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Time Time is the continued sequence of existence and event (philosophy), events that occurs in an apparently irreversible process, irreversible succession from the past, through the present, into the future. It is a component quantity of various me ...
in physics is defined by its
measurement Measurement is the quantification of attributes of an object or event, which can be used to compare with other objects or events. In other words, measurement is a process of determining how large or small a physical quantity is as compared ...
: time is what a
clock A clock or a timepiece is a device used to measure and indicate time. The clock is one of the oldest human inventions, meeting the need to measure intervals of time shorter than the natural units such as the day, the lunar month and ...
reads. In classical, non-relativistic physics, it is a scalar quantity (often denoted by the symbol t) and, like
length Length is a measure of distance. In the International System of Quantities, length is a quantity with dimension distance. In most systems of measurement a base unit for length is chosen, from which all other units are derived. In the Inte ...
,
mass Mass is an intrinsic property of a body. It was traditionally believed to be related to the quantity of matter in a physical body, until the discovery of the atom and particle physics. It was found that different atoms and different ele ...
, and charge, is usually described as a
fundamental quantity A base unit (also referred to as a fundamental unit) is a unit adopted for measurement of a '' base quantity''. A base quantity is one of a conventionally chosen subset of physical quantities, where no quantity in the subset can be expressed in ter ...
. Time can be combined mathematically with other
physical quantities A physical quantity is a physical property of a material or system that can be quantified by measurement. A physical quantity can be expressed as a ''value'', which is the algebraic multiplication of a ' Numerical value ' and a ' Unit '. For exam ...
to derive other concepts such as
motion In physics, motion is the phenomenon in which an object changes its position with respect to time. Motion is mathematically described in terms of displacement, distance, velocity, acceleration, speed and frame of reference to an observer and m ...
,
kinetic energy In physics, the kinetic energy of an object is the energy that it possesses due to its motion. It is defined as the work needed to accelerate a body of a given mass from rest to its stated velocity. Having gained this energy during its acce ...
and time-dependent fields. ''
Timekeeping Time is the continued sequence of existence and events that occurs in an apparently irreversible succession from the past, through the present, into the future. It is a component quantity of various measurements used to sequence events, to co ...
'' is a complex of technological and scientific issues, and part of the foundation of '' recordkeeping''.


Markers of time

Before there were clocks, time was measured by those physical processes which were understandable to each epoch of civilization: *the first appearance (see:
heliacal rising The heliacal rising ( ) or star rise of a star occurs annually, or the similar phenomenon of a planet, when it first becomes visible above the eastern horizon at dawn just before sunrise (thus becoming "the morning star") after a complete orbit o ...
) of
Sirius Sirius is the brightest star in the night sky. Its name is derived from the Greek word , or , meaning 'glowing' or 'scorching'. The star is designated α Canis Majoris, Latinized to Alpha Canis Majoris, and abbreviated Alpha CM ...
to mark the flooding of the Nile each year Otto Neugebauer ''The Exact Sciences in Antiquity''. Princeton: Princeton University Press, 1952; 2nd edition, Brown University Press, 1957; reprint, New York: Dover publications, 1969. Page 82. *the periodic succession of
night Night (also described as night time, unconventionally spelled as "nite") is the period of ambient darkness from sunset to sunrise during each 24-hour day, when the Sun is below the horizon. The exact time when night begins and ends depends ...
and
day A day is the time period of a full rotation of the Earth with respect to the Sun. On average, this is 24 hours, 1440 minutes, or 86,400 seconds. In everyday life, the word "day" often refers to a solar day, which is the length between two ...
, seemingly eternally *the position on the horizon of the first appearance of the sun at dawn *the position of the sun in the sky *the marking of the moment of noontime during the day *the length of the shadow cast by a
gnomon A gnomon (; ) is the part of a sundial that casts a shadow. The term is used for a variety of purposes in mathematics and other fields. History A painted stick dating from 2300 BC that was excavated at the astronomical site of Taosi is the ...
Eventually, it became possible to characterize the passage of time with instrumentation, using
operational definition An operational definition specifies concrete, replicable procedures designed to represent a construct. In the words of American psychologist S.S. Stevens (1935), "An operation is the performance which we execute in order to make known a concept." F ...
s. Simultaneously, our conception of time has evolved, as shown below.


