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Absolute space and time

Absolute space and time is a foundational concept in classical physics, introduced by Isaac Newton in his 1687 work Philosophiæ Naturalis Principia Mathematica, positing that space and time exist as absolute, independent entities unaffected by the presence of matter or observers.^[1] In the Scholium to the Definitions of the Principia, Newton distinguishes absolute space as remaining "similar and immovable" without relation to anything external, serving as an unchanging backdrop for all physical phenomena, in contrast to relative space, which is a movable dimension or measure arising from the positions of sensible bodies such as the Earth or stars.^[1] Similarly, absolute time, also termed "duration," flows equably and uniformly, independent of any external changes or motions, while relative time is an perceptible and approximate measure, like an hour or day, derived from the succession of ideas in the mind or observable celestial cycles.^[1] These notions underpin Newton's theory of motion, where absolute motion is defined as the translation of a body from one absolute place to another, detectable through its causes and effects—such as centrifugal forces in a rotating bucket of water—rather than mere changes in relation to surrounding objects.^[1] Newton's framework rejected earlier views, including Aristotle's idea of space as a plenum filled with matter and Descartes' identification of space with bodily extension, instead aligning with a revived atomistic tradition that allowed for void space.^[2] Historically, absolute space and time provoked intense debate among Newton's contemporaries and successors; for instance, Gottfried Wilhelm Leibniz critiqued them as unnecessary metaphysical entities, arguing instead for relational space and time defined solely by material relations.^[2] Despite such opposition, Newton's absolutes dominated Western physics for over two centuries, providing the geometric structure for his laws of motion and universal gravitation, until challenged by Albert Einstein's theory of relativity in the early 20th century, which reconceived space and time as intertwined and observer-dependent.^[2]

Historical Development

Early Concepts

The concept of space and time in ancient Greek philosophy laid foundational intuitions for later absolute notions, emphasizing unchanging frameworks underlying motion and change. Plato, in his dialogue Timaeus, introduced space as the chōra or receptacle—a formless, eternal matrix that receives and nurtures the ideal Forms, providing an invariant backdrop for the sensible world's becoming.^[3] This receptacle implies a stable spatial structure independent of the transient objects it contains, while time is depicted as a "moving image of eternity," created alongside the cosmos to mimic the timeless perfection of the Forms.^[3] Aristotle, building on but critiquing Platonic idealism, defined place (topos) in Physics Book IV as the innermost boundary of the containing body, serving as the arena for natural locomotion and motion.^[4] For Aristotle, space thus functions as a relational system of places ordered by the cosmos's spherical structure, with time as the measure of change in this plenum, where void has no existence.^[5] In medieval scholasticism, these Greek ideas were synthesized with Christian theology, positing an absolute divine dimension to space and time. Thomas Aquinas, in his Commentary on Aristotle's Physics, integrated Aristotelian physics by viewing place and time as real but created entities, subordinate to God's eternal immensity.^[6] Space, for Aquinas, reflects divine omnipresence as an infinite, immaterial expanse encompassing the finite Aristotelian universe, while time derives from mutable creation yet measures motion within God's unchanging eternity.^[6] This theological overlay elevated space to an absolute, God-sustained container, bridging Aristotelian relational places with a transcendent framework that ensures cosmic order under divine providence. Pre-scientific intuitions further reinforced absolute space as a fixed, empty backdrop against which objects and events occur, and time as a uniform, irreversible flow independent of observers. These everyday notions, evident in commonsense perceptions of a stable environment for daily motions and a steady progression of moments, predated rigorous analysis and permeated philosophical thought. During the Renaissance transition, Galileo Galilei shifted emphasis to kinematics in works like Two New Sciences, treating space as an isotropic Euclidean arena for describing uniform motion without explicitly invoking absoluteness, yet implicitly assuming a neutral frame for relative velocities.^[7] In the mid-17th century, René Descartes further developed these ideas in his Principia Philosophiae (1644), identifying space with the extension of matter and rejecting the existence of void; he treated space relationally as determined by the positions and relations among extended bodies, influencing the debates that Newton would later address.^[8]

