Philosophy of space and time is the branch of
philosophyPhilosophy is the study of general and fundamental problems concerning matters such as existence, knowledge, values, reason, mind, and language. Philosophy is distinguished from other ways of addressing these questions by its critical, generally systematic approach and its reliance on reasoned...
concerned with the issues surrounding the
ontologyOntology is the philosophical study of the nature of being, existence or reality in general, as well as of the basic categories of being and their relations...
,
epistemologyEpistemology or theory of knowledge is the branch of philosophy concerned with the nature and scope of knowledge...
, and character of
spaceSpace is the boundless, three-dimensional extent in which objects and events occur and have relative position and direction. Physical space is often conceived in three linear dimensions, although modern physicists usually consider it, with time, to be part of the boundless four-dimensional...
and
timeTime is a component of the measuring system used to sequence events, to compare the durations of events and the intervals between them, and to quantify the motions of objects...
. While such ideas have been central to philosophy from its inception, the philosophy of space and time was both an inspiration for and a central aspect of early
analytic philosophyAnalytic philosophy is a generic term for a style of philosophy that came to dominate English-speaking countries in the 20th century...
. The subject focuses on a number of basic issues, including—but not limited to—whether or not time and space exist independently of the mind, whether they exist independently of one another, what accounts for time's apparently unidirectional flow, whether times other than the present moment exist, and questions about the nature of identity (particularly the nature of identity over time).
Ancient and medieval views
The earliest recorded
Western philosophyWestern philosophy is the philosophical thought and work of the Western or Occidental world, as distinct from Eastern or Oriental philosophies and the varieties of indigenous philosophies....
of
timeTime is a component of the measuring system used to sequence events, to compare the durations of events and the intervals between them, and to quantify the motions of objects...
was expounded by the
ancient EgyptAncient Egypt was an ancient civilization of eastern North Africa, concentrated along the lower reaches of the Nile River in what is now the modern country of Egypt. The civilization coalesced around 3150 BC with the political unification of Upper and Lower Egypt under the first pharaoh, and...
ian thinker
PtahhotepPtahhotep, sometimes known as Ptahhotpe or Ptah-Hotep, was an ancient Egyptian official during the late 25th century BC to early 24th century BC. Ptahhotep was the city administrator and first minister during the reign of Djedkare Isesi in the Fifth Dynasty...
(c. 2650–2600 BC), who said: "Do not lessen the time of following desire, for the wasting of time is an abomination to the spirit." The
VedasThe Vedas are a large body of texts originating in Ancient India. The texts are composed in Vedic Sanskrit and form the oldest layer of Sanskrit literature, and the oldest sacred texts of Hinduism....
, the earliest texts on
Indian philosophyThe term Indian philosophy , may refer to any of several traditions of philosophical thought that originated in the Indian subcontinent, including Hindu philosophy, Buddhist philosophy, and Jain philosophy...
and
Hindu philosophyHindu philosophy is divided into six Sanskrit schools of thought, or darshanas , which accept the Vedas as supreme revealed scriptures, and three schools, which do not accept the Vedas as supreme...
dating back to the late
2nd millennium BCThe 2nd millennium BC marks the transition from the Middle to the Late Bronze Age.Its first half is dominated by the Middle Kingdom of Egypt and Babylonia. The alphabet develops. Indo-Iranian migration onto the Iranian plateau and onto the Indian subcontinent propagates the use of the chariot...
, describe ancient
Hindu cosmologyAccording to Hindu mythology and Vedic cosmology the universe is cyclically created and destroyed. The life span of Lord Brahma, the creator, is 100 'Brahma-Years'. One day in the life of Brahma is called a Kalpa or 4.32 billion years...
, in which the
universeThe Universe comprises everything that physically exists, the entirety of space and time, all forms of matter and energy, and the physical laws and constants that govern them...
goes through repeated cycles of creation, destruction and rebirth, with each cycle lasting 4,320,000 years.
AncientThis page lists some links to ancient philosophy. In Western philosophy, the spread of Christianity through the Roman Empire marked the end of Hellenistic philosophy and ushered in the beginnings of Medieval philosophy, whereas in Eastern philosophy, the spread of Islam through the Arab Empire...
Greek philosophersGreek philosophy focused on the role of reason and inquiry. Many philosophers today concede that Greek philosophy has shaped the entire Western thought since its inception...
, including
ParmenidesParmenides of Elea was an ancient Greek philosopher born in Elea, a Greek city on the southern coast of Italy. He was the founder of the Eleatic school of philosophy. Parmenides was also a priest of Apollo and iatromantis. The single known work of Parmenides is a poem which has survived only in...
and
HeraclitusHeraclitus of Ephesus was a pre-Socratic Greek philosopher, a native of Ephesus, Ionia, on the coast of Asia Minor. He was of distinguished parentage. Little is known about his early life and education, but he regarded himself as self-taught and a pioneer of wisdom...
, wrote essays on the nature of time.
In Book 11 of St. Augustine's
ConfessionsConfessions is the name of an autobiographical work, consisting of 13 books, by St. Augustine of Hippo, written between AD 397 and AD 398. Modern English translations of it are sometimes published under the title The Confessions of St...
, he ruminates on the nature of time, asking, "What then is time? If no one asks me, I know: if I wish to explain it to one that asketh, I know not." He settles on time being defined more by what it is not than what it is.