The unit of measurement of time: the second

In the
International System of Units The International System of Units, known by the international abbreviation SI in all languages and sometimes pleonastically as the SI system, is the modern form of the metric system and the world's most widely used system of measurement. ...
(SI), the unit of time is the
second The second (symbol: s) is the unit of time in the International System of Units (SI), historically defined as of a day – this factor derived from the division of the day first into 24 hours, then to 60 minutes and finally to 60 seconds ea ...
(symbol: \mathrm). It is a
SI base unit The SI base units are the standard units of measurement defined by the International System of Units (SI) for the seven base quantities of what is now known as the International System of Quantities: they are notably a basic set from which al ...
, and has been defined since 1967 as "the duration of yclesof the
radiation In physics, radiation is the emission or transmission of energy in the form of waves or particles through space or through a material medium. This includes: * ''electromagnetic radiation'', such as radio waves, microwaves, infrared, visi ...
corresponding to the transition between the two hyperfine levels of the
ground state The ground state of a quantum-mechanical system is its stationary state of lowest energy; the energy of the ground state is known as the zero-point energy of the system. An excited state is any state with energy greater than the ground state. ...
of the
caesium Caesium (IUPAC spelling) (or cesium in American English) is a chemical element with the symbol Cs and atomic number 55. It is a soft, silvery-golden alkali metal with a melting point of , which makes it one of only five elemental metals that a ...
133 atom". This definition is based on the operation of a caesium
atomic clock An atomic clock is a clock that measures time by monitoring the resonant frequency of atoms. It is based on atoms having different energy levels. Electron states in an atom are associated with different energy levels, and in transitions betwe ...
. These clocks became practical for use as primary reference standards after about 1955, and have been in use ever since.


The state of the art in timekeeping

The UTC
timestamp A timestamp is a sequence of characters or encoded information identifying when a certain event occurred, usually giving date and time of day, sometimes accurate to a small fraction of a second. Timestamps do not have to be based on some absolut ...
in use worldwide is an atomic time standard. The relative accuracy of such a time standard is currently on the order of 10−15 (corresponding to 1 second in approximately 30 million years). The smallest time step considered theoretically observable is called the Planck time, which is approximately 5.391×10−44 seconds - many orders of magnitude below the resolution of current time standards. The caesium 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.


Conceptions of time

Galileo Galileo di Vincenzo Bonaiuti de' Galilei (15 February 1564 – 8 January 1642) was an Italian astronomer, physicist and engineer, sometimes described as a polymath. Commonly referred to as Galileo, his name was pronounced (, ). He was ...
, Newton, and most people up until the 20th century thought that time was the same for everyone everywhere. This is the basis for
timeline A timeline is a display of a list of events in chronological order. It is typically a graphic design showing a long bar labelled with dates paralleling it, and usually contemporaneous events. Timelines can use any suitable scale represen ...
s, where time is a
parameter A parameter (), generally, is any characteristic that can help in defining or classifying a particular system (meaning an event, project, object, situation, etc.). That is, a parameter is an element of a system that is useful, or critical, when ...
. The modern understanding of time is based on
Einstein Albert Einstein ( ; ; 14 March 1879 – 18 April 1955) was a German-born Theoretical physics, theoretical physicist, widely acknowledged to be one of the greatest and most influential physicists of all time. Einstein is best known for d ...
's
theory of relativity The theory of relativity usually encompasses two interrelated theories by Albert Einstein: special relativity and general relativity, proposed and published in 1905 and 1915, respectively. Special relativity applies to all physical phenomena in ...
, in which rates of time run differently depending on relative motion, and
space Space is the boundless three-dimensional extent in which objects and events have relative position and direction. In classical physics, physical space is often conceived in three linear dimensions, although modern physicists usually consi ...
and time are merged into
spacetime In physics, spacetime is a mathematical model that combines the three dimensions of space and one dimension of time into a single four-dimensional manifold. Spacetime diagrams can be used to visualize relativistic effects, such as why differ ...
, where we live on a
world line The world line (or worldline) of an object is the path that an object traces in 4-dimensional spacetime. It is an important concept in modern physics, and particularly theoretical physics. The concept of a "world line" is distinguished from c ...
rather than a timeline. In this view time is a coordinate. According to the prevailing cosmological model of the
Big Bang The Big Bang event is a physical theory that describes how the universe expanded from an initial state of high density and temperature. Various cosmological models of the Big Bang explain the evolution of the observable universe from the ...
theory, time itself began as part of the entire
Universe The universe is all of space and time and their contents, including planets, stars, galaxies, and all other forms of matter and energy. The Big Bang theory is the prevailing cosmological description of the development of the univers ...
about 13.8 billion years ago.


