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The Ontological Crisis at the Heart of Einstein’s General Relativity Theory
1. Introduction
General relativity theory (GRT) allegedly stands as one of physics’ greatest predictive triumphs. Its account of gravitational lensing, perihelion precession, gravitational waves, and black holes has been cited as evidence of its success. Yet this empirical success masks a profound philosophical problem that has plagued the theory since 1915: Einstein never adequately explained how matter warps spacetime, and more fundamentally, he never established that spacetime is the sort of thing that can be warped. The substantivalist interpretation of spacetime—treating it as a real, causally efficacious entity—remains deeply problematic, and no amount of predictive accuracy can resolve what is essentially an ontological confusion.
2. The Substantivalist Assumption
When we read that “mass tells spacetime how to curve, and spacetime tells matter how to move,” we’re being sold a picture that presupposes substantivalism: the view that spacetime is a genuine substance that exists independently of the material objects and events within it (Earman, 1989). On this view, spacetime is not merely a mathematical structure we use to describe relations between events, but a real thing with its own properties and causal powers.
This assumption is so thoroughly baked into standard presentations of general relativity that it becomes invisible. Nerlich and other substantivalists argue that spacetime must be real because we need something to be curved, and because spacetime appears to act on matter, thereby constraining the paths objects can follow (Nerlich, 1994). But this reasoning is circular: it assumes spacetime must be real because the theory describes it as having properties, without ever justifying why we should reify the mathematical structure in the first place.
3. The Relationalist Alternative
The relationalist tradition, running from Leibniz through Mach to some contemporary philosophers, insists that space and time are not substances but rather systems of relations between physical events and objects (Barbour, 1982; Rovelli, 2010). On this view, there is no spacetime “container” that exists independently—there are only material configurations and the geometric relations between them.
The appeal of relationism is considerable. It eliminates the metaphysical extravagance of postulating a vast, invisible substance that somehow exists “beneath” or “alongside” matter. It makes better sense of the fact that we can only ever measure spatial and temporal relations between physical processes, never spacetime itself (Mach, 1883/1960). And it avoids the strange conclusion that the universe might contain two fundamentally different kinds of things: matter-energy on one hand, and spacetime on the other.
When relationalists look at Einstein’s field equations, they see a sophisticated mathematical description of how matter-energy configurations determine the geometric relations that will obtain between events. The “curvature” of spacetime is, on this reading, just a convenient way of talking about how these relations deviate from Euclidean flatness—not a description of something literally bending (Rovelli, 1997).
4. The Mechanism Problem
Even if we grant substantivalism for the sake of argument, GRT faces a deeper difficulty: it provides no mechanism whatsoever for how matter warps spacetime. The field equations relate the stress-energy tensor (describing matter-energy distribution) to the Einstein tensor (describing spacetime curvature), but this mathematical relationship does not constitute a causal explanation (Brown, 2005).
Consider an analogy: if someone told you that whenever there are more cars on a road, the road becomes more curved, you would reasonably ask how the cars cause this curvature. Do they press down on a flexible surface? Do they emit some influence that gradually bends the road? The mathematical correlation between car density and curvature would not satisfy your question about mechanism.
Yet this is precisely where GRT leaves us. The theory tells us that a distribution of matter-energy is always accompanied by a particular geometry of spacetime, but it says nothing about the process connecting them. Is there some field mediating the interaction? Does matter exert a force on spacetime? If so, how can an abstract geometrical structure be subject to forces? These questions reveal the theory’s explanatory gap (Janssen, 2009).
5. The Causal Bootstrapping Problem
The substantivalist picture faces an additional puzzle about the direction of causal influence. We’re told that matter curves spacetime, and curved spacetime determines how matter moves (Wheeler, 1990). But this creates a strange feedback loop: matter creates curvature, but matter’s behavior is determined by that very curvature, which depends on where the matter is, which is determined by the curvature, and so on.