In contrast to ancient Greek philosophers who believed that the universe had an infinite past with no beginning,
medieval philosophersMedieval philosophy is the philosophy of Europe and the Middle East in the era now known as medieval or the Middle Ages, the period roughly extending from the fall of the Roman Empire in the fifth century A.D. to the Renaissance in the sixteenth century...
and
theologiansThe term "theology" literally means the study of God, deriving from the Greek word theos, meaning 'God', and the suffix -ology from the Greek word logos meaning "discourse", "theory", or "reasoning"...
developed the concept of the universe having a
finite pastTemporal finitism is the idea that time is finite.The philosophy of Aristotle, expressed in such works as his Physics, held that although space was finite, with only void existing beyond the outermost sphere of the heavens, time was infinite...
with a beginning. This view was inspired by the creation myth shared by the three
Abrahamic religionsAbrahamic religions has become a popular and often used designation for the monotheistic faiths of Judaism, Christianity, and Islam, emphasizing their common origin and values. For some 1,300 years their histories and thought have been intertwined...
:
JudaismJudaism is a set of beliefs and practices originating in the Hebrew Bible , as later further explored and explained in the Talmud and other texts...
,
ChristianityChristianity is a monotheistic religion based on the life and teachings of Jesus of Nazareth as presented by the revelations in the New Testament....
and
IslamIslam Islam Islam ( al-’islām,
[There are ten pronunciations of Islam in English, differing in whether the first or second syllable has the stress, whether the s is or , and whether the a is pronounced as in father, as in cat, or (when the stress is on the i) as in the a of sofa...]
. The
Christian philosopherChristian philosophy is a term to describe the fusion of various fields of philosophy with the theological doctrines of Christianity.-Reconciling Christianity with philosophy:...
,
John PhiloponusJohn Philoponus , also known as John the Grammarian or John of Alexandria, was a Christian and Aristotelian commentator and the author of a considerable number of philosophical treatises and theological works...
, presented the first such argument against the ancient Greek notion of an infinite past. However, the most sophisticated medieval arguments against an infinite past were developed by the
early Muslim philosopherEarly Islamic philosophy or classical Islamic philosophy is a period of intense philosophical development beginning in the 2nd century AH of the Islamic calendar and lasting until the 6th century AH...
,
Al-Kindi' , also known to the West by the Latinized version of his name Alkindus, was an Arab Iraqi polymath: an Islamic philosopher, scientist, astrologer, astronomer, cosmologist, chemist, logician, mathematician, musician, physician, physicist, psychologist, and meteorologist...
(Alkindus); the
Jewish philosopherJewish philosophy refers to the conjunction between serious study of philosophy, Jewish scholasticism and Jewish theology. In one sense, it refers to all philosophical activity carried out by Jews or in relation to the religion of Judaism...
,
Saadia GaonSaʻadiah ben Yosef Gaon , , was a prominent rabbi, Jewish philosopher, and exegete of the Geonic period....
(Saadia ben Joseph); and the
Muslim theologianKalām is the Islamic philosophy of seeking Islamic theological principles through dialectic. In Arabic the word means "words, discussion, discourse". A scholar of kalam is referred to as a mutakallim...
,
Al-GhazaliAbū Ḥāmid Muḥammad ibn Muḥammad al-Ghazālī , often Algazel in English, was born and died in Tus, in the Khorasan province of Persia. He was an Islamic theologian, jurist, philosopher, cosmologist, psychologist and mystic of Persian origin, and remains one of the most celebrated scholars in the...
(Algazel). They developed two logical arguments against an infinite past, the first being the "argument from the impossibility of the existence of an actual infinite", which states:
- "An actual infinite cannot exist."
- "An infinite temporal regress of events is an actual infinite."
- "∴ An infinite temporal regress of events cannot exist."
The second argument, the "argument from the impossibility of completing an actual infinite by successive addition", states:
- "An actual infinite cannot be completed by successive addition."
- "The temporal series of past events has been completed by successive addition."
- "∴ The temporal series of past events cannot be an actual infinite."
Both arguments were adopted by later Christian philosophers and theologians, and the second argument in particular became more famous after it was adopted by
Immanuel KantImmanuel Kant was an 18th-century German philosopher from the Prussian city of Königsberg...
in his thesis of the first
antinomyAntinomy literally means the mutual incompatibility, real or apparent, of two laws. It is a term used in logic and epistemology....
concerning time.
In the early 11th century, the
Muslim physicistPhysics in medieval Islam included experimental physics, mathematical physics and theoretical physics.The fields of physics that were studied by Muslim scientists during this time also included optics and magnetism , mechanics , and astrophysics .These studies...
, Ibn al-Haytham (Alhacen or Alhazen), discussed
space perceptionDepth perception is the visual ability to perceive the world in three dimensions. Although any animal capable of moving around its environment must be able to sense the distance of objects in that environment, the term perception is reserved for humans, who are, as far as is known, the only beings...
and its
epistemologicalEpistemology or theory of knowledge is the branch of philosophy concerned with the nature and scope of knowledge...
implications in his
Book of OpticsThe Book of Optics was a seven-volume treatise on optics, physics, mathematics, anatomy and psychology written by the Iraqi Muslim scientist, Ibn al-Haytham , from 1011 to 1021, when he was under house arrest in Cairo, Egypt.The book...
(1021). His
experimentIn scientific research, an experiment is a method of investigating causal relationships among variables, or to test a hypothesis. An experiment is a cornerstone of the empirical approach to acquiring data about the world and is used in both natural sciences and social sciences...
al proof of the intromission model of vision led to changes in the way the
visual perceptionVisual perception is the ability to interpret information and surroundings from visible light reaching the eye. The resulting perception is also known as eyesight, sight or vision...
of space was understood, contrary to the previous
emission theory of visionEmission theory or extramission theory is the proposal that visual perception is accomplished by rays of light emitted by the eyes. This theory has been replaced by intromission theory, which states that visual perception comes from something representative of the object entering the eyes...
supported by
EuclidEuclid , fl. 300 BC, also known as Euclid of Alexandria, was a Greek mathematician and is often referred to as the "Father of Geometry." He was active in Hellenistic Alexandria during the reign of Ptolemy I...
and
PtolemyClaudius Ptolemaeus , known in English as Ptolemy , was a Roman citizen of Greek ancestry. He was a mathematician, astronomer, geographer, astrologer and a poet of a single epigram in the Greek Anthology. He lived in Egypt under the Roman Empire, and is believed to have been born in the town of...
