universe. Ernst Mach argued that Newton's bucket experiment, which Newton took to demonstrate absolute rotation, actually demonstrated only rotation relative to the fixed stars. If the stars were rotated around a stationary bucket, Mach contended, the water would bulge just the same. Einstein was deeply influenced by this principle in developing general relativity and initially believed his field equations embodied it. Relationists hold that even if Einstein's final theory does not fully incorporate Mach's Principle in every formulation, the aspiration remains the right one: inertial and gravitational structure should be determined by matter, not presupposed independently of it.
Einstein's own hole argument - later revived and sharpened by John Earman and John Norton in 1987 - poses a challenge for substantivalism which relationists regard as a serious challenge, and in some formulations as a decisive one. In a region of spacetime containing no matter (a “hole”), the field equations permit multiple diffeomorphically equivalent solutions that assign different metric values to the same spacetime points. If substantivalism is true and spacetime points are real individuals, these solutions represent distinct physical possibilities - yet no observation could distinguish them. Relationists argue the natural resolution is to deny that spacetime points have primitive identity: the apparent underdetermination dissolves once one accepts that only relational, diffeomorphism-invariant facts are physically real. The hole argument thus transforms from a problem into a vindication of the relationist framework.
A sophisticated substantivalist response - associated with John Earman, who defends what he calls “sophisticated substantivalism” - holds that spacetime points do exist but lack haecceistic identity; their identity is entirely structural. Relationists counter that this concession effectively abandons substantivalism in any meaningful sense. If spacetime points have no properties beyond their relational roles, it is unclear what work the posit of their independent existence is doing. On the pure relationist view, the metric tensor is not a field living on a pre-existing manifold but is itself the encoding of spatiotemporal relations among physical events. Matter and geometry are not two things but aspects of one relational structure.
Relationists argue that their interpretation is better positioned for the eventual reconciliation of general relativity with quantum mechanics. Loop quantum gravity, one of the leading research programs in quantum gravity, is explicitly background-independent: it does not assume a fixed spacetime geometry on which quantum fields propagate but attempts to quantize geometry itself. Relationists hold that this background independence is most naturally motivated by a relationist ontology. If spacetime were a substance, one would expect a privileged fixed background; the absence of any such background in the deep structure of the theory is, on this view, a signal that relationist foundations are correct.
The relationist tradition in natural philosophy predates general relativity by centuries. Leibniz's correspondence with Samuel Clarke (acting as Newton's proxy) in 1715-1716 set the terms of the debate between relational and absolute conceptions of space and time that persist to the present day. Leibniz held that space is the order of coexistent things, time the order of successive things - nothing more. Bishop Berkeley independently advanced similar arguments, attacking Newtonian absolute space as a metaphysical fiction unsupported by experience.
Mach's The Science of Mechanics (1883) brought the critique into the modern era, arguing that all mechanical concepts must be grounded in observable relations among bodies. Einstein read Mach carefully and credited him as a formative influence. In the early years after the publication of general relativity (1915), Einstein believed the theory vindicated Mach's Principle, though he later became less certain as cosmological solutions admitting empty spacetime geometries - such as the de Sitter solution - were discovered.
The philosophical debate intensified in the latter twentieth century following Earman and Norton's 1987 reconstruction of the hole argument. This prompted a large literature in philosophy of physics, with relationists such as Carlo Rovelli and Julian Barbour developing sophisticated modern versions of the position. Barbour's work, especially The End of Time (1999) and earlier technical papers with Bruno Bertotti, attempted to construct a fully Machian, relationist mechanics from first principles, culminating in his program of “shape dynamics.”
Gottfried Wilhelm Leibniz (1646-1716) - Philosopher and mathematician whose correspondence with Clarke articulated the classical case against Newtonian absolute space on grounds of sufficient reason and the identity of indiscernibles.
Ernst Mach (1838-1916) - Physicist and philosopher whose critique of Newtonian mechanics in The Science of Mechanics introduced what Einstein would later call Mach's Principle and directly influenced the development of general relativity.
Julian Barbour (b. 1937) - Independent physicist and philosopher whose work on relational mechanics, Machian dynamics, and shape dynamics represents the most technically developed modern attempt to ground spacetime physics in purely relational foundations. Author of The End of Time (1999) and The Janus Point (2020).
Carlo Rovelli (b. 1956) - Theoretical physicist and co-developer of loop quantum gravity. Rovelli has argued extensively in both technical and popular work - including Quantum Gravity (2004) and The Order of Time (2018) - that general relativity supports a relationist ontology and that background independence is the central conceptual lesson of the theory.
Harvey Brown - Philosopher of physics at Oxford whose work, particularly Physical Relativity (2005), argues for a dynamical interpretation of spacetime structure that aligns with relationist conclusions, holding that geometric structure is grounded in the behavior of matter rather than the reverse.
Lee Smolin (b. 1955) - Theoretical physicist and co-developer of loop quantum gravity who has argued for relationist and Leibnizian foundations for physics in works including Three Roads to Quantum Gravity (2001) and The Life of the Cosmos (1997).
Relationists disagree among themselves about whether general relativity as currently formulated actually embodies a thoroughgoing relationism or merely points toward one. Some, including Rovelli, argue that the theory's diffeomorphism invariance already commits it to a relational ontology. Others, including Barbour, hold that standard general relativity still smuggles in absolute structures - particularly absolute simultaneity in certain formulations and the fixed topology of the manifold - and that a genuinely relational theory would look somewhat different, as in his shape dynamics program.
A significant internal tension concerns whether the metric tensor should be treated as part of the material content of the universe or as a purely relational structure encoding distances among events. Rovelli tends to treat the gravitational field (encoded in the metric) as a physical field on par with the electromagnetic field - a material thing, not an empty stage. This threatens to slide toward a form of substantivalism about the gravitational field itself. More austere relationists resist this move, insisting that the metric encodes only relations and is not an additional physical entity.
Not all relationists fully endorse Mach's Principle in its strong form. The existence of cosmological solutions to Einstein's equations that contain no matter - or in which inertial structure does not appear to be determined by the matter distribution - is a standing challenge. Some relationists accept that standard general relativity only partially satisfies Machian desiderata and view this as a deficiency to be corrected in successor theories. Others argue that in the actual universe, with its observed matter content, the Machian conditions are satisfied well enough that the principle stands.
Some structural realist interpretations of general relativity push beyond traditional relationism by denying that the relata of spatiotemporal relations - the events or objects standing in those relations - need to be assumed as primitives. On this view, associated with ontic structural realism, only the relational structure itself is real. Traditional relationists may resist this as an overcorrection that abandons the commonsense foundation of the view, namely that relations hold among real physical things and events.