Time
Common symbols	t
SI unit	second (s)
Other units	seeunit of time
Dimension	${\displaystyle \mathsf{T}}$

Time
Major concepts Past Present Future Eternity of the world
Fields of study Archaeology Chronology History Horology Metrology Paleontology Futurology
Philosophy Presentism Eternalism Event Fatalism
Religion Mythology Creation End time Day of Judgement Immortality Afterlife Reincarnation Kalachakra
Measurement Standards ISO 8601 Metric Hexadecimal
Science Naturalism Chronobiology Cosmogony Evolution Radiometric dating Ultimate fate of the universe Time in physics
Related topics Motion Space Spacetime Time travel
v t e

Inphysics,time is defined by itsmeasurement: time is what aclock reads.^[1] In classical, non-relativistic physics, it is ascalar quantity (often denoted by the symbol${\displaystyle t}$) and, likelength,mass, andcharge, is usually described as afundamental quantity. Time can be combined mathematically with otherphysical quantities toderive other concepts such asmotion,kinetic energy and time-dependentfields.Timekeeping is a complex of technological and scientific issues, and part of the foundation ofrecordkeeping.

Before there were clocks, time was measured by those physical processes^[2] which were understandable to each epoch of civilization:^[3]

• the first appearance (see:heliacal rising) ofSirius to mark theflooding of the Nile each year^[3]
• the periodic succession ofnight andday, seemingly eternally^[4]
• the position on the horizon of the first appearance of the sun at dawn^[5]
• the position of the sun in the sky^[6]
• the marking of the moment ofnoontime during the day^[7]
• the length of the shadow cast by agnomon^[8]

Eventually,^[9][10] it became possible to characterize the passage of time with instrumentation, usingoperational definitions. Simultaneously, our conception of time has evolved, as shown below.^[11]

In theInternational System of Units (SI), the unit of time is thesecond (symbol: s). It has been defined since 1967 as "the duration of9192631770periods of theradiation corresponding to the transition between the twohyperfine levels of theground state of thecaesium 133 atom", and is anSI base unit.^[12] This definition is based on the operation of a caesiumatomic clock. These clocks became practical for use as primary reference standards after about 1955, and have been in use ever since.

TheUTCtimestamp in use worldwide is an atomic time standard. The relative accuracy of such a time standard is currently on the order of 10^−15[13] (corresponding to 1 second in approximately 30 million years). The smallest time step considered theoretically observable is called thePlanck time, which is approximately 5.391×10⁻⁴⁴ seconds – many orders of magnitude below the resolution of current time standards.

Thecaesium atomic clock became practical after 1950, when advances in electronics enabled reliable measurement of the microwave frequencies it generates. As further advances occurred,atomic clock research has progressed to ever-higher frequencies, which can provide higher accuracy and higher precision. Clocks based on these techniques have been developed, but are not yet in use as primary reference standards.

Galileo,Newton, and most people up until the 20th century thought that time was the same for everyone everywhere. This is the basis fortimelines, where time is aparameter. The modern understanding of time is based onEinstein'stheory of relativity, in which rates of time run differently depending on relative motion, andspace and time are merged intospacetime, where we live on aworld line rather than a timeline. In this view time is acoordinate. According to the prevailingcosmologicalmodel of theBig Bang theory, time itself began as part of the entireUniverse about 13.8 billion years ago.

In order to measure time, one can record the number of occurrences (events) of someperiodicphenomenon. The regular recurrences of theseasons, themotions of thesun,moon andstars were noted and tabulated for millennia, before thelaws of physics were formulated. The sun was the arbiter of the flow of time, buttime was known only to thehour formillennia, hence, the use of thegnomon was known across most of the world, especiallyEurasia, and at least as far southward as the jungles ofSoutheast Asia.^[15]

In particular, the astronomical observatories maintained for religious purposes became accurate enough to ascertain the regular motions of the stars, and even some of the planets.

At first,timekeeping was done by hand by priests, and then for commerce, with watchmen to note time as part of their duties.The tabulation of theequinoxes, thesandglass, and thewater clock became more and more accurate, and finally reliable. For ships at sea,marine sandglasses were used. These devices allowed sailors to call the hours, and to calculate sailing velocity.