Regularities in nature

In order to measure time, one can record the number of occurrences (events) of some periodic
phenomenon A phenomenon ( : phenomena) is an observable event. The term came into its modern philosophical usage through Immanuel Kant, who contrasted it with the noumenon, which ''cannot'' be directly observed. Kant was heavily influenced by Gottfrie ...
. The regular recurrences of the seasons, the
motion In physics, motion is the phenomenon in which an object changes its position with respect to time. Motion is mathematically described in terms of displacement, distance, velocity, acceleration, speed and frame of reference to an observer and m ...
s of the sun,
moon The Moon is Earth's only natural satellite. It is the fifth largest satellite in the Solar System and the largest and most massive relative to its parent planet, with a diameter about one-quarter that of Earth (comparable to the width of ...
and
star A star is an astronomical object comprising a luminous spheroid of plasma (physics), plasma held together by its gravity. The List of nearest stars and brown dwarfs, nearest star to Earth is the Sun. Many other stars are visible to the naked ...
s were noted and tabulated for millennia, before the laws of physics were formulated. The sun was the arbiter of the flow of time, but
time Time is the continued sequence of existence and event (philosophy), events that occurs in an apparently irreversible process, irreversible succession from the past, through the present, into the future. It is a component quantity of various me ...
was known only to the
hour An hour (symbol: h; also abbreviated hr) is a unit of time conventionally reckoned as of a day and scientifically reckoned between 3,599 and 3,601 seconds, depending on the speed of Earth's rotation. There are 60 minutes in an hour, and 24 ...
for millennia, hence, the use of the
gnomon A gnomon (; ) is the part of a sundial that casts a shadow. The term is used for a variety of purposes in mathematics and other fields. History A painted stick dating from 2300 BC that was excavated at the astronomical site of Taosi is the ...
was known across most of the world, especially
Eurasia Eurasia (, ) is the largest continental area on Earth, comprising all of Europe and Asia. Primarily in the Northern and Eastern Hemispheres, it spans from the British Isles and the Iberian Peninsula in the west to the Japanese archipelag ...
, and at least as far southward as the jungles of
Southeast Asia Southeast Asia, also spelled South East Asia and South-East Asia, and also known as Southeastern Asia, South-eastern Asia or SEA, is the geographical south-eastern region of Asia, consisting of the regions that are situated south of mainland ...
. 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 Time is the continued sequence of existence and events that occurs in an apparently irreversible succession from the past, through the present, into the future. It is a component quantity of various measurements used to sequence events, to co ...
was done by hand by priests, and then for commerce, with watchmen to note time as part of their duties. The tabulation of the
equinox A solar equinox is a moment in time when the Sun crosses the Earth's equator, which is to say, appears directly above the equator, rather than north or south of the equator. On the day of the equinox, the Sun appears to rise "due east" and se ...
es, the sandglass, and the
water clock A water clock or clepsydra (; ; ) is a timepiece by which time is measured by the regulated flow of liquid into (inflow type) or out from (outflow type) a vessel, and where the amount is then measured. Water clocks are one of the oldest time- ...
became more and more accurate, and finally reliable. For ships at sea, boys were used to turn the sandglasses and to call the hours.


