Philosophy of space and time
Encyclopedia
Philosophy of space and time is the branch of philosophy
concerned with the issues surrounding the ontology
, epistemology, and character of space
and time
. 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 philosophy
. 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).
of time
was expounded by the ancient Egypt
ian thinker Ptahhotep
(c. 2650–2600 BCE), who said: "Do not lessen the time of following desire, for the wasting of time is an abomination to the spirit." The Vedas
, the earliest texts on Indian philosophy
and Hindu philosophy
dating back to the late 2nd millennium BCE, describe ancient Hindu cosmology
, in which the universe
goes through repeated cycles of creation, destruction and rebirth, with each cycle lasting 4,320,000 years. Ancient
Greek philosophers
, including Parmenides
and Heraclitus
, wrote essays on the nature of time.
Incas regarded space and time as a single concept, named pacha .
Plato, in the Timaeus, identified time with the period of motion of the heavenly bodies, and space as that in which things come to be. Aristotle, in Book IV of his Physica defined time as the number of change with respect to before and after, and the space of an object as the innermost motionless boundary of that which surrounds it.
In Book 11 of St. Augustine's Confessions
, 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 philosophers
and theologians
developed the concept of the universe having a finite past
with a beginning. This view was inspired by the creation belief shared by the three Abrahamic religions
: Judaism
, Christianity
and Islam
. The Christian philosopher
, John Philoponus
, presented the first such argument against the ancient Greek notion of an infinite past. His were adopted by many including, most notably, early Muslim philosopher
, Al-Kindi
(Alkindus); the Jewish philosopher
, Saadia Gaon
(Saadia ben Joseph); and the Muslim theologian
, Al-Ghazali
(Algazel). They used his two logical arguments against an infinite past, the first being the "argument from the impossibility of the existence of an actual infinite", which states:
The second argument, the "argument from the impossibility of completing an actual infinite by successive addition", states:
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 Kant
in his thesis of the first antinomy
concerning time.
In the early 11th century, the Muslim physicist
, Ibn al-Haytham (Alhacen or Alhazen), discussed space perception
and its epistemological implications in his Book of Optics
(1021). His experiment
al proof of the intromission model of vision led to changes in the way the visual perception
of space was understood, contrary to the previous emission theory of vision
supported by Euclid
and Ptolemy
. 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."
position in ontology
is that time and space have existence apart from the human mind. Idealists
deny or doubt the existence of objects independent of the mind. Some anti-realists
whose ontological position is that objects outside the mind do exist, nevertheless doubt the independent existence of time and space.
Kant
, in the Critique of Pure Reason
, described time as an a priori
notion that, together with other a priori notions such as space
, allows us to comprehend sense experience. Kant denies that either space or time are substance
, entities in themselves, or learned by experience; he holds rather that both are elements of a systematic framework we use to structure our experience. Spatial measurement
s are used to quantify
how far apart object
s are, and temporal measurements are used to quantitatively compare the interval between (or duration of) events. Although
space and time are held to be transcendentally ideal in this sense, they are also empirically real, i.e. not mere illusions.
Idealist writers such as J. M. E. McTaggart
in The Unreality of Time
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 Leibniz
held that his monad
s existed, at least independently of the mind of the observer.
), began between physicists Isaac Newton
(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 experiment
s 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 reason
and the identity of indiscernibles
. 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 argument
:
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 account
. 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.
. 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 Principle
).
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 light
. 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 relativity
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 Principle
, 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 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 exactly the same type of independent existence.
, reacting to the creation of the new non-euclidean geometry
, 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-world
.
This view was developed and updated to include considerations from relativistic physics by Hans Reichenbach
. Reichenbach's conventionalism, applying to space and time, focuses around the idea of coordinative definition
.
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 wavelength
of cadmium
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.
have made up a large proportion of discussion within the philosophy of space and time, as well as the philosophy of physics
. The following is a short list of topics.
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 argument
to demonstrate that relativity predicts a block universe in which events are fixed in four dimensions.
draws a distinction between invariance upon mathematical transformation
and covariance upon transformation.
Invariance, or symmetry, applies to objects, i.e. the symmetry group
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 group
designates in which range of coordinate system
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 mechanics
will be any coordinate systems that are obtained from one another by shifts in position as well as other translations allowed by a Galilean transformation
.
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 general theory of relativity 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 general theory of relativity, unlike those 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 general theory of relativity is just the covariance group of every theory.
In these translations, a theory of space and time is seen as a 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 are incorporated in that theory, and as history progresses, more and more structure is removed.
For example, Aristotle
'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.
is known as the "hole argument
".
This is a technical mathematical argument but can be paraphrased as follows:
Define a function d as the identity function
over all elements over the manifold M, excepting a small neighbourhood
H belonging to M. Over H d comes to differ from identity by a smooth function
.
With use of this function d we can construct two mathematical model
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 foliation
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.
arises directly from two contradictory facts. Firstly, the fundamental physical laws are time-reversal invariant
; if a cinematographic film were taken of any process describable by means of the aforementioned laws and then played backwards, it would still portray a physically possible process. Secondly, our experience of time, at the macroscopic
level, is not time-reversal invariant. Glasses can fall and break, however shards of glass cannot reassemble and fly up onto 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.
view, in which the direction of time follows from an asymmetry of causation
. 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 main objections to 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 with this view is 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.