Richard of Wallingford (1292–1336), abbot of St. Albans Abbey, famously built amechanical clock as an astronomicalorrery about 1330.^[16][17]

By the time of Richard of Wallingford, the use ofratchets andgears allowed the towns of Europe to create mechanisms to display the time on their respective town clocks; by the time of the scientific revolution, the clocks became miniaturized enough for families to share a personal clock, or perhaps a pocket watch. At first, only kings could afford them.Pendulum clocks were widely used in the 18th and 19th century. They have largely been replaced in general use byquartz anddigital clocks.Atomic clocks can theoretically keep accurate time for millions of years. They are appropriate forstandards and scientific use.

In 1583,Galileo Galilei (1564–1642) discovered that apendulum's harmonic motion has a constant period, which he learned by timing the motion of a swaying lamp inharmonic motion atmass at the cathedral ofPisa, with hispulse.^[18]

In hisTwo New Sciences (1638),Galileo used awater clock to measure the time taken for a bronze ball to roll a known distance down aninclined plane; this clock was:^[19]

...a large vessel of water placed in an elevated position; to the bottom of this vessel was soldered a pipe of small diameter giving a thin jet of water, which we collected in a small glass during the time of each descent, whether for the whole length of the channel or for a part of its length; the water thus collected was weighed, after each descent, on a very accurate balance; the differences and ratios of these weights gave us the differences and ratios of the times, and this with such accuracy that although the operation was repeated many, many times, there was no appreciable discrepancy in the results.

Galileo's experimental setup to measure the literalflow of time, in order to describe the motion of a ball, precededIsaac Newton's statement in hisPrincipia, "I do not definetime,space,place andmotion, as being well known to all."^[20]

TheGalilean transformations assume that time is the same for allreference frames.

In or around 1665, whenIsaac Newton (1643–1727) derived the motion of objects falling undergravity, the first clear formulation formathematical physics of a treatment of time began: linear time, conceived as auniversal clock.

Absolute, true, and mathematical time, of itself, and from its own nature flows equably without regard to anything external, and by another name is called duration: relative, apparent, and common time, is some sensible and external (whether accurate or unequable) measure of duration by the means of motion, which is commonly used instead of true time; such as an hour, a day, a month, a year.^[21]

Thewater clock mechanism described by Galileo was engineered to providelaminar flow of the water during the experiments, thus providing a constant flow of water for the durations of the experiments, and embodying what Newton calledduration.

In this section, the relationships listed below treat time as a parameter which serves as an index to the behavior of the physical system under consideration. Because Newton'sfluents treat alinear flow of time (what he calledmathematical time), time could be considered to be a linearly varying parameter, an abstraction of the march of the hours on the face of a clock. Calendars and ship's logs could then be mapped to the march of the hours, days, months, years and centuries.

By 1798,Benjamin Thompson (1753–1814) had discovered that work could be transformed toheat without limit – a precursor of the conservation of energy or

• 1st law of thermodynamics

In 1824Sadi Carnot (1796–1832) scientifically analyzed thesteam engine with hisCarnot cycle, an abstract engine.Rudolf Clausius (1822–1888) noted a measure of disorder, orentropy, which affects the continually decreasing amount of free energy which is available to a Carnot engine in the:

• 2nd law of thermodynamics

Thus the continual march of a thermodynamic system, from lesser to greater entropy, at any given temperature, defines anarrow of time. In particular,Stephen Hawking identifies three arrows of time:^[22]

• Psychological arrow of time – our perception of an inexorable flow.
• Thermodynamic arrow of time – distinguished by the growth ofentropy.
• Cosmological arrow of time – distinguished by the expansion of the universe.

With time, entropy increases in an isolated thermodynamic system. In contrast,Erwin Schrödinger (1887–1961) pointed out thatlife depends on a"negative entropy flow".^[23]Ilya Prigogine (1917–2003) stated that other thermodynamic systems which, like life, are also far from equilibrium, can also exhibit stable spatio-temporal structures that reminisce life. Soon afterward, theBelousov–Zhabotinsky reactions^[24] were reported, which demonstrate oscillating colors in a chemical solution.^[25] These nonequilibrium thermodynamic branches reach abifurcation point, which is unstable, and another thermodynamic branch becomes stable in its stead.^[26]

In 1864,James Clerk Maxwell (1831–1879) presented a combined theory ofelectricity andmagnetism. He combined all the laws then known relating to those two phenomenon into four equations. These equations are known asMaxwell's equations forelectromagnetism; they allow for solutions in the form of electromagnetic waves and propagate at a fixed speed,c, regardless of the velocity of the electric charge that generated them.