. In "tying the visual perception of space to prior bodily experience, Alhacen unequivocally rejected the
intuitiveness of spatial perception and, therefore, the autonomy of vision. Without tangible notions of distance and size for
correlation, sight can tell us next to nothing about such things."
Realism and anti-realism
A traditional
realistContemporary philosophical realism is the belief in a reality that is completely ontologically independent of our conceptual schemes, linguistic practices, beliefs, etc. Philosophers who profess realism also typically believe that truth consists in a belief's correspondence to reality...
position in
ontologyOntology is the philosophical study of the nature of being, existence or reality in general, as well as of the basic categories of being and their relations...
is that time and space have existence apart from the human mind.
IdealistsIdealism is the philosophical theory that maintains that the ultimate nature of reality is based on mind or ideas. It holds that the so-called external or "real world" is inseparable from mind, consciousness, or perception...
deny or doubt the existence of objects independent of the mind. Some
anti-realistsIn philosophy, the term anti-realism is used to describe anyposition involving either the denial of an objective reality of entities of a certain type or the denial that verification-transcendent statements about a type of entity are either true or false...
whose ontological position is that objects outside the mind do exist, nevertheless doubt the independent existence of time and space.
KantImmanuel Kant was an 18th-century German philosopher from the Prussian city of Königsberg...
, in the
Critique of Pure ReasonThe Critique of Pure Reason by Immanuel Kant, first published in 1781, second edition 1787, is one of the most influential works in the history of philosophy...
, described time as an
a prioriThe terms "a priori" and "a posteriori" are used in philosophy to distinguish two types of knowledge, justifications or arguments...
notion that, together with other
a priori notions such as
spaceSpace is the boundless, three-dimensional extent in which objects and events occur and have relative position and direction. Physical space is often conceived in three linear dimensions, although modern physicists usually consider it, with time, to be part of the boundless four-dimensional...
, allows us to comprehend sense experience. For Kant, neither space nor time are conceived as
substancesSubstance theory, or substance attribute theory, is an ontological theory about objecthood, positing that a substance is distinct from its properties. This is part of essentialism in that ousia as a substance can also be a descriptor of an object's being and/or nature...
, but rather both are elements of a systematic
frameworkA framework is a basic conceptual structure used to solve or address complex issues. This very broad definition has allowed the term to be used as a buzzword, especially in a software context....
we use to structure our experience. Spatial
measurementIn science, measurement is the process of obtaining the magnitude of a quantity, such as length or mass, relative to a unit of measurement, such as a meter or a kilogram...
s are used to
quantifyQuantity is a kind of property which exists as magnitude or multitude. It is among the basic classes of things along with quality, substance, change, and relation. Quantity was first introduced as quantum, an entity having quantity. Being a fundamental term, quantity is used to refer to any type of...
how far apart
objectIn physics, a physical body or physical object is a collection of masses, taken to be one...
s are, and temporal measurements are used to quantitatively compare the interval between (or duration of) events.
Idealist writers such as
J. M. E. McTaggartJohn McTaggart Ellis McTaggart was an Idealist metaphysician. For most of his life McTaggart was a lecturer at Trinity College, Cambridge...
in
The Unreality of TimeIn the philosophy of space and time, "The Unreality of Time" is the following article:McTaggart, John McTaggart Ellis, 1908, "The Unreality of Time," Mind: A Quarterly Review of Psychology and Philosophy 17: 456-73....
have argued that time is an illusion (see also The flow of time below).
The writers discussed here are for the most part realists in this regard; for instance,
Gottfried LeibnizGottfried Wilhelm Leibniz was a German philosopher, polymath and mathematician who wrote primarily in Latin and French....
held that his monads existed, at least independently of the mind of the observer.
Leibniz and Newton
The great debate between defining notions of space and time as real objects themselves (
absoluteThe term Absolutism may refer to:* Absolute idealism, an ontologically monistic philosophy attributed to G.W.F. Hegel. It is Hegel's account of how being is ultimately comprehensible as an all-inclusive whole...
), or whether they are merely orderings upon actual objects (
relationalRelationism can refer to a framework of social thought governing political, economic and social behaviour; or to a particular philosophical position on the ontology of fundamental quantities of physics.- Relationism in social thought :...
), began between physicists
Isaac NewtonSir Isaac Newton FRS was an English physicist, mathematician, astronomer, natural philosopher, alchemist, and theologian who is perceived and considered by a substantial number of scholars and the general public as one of the most influential men in history...
(via his spokesman, Samuel Clarke) and Gottfried Leibniz in the papers of the Leibniz-Clarke Correspondence.
Arguing against the absolutist position, Leibniz offers a number of thought experiments with the purpose of showing that there is contradiction in assuming the existence of facts such as absolute location and velocity. These arguments trade heavily on two principles central to his philosophy: the
principle of sufficient reasonThe principle of sufficient reason states that anything that happens does so for a definite reason. In virtue of which no fact can be real or no statement true unless it has sufficient reason why it should not be otherwise...
and the
identity of indiscerniblesThe identity of indiscernibles is an ontological principle which states that two or more objects or entities are identical , if they have all their properties in common. That is, entities x and y are identical if any predicate possessed by x is also possessed by y and vice versa...
. The principle of sufficient reason holds that for every fact there is a reason that is sufficient to explain what and why it is the way it is and not otherwise. The identity of indiscernibles states that if there is no way of telling two entities apart then they are one and the same thing.
The example Leibniz uses involves two proposed universes situated in absolute space. The only discernible difference between them is that the latter is positioned five feet to the left of the first. The possibility of the example is only available if such a thing as absolute space exists. Such a situation, however, is not possible according to Leibniz, for if it were, where a universe was positioned in absolute space would have no sufficient reason, as it might very well have been anywhere else. Therefore, it is contradicting the principle of sufficient reason, and there could exist two distinct universes that were in all ways indiscernible, thus contradicting the identity of indiscernibles.