However, asymmetry of causation can be observed in a non-arbitrary way which is not metaphysical in the case of a human hand dropping a cup of water which smashes into fragments on a hard floor, spilling the liquid. In this order, the causes of the resultant pattern of cup fragments and water spill is easily attributable in terms of the trajectory of the cup, irregularities in its structure, angle of its impact on the floor, etc. However, applying the same event in reverse, it is difficult to explain why the various pieces of the cup should fly up into the human hand and reassemble precisely into the shape of a cup, or why the water should position itself entirely within the cup. The causes of the resultant structure and shape of the cup and the encapsulation of the water by the hand within the cup are not easily attributable, as neither hand nor floor can achieve such formations of the cup or water. This asymmetry is perceivable on account of two features:- i) the relationship between the agent capacities of the human hand (i.e., what it is and is not capable of & what it is for) and non-animal agency (i.e., what floors are and are not capable of and what they are for) and ii) that the pieces of cup came to possess exactly the nature and number of those of a cup before assembling. In short, such asymmetry is attributable to the relationship between temporal direction on the one hand and the implications of form and functional capacity on the other.
The application of these ideas of form and functional capacity only dictates temporal direction in relation to complex scenarios involving specific, non-metaphysical agency which is not merely dependent on human perception of time. However, this last observation in itself is not sufficient to invalidate the implications of the example for the progressive nature of time in general.
The answer from classical thermodynamics
states that while our basic physical theory is, in fact, time-reversal symmetric, thermodynamics is not. In particular, the second law of thermodynamics
states that the net entropy
of a closed system never decreases, and this explains why we often see glass breaking, but not coming back together.
But in statistical mechanics
things get more complicated. On one hand, statistical mechanics is far superior to classical thermodynamics, in that thermodynamic behavior, such as 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.
, 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 quantum mechanics are too few to account for the uniformity of macroscopic time-asymmetry and 2) it relies on the assumption that quantum mechanics is the final or correct description of physical processes.
One recent proponent of the laws solution is Tim Maudlin who argues that, the fundamental laws of physics are laws of temporal evolution (see Maudlin [2007]). However, elsewhere Maudlin argues: "[the] passage of time is an intrinsic asymmetry in the temporal structure of the world... It is the asymmetry that grounds the distinction between sequences that runs from past to future and sequences which run from future to past" [ibid, 2010 edition, p.108]. Thus it is arguably difficult to assess whether Maudlin is suggesting that the direction of time is a consequence of the laws or is itself primitive.
. 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-series
. The A-series orders events according to their being in the past, present or future, simpliciter and in comparison to each other. The B-series
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 Time
, 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.
models have shown that it is possible for theories in two different spacetime backgrounds, like AdS/CFT or T-duality
, to be equivalent.
, time is an ordering of various realities
. 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 Homer
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).
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 perdurantist
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 pre-philosophical 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 Presentists
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.
According Z-Theory time related phenomena are not more than a process caused by relative motion of an object and the conservative field that surrounds that object. Explanations and calculations given to each describing phenomena cover wide range of events from molecular to galaxy scale.
That hidden universal process causes a lot of recognizable consequences including appearance-disappearance of moving objects (including man made vehicles) following by time shift effect observing as difference in readings of the time keeping devices of the moving vehicles and the identical devices located motionlessly.
Same process is responsible for unusual object appearances outside of its natural location in space and time.
Z-Theory solves many theoretical problems derived from basic question about nature of time.
Philosophy
Philosophy is the study of general and fundamental problems, such as those connected with existence, knowledge, values, reason, mind, and language. Philosophy is distinguished from other ways of addressing such problems by its critical, generally systematic approach and its reliance on rational...
concerned with the issues surrounding the ontology
Ontology
Ontology is the philosophical study of the nature of being, existence or reality as such, as well as the basic categories of being and their relations...
, epistemology, and character of space
Space
Space 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 a boundless four-dimensional continuum...
and time
Time
Time is a part of the measuring system used to sequence events, to compare the durations of events and the intervals between them, and to quantify rates of change such as 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 philosophy
Analytic philosophy
Analytic 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
Western 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 time
Time
Time is a part of the measuring system used to sequence events, to compare the durations of events and the intervals between them, and to quantify rates of change such as the motions of objects....
was expounded by the ancient Egypt
Ancient Egypt
Ancient Egypt was an ancient civilization of Northeastern Africa, concentrated along the lower reaches of the Nile River in what is now the modern country of Egypt. Egyptian civilization coalesced around 3150 BC with the political unification of Upper and Lower Egypt under the first pharaoh...
ian thinker Ptahhotep
Ptahhotep
Ptahhotep, sometimes known as Ptahhotpe or Ptah-Hotep, was an ancient Egyptian official during the late 25th century BC and early 24th century BC.-Life:...