The fact that light is predicted to always travel at speedc would be incompatible with Galilean relativity if Maxwell's equations were assumed to hold in anyinertial frame (reference frame with constant velocity), because the Galilean transformations predict the speed to decrease (or increase) in the reference frame of an observer traveling parallel (or antiparallel) to the light.

It was expected that there was one absolute reference frame, that of theluminiferous aether, in which Maxwell's equations held unmodified in the known form.

TheMichelson–Morley experiment failed to detect any difference in the relative speed of light due to the motion of the Earth relative to the luminiferous aether, suggesting that Maxwell's equations did, in fact, hold in all frames. In 1875,Hendrik Lorentz (1853–1928) discoveredLorentz transformations, which left Maxwell's equations unchanged, allowing Michelson and Morley's negative result to be explained.Henri Poincaré (1854–1912) noted the importance of Lorentz's transformation and popularized it. In particular, the railroad car description can be found inScience and Hypothesis,^[27] which was published before Einstein's articles of 1905.

The Lorentz transformation predictedspace contraction andtime dilation; until 1905, the former was interpreted as a physical contraction of objects moving with respect to the aether, due to the modification of the intermolecular forces (of electric nature), while the latter was thought to be just a mathematical stipulation.^{[citation needed]}

Albert Einstein's 1905special relativity challenged the notion of absolute time, and could only formulate a definition ofsynchronization for clocks that mark a linear flow of time:

If at the point A of space there is a clock, an observer at A can determine the time values of events in the immediate proximity of A by finding the positions of the hands which are simultaneous with these events. If there is at the point B of space another clock in all respects resembling the one at A, it is possible for an observer at B to determine the time values of events in the immediate neighbourhood of B.

But it is not possible without further assumption to compare, in respect of time, an event at A with an event at B. We have so far defined only an "A time" and a "B time".

We have not defined a common "time" for A and B, for the latter cannot be defined at all unless we establishby definition that the "time" required by light to travel from A to B equals the "time" it requires to travel from B to A. Let a ray of light start at the "A time"t_A from A towards B, let it at the "B time"t_B be reflected at B in the direction of A, and arrive again at A at the “A time”t′_A.

In accordance with definition the two clocks synchronize if

${\displaystyle t_{\text{B}}-t_{\text{A}}=t_{\text{A}}^{\prime }-t_{\text{B}}\text{.}}$

We assume that this definition of synchronism is free from contradictions, and possible for any number of points; and that the following relations are universally valid:—

1. If the clock at B synchronizes with the clock at A, the clock at A synchronizes with the clock at B.
2. If the clock at A synchronizes with the clock at B and also with the clock at C, the clocks at B and C also synchronize with each other.

Einstein showed that if the speed of light is not changing between reference frames, space and time must be so that the moving observer will measure the same speed of light as the stationary one because velocity isdefined by space and time:

${\displaystyle \mathbf{v}=\frac{d\mathbf{r}}{dt}\text{,}}$ wherer is position andt is time.

Indeed, the Lorentz transformation (for two reference frames in relative motion, whosex axis is directed in the direction of the relative velocity)

can be said to "mix" space and time in a way similar to the way a Euclidean rotation around thez axis mixesx andy coordinates. Consequences of this includerelativity of simultaneity.

More specifically, the Lorentz transformation is a hyperbolic rotation

which is a change of coordinates in the four-dimensionalMinkowski space, a dimension of which isct. (InEuclidean space an ordinary rotation

is the corresponding change of coordinates.) The speed of lightc can be seen as just a conversion factor needed because we measure the dimensions of spacetime in different units; since themetre is currently defined in terms of the second, it has theexact value of299 792 458 m/s. We would need a similar factor in Euclidean space if, for example, we measured width in nautical miles and depth in feet. In physics, sometimesunits of measurement in whichc = 1 are used to simplify equations.

Time in a "moving" reference frame is shown to run more slowly than in a "stationary" one by the following relation (which can be derived by the Lorentz transformation by putting ∆x′ = 0, ∆τ = ∆t′):

${\displaystyle \mathrm{\Delta }t=\frac{\mathrm{\Delta }\tau }{\sqrt{1-v^2/c^2}}}$

where:

• ${\displaystyle \mathrm{\Delta }\tau }$ is the time between two events as measured in the moving reference frame in which they occur at the same place (e.g. two ticks on a moving clock); it is called theproper time between the two events;
• ${\displaystyle \mathrm{\Delta }}$t is the time between these same two events, but as measured in the stationary reference frame;
• v is the speed of the moving reference frame relative to the stationary one;
• c is thespeed of light.