Newton's Formulation

Isaac Newton introduced his concepts of absolute space and time in the Scholium following the Definitions in his Philosophiæ Naturalis Principia Mathematica, published in 1687 during the Scientific Revolution.^[1] There, he defined absolute space as "of its own nature, without relation to anything external, always remains similar and immovable," distinguishing it from relative space, which is "some movable dimension or measure of the absolute space" perceptible through positions relative to bodies.^[1] Similarly, absolute time was described as "of itself, and from its own nature, [flowing] equably without relation to anything external," in contrast to relative time, which serves as a "sensible and external measure of duration by means of motion."^[1] These definitions provided a foundational framework for Newton's mechanics, independent of observable changes or moving objects. Newton integrated absolute space into his first law of motion, stating that a body persists in its state of rest or uniform rectilinear motion unless compelled to change by impressed forces, with such motion understood relative to absolute space. This absolute reference frame was essential for distinguishing true motion from apparent motion, as relative motions alone could not account for inertial effects. To illustrate, Newton invoked the rotating bucket experiment: a bucket filled with water, suspended by a twisted cord and released to spin, initially keeps the water surface flat while the bucket rotates, but as the water acquires the rotation, its surface becomes concave due to centrifugal forces arising from rotation relative to absolute space, not merely relative to the bucket or surroundings.^[1] This demonstrates that true rotational motion produces observable effects independent of external relations, affirming the existence of an immovable absolute space. Underlying these scientific formulations were Newton's theological views, where absolute space served as the divine medium for God's omnipresence. In the General Scholium of the Principia, he asserted that God "endures from eternity to eternity, and is present from infinity to infinity," constituting duration and space as emanations of His being. Newton further elaborated this in the Opticks (1704), describing infinite space as God's "sensorium," an immaterial perceptive organ through which the divine intimately senses all things without reliance on material intermediaries. This perspective reconciled the immutability of absolute space and time with a theistic cosmology, positioning them as eternal attributes enabling God's eternal governance over the universe.

Philosophical Debates

Relational Alternatives

Relational theories of space and time, in contrast to absolute conceptions, posit that space and time emerge solely from the relations among material objects and events, lacking any independent existence. Gottfried Wilhelm Leibniz articulated this relationalist view in the early 18th century, defining space as the order of coexistences among phenomena and time as the order of non-coexistences or successive phenomena.^[9] According to Leibniz, these relational orders are ideal abstractions derived from the positions and sequences of bodies, rather than entities subsisting on their own.^[10] This perspective came into sharp focus during the 1715–1716 correspondence between Leibniz and Samuel Clarke, who defended Isaac Newton's absolute views. Clarke argued that absolute space was essential to God's immensity, equating infinite space with divine omnipresence and warning that Leibniz's relationalism would reduce God to a limited, material-dependent being.^[11] Leibniz countered that space and time as relations preserved God's transcendence, avoiding the notion of an empty, infinite container that might imply divine limitation or multiplicity.^[12] In the late 19th century, Ernst Mach revived and extended relational critiques in his 1883 work The Science of Mechanics, challenging the Newtonian idea of inertia as defined relative to absolute space. Mach proposed instead that inertial effects arise from the relative motions of bodies with respect to the entire fixed distribution of distant stars and matter in the universe.^[13] This "Machian" relationalism emphasized that all motion, including inertial frames, must be empirically grounded in observable cosmic relations, influencing later thinkers like Albert Einstein.^[14] Philosophically, relationalism resolves paradoxes associated with absolute space, such as the unintelligibility of empty space existing without objects to relate, by deriving spatial and temporal structures entirely from material interactions.^[15] It also aligns with empiricist principles, as space and time become verifiable through the observable relations between events and bodies, eschewing unobservable absolute entities.^[10]