(c. 2650–2600 BCE), who said: "Do not lessen the time of following desire, for the wasting of time is an abomination to the spirit." The Vedas
Vedas
The Vedas are a large body of texts originating in ancient India. Composed in Vedic Sanskrit, the texts constitute the oldest layer of Sanskrit literature and the oldest scriptures of Hinduism....
, the earliest texts on Indian philosophy
Indian philosophy
India has a rich and diverse philosophical tradition dating back to ancient times. According to Radhakrishnan, the earlier Upanisads constitute "...the earliest philosophical compositions of the world."...
and Hindu philosophy
Hindu philosophy
Hindu philosophy is divided into six schools of thought, or , which accept the Vedas as supreme revealed scriptures. Three other schools do not accept the Vedas as authoritative...
dating back to the late 2nd millennium BCE, describe ancient Hindu cosmology
Hindu cosmology
In Hindu cosmology the universe is, according to Hindu mythology and Vedic cosmology, cyclically created and destroyed.-Description:The Hindu cosmology and timeline is the closest to modern scientific timelines and even more which might indicate that the Big Bang is not the beginning of everything...
, in which the universe
Universe
The Universe is commonly defined as the totality of everything that exists, including all matter and energy, the planets, stars, galaxies, and the contents of intergalactic space. Definitions and usage vary and similar terms include the cosmos, the world and nature...
goes through repeated cycles of creation, destruction and rebirth, with each cycle lasting 4,320,000 years. Ancient
Ancient philosophy
This page lists some links to ancient philosophy. In Western philosophy, the spread of Christianity through the Roman Empire marked the ending of Hellenistic philosophy and ushered in the beginnings of Medieval philosophy, whereas in Eastern philosophy, the spread of Islam through the Arab Empire...
Greek philosophers
Greek philosophy
Ancient Greek philosophy arose in the 6th century BCE and continued through the Hellenistic period, at which point Ancient Greece was incorporated in the Roman Empire...
, including Parmenides
Parmenides
Parmenides 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. The single known work of Parmenides is a poem, On Nature, which has survived only in fragmentary form. In this poem, Parmenides...
and Heraclitus
Heraclitus
Heraclitus of Ephesus was a pre-Socratic Greek philosopher, a native of the Greek city 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.
Incas regarded space and time as a single concept, named pacha .
Plato, in the Timaeus, identified time with the period of motion of the heavenly bodies, and space as that in which things come to be. Aristotle, in Book IV of his Physica defined time as the number of change with respect to before and after, and the space of an object as the innermost motionless boundary of that which surrounds it.
In Book 11 of St. Augustine's Confessions
Confessions (St. Augustine)
Confessions 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 philosophers
Medieval philosophy
Medieval philosophy is the philosophy in the era now known as medieval or the Middle Ages, the period roughly extending from the fall of the Western Roman Empire in the fifth century AD to the Renaissance in the sixteenth century...
and theologians
Theology
Theology is the systematic and rational study of religion and its influences and of the nature of religious truths, or the learned profession acquired by completing specialized training in religious studies, usually at a university or school of divinity or seminary.-Definition:Augustine of Hippo...
developed the concept of the universe having a finite past
Temporal finitism
Temporal finitism is the idea that time is finite. The context of the idea is the pre-modern era, before mathematicians had understood the concept of infinity and before physical cosmology....
with a beginning. This view was inspired by the creation belief shared by the three Abrahamic religions
Abrahamic religions
Abrahamic religions are the monotheistic faiths emphasizing and tracing their common origin to Abraham or recognizing a spiritual tradition identified with him...
: Judaism
Judaism
Judaism ) is the "religion, philosophy, and way of life" of the Jewish people...
, Christianity
Christianity
Christianity is a monotheistic religion based on the life and teachings of Jesus as presented in canonical gospels and other New Testament writings...
and Islam
Islam
Islam . The most common are and . : Arabic pronunciation varies regionally. The first vowel ranges from ~~. The second vowel ranges from ~~~...
. The Christian philosopher
Christian philosophy
Christian philosophy may refer to any development in philosophy that is characterised by coming from a Christian tradition.- Origins of Christian philosophy :...
, John Philoponus
John Philoponus
John 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. His were adopted by many including, most notably, early Muslim philosopher
Early Islamic philosophy
Early 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
Al-Kindi
' , known as "the Philosopher of the Arabs", was a Muslim Arab philosopher, mathematician, physician, and musician. Al-Kindi was the first of the Muslim peripatetic philosophers, and is unanimously hailed as the "father of Islamic or Arabic philosophy" for his synthesis, adaptation and promotion...
(Alkindus); the Jewish philosopher
Jewish philosophy
Jewish philosophy , includes all philosophy carried out by Jews, or, in relation to the religion of Judaism. Jewish philosophy, until modern Enlightenment and Emancipation, was pre-occupied with attempts to reconcile coherent new ideas into the tradition of Rabbinic Judaism; thus organizing...
, Saadia Gaon
Saadia Gaon
Saʻadiah ben Yosef Gaon was a prominent rabbi, Jewish philosopher, and exegete of the Geonic period.The first important rabbinic figure to write extensively in Arabic, he is considered the founder of Judeo-Arabic literature...