Moving objects therefore are said toshow a slower passage of time. This is known astime dilation.

These transformations are only valid for two frames atconstant relative velocity. Naively applying them to other situations gives rise to suchparadoxes as thetwin paradox.

That paradox can be resolved using for instance Einstein'sGeneral theory of relativity, which usesRiemannian geometry, geometry in accelerated, noninertial reference frames. Employing themetric tensor which describesMinkowski space:

${\displaystyle \left[(d{x}^1{)}^2+(d{x}^2{)}^2+(d{x}^3{)}^2-c(dt{)}^2)\right],}$

Einstein developed a geometric solution to Lorentz's transformation that preservesMaxwell's equations. Hisfield equations give an exact relationship between the measurements of space and time in a given region ofspacetime and the energy density of that region.

Einstein's equations predict that time should be altered by the presence ofgravitational fields (see theSchwarzschild metric):

${\displaystyle T=\frac{dt}{\sqrt{\left(1-\frac{2GM}{r{c}^2}\right)d{t}^2-\frac{1}{c^2}{\left(1-\frac{2GM}{r{c}^2}\right)}^{-1}d{r}^2-\frac{r^2}{c^2}d{\theta }^2-\frac{r^2}{c^2}{\sin }^2\theta d{\varphi }^2}}}$

where:

• ${\displaystyle T}$ is thegravitational time dilation of an object at a distance of${\displaystyle r}$.
• ${\displaystyle dt}$ is the change in coordinate time, or the interval of coordinate time.
• ${\displaystyle G}$ is thegravitational constant
• ${\displaystyle M}$ is themass generating the field
• ${\displaystyle \sqrt{\left(1-\frac{2GM}{r{c}^2}\right)d{t}^2-\frac{1}{c^2}{\left(1-\frac{2GM}{r{c}^2}\right)}^{-1}d{r}^2-\frac{r^2}{c^2}d{\theta }^2-\frac{r^2}{c^2}{\sin }^2\theta d{\varphi }^2}}$ is the change inproper time${\displaystyle d\tau }$, or the interval ofproper time.

Or one could use the following simpler approximation:

${\displaystyle \frac{dt}{d\tau }=\frac{1}{\sqrt{1-\left(\frac{2GM}{r{c}^2}\right)}}.}$

That is, the stronger the gravitational field (and, thus, the larger theacceleration), the more slowly time runs. The predictions of time dilation are confirmed byparticle acceleration experiments andcosmic ray evidence, where moving particlesdecay more slowly than their less energetic counterparts. Gravitational time dilation gives rise to the phenomenon ofgravitational redshift andShapiro signal travel time delays near massive objects such as the sun. TheGlobal Positioning System must also adjust signals to account for this effect.

According to Einstein's general theory of relativity, a freely moving particle traces a history in spacetime that maximises its proper time. This phenomenon is also referred to as the principle of maximal aging, and was described byTaylor andWheeler as:^[29]

"Principle of Extremal Aging: The path a free object takes between two events in spacetime is the path for which the time lapse between these events, recorded on the object's wristwatch, is an extremum."

Einstein's theory was motivated by the assumption that every point in the universe can be treated as a 'center', and that correspondingly, physics must act the same in all reference frames. His simple and elegant theory shows that time is relative to aninertial frame. In an inertial frame,Newton's first law holds; it has its own local geometry, and therefore itsown measurements of space and time;there is no 'universal clock'. An act of synchronization must be performed between two systems, at the least.

There is a time parameter in the equations ofquantum mechanics. TheSchrödinger equation^[30] is

${\displaystyle H(t)|\psi (t)⟩=i\hslash \frac{\mathrm{\partial }}{\mathrm{\partial }t}|\psi (t)⟩}$

One solution can be

${\displaystyle |{\psi }_e(t)⟩=e^{-iHt/\hslash }|{\psi }_e(0)⟩}$.

where${\displaystyle e^{-iHt/\hslash }}$is called thetime evolution operator, andH is theHamiltonian.