Standing out in Clarke’s (and Newton’s) response to Leibniz arguments is the
bucket argumentIsaac Newton's rotating bucket argument was designed to demonstrate that true rotational motion cannot be defined as the relative rotation of the body with respect to the immediately surrounding bodies...
:
Water in a bucket, hung from a rope and set to spin, will start with a flat surface. As the water begins to spin in the bucket, the surface of the water will become concave. If the bucket is stopped, the water will continue to spin, and while the spin continues the surface will remain concave. The concave surface is apparently not the result of the interaction of the bucket and the water, since the water is flat when the bucket first starts to spin, becomes concave as the water starts to spin, and remains concave as the bucket stops.
In this response, Clarke argues for the necessity of the existence of absolute space to account for phenomena like rotation and acceleration that cannot be accounted for on a purely
relationalist accountRelationism can refer to a framework of social thought governing political, economic and social behaviour; or to a particular philosophical position on the ontology of fundamental quantities of physics.- Relationism in social thought :...
. Clarke argues that since the curvature of the water occurs in the rotating bucket as well as in the stationary bucket containing spinning water, it can only be explained by stating that the water is rotating in relation to the presence of some third thing—absolute space.
Leibniz describes a space that exists only as a relation between objects, and which has no existence apart from the existence of those objects. Motion exists only as a relation between those objects. Newtonian space provided the absolute frame of reference within which objects can have motion. In Newton’s system the frame of reference exists independently of the objects which are contained in it. These objects can be described as moving in relation to space itself. For many centuries, the evidence of a concave water surface held authority.
Mach
Another important figure in this debate is 19th century physicist,
Ernst MachErnst Mach was an Austrian physicist and philosopher, remembered for his contributions to physics such as the Mach number and the study of shock waves...
. While he did not deny the existence of phenomena like that seen in the bucket argument, he still denied the absolutist conclusion by offering a different answer as to what the bucket was rotating in relation to: the fixed stars.
Mach suggested that thought experiments like the bucket argument are problematic. If we were to imagine a universe that only contains a bucket, on Newton’s account, this bucket could be set to spin relative to absolute space, and the water it contained would form the characteristic concave surface. But, in the absence of anything else in the universe it would be difficult to confirm that the bucket was indeed spinning. It seems equally possible that the surface of the water in the bucket would remain flat.
Mach argued that, in effect, the water experiment in an otherwise empty universe would remain flat. But if another object was introduced into this universe, perhaps a distant star, there is now something relative to which the bucket could be seen as rotating. The water inside the bucket could possibly have a slight curve. To account for the curve that we observe, an increase in the number of objects in the universe also increases the curvature in the water. Mach argued that the momentum of an object, whether angular or linear, exists as a result of the sum of the effects of other objects in the universe (
Mach's PrincipleIn theoretical physics, particularly in discussions of gravitation theories, Mach's principle is the name given by Einstein to an imprecise hypothesis often credited to the physicist and philosopher Ernst Mach....
).
Einstein
EinsteinAlbert Einstein was a theoretical physicist. His many contributions to physics include the special and general theories of relativity, the founding of relativistic cosmology, the first post-Newtonian expansion, explaining the perihelion advance of Mercury, prediction of the deflection of...
, a prominent physicist in the 20th century, proposed that relativistics are based on the principle of relativity. This theory holds that the rules of physics must be the same for all observers, regardless of the frame of reference that is used, and that light propagates at the same speed in all reference frames. This theory was motivated by Maxwell’s equations. These equations show that electromagnetic waves propagate in a vacuum at the
speed of lightIn physics, the speed of light is a physical constant, the speed at which electromagnetic radiation, such as light, travels in free space . Its value is 299,792,458 metres per second...
. However, Maxwell's equations give no indication of what this speed is relative to. Prior to Einstein, it was thought that this speed was relative to a fixed medium, called the luminiferous ether. In contrast, the theory of special relativity postulates that light propagates at the speed of light in all inertial frames, and examines the implications of this postulate.
All attempts to measure any speed relative to this ether failed, which can be seen as a confirmation of Einstein's postulate that light propagates at the same speed in all reference frames.
Special relativitySpecial relativity is the physical theory of measurement in inertial frames of reference proposed in 1905 by Albert Einstein in the paper "On the Electrodynamics of Moving Bodies"...
is a formalization of the principle of relativity which does not contain a privileged inertial frame of reference such as the luminiferous ether or absolute space, from which Einstein inferred that no such frame exists.
Einstein generalized relativity to frames of reference that were non-inertial. He achieved this by positing the
Equivalence PrincipleIn the physics of general relativity, the equivalence principle refers to several related concepts dealing with the equivalence of gravitational and inertial mass, and to Albert Einstein's assertion that the gravitational "force" as experienced locally while standing on a massive body is actually...
, which states that the force felt by an observer in a given gravitational field and that felt by an observer in an accelerating frame of reference are indistinguishable. This led to the conclusion that the mass of an object warps the geometry of the space-time surrounding it, as described in Einstein’s field equations.
In classical physics, an inertial reference frame is one in which an object that experiences no forces does not accelerate. In general relativity, an inertial frame of reference is one that is following a
geodesicIn general relativity, a geodesic generalizes the notion of a "straight line" to curved spacetime. Importantly, the world line of a particle free from all external force is a particular type of geodesic...
of space-time. An object that moves against a geodesic experiences a force. An object in free fall does not experience a force, because it is following a geodesic. An object standing on the earth, however, will experience a force, as it is being held against the geodesic by the surface of the planet. In light of this, the bucket of water rotating in empty space will experience a force because it rotates with respect to the geodesic. The water will become concave, not because it is rotating with respect to the distant stars, but because it is rotating with respect to the geodesic.