(Saadia ben Joseph); and the Muslim theologian
Kalam
ʿIlm al-Kalām is the Islamic philosophical discipline of seeking theological principles through dialectic. Kalām in Islamic practice relates to the discipline of seeking theological knowledge through debate and argument. A scholar of kalām is referred to as a mutakallim...
, Al-Ghazali
Al-Ghazali
Abu Hāmed Mohammad ibn Mohammad al-Ghazzālī , known as Algazel to the western medieval world, born and died in Tus, in the Khorasan province of Persia was a Persian Muslim theologian, jurist, philosopher, and mystic....
(Algazel). They used his 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 Kant
Immanuel Kant
Immanuel Kant was a German philosopher from Königsberg , researching, lecturing and writing on philosophy and anthropology at the end of the 18th Century Enlightenment....
in his thesis of the first antinomy
Antinomy
Antinomy 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 physicist
Islamic physics
Physics in medieval Islam is the development of physics in the medieval Islamic world in the history of physics. In the course of the expansion of the Islamic world, Muslim scholars encountered the science, mathematics, and medicine of antiquity through the works of Aristotle, Archimedes, Galen,...
, Ibn al-Haytham (Alhacen or Alhazen), discussed space perception
Depth perception
Depth perception is the visual ability to perceive the world in three dimensions and the distance of an object. Depth sensation is the ability to move accurately, or to respond consistently, based on the distances of objects in an environment....
and its epistemological implications in his Book of Optics
Book of Optics
The Book of Optics ; ; Latin: De Aspectibus or Opticae Thesaurus: Alhazeni Arabis; Italian: Deli Aspecti) is a seven-volume treatise on optics and other fields of study composed by the medieval Muslim scholar Alhazen .-See also:* Science in medieval Islam...
(1021). His experiment
Experiment
An experiment is a methodical procedure carried out with the goal of verifying, falsifying, or establishing the validity of a hypothesis. Experiments vary greatly in their goal and scale, but always rely on repeatable procedure and logical analysis of the results...
al proof of the intromission model of vision led to changes in the way the visual perception
Visual perception
Visual perception is the ability to interpret information and surroundings from the effects of 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 vision
Emission theory (vision)
Emission 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 Euclid
Euclid
Euclid , fl. 300 BC, also known as Euclid of Alexandria, was a Greek mathematician, often referred to as the "Father of Geometry". He was active in Alexandria during the reign of Ptolemy I...
and Ptolemy
Ptolemy
Claudius Ptolemy , was a Roman citizen of Egypt who wrote in Greek. He was a mathematician, astronomer, geographer, astrologer, and poet of a single epigram in the Greek Anthology. He lived in Egypt under Roman rule, and is believed to have been born in the town of Ptolemais Hermiou in the...
. 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 realistPhilosophical realism
Contemporary philosophical realism is the belief that our reality, or some aspect of it, is ontologically independent of our conceptual schemes, linguistic practices, beliefs, etc....
position in ontology
Ontology
Ontology is the philosophical study of the nature of being, existence or reality as such, as well as the basic categories of being and their relations...
is that time and space have existence apart from the human mind. Idealists
Idealism
In philosophy, idealism is the family of views which assert that reality, or reality as we can know it, is fundamentally mental, mentally constructed, or otherwise immaterial. Epistemologically, idealism manifests as a skepticism about the possibility of knowing any mind-independent thing...
deny or doubt the existence of objects independent of the mind. Some anti-realists
Anti-realism
In analytic philosophy, the term anti-realism is used to describe any position 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.
Kant
Immanuel Kant
Immanuel Kant was a German philosopher from Königsberg , researching, lecturing and writing on philosophy and anthropology at the end of the 18th Century Enlightenment....
, in the Critique of Pure Reason
Critique of Pure Reason
The Critique of Pure Reason by Immanuel Kant, first published in 1781, second edition 1787, is considered one of the most influential works in the history of philosophy. Also referred to as Kant's "first critique," it was followed by the Critique of Practical Reason and the Critique of Judgement...
, described time as an a priori
A priori and a posteriori (philosophy)
The 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 space
Space
Space 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 a boundless four-dimensional continuum...
, allows us to comprehend sense experience. Kant denies that either space or time are substance
Substance theory
Substance theory, or substance attribute theory, is an ontological theory about objecthood, positing that a substance is distinct from its properties. A thing-in-itself is a property-bearer that must be distinguished from the properties it bears....
, entities in themselves, or learned by experience; he holds rather that both are elements of a systematic framework we use to structure our experience. Spatial measurement
Measurement
Measurement is the process or the result of determining the ratio of a physical quantity, such as a length, time, temperature etc., to a unit of measurement, such as the metre, second or degree Celsius...
s are used to quantify
Quantity
Quantity is a property that can exist as a magnitude or multitude. Quantities can be compared in terms of "more" or "less" or "equal", or by assigning a numerical value in terms of a unit of measurement. Quantity is among the basic classes of things along with quality, substance, change, and relation...
how far apart object
Physical body
In 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. Although
space and time are held to be transcendentally ideal in this sense, they are also empirically real, i.e. not mere illusions.