Mechanical clocks

Richard of Wallingford (1292–1336), abbot of St. Alban's abbey, famously built a
mechanical clock A clock or a timepiece is a device used to measure and indicate time. The clock is one of the oldest human inventions, meeting the need to measure intervals of time shorter than the natural units such as the day, the lunar month and th ...
as an astronomical
orrery An orrery is a mechanical model of the Solar System that illustrates or predicts the relative positions and motions of the planets and moons, usually according to the heliocentric model. It may also represent the relative sizes of these bodies ...
about 1330. By the time of Richard of Wallingford, the use of ratchets and
gear A gear is a rotating circular machine part having cut teeth or, in the case of a cogwheel or gearwheel, inserted teeth (called ''cogs''), which mesh with another (compatible) toothed part to transmit (convert) torque and speed. The basic ...
s 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 clock A pendulum clock is a clock that uses a pendulum, a swinging weight, as its timekeeping element. The advantage of a pendulum for timekeeping is that it is a harmonic oscillator: It swings back and forth in a precise time interval dependent on i ...
s were widely used in the 18th and 19th century. They have largely been replaced in general use by
quartz Quartz is a hard, crystalline mineral composed of silica ( silicon dioxide). The atoms are linked in a continuous framework of SiO4 silicon-oxygen tetrahedra, with each oxygen being shared between two tetrahedra, giving an overall chemical f ...
and
digital clock A digital clock is a type of clock that displays the time digitally (i.e. in numerals or other symbols), as opposed to an analogue clock. Digital clocks are often associated with electronic drives, but the "digital" description refers only t ...
s. Atomic clocks can theoretically keep accurate time for millions of years. They are appropriate for standards and scientific use.