Einstein partially advocates Mach’s principle in that distant stars explain inertia because they provide the gravitational field against which acceleration and inertia occur. But contrary to Leibniz’ account, this warped space-time is as integral a part of an object as are its other defining characteristics such as volume and mass. If one holds, contrary to idealist beliefs, that objects exist independently of the mind, it seems that Relativistics commits them to also hold that space and temporality have the exact same type of independent existence.
Conventionalism
The position of conventionalism states that there is no fact of the matter as to the geometry of space and time, but that it is decided by convention. The first proponent of such a view,
Henri PoincaréJules Henri Poincaré was a French mathematician and theoretical physicist, and a philosopher of science...
, reacting to the creation of the new
non-euclidean geometryA non-Euclidean geometry is characterized by a non-vanishing Riemann curvature tensor. Examples of non-Euclidean geometries include the hyperbolic and elliptic geometry, which are contrasted with a Euclidean geometry. The essential difference between Euclidean and non-Euclidean geometry is the...
, argued that which geometry applied to a space was decided by convention, since different geometries will describe a set of objects equally well, based on considerations from his
sphere-worldThe idea of a sphere-world was constructed by Henri Poincaré while pursuing his argument for conventionalism , offered a thought experiment about a sphere with strange properties....
.
This view was developed and updated to include considerations from relativistic physics by
Hans ReichenbachHans Reichenbach was a leading philosopher of science, educator and proponent of logical empiricism...
. Reichenbach's conventionalism, applying to space and time, focuses around the idea of
coordinative definitionA coordinative definition is a postulate which assigns a partial meaning to the theoretical terms of a scientific theory by correlating the mathematical objects of the pure or formal/syntactical aspects of a theory with physical objects in the world...
.
Coordinative definition has two major features. The first has to do with coordinating units of length with certain physical objects. This is motivated by the fact that we can never directly apprehend length. Instead we must choose some physical object, say the Standard Metre at the Bureau International des Poids et Mesures (International Bureau of Weights and Measures), or the
wavelengthIn physics, the wavelength of a sinusoidal wave is the spatial period of the wave – the distance over which the wave's shape repeats.It is usually determined by considering the distance between consecutive corresponding points of the same phase, such as crests, troughs, or zero crossings, and is a...
of
cadmiumCadmium is a chemical element with the symbol Cd and atomic number 48. The soft, bluish-white transition metal is chemically similar to the two other metals in group 12, zinc and mercury. Similar to zinc it prefers oxidation state +2 in most of its compounds and similar to mercury it shows a low...
to stand in as our unit of length. The second feature deals with separated objects. Although we can, presumably, directly test the equality of length of two measuring rods when they are next to one another, we can not find out as much for two rods distant from one another. Even supposing that two rods, whenever brought near to one another are seen to be equal in length, we are not justified in stating that they are always equal in length. This impossibility undermines our ability to decide the equality of length of two distant objects. Sameness of length, to the contrary, must be set by definition.
Such a use of coordinative definition is in effect, on Reichenbach's conventionalism, in the General Theory of Relativity where light is assumed, i.e. not discovered, to mark out equal distances in equal times. After this setting of coordinative definition, however, the geometry of spacetime is set.
As in the absolutism/relationalism debate, contemporary philosophy is still in disagreement as to the correctness of the conventionalist doctrine. While conventionalism still holds many proponents, cutting criticisms concerning the coherence of Reichenbach's doctrine of coordinative definition have led many to see the conventionalist view as untenable.
The structure of spacetime
Building from a mix of insights from the historical debates of absolutism and conventionalism as well as reflecting on the import of the technical apparatus of the General Theory of Relativity, details as to the structure of
spacetimeIn physics, spacetime is any mathematical model that combines space and time into a single continuum. Spacetime is usually interpreted with space being three-dimensional and time playing the role of a fourth dimension that is of a different sort than the spatial dimensions...
have made up a large proportion of discussion within the philosophy of space and time, as well as the
philosophy of physicsIn philosophy, the philosophy of physics studies the fundamental philosophical questions underlying modern physics, the study of matter and energy and how they interact. The philosophy of physics begins by reflecting on the basic metaphysical and epistemological questions posed by physics:...
. The following is a short list of topics.
The relativity of simultaneity
According to
special relativitySpecial relativity is the physical theory of measurement in inertial frames of reference proposed in 1905 by Albert Einstein in the paper "On the Electrodynamics of Moving Bodies"...
each point in the universe can have a different set of events that compose its present instant. This has been used in the
Rietdijk-Putnam argumentIf special relativity is true, then each observer will have their own plane of simultaneity, which contains a unique set of events that constitutes the observer's present moment. Observers moving at different relative velocities have different planes of simultaneity hence different sets of events...
to demonstrate that relativity predicts a block universe in which events are fixed in four dimensions.
Invariance vs. covariance
Bringing to bear the lessons of the absolutism/relationalism debate with the powerful mathematical tools invented in the 19th and 20th century,
Michael FriedmanMichael Friedman may refer to:*Michael Jan Friedman, author*Mike Friedman, cyclist*Michael Friedman -See also:*Michael Freedman, mathematician*Michael Freeman...
draws a distinction between invariance upon mathematical
transformationIn mathematics, a transformation could be any function mapping a set X on to another set or on to itself. However, often the set X has some additional algebraic or geometric structure and the term "transformation" refers to a function from X to itself which preserves this structure.Examples include...
and covariance upon transformation.
Invariance, or symmetry, applies to
objects, i.e. the
symmetry groupThe symmetry group of an object is the group of all isometries under which it is invariant with composition as the operation...
of a space-time theory designates what features of objects are invariant, or absolute, and which are dynamical, or variable.