Idealist writers such as J. M. E. McTaggart
J. M. E. McTaggart
John McTaggart was an idealist metaphysician. For most of his life McTaggart was a fellow and lecturer in philosophy at Trinity College, Cambridge. He was an exponent of the philosophy of Hegel and among the most notable of the British idealists.-Personal life:J. M. E. McTaggart was born in 1866...
in The Unreality of Time
The Unreality of Time
The Unreality of Time is the best-known philosophical work of the Cambridge idealist J. M. E. McTaggart. In the paper, first published in 1908 in Mind 17: 457-73, McTaggart argues that time is unreal because our descriptions of time are either contradictory, circular, or insufficient...
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 Leibniz
Gottfried Leibniz
Gottfried Wilhelm Leibniz was a German philosopher and mathematician. He wrote in different languages, primarily in Latin , French and German ....
held that his monad
Monadology
The Monadology is one of Gottfried Leibniz’s best known works representing his later philosophy. It is a short text which sketches in some 90 paragraphs a metaphysics of simple substances, or monads.- Text :...
s 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 (absolute), or whether they are merely orderings upon actual objects (relationalRelationism
Relationism can refer to:*In social thought, Karl Mannheim pioneered the idea of Relationism, in the development of his theories on the Sociology of Knowledge...
), began between physicists Isaac Newton
Isaac Newton
Sir Isaac Newton PRS was an English physicist, mathematician, astronomer, natural philosopher, alchemist, and theologian, who has been "considered by many to be the greatest and most influential scientist who ever lived."...
(via his spokesman, Samuel Clarke) and Gottfried Leibniz in the papers of the Leibniz-Clarke correspondence
Leibniz-Clarke correspondence
The Leibniz–Clarke correspondence was a scientific, theological and philosophical debate conducted in an exchange of letters between the German thinker Gottfried Wilhelm Leibniz and Samuel Clarke, an English supporter of Isaac Newton during the years 1715 and 1716...
.
Arguing against the absolutist position, Leibniz offers a number of thought experiment
Thought experiment
A thought experiment or Gedankenexperiment considers some hypothesis, theory, or principle for the purpose of thinking through its consequences...
s 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 reason
Principle of sufficient reason
The principle of sufficient reason states that anything that happens does so for a reason: no state of affairs can obtain, and no statement can be true unless there is sufficient reason why it should not be otherwise...
and the identity of indiscernibles
Identity of indiscernibles
The 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 argument
Bucket argument
Isaac 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 account
Relationism
Relationism can refer to:*In social thought, Karl Mannheim pioneered the idea of Relationism, in the development of his theories on the Sociology of Knowledge...
. 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
Ernst Mach was an Austrian physicist and philosopher, noted 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 Principle
Mach's principle
In 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
Albert EinsteinAlbert Einstein
Albert Einstein was a German-born theoretical physicist who developed the theory of general relativity, effecting a revolution in physics. For this achievement, Einstein is often regarded as the father of modern physics and one of the most prolific intellects in human history...
proposed that relativistics are based on the principle of relativity
Principle of relativity
In physics, the principle of relativity is the requirement that the equations describing the laws of physics have the same form in all admissible frames of reference....
. 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 light
Speed of light
The speed of light in vacuum, usually denoted by c, is a physical constant important in many areas of physics. Its value is 299,792,458 metres per second, a figure that is exact since the length of the metre is defined from this constant and the international standard for time...
. 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 relativity
Special relativity
Special relativity is the physical theory of measurement in an inertial frame of reference proposed in 1905 by Albert Einstein in the paper "On the Electrodynamics of Moving Bodies".It generalizes Galileo's...
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 Principle
Equivalence principle
In the physics of general relativity, the equivalence principle is any of 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 geodesic
Geodesic (general relativity)
In 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, non-gravitational, 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
Free fall
Free fall is any motion of a body where gravity is the only force acting upon it, at least initially. These conditions produce an inertial trajectory so long as gravity remains the only force. Since this definition does not specify velocity, it also applies to objects initially moving upward...
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 exactly the 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 PoincaréHenri Poincaré
Jules Henri Poincaré was a French mathematician, theoretical physicist, engineer, and a philosopher of science...
, reacting to the creation of the new non-euclidean geometry
Non-Euclidean geometry
Non-Euclidean geometry is the term used to refer to two specific geometries which are, loosely speaking, obtained by negating the Euclidean parallel postulate, namely hyperbolic and elliptic geometry. This is one term which, for historical reasons, has a meaning in mathematics which is much...
, 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-world
Sphere-world
The idea of a sphere-world was constructed by Henri Poincaré who, 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 Reichenbach
Hans Reichenbach
Hans 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 definition
Coordinative definition
A 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 wavelength
Wavelength
In 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 cadmium
Cadmium
Cadmium is a chemical element with the symbol Cd and atomic number 48. This soft, bluish-white metal is chemically similar to the two other stable 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 spacetimeSpacetime
In physics, spacetime is any mathematical model that combines space and time into a single continuum. Spacetime is usually interpreted with space as being three-dimensional and time playing the role of a fourth dimension that is of a different sort from the spatial dimensions...
have made up a large proportion of discussion within the philosophy of space and time, as well as the philosophy of physics
Philosophy of physics
In 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
Special relativity is the physical theory of measurement in an inertial frame of reference proposed in 1905 by Albert Einstein in the paper "On the Electrodynamics of Moving Bodies".It generalizes Galileo's...