Galileo: the flow of time

In 1583,
Galileo Galilei Galileo di Vincenzo Bonaiuti de' Galilei (15 February 1564 – 8 January 1642) was an Italian astronomer, physicist and engineer, sometimes described as a polymath. Commonly referred to as Galileo, his name was pronounced (, ). He ...
(1564–1642) discovered that a pendulum's harmonic motion has a constant period, which he learned by timing the motion of a swaying lamp in harmonic motion at
mass Mass is an intrinsic property of a body. It was traditionally believed to be related to the quantity of matter in a physical body, until the discovery of the atom and particle physics. It was found that different atoms and different ele ...
at the cathedral of
Pisa Pisa ( , or ) is a city and ''comune'' in Tuscany, central Italy, straddling the Arno just before it empties into the Ligurian Sea. It is the capital city of the Province of Pisa. Although Pisa is known worldwide for its leaning tower, the ci ...
, with his pulse. In his '' Two New Sciences'' (1638),
Galileo Galileo di Vincenzo Bonaiuti de' Galilei (15 February 1564 – 8 January 1642) was an Italian astronomer, physicist and engineer, sometimes described as a polymath. Commonly referred to as Galileo, his name was pronounced (, ). He was ...
used a
water clock A water clock or clepsydra (; ; ) is a timepiece by which time is measured by the regulated flow of liquid into (inflow type) or out from (outflow type) a vessel, and where the amount is then measured. Water clocks are one of the oldest time- ...
to measure the time taken for a bronze ball to roll a known distance down an
inclined plane An inclined plane, also known as a ramp, is a flat supporting surface tilted at an angle from the vertical direction, with one end higher than the other, used as an aid for raising or lowering a load. The inclined plane is one of the six cla ...
; this clock was:
Galileo Galileo di Vincenzo Bonaiuti de' Galilei (15 February 1564 – 8 January 1642) was an Italian astronomer, physicist and engineer, sometimes described as a polymath. Commonly referred to as Galileo, his name was pronounced (, ). He was ...
1638 ''Discorsi e dimostrazioni matematiche, intorno á due nuoue scienze'' 213, Leida, Appresso gli Elsevirii (Louis Elsevier), or ''Mathematical discourses and demonstrations, relating to Two New Sciences'', English translation by Henry Crew and Alfonso de Salvio 1914. Section 213 is reprinted on pages 534-535 of ''On the Shoulders of Giants'':The Great Works of Physics and Astronomy (works by
Copernicus Nicolaus Copernicus (; pl, Mikołaj Kopernik; gml, Niklas Koppernigk, german: Nikolaus Kopernikus; 19 February 1473 – 24 May 1543) was a Renaissance polymath, active as a mathematician, astronomer, and Catholic canon, who formulat ...
,
Kepler Johannes Kepler (; ; 27 December 1571 – 15 November 1630) was a German astronomer, mathematician, astrologer, natural philosopher and writer on music. He is a key figure in the 17th-century Scientific Revolution, best known for his laws o ...
,
Galileo Galileo di Vincenzo Bonaiuti de' Galilei (15 February 1564 – 8 January 1642) was an Italian astronomer, physicist and engineer, sometimes described as a polymath. Commonly referred to as Galileo, his name was pronounced (, ). He was ...
, Newton, and
Einstein Albert Einstein ( ; ; 14 March 1879 – 18 April 1955) was a German-born Theoretical physics, theoretical physicist, widely acknowledged to be one of the greatest and most influential physicists of all time. Einstein is best known for d ...
). Stephen Hawking, ed. 2002
...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 literal '' flow of time'', in order to describe the motion of a ball, preceded
Isaac Newton Sir Isaac Newton (25 December 1642 – 20 March 1726/27) was an English mathematician, physicist, astronomer, alchemist, Theology, theologian, and author (described in his time as a "natural philosophy, natural philosopher"), widely ...
's statement in his Principia, "I do not define
time Time is the continued sequence of existence and event (philosophy), events that occurs in an apparently irreversible process, irreversible succession from the past, through the present, into the future. It is a component quantity of various me ...
,
space Space is the boundless three-dimensional extent in which objects and events have relative position and direction. In classical physics, physical space is often conceived in three linear dimensions, although modern physicists usually consi ...
,
place Place may refer to: Geography * Place (United States Census Bureau), defined as any concentration of population ** Census-designated place, a populated area lacking its own municipal government * "Place", a type of street or road name ** O ...
and
motion In physics, motion is the phenomenon in which an object changes its position with respect to time. Motion is mathematically described in terms of displacement, distance, velocity, acceleration, speed and frame of reference to an observer and m ...
, as being well known to all." Newton 1687 ''
Philosophiae Naturalis Principia Mathematica Philosophy (from , ) is the systematized study of general and fundamental questions, such as those about existence, reason, knowledge, values, mind, and language. Such questions are often posed as problems to be studied or resolved. S ...
'', Londini, Jussu Societatis Regiae ac Typis J. Streater, or '' The Mathematical Principles of Natural Philosophy'',
London London is the capital and List of urban areas in the United Kingdom, largest city of England and the United Kingdom, with a population of just under 9 million. It stands on the River Thames in south-east England at the head of a estuary dow ...
, English translation by Andrew Motte 1700s. From part of the Scholium, reprinted on page 737 of ''On the Shoulders of Giants'':The Great Works of Physics and Astronomy (works by
Copernicus Nicolaus Copernicus (; pl, Mikołaj Kopernik; gml, Niklas Koppernigk, german: Nikolaus Kopernikus; 19 February 1473 – 24 May 1543) was a Renaissance polymath, active as a mathematician, astronomer, and Catholic canon, who formulat ...
,
Kepler Johannes Kepler (; ; 27 December 1571 – 15 November 1630) was a German astronomer, mathematician, astrologer, natural philosopher and writer on music. He is a key figure in the 17th-century Scientific Revolution, best known for his laws o ...
,
Galileo Galileo di Vincenzo Bonaiuti de' Galilei (15 February 1564 – 8 January 1642) was an Italian astronomer, physicist and engineer, sometimes described as a polymath. Commonly referred to as Galileo, his name was pronounced (, ). He was ...
, Newton, and
Einstein Albert Einstein ( ; ; 14 March 1879 – 18 April 1955) was a German-born Theoretical physics, theoretical physicist, widely acknowledged to be one of the greatest and most influential physicists of all time. Einstein is best known for d ...
). Stephen Hawking, ed. 2002
The
Galilean transformation In physics, a 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. These transformations together with spatial rotat ...
s assume that time is the same for all reference frames.