Key Criticisms

One of the primary logical challenges to Newton's concept of absolute space arose from its inherent unobservability, rendering it undetectable through sensory experience or empirical means. George Berkeley, in his 1721 treatise De Motu, argued that absolute space and motion are metaphysical fictions, as they cannot be perceived or distinguished from relative positions and motions; instead, all motion is relative to other bodies, aligning with an idealist critique that dismissed absolute space as an unnecessary and unverifiable entity beyond human perception.^[16] This detectability problem highlighted a fundamental flaw: if absolute space exists, it should in principle allow for the identification of true motion independent of relative observations, yet no such distinction proves possible in practice. Empirical critiques further undermined absolute space by demonstrating that rotational motion, posited by Newton as evidence of absolute rotation, lacked clear observable markers distinguishing it from relative effects. Christiaan Huygens, in his analysis of pendulum behavior in rotating systems during the late 17th century, questioned whether absolute rotation could be confirmed without reference to surrounding matter, noting that phenomena like centrifugal deviation in a rotating pendulum could be interpreted as relative interactions rather than proof of an absolute frame; this suggested that no experiment could unequivocally isolate absolute rotation from observable relative differences.^[17] Huygens's work thus challenged Newton's bucket experiment by proposing that rotational dynamics are better understood through relative inertial structures defined by the distribution of matter, rather than an unobservable absolute space.^[18] Metaphysical objections portrayed absolute space as an occult, superfluous substance that contravened principles of parsimony, such as Occam's razor, by introducing an invisible, infinite entity without explanatory necessity. In the 18th century, philosophers like Gottfried Wilhelm Leibniz, through his correspondence with Samuel Clarke (Newton's defender), contended that positing absolute space as a real, independent being multiplied entities beyond what relative relations between bodies required, violating the principle of sufficient reason and rendering space akin to a hidden, god-like medium devoid of empirical warrant.^[19] This view framed absolute space as an extravagant hypothesis, preferable only if relative alternatives failed, but ultimately dismissed as an unnecessary complication to the observable order of coexistences. By the 19th century, tensions from electromagnetism intensified these challenges, as James Clerk Maxwell's equations (1860s) necessitated a luminiferous ether as the medium for light propagation at a constant speed, implying a preferred absolute rest frame that clashed with the idea of space's uniform fixity. However, the ether's hypothesized immobility in absolute space raised paradoxes, since planetary motions through it should produce detectable drags or variations in light speed, yet early experiments hinted at no such effects, indirectly eroding confidence in absolute space's role as an unchanging backdrop.^[20] These developments, peaking during the Enlightenment and extending into Victorian physics, collectively exposed absolute space and time as increasingly untenable, paving the way for paradigm shifts while relational alternatives, such as Leibniz's, emerged as a key form of opposition.^[21]

Mathematical Framework

Definitions of Absolute Space

In classical physics, absolute space is defined as a fixed, three-dimensional Euclidean manifold that endures without alteration, independent of any external relations or observers, providing an unchanging arena for the description of physical motions. This conceptual structure posits space as a rigid, homogeneous entity where positions are measured against an immutable grid of coordinates, homogeneous and isotropic, with a preferred frame for absolute rest, though kinematically undetectable.^[15] The absoluteness of this space is preserved under Galilean transformations, which connect coordinates between inertial reference frames differing by constant relative velocity \mathbf{v}. These transformations take the form \mathbf{x}' = \mathbf{x} - \mathbf{v}t, t' = t, ensuring that spatial distances remain invariant and no phenomena such as length contraction occur, thereby maintaining the fixed geometry of the manifold across frames.^[22] Absolute motion within this framework is quantified by the second time derivative of position, \frac{d^2 \mathbf{x}}{dt^2}, representing acceleration, which proves invariant across all inertial reference frames due to the linearity of Galilean transformations. This independence underscores acceleration as an absolute kinematic quantity, distinguishable from relative velocities that vary between observers. The implications for dynamics are profound: forces acting on bodies are inherently defined relative to this absolute space, permitting the universal applicability of laws like \mathbf{F} = m \frac{d^2 \mathbf{x}}{dt^2}, where the right-hand side captures true, frame-independent acceleration and enables consistent predictions of mechanical behavior irrespective of the observer's motion.^[2] This mathematical precision of absolute space received further formalization in the analytic mechanics developed during the 18th and 19th centuries by Joseph-Louis Lagrange and William Rowan Hamilton. Lagrange's Mécanique Analytique (1788) embeds the system's configuration space within the fixed Euclidean manifold, deriving equations of motion through variational principles that presuppose the unchanging spatial structure for generalized coordinates. Hamilton's subsequent reformulation in terms of phase space and the Hamiltonian function (circa 1830s) similarly relies on this absolute backdrop to define canonical momenta and evolve the system deterministically, reinforcing the foundational role of the immutable 3D geometry in classical dynamics.^[13]