This isn’t merely circular—it’s a bootstrap operation where spacetime and matter must somehow mutually determine each other at every instant. How is this supposed to work? Does spacetime respond to matter’s presence with some time lag, or instantaneously? If instantaneously, how do we square this with relativity’s prohibition on instantaneous action-at-a-distance? If with a lag, what equations govern the dynamics of spacetime’s response?
GRT provides no answers because it’s not formulated as a causal theory with distinct influences propagating from sources to effects. It’s a constraint equation: given a matter distribution, there exists a spacetime geometry that satisfies the field equations. But constraint equations don’t tell causal stories (Brown, 2005).
6. The Hole Argument and Haecceitism
The philosophical difficulties deepen when we consider Einstein’s own “hole argument,” which he initially thought refuted his theory—before later claiming it refuted substantivalism instead. The argument reveals that if spacetime points have primitive identity independent of the events occurring at them, then GRT is radically indeterministic (Earman and Norton, 1987; Norton, 1988).
Here’s why. Take a solution to Einstein’s equations—a complete specification of the metric field across spacetime, along with the matter distribution. Now perform a “hole diffeomorphism”: in some region of spacetime, smoothly move all the matter and fields to slightly different spacetime points while leaving them unchanged outside that region. This generates a physically distinct solution (if spacetime points have intrinsic identity) that agrees with the original solution about everything that happens before the hole region.
This means the theory cannot predict which of infinitely many different futures will occur—a devastating failure of determinism. The standard response is to deny that spacetime points have primitive identity (reject “haecceitism”), but this severely undermines substantivalism (Pooley, 2013). If spacetime points have no identity apart from the metric and matter fields, in what sense is spacetime a substance? Substances are supposed to have identity conditions independent of their contingent states.
7. The Problem of Nothingness
Here is a related ontological puzzle: what is the status of spacetime in regions containing no matter-energy? Is there literally nothing there, or is there still spacetime? Substantivalists must say spacetime persists even in perfect vacuum, which seems to require that spacetime can exist in various states (flat, curved, etc.) entirely independently of matter—a puzzling claim about something that’s supposed to be causally connected to matter (Field, 1985).
Relationalists avoid this problem: in regions without matter, there simply are no spatial or temporal relations to speak of. But they face their own difficulty in making sense of vacuum solutions to Einstein’s equations, like gravitational waves propagating through empty space. What relations are these waves relations of, if there’s nothing there? (Earman, 1989).
8. Predictive Success Does Not Resolve Ontological Confusion
Defenders of GRT often respond to these philosophical worries by pointing to the theory’s empirical achievements. We’ve detected gravitational waves, confirmed frame-dragging, observed light bending around massive objects—all exactly as the theory predicts (Abbott et al., 2016; Will, 2014). Doesn’t this vindicate Einstein’s picture?
This response misunderstands the nature of the philosophical problem. No one doubts that Einstein’s field equations are extraordinarily accurate instruments of prediction. The question is what these equations are about—what features of reality they correctly describe (van Fraassen, 1980)? Empirical success shows that the mathematical structure captures something important about nature, but it doesn’t tell us whether that something is a real substantival spacetime or merely geometric relations between material processes.
Consider an analogy from the history of science: Ptolemaic astronomy, with its epicycles and deferents, made excellent predictions about planetary positions for over a millennium. But it was fundamentally wrong about what planets are and how they move. Similarly, GRT’s predictive power doesn’t automatically validate its implicit ontology (Laudan, 1981).
Indeed, we have historical reasons to be cautious. Newtonian mechanics was supremely successful for two centuries, and it too seemed to require absolute space as a real container. Yet we now recognize that Newton’s absolute space was an unnecessary metaphysical addition—the theory’s predictions could be preserved while abandoning the substantival interpretation (Sklar, 1974). General relativity may face a similar revision.
9. Alternative Formulations and the Underdetermination Problem
The existence of alternative formulations of GRT further undermines the claim that predictive success establishes substantivalism. Einstein’s equations can be reformulated in ways that make spacetime geometry look more like a derived quantity than a fundamental one.
