Newton or Leibniz? Modern Physics and Two Concepts of Reality

Newton or Leibniz? Modern Physics and Two Concepts of Reality

The old dispute between Newton and Leibniz is often treated as a historical curiosity. It should not be. Modern physics has not left that dispute behind; it has made its central contrast newly vivid.

Newton and Leibniz did not merely disagree about technical physics. They disagreed about what sort of reality physics describes.

In the Newtonian picture, space and time are real frameworks that do not depend upon the material bodies situated within them. Absolute time passes independently of physical change, while absolute space provides the structure relative to which true motion can be defined. Newton did not regard space as an ordinary substance. In De gravitatione, he explicitly says that extension fits neither the category of substance nor that of accident. Nevertheless, space and time possess a reality and independence that distinguish Newton’s view sharply from Leibniz’s.

For Leibniz, space is the order of coexistences and time the order of successions. They are not self-subsistent containers but expressions of relations among things. Remove the things and their possible relations, and no independently existing spatial or temporal receptacle remains.

This is not a minor philosophical difference. It is a difference in ontology.

Modern physics has not straightforwardly confirmed Leibniz. That would be too simple. Special relativity abandoned absolute simultaneity and the Newtonian division between absolute space and universal time, but it retained a fixed Minkowski geometry. It therefore did not simply replace Newtonian substantivalism with Leibnizian relationism. General relativity went further: the metric field that determines spacetime geometry became dynamical and responsive to matter and energy. Even here, however, the metaphysical interpretation remains contested.

Between Leibniz and relativity stands Mach, whose critique of Newton’s bucket and absolute space strongly influenced Einstein’s search for a general theory. General relativity does not, however, straightforwardly satisfy any single agreed formulation of “Mach’s principle,” and Einstein’s own commitment to Machian ideas changed over time. Barbour and Bertotti’s best-matching programme, later extended within the shape-dynamics programme, is among the clearest contemporary attempts to turn this Leibnizian–Machian relational impulse into an explicit dynamics.

The hole argument makes the older dispute especially concrete. Leibniz’s global “shift” arguments are clear conceptual ancestors of its reasoning. In the correspondence with Clarke, Leibniz considers transformations of the entire universe that preserve every relation among bodies. A wholesale displacement would produce no observable difference and, he argues, there could be no sufficient reason for God to choose one placement rather than another. In his later letters he explicitly connects such indiscernibility with identity and applies the same reasoning to the uniform motion of the universe as a whole.

Earman and Norton formulate the modern parallel as “Leibniz Equivalence”: diffeomorphically related models represent the same physical situation. The hole argument adds an important local and dynamical feature. Its transformation can be confined to a particular spacetime region, creating the threat of radical indeterminism if manifold points are assumed to possess physical identities independently of the metric and matter fields. This presses against naïve manifold substantivalism, but it does not by itself prove relationism. More sophisticated substantivalist and structuralist interpretations remain possible.

This is one reason the Newton–Leibniz dispute is still alive.

Quantum theory deepens the issue, though in a different way. Its significance here is not that it proves idealism, theology, or a relational metaphysics. It does none of those things. Standard nonrelativistic quantum mechanics ordinarily presupposes an external time parameter, while quantum field theories are normally formulated on a given spacetime background. Quantum theory therefore does not complete the relational transformation of space and time initiated by relativity. Some approaches to quantum gravity pursue that transformation further by seeking a background-independent quantum description, although no consensus theory has yet completed the task.

What quantum theory does challenge is the classical expectation that every physical system must possess a complete set of determinate, context-independent properties. The lesson one draws from this depends upon one’s interpretation, but it is one reason relational interpretations continue to attract attention.

Carlo Rovelli’s relational quantum mechanics is directly relevant here. In this interpretation, the value of a physical variable need not be an absolute possession of a system valid relative to every other system. It may instead be a fact relative to another physical system, actualized through their interaction. The “observer” need not be conscious: any physical system can occupy that role.

This does not revive Leibniz’s metaphysics as a whole. The difference is substantial. Leibnizian monads do not physically interact, whereas interaction is fundamental to relational quantum mechanics. Nor should Rovelli’s relative facts simply be identified with Leibnizian perceptions. The point of contact is more limited but still important: both views resist the idea that reality is exhaustively described as a collection of wholly self-sufficient objects bearing absolute intrinsic properties.

Quantum-reference-frame formalisms make another aspect of this relational turn mathematically explicit. They construct transformations between descriptions relative to different quantum systems and extend the idea of covariance to cases in which the reference frame is itself quantum mechanical. Properties such as superposition and entanglement may then depend upon the chosen quantum frame. In the subsequent perspective-neutral framework, choosing a frame can be represented as fixing a symmetry redundancy, while changing frames corresponds to a transformation between perspectives. These frameworks should not automatically be identified with relational quantum mechanics, still less with conscious viewpoints. Nevertheless, they provide a particularly clear formal example of how descriptions can vary with perspective while remaining connected by objective transformation rules.