Covariance applies to
formulations of theories, i.e. the
covariance groupIn mathematics, a group is an algebraic structure consisting of a set together with an operation that combines any two of its elements to form a third element. To qualify as a group, the set and the operation must satisfy a few conditions called group axioms, namely closure, associativity, identity...
designates in which range of
coordinate systemIn mathematics and its applications, a coordinate system is a system for assigning an n-tuple of numbers or scalars to each point in an n-dimensional space. This concept is part of the theory of manifolds. "Scalars" in many cases means real numbers, but, depending on context, can mean complex...
s the laws of physics hold.
This distinction can be illustrated by revisiting Leibniz's thought experiment, in which the universe is shifted over five feet. In this example the position of an object is seen not to be a property of that object, i.e. location is not invariant. Similarly, the covariance group for
classical mechanicsIn the fields of physics, classical mechanics is one of the two major sub-fields of study in the science of mechanics, which is concerned with the set of physical laws governing and mathematically describing the motions of bodies and aggregates of bodies geometrically distributed within a certain...
will be any coordinate systems that are obtained from one another by shifts in position as well as other translations allowed by a
Galilean transformationThe Galilean transformation is used to transform between the coordinates of two reference frames which differ only by constant relative motion within the constructs of Newtonian physics. This is the passive transformation point of view...
.
In the classical case, the invariance, or symmetry, group and the covariance group coincide, but, interestingly enough, they part ways in relativistic physics. The symmetry group of the GTR includes all differentiable transformations, i.e. all properties of an object are dynamical, in other words there are no absolute objects. The formulations of the GTR, unlike that of classical mechanics, do not share a standard, i.e. there is no single formulation paired with transformations. As such the covariance group of the GTR is just the covariance group of every theory.
Historical frameworks
A further application of the modern mathematical methods, in league with the idea of invariance and covariance groups, is to try to interpret historical views of space and time in modern, mathematical language.
In these translations, a theory of space and time is seen as a
manifoldIn mathematics, more specifically in differential geometry and topology, a manifold is a mathematical space that on a small enough scale resembles the Euclidean space of a certain dimension, called the dimension of the manifold....
paired with vector spaces, the more vector spaces the more facts there are about objects in that theory. The historical development of spacetime theories is generally seen to start from a position where many facts about objects or incorporated in that theory, and as history progresses, more and more structure is removed.
For example,
AristotleAristotle was a Greek philosopher, a student of Plato and teacher of Alexander the Great. He wrote on many subjects, including physics, metaphysics, poetry, theater, music, logic, rhetoric, politics, government, ethics, biology, and zoology.Together with Plato and Socrates , Aristotle is one of...
's theory of space and time holds that not only is there such a thing as absolute position, but that there are special places in space, such as a center to the universe, a sphere of fire, etc. Newtonian spacetime has absolute position, but not special positions. Galilean spacetime has absolute acceleration, but not absolute position or velocity. And so on.
Holes
With the GTR, the traditional debate between absolutism and relationalism has been shifted to whether or not spacetime is a substance, since the GTR largely rules out the existence of, e.g., absolute positions. One powerful argument against spacetime substantivalism, offered by
John EarmanJohn Earman is a philosopher of physics. He is currently a professor in the History and Philosophy of Science department at the University of Pittsburgh. He has also taught at UCLA, the Rockefeller University, and the University of Minnesota, and is president of the Philosophy of Science...
is known as the "
hole argumentIn general relativity, the hole argument is a "paradox" which much troubled Albert Einstein while developing his famous field equation.It is interpreted by some philosophers as an argument against manifold substantialism, a doctrine that the manifold of events in spacetime are a "substance" which...
".
This is a technical mathematical argument but can be paraphrased as follows:
Define a function
d as the
identity functionIn mathematics, an identity function, also called identity map or identity transformation, is a function that always returns the same value that was used as its argument...
over all elements over the manifold M, excepting a small
neighbourhoodIn topology and related areas of mathematics, a neighbourhood is one of the basic concepts in a topological space. Intuitively speaking, a neighbourhood of a point is a set containing the point where you can move that point some amount without leaving the set.This concept is closely related to the...
H belonging to M. Over H
d comes to differ from identity by a
smooth functionIn mathematical analysis, a differentiability class is a classification of functions according to the properties of their derivatives. Higher order differentiability classes correspond to the existence of more derivatives. Functions that have derivatives of all orders are called smooth.Most of...
.
With use of this function
d we can construct two
mathematical modelA mathematical model uses mathematical language to describe a system. Mathematical models are used not only in the natural sciences and engineering disciplines but also in the social sciences ; physicists, engineers, computer scientists, and economists use...
s, where the second is generated by applying
d to proper elements of the first, such that the two models are identical prior to the time
t=0, where
t is a time function created by a
foliationIn mathematics, a foliation is a geometric device used to study manifolds, consisting of an integrable subbundle of the tangent bundle. A foliation looks locally like a decomposition of the manifold as a union of parallel submanifolds of smaller dimension....
of spacetime, but differ after
t=0.
These considerations show that, since substantivalism allows the construction of holes, that the universe must, on that view, be indeterministic. Which, Earman argues, is a case against substantivalism, as the case between determinism or indeterminism should be a question of physics, not of our commitment to substantivalism.
The direction of time
The problem of the
direction of timeIn the natural sciences, arrow of time, or time’s arrow, is a term coined in 1927 by British astronomer Arthur Eddington used to distinguish a direction of time on a four-dimensional relativistic map of the world, which, according to Eddington, can be determined by a study of organizations of...
arises directly from two contradictory facts. First, the fundamental physical laws are time-reversal
invariantInvariant and invariance may have several meanings, among which are:* Invariant , an expression whose value doesn't change during program execution* In computer science, a type in overriding that is neither covariant nor contravariant...