In certain approaches to quantum gravity, for instance, spacetime is treated as emergent from more fundamental non-spatiotemporal structures. Loop quantum gravity discretizes space into quantum networks (Rovelli, 2004); string theory derives spacetime from the dynamics of extended objects (Polchinski, 2005); and causal set theory builds spacetime from discrete causal relations (Sorkin, 2005). These programs take seriously the possibility that the smooth spacetime manifold of general relativity is merely an effective description, valid at large scales, of something quite different at the fundamental level.
If spacetime can be emergent in this way—if the same predictions can be generated by theories that don’t treat spacetime as fundamental—then empirical success cannot adjudicate between substantivalist and non-substantivalist interpretations. We face an underdetermination problem: the evidence is compatible with multiple metaphysical pictures (Huggett and Wüthrich, 2013).
10. The Mathematical Structure Fallacy
There’s a general methodological error underlying much substantivalist reasoning: the inference from “our best theory represents X mathematically” to “X must be real.” This fallacy appears throughout physics. Complex numbers are essential to quantum mechanics, but few people think imaginary numbers are real physical entities. Configuration space is central to analytical mechanics, but it’s obviously a mathematical convenience, not a real space in which particles live (Albert, 1996).
Why should we treat the spacetime manifold differently? Just because GRT uses differential geometry to represent gravitational phenomena doesn’t mean that there really exists a four-dimensional pseudo-Riemannian manifold “out there” in nature. The manifold might be merely a representational tool—an effective way of encoding information about geometric relations between events (Mundy, 1983).
Substantivalists need to explain what distinguishes spacetime from other mathematical structures in our theories, justifying why this particular structure deserves reification while others don’t. Without such an explanation, substantivalism looks like an arbitrary choice to take one part of our mathematical formalism literally.
11. The Incompleteness of General Relativity Theory
Finally, we must acknowledge that GRT is almost certainly not the final word on gravity and geometry. The theory is incompatible with quantum mechanics, and singularities in the theory signal its own breakdown (Penrose, 1969; Hawking and Penrose, 1970). Any future theory of quantum gravity will necessarily revise our understanding of spacetime at fundamental scales.
This incompleteness should make us epistemically humble about interpreting general relativity’s ontology. Why invest heavily in substantivalist metaphysics for a theory we know to be provisional? The wiser course is to remain agnostic about whether spacetime is real or relational until we have a more fundamental theory (Wüthrich, 2005).
Moreover, the quantum gravity problem itself reveals how poorly we understand spacetime’s nature. If spacetime were simply a substance with well-defined properties, it’s unclear why quantizing it should be so problematic. The difficulties in developing quantum gravity may stem partly from trying to quantize something that isn’t fundamental—like trying to find the quantum mechanics of temperature rather than recognizing temperature as emergent from molecular motion (Huggett & Wüthrich, 2013).
12. The Einsteinian Paradox: Ontological Hypocrisy?
There is a profound historical irony in the ontological status of GRT when viewed through the lens of Einstein’s own philosophical commitments. Throughout the 1920s and 30s, Einstein remained the most formidable critic of Quantum Mechanics (QM), famously arguing that the theory was “incomplete.” His objection was not that QM failed to predict outcomes—it did so with terrifying precision—but that it failed to provide a “realist” foundation. He could not tolerate a physics that reduced reality to a “black box” of mathematical probabilities without a corresponding physical story of what was occurring in the absence of measurement.
Yet, as we have seen, GRT occupies the exact same “incomplete” ground for which Einstein condemned the quantum theorists. This “Einsteinian Paradox” can be broken down into three specific points of failure:
1. The “Shut Up and Calculate” of Gravity
Einstein derided the Copenhagen interpretation of QM for its “shut up and calculate” ethos. However, the standard substantivalist reading of GTR demands the same intellectual surrender. We are given the field equations—the mathematical correlations between the stress-energy tensor and the metric tensor—but we are offered no physical “how.” If QM is incomplete because it lacks a realist mechanism for wave-function collapse, GTR is equally incomplete for lacking a realist mechanism for spacetime deformation. In both cases, the math is used as a shroud to hide an ontological void.