But theSchrödinger picture shown above is equivalent to theHeisenberg picture, which enjoys a similarity to the Poisson brackets of classical mechanics. ThePoisson brackets are superseded by a nonzerocommutator, say [H,A] forobservableA, and Hamiltonian H:

${\displaystyle \frac{d}{dt}A=(i\hslash {)}^{-1}[A,H]+{\left(\frac{\mathrm{\partial }A}{\mathrm{\partial }t}\right)}_{\mathrm{c}\mathrm{l}\mathrm{a}\mathrm{s}\mathrm{s}\mathrm{i}\mathrm{c}\mathrm{a}\mathrm{l}}.}$

This equation denotes anuncertainty relation in quantum physics. For example, withtime (the observableA), the energyE (from the HamiltonianH) gives:

${\displaystyle \mathrm{\Delta }E\mathrm{\Delta }T\ge \frac{\hslash }{2}}$

where

• ${\displaystyle \mathrm{\Delta }E}$ is the uncertainty in energy
• ${\displaystyle \mathrm{\Delta }T}$ is the uncertainty in time
• ${\displaystyle \hslash }$ is the reducedPlanck constant

The moreprecisely one measures the duration of asequence of events, the less precisely one can measure the energy associated with that sequence, and vice versa. This equation is different from the standard uncertainty principle, because time is not anoperator in quantum mechanics.

Correspondingcommutator relations also hold for momentump and positionq, which areconjugate variables of each other, along with a corresponding uncertainty principle in momentum and position, similar to the energy and time relation above.

Quantum mechanics explains the properties of theperiodic table of theelements. Starting withOtto Stern's andWalter Gerlach's experiment withmolecular beams in a magnetic field,Isidor Rabi (1898–1988), was able tomodulate the magnetic resonance of the beam. In 1945 Rabi then suggested that this technique be the basis of a clock^[31] using theresonant frequency of an atomic beam.In 2021 Jun Ye of JILA in Boulder Colorado observedtime dilatation in the difference in the rate of optical lattice clock ticks at the top of a cloud of strontium atoms, than at the bottom of that cloud, a column one millimeter tall, under the influence of gravity.^[32]

One could say that time is aparameterization of adynamical system that allows the geometry of the system to be manifested and operated on. It has been asserted thattime is an implicit consequence ofchaos (i.e.nonlinearity/irreversibility): thecharacteristic time, or rate ofinformation entropy production, of asystem.Mandelbrot introducesintrinsic time in his bookMultifractals and1/f noise.

Khemani, Moessner, and Sondhi define a time crystal as a "stable, conservative, macroscopic clock".^[33]: 7

Signalling is one application of theelectromagnetic waves described above. In general, a signal is part ofcommunication between parties and places. One example might be ayellow ribbon tied to a tree, or the ringing of achurch bell. A signal can be part of aconversation, which involves aprotocol. Another signal might be the position of the hour hand on a town clock or a railway station. An interested party might wish to view that clock, to learn the time. See:Time ball, an early form ofTime signal.

We as observers can still signal different parties and places as long as we live within theirpastlight cone. But we cannot receive signals from those parties and places outside ourpast light cone.

Along with the formulation of the equations for the electromagnetic wave, the field oftelecommunication could be founded.

In 19th centurytelegraphy,electrical circuits, some spanningcontinents andoceans, could transmitcodes - simple dots, dashes and spaces. From this, a series of technical issues have emerged; seeCategory:Synchronization. But it is safe to say that our signalling systems can be only approximatelysynchronized, aplesiochronous condition, from whichjitter need be eliminated.

That said,systemscan be synchronized (at an engineering approximation), using technologies likeGPS. The GPS satellites must account for the effects of gravitation and other relativistic factors in their circuitry. See:Self-clocking signal.

Theprimary time standard in the U.S. is currentlyNIST-F1, alaser-cooledCs fountain,^[34] the latest in a series of time and frequency standards, from theammonia-based atomic clock (1949) to thecaesium-based NBS-1 (1952) to NIST-7 (1993). The respective clock uncertainty declined from 10,000 nanoseconds per day to 0.5 nanoseconds per day in 5 decades.^[35] In 2001 the clock uncertainty for NIST-F1 was 0.1 nanoseconds/day. Development of increasingly accurate frequency standards is underway.

In this time and frequency standard, a population of caesium atoms is laser-cooled to temperatures of onemicrokelvin. The atoms collect in a ball shaped by six lasers, two for each spatial dimension, vertical (up/down), horizontal (left/right), and back/forth. The vertical lasers push the caesium ball through a microwave cavity. As the ball is cooled, the caesium population cools to its ground state and emits light at its natural frequency, stated in the definition ofsecond above. Eleven physical effects are accounted for in the emissions from the caesium population, which are then controlled for in the NIST-F1 clock. These results are reported toBIPM.