Absolute Time and Dynamics

In Newtonian mechanics, absolute time is defined as a universal parameter t that flows equably without regard to anything external, serving as an invariant measure of duration independent of motion, events, or observers.^[1] This concept, articulated in the scholium to the definitions in Newton's Philosophiæ Naturalis Principia Mathematica, distinguishes absolute time from relative time, which is sensible and measured by means like the apparent motion of the sun or mechanical clocks.^[23] The infinitesimal interval dt remains constant across all frames, providing a fixed temporal backdrop for physical processes.^[13] Absolute time integrates with absolute space in Newtonian dynamics to form a separable 4D spacetime structure, where the full state of a system is specified by position \mathbf{x} and time t, but space and time remain ontologically distinct rather than unified.^[13] In this framework, time acts as a scalar parameter parameterizing the evolution of spatial configurations, enabling the laws of motion to describe changes uniformly.^[2] For instance, the kinetic energy of a particle of mass m moving with velocity \mathbf{v} relative to absolute space is given by

T = \frac{1}{2} m v^2,

where v = |\mathbf{v}| and \mathbf{v} = d\mathbf{x}/dt, with time t serving as the independent variable driving the dynamics.^[24] This absolute progression of time underpins classical dynamics, as seen in the example of planetary orbits under gravitational forces, where the uniform flow of t allows for precise predictions of elliptical paths and periods without dependence on local observers.^[25] In the 19th century, absolute time found refinements in celestial mechanics through Pierre-Simon Laplace's Mécanique Céleste, which extended Newtonian principles to compute long-term solar system stability using uniform temporal parameterization.^[26] In thermodynamics, the second law, formulated by Rudolf Clausius, introduces a unidirectional arrow of time through entropy increase as an irreversible process, operating within the framework of absolute time in classical physics.^[27]

Relativity's Paradigm Shift

Special Relativity

The Michelson-Morley experiment of 1887 sought to detect the Earth's motion through the hypothetical luminiferous ether by measuring differences in the speed of light in perpendicular directions, but yielded a null result, failing to reveal any such motion. This outcome challenged the classical notion of an absolute medium for light propagation and paved the way for a reevaluation of space and time. In 1905, Albert Einstein published his seminal paper "On the Electrodynamics of Moving Bodies," which resolved these issues by formulating special relativity without invoking the ether.^[28] Einstein's theory rests on two fundamental postulates: the laws of physics are identical in all inertial reference frames, and the speed of light in vacuum is constant for all observers regardless of the motion of the source or observer.^[28] These principles imply the relativity of simultaneity, where events simultaneous in one inertial frame may not be in another moving relative to it, thus eliminating absolute time.^[28] To reconcile measurements across frames, Einstein derived the Lorentz transformations, which supersede the Galilean transformations of classical mechanics:

x' = \gamma (x - vt), \quad t' = \gamma \left( t - \frac{vx}{c^2} \right),

where \gamma = \frac{1}{\sqrt{1 - \frac{v^2}{c^2}}}, v is the relative velocity, c is the speed of light, and primed coordinates denote the moving frame.^[28] These equations demonstrate that space and time coordinates mix, rendering both observer-dependent. In 1908, Hermann Minkowski reformulated special relativity geometrically as a four-dimensional spacetime continuum, a flat manifold with the invariant metric

ds^2 = -c^2 dt^2 + dx^2 + dy^2 + dz^2.

This Minkowski spacetime unifies space and time into a single entity, where intervals are absolute but coordinates are relative.^[29] Key consequences include time dilation, where the time interval \Delta t in a frame moving at velocity v relative to a stationary observer relates to the proper time \Delta \tau by \Delta t = \gamma \Delta \tau, and length contraction, where the length L of an object in the direction of motion is L = L_0 / \gamma with L_0 its proper length.^[28] Together, these effects preclude any absolute rest frame, as all inertial frames are equivalent, fundamentally undermining Newton's concepts of absolute space and time.^[28]