. In other words, anything that can happen moving forward through time is just as possible moving backwards in time. Or, put in another way, through the eyes of physics, there will be no distinction, in terms of possibility, between what happens in a movie if the film is run forward, or if the film is run backwards. Second, our experience of time, at the
macroscopicMacroscopic is a word commonly used to describe physical objects that are measurable and observable by the naked eye.When applied to phenomena and abstract objects, it describes existence in the world as we perceive it, often in contrast to experiences or theories considering objects of geometric...
level, is
not time-reversal invariant. Glasses fall and break all the time, but shards of glass do not put themselves back together and fly up on tables. We have memories of the past, and none of the future. We feel we can't change the past but can influence the future.
The causation solution
One solution to this problem takes a
metaphysicalMetaphysics investigates principles of reality transcending those of any particular science. Cosmology and ontology are traditional branches of metaphysics. It is concerned with explaining the fundamental nature of being and the world...
view, in which the direction of time follows from an asymmetry of
causationCausality is the relationship between an event and a second event , where the second event is a direct consequence of the first....
. We know more about the past because the elements of the past are causes for the effect that is our perception. We feel we can't affect the past and can affect the future because we
can't affect the past and
can affect the future.
There are two major difficulties with this view. First is the problem of distinguishing the cause from the effect in a non-arbitrary way. The use of causation in constructing a temporal ordering could easily become circular. The second problem is with not the consistency of this view, but its explanatory power. While the causation account, if successful may account for some time-asymmetric phenomena like perception and action, it does not account for many others, like the breaking glass described above.
The thermodynamics solution
The second major family of solutions to this problem, and by far the one that has generated the most literature, finds the existence of the direction of time as relating to the nature of thermodynamics.
The answer from classical
thermodynamicsIn physics, thermodynamics is the study of the conversion of energy into work and heat and its relation to macroscopic variables such as temperature, volume and pressure...
states that while our basic physical theory is, in fact, time-reversal symmetric, thermodynamics is not. In particular, the
second law of thermodynamicsThe second law of thermodynamics is an expression of the universal principle of entropy, stating that the entropy of an isolated system which is not in equilibrium will tend to increase over time, approaching a maximum value at equilibrium, and that the entropy change dS of a system undergoing any...
states that the net
entropyEntropy is a concept of information maintaining great importance in physics, chemistry, and information theory...
of a closed system never decreases, and this explains why we often see glass breaking, but not coming back together.
But in
statistical mechanicsStatistical mechanics is the application of probability theory, which includes mathematical tools for dealing with large populations, to the field of mechanics, which is concerned with the motion of particles or objects when subjected to a force...
things get more complicated. On one hand, statistical mechanics is far superior to classical thermodynamics, in that thermodynamic behavior, glass breaking, can be explained by the fundamental laws of physics paired with a statistical postulate. But statistical mechanics, unlike classical thermodynamics, is time-reversal symmetric. The second law of thermodynamics, as it arises in statistical mechanics, merely states that it is
overwhelmingly likely that net entropy will increase, but it is not an absolute law.
Current thermodynamic solutions to the problem of the direction of time aim to find some further fact, or feature of the laws of nature to account for this discrepancy.
The laws solution
A third type of solution to the problem of the direction of time, although much less represented, argues that the laws are not time-reversal symmetric. For example, certain processes in
quantum mechanicsQuantum mechanics is a set of principles describing the physical reality at the atomic level of matter and the subatomic . These descriptions include the simultaneous wave-like and particle-like behavior of both matter and radiation...
, relating to the weak nuclear force, are not time-reversible, keeping in mind that when dealing with quantum mechanics time-reversibility comprises a more complex definition.
But this type of solution is insufficient because 1) the time-asymmetric phenomena in QM are too few to account for the uniformity of macroscopic time-asymmetry and 2) it relies on the assumption that QM is the final or correct description of physical processes.
One recent proponent of the laws solution is Tim Maudlin who argues that, in addition to quantum mechanical phenomena, our basic spacetime physics (
general relativityGeneral relativity or the general theory of relativity is the geometric theory of gravitation published by Albert Einstein in 1916. It is the current description of gravitation in modern physics. It unifies special relativity and Newton's law of universal gravitation, and describes gravity as a...
) is time-reversal asymmetric. He denies the definitions, often quite complicated, that underlie time-reversal symmetries, arguing that these definitions themselves cause the appearance of a problem of the direction of time.
The flow of time
The problem of the flow of time, as it has been treated in analytic philosophy, owes its beginning to a paper written by
J. M. E. McTaggartJohn McTaggart Ellis McTaggart was an Idealist metaphysician. For most of his life McTaggart was a lecturer at Trinity College, Cambridge...
. In this paper McTaggart proposes two "temporal series". The first series, which means to account for our intuitions about temporal becoming, or the moving Now, is called the
A-seriesA-series and B-series are terms introduced by the Scottish idealist philosopher John McTaggart in 1908 which have become classic terms of reference in modern discussions of the philosophy of time, even outside the analytic tradition....
. The A-series orders events according to their being in the past, present or future,
simpliciter and in comparison to each other. The
B-seriesA-series and B-series are terms introduced by the Scottish idealist philosopher John McTaggart in 1908 which have become classic terms of reference in modern discussions of the philosophy of time, even outside the analytic tradition....
eliminates all reference to the present, and the associated temporal modalities of past and future, and orders all events by the temporal relations
earlier than and
later than.
McTaggart, in his paper
The Unreality of TimeIn the philosophy of space and time, "The Unreality of Time" is the following article:McTaggart, John McTaggart Ellis, 1908, "The Unreality of Time," Mind: A Quarterly Review of Psychology and Philosophy 17: 456-73....
, argues that time is unreal since a) the A-series is inconsistent and b) the B-series alone cannot account for the nature of time as the A-series describes an essential feature of it.