Additionally, a referencehydrogen maser is also reported to BIPM as a frequency standard forTAI (international atomic time).

The measurement of time is overseen byBIPM (Bureau International des Poids et Mesures), located inSèvres, France, which ensures uniformity of measurements and their traceability to theInternational System of Units (SI) worldwide. BIPM operates under authority of theMetre Convention, a diplomatic treaty between fifty-one nations, the Member States of the Convention, through a series of Consultative Committees, whose members are the respective nationalmetrology laboratories.

The equations of general relativity predict a non-static universe. However, Einstein accepted only a static universe, and modified the Einstein field equation to reflect this by adding thecosmological constant, which he later described as his "biggest blunder". But in 1927,Georges Lemaître (1894–1966) argued, on the basis ofgeneral relativity, that the universe originated in a primordial explosion. At the fifthSolvay conference, that year, Einstein brushed him off with "Vos calculs sont corrects, mais votre physique est abominable."^[36] (“Your math is correct, but your physics is abominable”). In 1929,Edwin Hubble (1889–1953) announced his discovery of theexpanding universe. The current generally accepted cosmological model, theLambda-CDM model, has a positive cosmological constant and thus not only an expanding universe but an accelerating expanding universe.

If the universe were expanding, then it must have been much smaller and therefore hotter and denser in the past.George Gamow (1904–1968) hypothesized that the abundance of the elements in the Periodic Table of the Elements, might be accounted for by nuclear reactions in a hot dense universe. He was disputed byFred Hoyle (1915–2001), who invented the term 'Big Bang' to disparage it.Fermi and others noted that this process would have stopped after only the light elements were created, and thus did not account for the abundance of heavier elements.

Gamow's prediction was a 5–10-kelvinblack-body radiation temperature for the universe, after it cooled during the expansion. This was corroborated byPenzias and Wilson in 1965. Subsequent experiments arrived at a 2.7 kelvins temperature, corresponding to anage of the universe of 13.8 billion years after the Big Bang.

This dramatic result has raised issues: what happened between the singularity of the Big Bang and the Planck time, which, after all, is the smallest observable time. When might have time separated out from thespacetime foam;^[38] there are only hints based on broken symmetries (seeSpontaneous symmetry breaking,Timeline of the Big Bang, and the articles inCategory:Physical cosmology).

General relativity gave us our modern notion of the expanding universe that started in the Big Bang. Using relativity and quantum theory we have been able to roughly reconstruct the history of the universe. In ourepoch, during which electromagnetic waves can propagate without being disturbed by conductors or charges, we can see the stars, at great distances from us, in the night sky. (Before this epoch, there was a time, before the universe cooled enough for electrons and nuclei to combine into atoms about 377,000 years after theBig Bang, during which starlight would not have been visible over large distances.)

Ilya Prigogine's reprise is"Time precedesexistence". In contrast to the views of Newton, of Einstein, and of quantum physics, which offer a symmetric view of time (as discussed above), Prigogine points out that statistical and thermodynamic physics can explainirreversible phenomena,^[39] as well as thearrow of time and theBig Bang.

• Relativistic dynamics
• Category:systems of units
• Time in astronomy

• Boorstein, Daniel J.,The Discoverers. Vintage. February 12, 1985.ISBN 0-394-72625-1
• Dieter Zeh, H.,The physical basis of the direction of time. Springer.ISBN 978-3-540-42081-1
• Kuhn, Thomas S.,The Structure of Scientific Revolutions.ISBN 0-226-45808-3
• Mandelbrot, Benoît,Multifractals and 1/f noise. Springer Verlag. February 1999.ISBN 0-387-98539-5
• Prigogine, Ilya (1984),Order out of Chaos.ISBN 0-394-54204-5
• Serres, Michel, et al., "Conversations on Science, Culture, and Time (Studies in Literature and Science)". March, 1995.ISBN 0-472-06548-3
• Stengers, Isabelle, and Ilya Prigogine,Theory Out of Bounds. University of Minnesota Press. November 1997.ISBN 0-8166-2517-4

• Media related toTime in physics at Wikimedia Commons

• Time in physics
• Philosophy of physics
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