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 argument
Rietdijk-Putnam Argument
In philosophy, the Rietdijk–Putnam argument, named after C. W. Rietdijk and Hilary Putnam, uses 20th-century findings in physics—specifically in special relativity—to support the philosophical position known as four-dimensionalism....
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 (philosopher)
Michael Friedman is a philosopher of science interested in Immanuel Kant and the post-analytic movement in philosophy. Friedman earned his A.B from Queen's College in New York and his PhD from Princeton University. He is Frederick P. Rehmus Family Professor of Humanities at Stanford University...
draws a distinction between invariance upon mathematical transformation
Transformation (mathematics)
In 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 that preserves this structure.Examples include...
and covariance upon transformation.
Invariance, or symmetry, applies to objects, i.e. the symmetry group
Symmetry group
The 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 group
Group (mathematics)
In 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 system
Coordinate system
In geometry, a coordinate system is a system which uses one or more numbers, or coordinates, to uniquely determine the position of a point or other geometric element. The order of the coordinates is significant and they are sometimes identified by their position in an ordered tuple and sometimes by...
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 mechanics
Classical mechanics
In physics, classical mechanics is one of the two major sub-fields of mechanics, which is concerned with the set of physical laws describing the motion of bodies under the action of a system of forces...
will be any coordinate systems that are obtained from one another by shifts in position as well as other translations allowed by a Galilean transformation
Galilean transformation
The 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 general theory of relativity 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 general theory of relativity, unlike those 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 general theory of relativity 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 manifold
Manifold
In mathematics , a manifold is a topological space that on a small enough scale resembles the Euclidean space of a specific 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 are incorporated in that theory, and as history progresses, more and more structure is removed.
For example, Aristotle
Aristotle
Aristotle was a Greek philosopher and polymath, a student of Plato and teacher of Alexander the Great. His writings cover many subjects, including physics, metaphysics, poetry, theater, music, logic, rhetoric, linguistics, politics, government, ethics, biology, and zoology...
'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 general theory of relativity, the traditional debate between absolutism and relationalism has been shifted to whether or not spacetime is a substance, since the general theory of relativity largely rules out the existence of, e.g., absolute positions. One powerful argument against spacetime substantivalism, offered by John EarmanJohn Earman
John Earman is a philosopher of physics. He is currently an emeritus 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 was president of the Philosophy of...
is known as the "hole argument
Hole argument
In general relativity, the hole argument is a "paradox" which much troubled Albert Einstein while developing his famous field equation.It is incorrectly interpreted by some philosophers as an argument against manifold substantialism, a doctrine that the manifold of events in spacetime are a...
".
This is a technical mathematical argument but can be paraphrased as follows:
Define a function d as the identity function
Identity function
In 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 neighbourhood
Neighbourhood (mathematics)
In 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 function
Smooth function
In 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 model
Mathematical model
A mathematical model is a description of a system using mathematical concepts and language. The process of developing a mathematical model is termed mathematical modeling. Mathematical models are used not only in the natural sciences and engineering disciplines A mathematical model is a...
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 foliation
Foliation
In 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 timeArrow of time
The arrow of time, or time’s arrow, is a term coined in 1927 by the British astronomer Arthur Eddington to describe the "one-way direction" or "asymmetry" of time...
arises directly from two contradictory facts. Firstly, the fundamental physical laws are time-reversal invariant
Invariant (physics)
In mathematics and theoretical physics, an invariant is a property of a system which remains unchanged under some transformation.-Examples:In the current era, the immobility of polaris under the diurnal motion of the celestial sphere is a classical illustration of physical invariance.Another...
; if a cinematographic film were taken of any process describable by means of the aforementioned laws and then played backwards, it would still portray a physically possible process. Secondly, our experience of time, at the macroscopic
Macroscopic
The macroscopic scale is the length scale on which objects or processes are of a size which is measurable and observable by the naked eye.When applied to phenomena and abstract objects, the macroscopic scale describes existence in the world as we perceive it, often in contrast to experiences or...
level, is not time-reversal invariant. Glasses can fall and break, however shards of glass cannot reassemble and fly up onto 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
Metaphysics is a branch of philosophy concerned with explaining the fundamental nature of being and the world, although the term is not easily defined. Traditionally, metaphysics attempts to answer two basic questions in the broadest possible terms:...
view, in which the direction of time follows from an asymmetry of causation
Causality
Causality is the relationship between an event and a second event , where the second event is understood as a 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 main objections to 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 with this view is 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.