2. Geometric “Spooky Action”
Einstein’s famous dismissal of quantum entanglement as “spooky action at a distance” rested on the requirement of locality—that physical effects must have a local, mechanical cause. Paradoxically, GTR’s account of gravity replaces Newton’s “spooky force” with a “spooky geometry.” To say that a planet moves because the “geometry” of a manifold is curved—without explaining how a non-material manifold exerts pressure on a material object—is to replace one ghost with another. The “feedback loop” where matter and space mysteriously mutually determine each other instantaneously—the bootstrapping problem—mirrors the very non-locality Einstein found so repugnant in the micro-world.
3. The Realism Double Standard
Einstein famously asked if the moon still existed when no one was looking, defending the idea of an objective reality independent of the observer. However, if we move toward a relationalist view of GRT—where spacetime is merely a system of relations between events—then “spacetime” itself disappears the moment the events do. By reifying the manifold into a “thing” (substantivalism) simply to give his equations a “stage” to act upon, Einstein committed the very sin he accused the quantum physicists of: he mistook a mathematical convenience for a physical reality.
Ultimately, the “ontological crisis” at the heart of GTR reveals that Einstein was a realist regarding the small but, perhaps inadvertently, an instrumentalist regarding the large. By his own standards for quantum mechanics, GRT must be viewed not as a final description of reality, but as a spectacular mathematical “map” that has yet to locate its “territory.” Until we bridge the gap between the tensor calculus and a concrete physical mechanism, GRT remains an extraordinary predictive tool masking an ontological mystery—a “complete” set of equations for an “incomplete” universe.
13. Conclusion: An Unresolved Foundational Crisis
GRT’s empirical success is undeniable and remarkable. But predictive accuracy does not resolve—and cannot resolve—the deep ontological questions about what spacetime is and how it interacts with matter. The theory’s substantivalist interpretation remains philosophically problematic for multiple independent reasons:
It presupposes without justification that spacetime is a real substance rather than a system of relations. It provides no mechanism for matter-spacetime interaction, offering only mathematical correlations. It generates puzzles about causal structure, determinism, and the identity of spacetime points. It faces underdetermination from empirically equivalent relationalist interpretations and emergent spacetime approaches. And it commits the fallacy of reifying mathematical structures merely because they appear in our best theories.
These are not minor interpretive quibbles—they strike at the heart of what general relativity is telling us about reality. A theory that cannot explain its own fundamental ontology, that leaves the nature of its central entity radically unclear, harbors a philosophical crisis beneath its empirical success. Until physics provides either a mechanism for matter-spacetime interaction or a fully worked-out relationalist alternative, general relativity will remain explanatorily incomplete at its very foundations.
The path forward likely requires moving beyond the classical framework entirely. Quantum gravity research might ultimately reveal that spacetime substantivalism was a wrong turn—a natural but mistaken interpretation of a mathematical structure that’s really describing something else. Or it might vindicate substantivalism by showing how spacetime emerges from quantum degrees of freedom with genuine causal powers. Either way, general relativity as currently understood leaves the central question unanswered: what is spacetime, really? And that question will haunt the theory no matter how many more predictions it gets right.
REFERENCES
(Abbott et al., 2016) Abbott, B.P. et al. “Observation of Gravitational Waves from a Binary Black Hole Merger.” Physical Review Letters 116, 6: 061102.
(Albert, 1996). Albert, D.Z. “Elementary Quantum Metaphysics.” In J.T. Cushing et al. (eds.), Bohmian Mechanics and Quantum Theory: An Appraisal. Dordrecht: Kluwer. Pp. 277-284.
(Barbour, 1982). Barbour, J.B. “Relational Concepts of Space and Time.” British Journal for the Philosophy of Science 33, 3: 251-274.
(Brown, 2005). Brown, H.R. (2005). Physical Relativity: Space-Time Structure from a Dynamical Perspective. Oxford: Oxford Univ. Press.
(Earman, 1989). Earman, J. World Enough and Space-Time: Absolute Versus Relational Theories of Space and Time. Cambridge MA: MIT Press.