Weyl saw, with unusual clarity, that modern physics had moved away from the older image of space and time as fixed containers. What matters in Weyl is not merely his authority, but his recognition that objectivity in modern physics is connected with invariance, relation, and structure. In Symmetry, he expressed the point concisely: “objectivity means invariance with respect to the group of automorphisms” (p. 132). Related ideas run through Space–Time–Matter and Philosophy of Mathematics and Natural Science.

A structural realist can treat this as a third possibility between a world made from intrinsically identified substances and a world reduced to relations among already constituted objects. On such a view, the objective content of a theory lies primarily in the structure preserved across admissible transformations. The path from Weylian invariance through structural realism to transformations between observer-relative descriptions is not a deductive proof, but it is conceptually natural.

At this point the theological question enters, but it must enter carefully. I discuss the broader methodological question of how science and spirituality can enter into dialogue without collapsing their distinct levels in When Science Meets Spirituality: Dialogue, Synthesis, and the Direction of Inference.

Newton believed in God, and Newton’s own theology should not be reduced to the image of a distant clockmaker. His God continually sustains and governs the world, and his discussions of divine omnipresence were closely connected with his understanding of space. Nevertheless, the later Newtonian picture of nature as bodies moving within an independently given framework readily lends itself to an image of God as external engineer: a supernatural agent standing over against a natural order that could otherwise be described on its own. Much popular atheistic discourse still targets some version of this picture, although sophisticated philosophical atheism need not depend upon it.

A Leibnizian picture suggests something different. God is not one being alongside other beings, nor merely a force intervening in the world from outside. God is the ultimate sufficient reason for there being a world at all and for this world being actual rather than merely possible. Spatial expressions such as “outside” and “above” are therefore already misleading, because the relation between God and the world is not itself a spatial relation.

This does not erase the distinction between natural and supernatural, and it does not turn God into a physical field or hidden component of nature. It changes the metaphysical grammar of the question. God is not introduced as an additional physical cause competing with natural causes, but as the ground upon which the existence and intelligibility of any natural order depend.

This does not establish theism. But it does show that different ontologies generate different concepts of God—and that a rejection of one concept need not amount to a rejection of every possible form of theism.

The same need for conceptual care applies to consciousness.

Materialism is not logically committed to Newtonian space and time. Nevertheless, some influential forms of modern materialism inherited an image of reality composed of externally related objects whose intrinsic properties are already complete. Consciousness must then appear at a later stage as something produced by otherwise nonperspectival matter.

Leibniz begins elsewhere. Every monad has perception in the broad sense of representing multiplicity within unity, although not every monad possesses conscious awareness. Leibniz distinguishes perception from apperception, the reflective awareness of perception. His metaphysics therefore should not be summarized by saying that everything is conscious. Its more relevant feature here is that perspective belongs to the basic constitution of reality rather than being added only after a nonperspectival world has been completed.

One need not accept the monadology to recognize how different this starting point is.

Von Neumann becomes relevant here, though precision matters. In chapter VI of Mathematical Foundations of Quantum Mechanics, he treats the observed system, measuring apparatus, and observer as a chain whose boundary can be displaced without changing the measurement statistics. The boundary may be drawn between the system and the apparatus-plus-observer, or between the system-plus-apparatus and the observer. In its most inward placement, even the observer’s retina, optic nerve, and brain can be included on the physical side, leaving what von Neumann calls the observer’s abstract “ego” outside the calculation.

This does not amount to the claim that consciousness physically causes state-vector reduction. Von Neumann’s central result is the formal mobility of the boundary, not the identification of consciousness as a collapse mechanism. A stronger causal role for consciousness was developed by London and Bauer and, most explicitly, in Wigner’s 1961 proposal. Wigner later distanced himself from that proposal. Decoherence now helps explain the effective stability of macroscopic records and why the precise placement of the boundary is often practically insignificant, but decoherence does not by itself select one unique outcome from the quantum state.

More recent extended Wigner’s-friend results have sharpened the problem. Frauchiger and Renner showed that, under their assumptions, universally applicable quantum reasoning, consistency between agents, and single outcomes cannot all be retained. Bong and collaborators derived a related “local friendliness” theorem: if coherent quantum control can be extended to observers, quantum predictions conflict with the conjunction of locality, freedom of measurement settings, and absolute observed events. Their experiment was a photonic proof of principle in which a photon’s path represented the “observer,” not an experiment involving a conscious or macroscopic friend. These results therefore do not prove that consciousness creates reality, but they make the status of observer-independent facts harder to treat as philosophically trivial.

This is where the older metaphysical terrain becomes visible again.

The modest claim is not that Leibniz has been proved right. Relativity does not establish relationism, quantum theory does not demonstrate idealism, and no physical experiment establishes God as the ground of being. The conclusions of physics, the interpretation of physical theories, and the construction of a general metaphysics remain distinguishable levels of argument.

For my own part, I would go somewhat further. I take the relational reading of modern physics to be not merely attractive but compelled by the deeper structure of the theories. That is a stronger claim and requires an argument of its own.