However, asymmetry of causation can be observed in a non-arbitrary way which is not metaphysical in the case of a human hand dropping a cup of water which smashes into fragments on a hard floor, spilling the liquid. In this order, the causes of the resultant pattern of cup fragments and water spill is easily attributable in terms of the trajectory of the cup, irregularities in its structure, angle of its impact on the floor, etc. However, applying the same event in reverse, it is difficult to explain why the various pieces of the cup should fly up into the human hand and reassemble precisely into the shape of a cup, or why the water should position itself entirely within the cup. The causes of the resultant structure and shape of the cup and the encapsulation of the water by the hand within the cup are not easily attributable, as neither hand nor floor can achieve such formations of the cup or water. This asymmetry is perceivable on account of two features:- i) the relationship between the agent capacities of the human hand (i.e., what it is and is not capable of & what it is for) and non-animal agency (i.e., what floors are and are not capable of and what they are for) and ii) that the pieces of cup came to possess exactly the nature and number of those of a cup before assembling. In short, such asymmetry is attributable to the relationship between temporal direction on the one hand and the implications of form and functional capacity on the other.
The application of these ideas of form and functional capacity only dictates temporal direction in relation to complex scenarios involving specific, non-metaphysical agency which is not merely dependent on human perception of time. However, this last observation in itself is not sufficient to invalidate the implications of the example for the progressive nature of time in general.
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 thermodynamics
Thermodynamics
Thermodynamics is a physical science that studies the effects on material bodies, and on radiation in regions of space, of transfer of heat and of work done on or by the bodies or radiation...
states that while our basic physical theory is, in fact, time-reversal symmetric, thermodynamics is not. In particular, the second law of thermodynamics
Second law of thermodynamics
The second law of thermodynamics is an expression of the tendency that over time, differences in temperature, pressure, and chemical potential equilibrate in an isolated physical system. From the state of thermodynamic equilibrium, the law deduced the principle of the increase of entropy and...
states that the net entropy
Entropy
Entropy is a thermodynamic property that can be used to determine the energy available for useful work in a thermodynamic process, such as in energy conversion devices, engines, or machines. Such devices can only be driven by convertible energy, and have a theoretical maximum efficiency when...
of a closed system never decreases, and this explains why we often see glass breaking, but not coming back together.
But in statistical mechanics
Statistical mechanics
Statistical mechanics or statistical thermodynamicsThe terms statistical mechanics and statistical thermodynamics are used interchangeably...
things get more complicated. On one hand, statistical mechanics is far superior to classical thermodynamics, in that thermodynamic behavior, such as 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
Quantum mechanics, also known as quantum physics or quantum theory, is a branch of physics providing a mathematical description of much of the dual particle-like and wave-like behavior and interactions of energy and matter. It departs from classical mechanics primarily at the atomic and subatomic...
, 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 quantum mechanics are too few to account for the uniformity of macroscopic time-asymmetry and 2) it relies on the assumption that quantum mechanics is the final or correct description of physical processes.
One recent proponent of the laws solution is Tim Maudlin who argues that, the fundamental laws of physics are laws of temporal evolution (see Maudlin [2007]). However, elsewhere Maudlin argues: "[the] passage of time is an intrinsic asymmetry in the temporal structure of the world... It is the asymmetry that grounds the distinction between sequences that runs from past to future and sequences which run from future to past" [ibid, 2010 edition, p.108]. Thus it is arguably difficult to assess whether Maudlin is suggesting that the direction of time is a consequence of the laws or is itself primitive.
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. McTaggartJ. M. E. McTaggart
John McTaggart was an idealist metaphysician. For most of his life McTaggart was a fellow and lecturer in philosophy at Trinity College, Cambridge. He was an exponent of the philosophy of Hegel and among the most notable of the British idealists.-Personal life:J. M. E. McTaggart was born in 1866...
. 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-series
A-series and B-series
A-series and B-series are two different descriptions of the temporal ordering relation among events. The two series differ principally in their use of tense to describe the temporal relation between events...
. The A-series orders events according to their being in the past, present or future, simpliciter and in comparison to each other. The B-series
A-series and B-series
A-series and B-series are two different descriptions of the temporal ordering relation among events. The two series differ principally in their use of tense to describe the temporal relation between events...
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 Time
The Unreality of Time
The Unreality of Time is the best-known philosophical work of the Cambridge idealist J. M. E. McTaggart. In the paper, first published in 1908 in Mind 17: 457-73, McTaggart argues that time is unreal because our descriptions of time are either contradictory, circular, or insufficient...
, 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
Quantum field theory provides a theoretical framework for constructing quantum mechanical models of systems classically parametrized by an infinite number of dynamical degrees of freedom, that is, fields and many-body systems. It is the natural and quantitative language of particle physics and...
models have shown that it is possible for theories in two different spacetime backgrounds, like AdS/CFT or T-duality
T-duality
T-duality is a symmetry of quantum field theories with differing classical descriptions, of which the relationship between small and large distances in various string theories is a special case. Discussion of the subject originated in a paper by T. S. Buscher and was further developed by Martin...
, to be equivalent.
Presentism and Eternalism
According to PresentismPresentism (philosophy of time)
Saint Augustine proposed that the present is a knife edge between the past and the future and could not contain any extended period of time. This seems evident because, if the present is extended, it must have separate parts - but these must be simultaneous if they are truly part of the present...
, time is an ordering of various realities
Reality
In philosophy, reality is the state of things as they actually exist, rather than as they may appear or might be imagined. In a wider definition, reality includes everything that is and has been, whether or not it is observable or comprehensible...