General Relativity

General relativity, formulated by Albert Einstein in 1915, represents a profound departure from the notions of absolute space and time by positing that gravity arises from the curvature of spacetime caused by mass and energy, rendering the geometry dynamic rather than fixed.^[30] In this framework, spacetime is not an inert stage but a malleable entity whose structure is determined by the distribution of matter and energy, eliminating any privileged, unchanging backdrop.^[30] This theory builds briefly on special relativity as its limit in the absence of gravity, but incorporates the effects of acceleration and gravitation to describe the universe on cosmic scales.^[30] Central to general relativity is the equivalence principle, which asserts that the effects of gravity are locally indistinguishable from those of acceleration in a non-inertial frame, such as an elevator in free fall.^[30] This principle implies that gravitational fields can be transformed away locally through a suitable choice of coordinates, leading to the requirement of general covariance: the laws of physics must hold in all coordinate systems, without reliance on an absolute space or time.^[30] By equating inertial and gravitational mass, it undermines Newton's absolute framework, where gravity acts instantaneously across empty space, and instead suggests that geometry itself encodes gravitational influence.^[30] The core of the theory is encapsulated in the Einstein field equations, which relate the curvature of spacetime to the stress-energy content of matter:

G_{\mu\nu} = \frac{8\pi [G](/page/G)}{c^4} T_{\mu\nu}

Here, G_{\mu\nu} is the Einstein tensor representing spacetime curvature, derived from the Ricci tensor and scalar, while T_{\mu\nu} is the stress-energy tensor describing the distribution of mass, energy, momentum, and stress; [G](/page/G) is the gravitational constant, and c is the speed of light. These equations, first presented in their final form on November 25, 1915, dictate that spacetime curvature responds dynamically to matter-energy, with no underlying absolute metric. The geometry of spacetime is described by the metric tensor g_{\mu\nu}, a 4x4 symmetric array that defines distances and intervals locally at each point, varying according to the nearby presence of mass-energy rather than adhering to a universal, flat structure.^[30] Unlike absolute space, which provides a fixed arena independent of contents, the metric in general relativity emerges relationally from interactions, ensuring that spatial and temporal measurements are context-dependent.^[30] Key implications include the absence of absolute time, manifested in gravitational time dilation where clocks run slower in stronger gravitational fields, as time intervals stretch with the metric component g_{00}.^[30] Similarly, space becomes relational, its configuration shaped by the global distribution of matter, such that distances and simultaneity vary without a rigid grid.^[30] These features were empirically validated during the 1919 solar eclipse expeditions led by Arthur Eddington, which measured the deflection of starlight by the Sun's gravity at approximately 1.75 arcseconds, matching general relativity's prediction and contradicting Newtonian expectations.^[31]