One way of formulating that argument is through what I call observer equivariance. If two admissible observers or reference systems are related by a transformation, their descriptions need not be identical, but they should transform coherently while preserving shared physical content. Objectivity would then consist not in a description from nowhere, but in the lawful equivalence of descriptions from different perspectives. I develop this idea more fully in Objectivity Between Perspectives and in the accompanying technical preprint.

This proposal should not be presented as a consequence already established by relativity, relational quantum mechanics, or quantum-reference-frame theory. It is a philosophical attempt to draw their structural lesson together. Its affinity with Leibniz lies not in any direct recovery of the monadology, but in the thought that perspective and objectivity need not be opposites. Objective reality may be what remains coherent across perspectives rather than what can be described without any perspective at all.

The stronger Leibnizian package—relational space and time, centres of perspective, and God as metaphysical ground—is not something physics straightforwardly demonstrates. But physics may make that package newly thinkable.

That, to me, is the real significance of the old debate.

The question is not merely whether Newton or Leibniz was “right.” The physical question is what sort of world modern physics leaves us with: one still best understood through container, mechanism, intrinsic property, and external viewpoint, or one that points instead toward relation, perspective, transformation, and structure.

A further metaphysical question then arises: whether such a world is self-sufficient or depends upon a deeper ground. Modern physics may alter the terms in which that question is asked, but it cannot settle the question by itself.

Both questions remain open.

And they may be more pressing now than they have been for a very long time.

References

Isaac Newton, “De gravitatione et aequipondio fluidorum,” in Andrew Janiak, ed., Newton: Philosophical Writings (Cambridge: Cambridge University Press, 2004).

Isaac Newton, The Principia: Mathematical Principles of Natural Philosophy, trans. I. Bernard Cohen and Anne Whitman (Berkeley: University of California Press, 1999), Scholium to the Definitions and General Scholium.

G. W. Leibniz and Samuel Clarke, The Leibniz–Clarke Correspondence, ed. H. G. Alexander (Manchester: Manchester University Press, 1956), especially Leibniz’s Third Paper and Fourth Paper.

G. W. Leibniz, “The Monadology,” especially §14, in Roger Ariew and Daniel Garber, trans. and eds., Philosophical Essays (Indianapolis: Hackett, 1989).

Ernst Mach, The Science of Mechanics.

Julian B. Barbour and Bruno Bertotti, “Mach’s Principle and the Structure of Dynamical Theories,” Proceedings of the Royal Society of London A 382 (1982): 295–306. https://doi.org/10.1098/rspa.1982.0102.

John Earman and John D. Norton, “What Price Spacetime Substantivalism? The Hole Story,” The British Journal for the Philosophy of Science 38 (1987): 515–525. https://doi.org/10.1093/bjps/38.4.515.

Hermann Weyl, Space–Time–Matter.

Hermann Weyl, Philosophy of Mathematics and Natural Science.

Hermann Weyl, Symmetry (Princeton: Princeton University Press, 1952), especially p. 132.

Carlo Rovelli, “Relational Quantum Mechanics,” International Journal of Theoretical Physics 35 (1996): 1637–1678. https://doi.org/10.1007/BF02302261.

Flaminia Giacomini, Esteban Castro-Ruiz, and Časlav Brukner, “Quantum Mechanics and the Covariance of Physical Laws in Quantum Reference Frames,” Nature Communications 10 (2019): 494. https://doi.org/10.1038/s41467-018-08155-0.

Augustin Vanrietvelde, Philipp A. Höhn, Flaminia Giacomini, and Esteban Castro-Ruiz, “A Change of Perspective: Switching Quantum Reference Frames via a Perspective-Neutral Framework,” Quantum 4 (2020): 225. https://doi.org/10.22331/q-2020-01-27-225.

John von Neumann, Mathematical Foundations of Quantum Mechanics, trans. Robert T. Beyer (Princeton: Princeton University Press, 1955), chapter VI, especially pp. 418–421.

Eugene P. Wigner, “Remarks on the Mind–Body Question,” in I. J. Good, ed., The Scientist Speculates (London: William Heinemann, 1961), 284–302.

Maximilian Schlosshauer, “Decoherence, the Measurement Problem, and Interpretations of Quantum Mechanics,” Reviews of Modern Physics 76 (2004): 1267–1305. https://doi.org/10.1103/RevModPhys.76.1267.

Daniela Frauchiger and Renato Renner, “Quantum Theory Cannot Consistently Describe the Use of Itself,” Nature Communications 9 (2018): 3711. https://doi.org/10.1038/s41467-018-05739-8.

Kok-Wei Bong et al., “A Strong No-Go Theorem on the Wigner’s Friend Paradox,” Nature Physics 16 (2020): 1199–1205. https://doi.org/10.1038/s41567-020-0990-x.

Gustaf Ullman, “Observer Equivariance as a Condition for Shared Physical Law: A Lean-Verified Categorical Model” (2026). https://doi.org/10.5281/zenodo.20589336.