. 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 Homer
Homer
In the Western classical tradition Homer , is the author of the Iliad and the Odyssey, and is revered as the greatest ancient Greek epic poet. These epics lie at the beginning of the Western canon of literature, and have had an enormous influence on the history of literature.When he lived is...
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
Endurantism 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 perdurantist
Perdurantism
Perdurantism or perdurance theory is a philosophical theory of persistence and identity. The perdurantist view is that an individual has distinct temporal parts throughout its existence....
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 pre-philosophical 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 Presentists
Presentism (philosophy of time)
Saint Augustine proposed that the present is a knife edge between the past and the future and could not contain any extended period of time. This seems evident because, if the present is extended, it must have separate parts - but these must be simultaneous if they are truly part of the present...
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.
Space and Time in Z-Theory
Among many theories mentioned above there is one new theory that uses concept of space and time. It supports basic principles of physics but uses conservative fields as primary cause of describing phenomena.According Z-Theory time related phenomena are not more than a process caused by relative motion of an object and the conservative field that surrounds that object. Explanations and calculations given to each describing phenomena cover wide range of events from molecular to galaxy scale.
That hidden universal process causes a lot of recognizable consequences including appearance-disappearance of moving objects (including man made vehicles) following by time shift effect observing as difference in readings of the time keeping devices of the moving vehicles and the identical devices located motionlessly.
Same process is responsible for unusual object appearances outside of its natural location in space and time.
Z-Theory solves many theoretical problems derived from basic question about nature of time.
See also
- Eternalism (philosophy of time)
- Presentism (philosophy of time)Presentism (philosophy of time)Saint Augustine proposed that the present is a knife edge between the past and the future and could not contain any extended period of time. This seems evident because, if the present is extended, it must have separate parts - but these must be simultaneous if they are truly part of the present...
- Arrow of timeArrow of timeThe arrow of time, or time’s arrow, is a term coined in 1927 by the British astronomer Arthur Eddington to describe the "one-way direction" or "asymmetry" of time...
- MetaphysicsMetaphysicsMetaphysics is a branch of philosophy concerned with explaining the fundamental nature of being and the world, although the term is not easily defined. Traditionally, metaphysics attempts to answer two basic questions in the broadest possible terms:...
- Time travelTime travelTime travel is the concept of moving between different points in time in a manner analogous to moving between different points in space. Time travel could hypothetically involve moving backward in time to a moment earlier than the starting point, or forward to the future of that point without the...
in science and Time travel in fictionTime 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, to experience the future, or the past.-Literature:... - Zeno's paradoxesZeno's paradoxesZeno's paradoxes are a set of problems generally thought to have been devised by Greek philosopher 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...
- Identity and changeIdentity and changeThe relationship between identity and change in the philosophical field of metaphysics seems, at first glance, deceptively simple, and belies the complexity of the issues involved. This article explores "the problem of change and identity".- Change :...
- Temporal partsTemporal partsTemporal parts is a concept used in contemporary metaphysics in the debate over the persistence of material objects. Objects typically have parts that exist in space—a human body, for example, has spatial parts like hands, feet, and legs. Some metaphysicians believe objects have temporal parts as...
- PerdurantismPerdurantismPerdurantism or perdurance theory is a philosophical theory of persistence and identity. The perdurantist view is that an individual has distinct temporal parts throughout its existence....
- EndurantismEndurantismEndurantism 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...
- Milič Čapek
- Quentin SmithQuentin SmithQuentin Persifor Smith is an American contemporary philosopher, scholar and professor of philosophy at Western Michigan University in Kalamazoo, Michigan. He has worked in the philosophy of time, philosophy of language, philosophy of physics and philosophy of religion...
- William Lane CraigWilliam Lane CraigWilliam Lane Craig is an American analytic philosopher, philosophical theologian, and Christian apologist. He is known for his work on the philosophy of time and the philosophy of religion, specifically the existence of God and the defense of Christian theism...
- Alfred North WhiteheadAlfred North WhiteheadAlfred North Whitehead, OM FRS was an English mathematician who became a philosopher. He wrote on algebra, logic, foundations of mathematics, philosophy of science, physics, metaphysics, and education...
External links
- Stanford Encyclopedia of PhilosophyStanford Encyclopedia of PhilosophyThe 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...
:- "Time" by Ned Markosian;
- "Being and Becoming in Modern Physics" by Steven Savitt;
- "Absolute and Relational Theories of Space and Motion" by Nick Huggett and Carl Hoefer.
- Internet Encyclopedia of PhilosophyInternet Encyclopedia of PhilosophyThe 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...
: "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 presentismPresentism (philosophy of time)Saint Augustine proposed that the present is a knife edge between the past and the future and could not contain any extended period of time. This seems evident because, if the present is extended, it must have separate parts - but these must be simultaneous if they are truly part of the present...
and four-dimensionalism. - CEITT - Time and Temporality Research Center. "Time and Temporality".
- http://www.exactspent.com/philosophy_of_space_and_time.htm and related subjects
- "Gods and the Universe in Buddhist Perspective, Essays on Buddhist Cosmology" by Francis Story.