(Earman and Norton, 1987). Earman, J. and Norton, J. “What Price Spacetime Substantivalism? The Hole Story.” British Journal for the Philosophy of Science 38, 4: 515-525.
(Field, 1984). Field, H. “Can We Dispense with Space-Time?” PSA: Proceedings of the Biennial Meeting of the Philosophy of Science Association. Pp. 33-90.
(Hawking and Penrose, 1970). Hawking, S. and Penrose, R. “The Singularities of Gravitational Collapse and Cosmology.” Proceedings of the Royal Society of London A 314, 1519: 529-548.
(Huggett and Wüthrich, 2013). Huggett, N. and Wüthrich, C. “Emergent Spacetime and Empirical (In)coherence.” Studies in History and Philosophy of Modern Physics 44, 3: 276-285.
(Janssen, 2009). Janssen, M. “Drawing the Line between Kinematics and Dynamics in Special Relativity.” Studies in History and Philosophy of Modern Physics 40, 1: 26-52.
(Laudan, 1981). Laudan, L. “A Confutation of Convergent Realism.” Philosophy of Science 48, 1: 19-49.
(Mach, 1883/1960). Mach, E. The Science of Mechanics. Trans. J. McCormack. La Salle IL: Open Court.
(Mundy, 1983). Mundy, B. “Relational Theories of Euclidean Space and Minkowski Space-Time.” Philosophy of Science 50, 2: 205-226.
(Nerlich, 1994). Nerlich, G. (1994). The Shape of Space. 2nd edn., Cambridge: Cambridge Univ. Press.
(Norton, 1988). Norton, J.D. “The Hole Argument.” PSA: Proceedings of the Biennial Meeting of the Philosophy of Science Association. Pp. 56-64.
(Penrose, 1969). Penrose, R. “Gravitational Collapse: The Role of General Relativity.” Rivista del Nuovo Cimento 1: 252-276.
(Polchinski, 2005). Polchinski, J. String Theory, Vol. 1. Cambridge: Cambridge Univ. Press.
(Pooley, 2013). Pooley, O. “Substantivalist and Relationalist Approaches to Spacetime.” In R. Batterman (ed.), The Oxford Handbook of Philosophy of Physics. Oxford: Oxford Univ. Press. Pp. 522-586.
(Rovelli, 1997). Rovelli, C. “Halfway Through the Woods: Contemporary Research on Space and Time.” In J. Earman and J. Norton (eds.), The Cosmos of Science. Pittsburgh PA: Univ. of Pittsburgh Press. Pp. 180-223.
(Rovelli, 2010). Rovelli, C. Quantum Gravity. Cambridge Univ. Press.
(Sklar, 1974). Sklar, L. Space, Time, and Spacetime. Berkeley CA: Univ. of California Press.
(Sorkin, 2005). Sorkin, R.D. “Causal Sets: Discrete Gravity.” In A. Gomberoff and D. Marolf (eds.), Lectures on Quantum Gravity. New York: Springer. Pp. 305-327.
(van Fraassen, 1980). van Fraassen, B. The Scientific Image. Oxford: Oxford Univ. Press.
(Wheeler, 1990). Wheeler, J.A. “Information, Physics, Quantum: The Search for Links.” In W.H. Zurek (ed.), Complexity, Entropy, and the Physics of Information. Redwood City CA: Addison-Wesley. Pp. 309-336.
(Will, 2014). Will, C.M. “The Confrontation between General Relativity and Experiment.” Living Reviews in Relativity 17, 1: 4.
(Wolpert, 2019). Wolpert, S. “Einstein’s General Relativity Theory is Questioned But Still Stands ‘For Now,’ Team Reports.” UCLA Newsroom. 25 July. Available online at URL = <https://newsroom.ucla.edu/releases/einstein-general-relativity-theory-questioned-ghez>.
(Wüthrich, 2005). Wüthrich, C. “To Quantize or Not to Quantize: Fact and Folklore in Quantum Gravity.” Philosophy of Science 72, 5: 777-788.
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