References

[1]
[PDF] isaac newton - the principia - LSE
Absolute space, of its own nature without reference to anything ex- ternal ... In astronomy, absolute time is distinguished from relative time by the.
[2]
Newton's views on space, time, and motion
Aug 12, 2004 · Isaac Newton founded classical mechanics on the view that space is distinct from body and that time passes uniformly without regard to whether anything happens ...
[3]
Plato's Timaeus - Stanford Encyclopedia of Philosophy
Oct 25, 2005 · In the Timaeus Plato presents an elaborately wrought account of the formation of the universe and an explanation of its impressive order and beauty.
[4]
Topoi on Topos: The Development of Aristotle's Concept of Place
Aristotle's notion of place receives its fullest development in Physics A 1-5, where he argues that place is the inner limit of a containing body. The.
[5]
Development of the Concept of Space up to Newton - MDPI
Aug 23, 2022 · Aristotle's universe, which he called Heaven, is finite and spherical in shape and is a plenum in which void has no place. More precisely, it is ...
[6]
Thomas Aquinas - Stanford Encyclopedia of Philosophy
Dec 7, 2022 · Not time, because Aquinas accepts Aristotle's definition of time as the measure of motion.<|control11|><|separator|>
[7]
Time | Internet Encyclopedia of Philosophy
Now, for much of the history of science, that intuitive picture of time as something that flows has been reflected in the way in which we do physics.
[8]
Galileo Galilei - Stanford Encyclopedia of Philosophy
Jun 4, 2021 · Galileo Galilei (1564–1642) has always played a key role in any history of science, as well as many histories of philosophy.
[9]
Space and Time as Relations: The Theoretical Approach of Leibniz
Space is an order of coexisting phenomena, as time is an order of successive phenomena. Today we call this view Relationalism: spatial and temporal ...
[10]
Leibniz's Philosophy of Physics
Dec 17, 2007 · ... Leibniz saw his relationalism about space and time as dovetailing with the foundations of his monadic metaphysics. Beyond arguing that space ...
[11]
[PDF] GW Leibniz and Samuel Clarke - LSE
Clarke refers to Newton, Principia, scholium to Definition 8: "As the order of the parts of time is immutable, so also is the order of the parts of space.
[12]
[PDF] Exchange of papers between Leibniz and Clarke - Early Modern Texts
Clarke first published this 'collection of papers' (not 'correspondence', not 'letters') in 1717, using his own fairly good translations of Leibniz's papers.
[13]
absolute and relational space and motion, post-Newtonian theories
Aug 11, 2006 · In this article, we explore the ways in which the selfsame issues have been taken up by contemporary authors, beginning with Mach, moving on to Einstein.2. Einstein · 3. Shape Dynamics · 4. The Dynamical Approach
[14]
The Forgotten Mystery of Inertia | American Scientist
A century after Ernst Mach and Albert Einstein cast doubt on absolute space, we still don't know how a gyroscope stays pointed in a fixed direction.This Article From Issue · November-December 2017 · Relative RevolutionsMissing: critique | Show results with:critique
[15]
Absolute and Relational Space and Motion: Classical Theories
Jul 19, 2021 · Leibniz argued (rather inconsistently, as we shall see) that since differences in absolute velocity are unobservable, they are not be genuine ...
[16]
Berkeley's Criticism of Newton on Space and Motion - jstor
De motu (1721;. 2nd ed., 1752). De motu is quoted from the translation by A. A. Luce in Vol. IV of the standard edition of The Works of George Berke- ley ...
[17]
Huygens on Inertial Structure and Relativity | Philosophy of Science
Jan 1, 2022 · Thereby his concept obviates the need for Newton's absolute space. Thus, his account is a powerful foundation for mechanics, although not ...Missing: critique | Show results with:critique
[18]
[PDF] Huygens on Inertial Structure and Relativity - PhilArchive
An alternative explanation: Huygens used to think rotation is motion in Absolute. Space but later came to see that it is relative to matter (Stein 1977, 10).Missing: critique | Show results with:critique
[19]
Leibniz's Theory of Space in the Correspondence with Clarke and ...
So far we have seen, that for Leibniz space is an abstraction from distances between physical objects in time, which is made up by the human mind and thus only ...Missing: relationalism | Show results with:relationalism
[20]
[PDF] Search for the aether
Feb 15, 2024 · If the aether takes over the role of absolute space, there is now just one reference frame in which you can use the simple laws of physics ( ...
[21]
[PDF] 09. The Leibniz-Clarke Correspondence - Research
Series of letters written in 1715-1716. Samuel Clarke. (1675-1729) ... Leibniz's Arguments Against Absolute Space. • First note: Newton's absolute ...
[22]
Newton's Scholium on Time, Space, Place and Motion
I do not define time, space, place, and motion, as being well known to all. Only I must observe, that the common people conceive those quantities under no other ...
[23]
Newton's Philosophiae Naturalis Principia Mathematica
Dec 20, 2007 · The distinctions between “absolute, true, and mathematical” and “relative, apparent, and common” time and space are the conceptual basis Newton ...“Definitions” and absolute... · Book 1 of the Principia · Book 3 of the Principia
[24]
https://plato.stanford.edu/entries/newton-principia/
[25]
Mécanique céleste : Laplace, Pierre Simon, marquis de, 1749-1827
Sep 26, 2019 · Mécanique céleste. by: Laplace, Pierre Simon, marquis de, 1749-1827 ... 1.7G. 4 v. 29 cm. Translated from the French: Traité de mécanique céleste
[26]
Thermodynamic Asymmetry in Time
Nov 15, 2001 · The thermodynamic time asymmetry is one of the most salient and consequential features of the physical universe.
[27]
[PDF] ON THE ELECTRODYNAMICS OF MOVING BODIES - Fourmilab
This edition of Einstein's On the Electrodynamics of Moving Bodies is based on the English translation of his original 1905 German-language paper. (published as ...
[28]
[PDF] Space and Time - UCSD Math
He also simply stated that the luminiferous ether was superfluous without any ex- planation, that is, he merely postulated that absolute motion does not exist.Missing: critique | Show results with:critique
[29]
Albert Einstein's 1916 Review Article on General Relativity - arXiv
May 13, 2004 · The first comprehensive overview of the final version of the general theory of relativity was published by Einstein in 1916.