Building from this framework, two camps of solution have been offered. The first, the A-theorist solution, takes becoming as the central feature of time, and tries to construct the B-series from the A-series by offering an account of how B-facts come to be out of A-facts. The second camp, the B-theorist solution, takes as decisive McTaggart's arguments against the A-series and tries to construct the A-series out of the B-series, for example, by temporal indexicals.
Dualities
Quantum field theoryQuantum field theory provides a theoretical framework for constructing quantum mechanical models of systems classically described by fields or of many-body systems. It is widely used in particle physics and condensed matter physics...
models have shown that it is possible for theories in two different spacetime backgrounds, like AdS/CFT or
T-dualityT-duality is a symmetry of string theory relating small and large distances. T-duality is not present in ordinary particle theory, indicating that strings experience spacetime in a way that is fundamentally distinct than the way particles do. It relates different string theories that were thought...
, to be equivalent.
Presentism and Eternalism
According to
PresentismIn the philosophy of time, presentism is the theory that only present things exist, and future and past things are unreal. Past and future "entities" are to be construed as logical constructions or fictions. The opposite of presentism is 'eternalism', which is the belief that things in the past and...
, time is an ordering of various
realitiesReality, in everyday usage, means "the state of things as they actually exist." Literally, the term denotes what is real; in its widest sense, this includes everything that is, whether or not it is observable or comprehensible. Reality in this sense includes being and sometimes is considered to...
. At a certain time some things exist and others do not. This is the only reality we can deal with and we cannot for example say that
HomerHomer is a legendary ancient Greek epic poet, traditionally said to be the author of the epic poems the Iliad and the Odyssey...
exists because at the present time he does not. An Eternalist, on the other hand, holds that time is a dimension of reality on a par with the three spatial dimensions, and hence that all things—past present and future—can be said to be just as real as things in the present are. According to this theory, then, Homer really
does exist, though we must still use special language when talking about somebody who exists at a distant time—just as we would use special language when talking about something a long way away (the very words near, far, above, below, over there, and such are directly comparable to phrases such as in the past, a minute ago, and so on).
Endurantism and perdurantism
The positions on the persistence of objects are somewhat similar. An
endurantistEndurantism or endurance theory is a philosophical theory of persistence and identity. According to the endurantist view material objects are persisting three-dimensional individuals wholly present at every moment of their existence...
holds that for an object to persist through time is for it to exist completely at different times (each instance of existence we can regard as somehow separate from previous and future instances, though still numerically identical with them). A
perdurantistPerdurantism or perdurance theory is a philosophical theory of persistence and identity. The perdurantist view is often defined as being the claim that objects have distinct temporal parts as opposed to endurantism...
on the other hand holds that for a thing to exist through time is for it to exist as a continuous reality, and that when we consider the thing as a whole we must consider an aggregate of all its "temporal parts" or instances of existing. Endurantism is seen as the conventional view and flows out of our innate ideas (when I talk to somebody I think I am talking to that person as a complete object, and not just a part of a cross-temporal being), but perduranists have attacked this position. (An example of a perdurantist is David Lewis.) One argument perdurantists use to state the superiority of their view is that perdurantism is able to take account of change in objects.
The relations between these two questions mean that on the whole
PresentistsIn the philosophy of time, presentism is the theory that only present things exist, and future and past things are unreal. Past and future "entities" are to be construed as logical constructions or fictions. The opposite of presentism is 'eternalism', which is the belief that things in the past and...
are also endurantists and Eternalists are also perdurantists (and vice versa), but this is not a necessary connection and it is possible to claim, for instance, that time's passage indicates a series of ordered realities, but that objects within these realities somehow exist outside of the reality as a whole, even though the realities as wholes are not related. However, such positions are rarely adopted.
See also
- Metaphysics
Metaphysics investigates principles of reality transcending those of any particular science. Cosmology and ontology are traditional branches of metaphysics. It is concerned with explaining the fundamental nature of being and the world...
- Time travel
Time travel is the concept of moving between different moments in time in a manner analogous to moving between different points in space, either sending objects backwards in time to a moment before the present, or sending objects forward from the present to the future without the need to...
in science and Time travel in fictionTime travel is a common theme in science fiction and is depicted in a variety of media. It simply means either going forward in time or backward, like seeing the future, or the past.- Literature :...
- Zeno's paradoxes
Zeno's paradoxes are a set of problems generally thought to have been devised by Zeno of Elea to support Parmenides's doctrine that "all is one" and that, contrary to the evidence of our senses, the belief in plurality and change is mistaken, and in particular that motion is nothing but an illusion...
- Arrow of time
In the natural sciences, arrow of time, or time’s arrow, is a term coined in 1927 by British astronomer Arthur Eddington used to distinguish a direction of time on a four-dimensional relativistic map of the world, which, according to Eddington, can be determined by a study of organizations of...
External links
- Stanford Encyclopedia of Philosophy
The Stanford Encyclopedia of Philosophy is a freely-accessible online encyclopedia of philosophy maintained by Stanford University. Each entry is written and maintained by an expert in the field, including professors from over 65 academic institutions worldwide...
:
- Internet Encyclopedia of Philosophy
The Internet Encyclopedia of Philosophy is a free online encyclopedia on philosophical topics and philosophers founded by James Fieser in 1995. The current general editors are James Fieser and Bradley Dowden. The staff also includes numerous area editors as well as volunteers...
: "Time" by Bradley Dowden.
- Brown, C.L., 2006, "What is Space?" A largely Wittgensteinian, approach towards a dissolution of the question: "What is space?"
- Rea, M. C., "Four Dimensionalism" in The Oxford Handbook for Metaphysics. Oxford Univ. Press. Describes presentism
In the philosophy of time, presentism is the theory that only present things exist, and future and past things are unreal. Past and future "entities" are to be construed as logical constructions or fictions. The opposite of presentism is 'eternalism', which is the belief that things in the past and...
and four dimensionalism.