Newton's physics: linear time

In or around 1665, when
Isaac Newton Sir Isaac Newton (25 December 1642 – 20 March 1726/27) was an English mathematician, physicist, astronomer, alchemist, Theology, theologian, and author (described in his time as a "natural philosophy, natural philosopher"), widely ...
(1643–1727) derived the motion of objects falling under
gravity In physics, gravity () is a fundamental interaction which causes mutual attraction between all things with mass or energy. Gravity is, by far, the weakest of the four fundamental interactions, approximately 1038 times weaker than the stro ...
, the first clear formulation for
mathematical physics Mathematical physics refers to the development of mathematical methods for application to problems in physics. The '' Journal of Mathematical Physics'' defines the field as "the application of mathematics to problems in physics and the developm ...
of a treatment of time began: linear time, conceived as a ''universal 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. Newton 1687 page 738.
The
water clock A water clock or clepsydra (; ; ) is a timepiece by which time is measured by the regulated flow of liquid into (inflow type) or out from (outflow type) a vessel, and where the amount is then measured. Water clocks are one of the oldest time- ...
mechanism described by Galileo was engineered to provide
laminar flow In fluid dynamics, laminar flow is characterized by fluid particles following smooth paths in layers, with each layer moving smoothly past the adjacent layers with little or no mixing. At low velocities, the fluid tends to flow without lateral mi ...
of the water during the experiments, thus providing a constant flow of water for the durations of the experiments, and embodying what Newton called ''duration''. 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's fluents treat a ''linear flow of time'' (what he called ''mathematical 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.


Thermodynamics and the paradox of irreversibility

By 1798,
Benjamin Thompson Sir Benjamin Thompson, Count Rumford, FRS (german: Reichsgraf von Rumford; March 26, 1753August 21, 1814) was an American-born British physicist and inventor whose challenges to established physical theory were part of the 19th-century revolut ...
(1753–1814) had discovered that work could be transformed to
heat In thermodynamics, heat is defined as the form of energy crossing the boundary of a thermodynamic system by virtue of a temperature difference across the boundary. A thermodynamic system does not ''contain'' heat. Nevertheless, the term is ...
without limit - a precursor of the conservation of energy or * 1st law of thermodynamics In 1824 Sadi Carnot (1796–1832) scientifically analyzed the
steam engine A steam engine is a heat engine that performs mechanical work using steam as its working fluid. The steam engine uses the force produced by steam pressure to push a piston back and forth inside a cylinder. This pushing force can be ...
with his
Carnot cycle A Carnot cycle is an ideal thermodynamic cycle proposed by French physicist Sadi Carnot in 1824 and expanded upon by others in the 1830s and 1840s. By Carnot's theorem, it provides an upper limit on the efficiency of any classical thermodyna ...
, an abstract engine.
Rudolf Clausius Rudolf Julius Emanuel Clausius (; 2 January 1822 – 24 August 1888) was a German physicist and mathematician and is considered one of the central founding fathers of the science of thermodynamics. By his restatement of Sadi Carnot's princip ...
(1822–1888) noted a measure of disorder, or
entropy Entropy is a scientific concept, as well as a measurable physical property, that is most commonly associated with a state of disorder, randomness, or uncertainty. The term and the concept are used in diverse fields, from classical thermodyna ...
, which affects the continually decreasing amount of free energy which is available to a Carnot engine in the: *
2nd law of thermodynamics The second law of thermodynamics is a physical law based on universal experience concerning heat and energy interconversions. One simple statement of the law is that heat always moves from hotter objects to colder objects (or "downhill"), unles ...
Thus the continual march of a thermodynamic system, from lesser to greater entropy, at any given temperature, defines an
arrow of time The arrow of time, also called time's arrow, is the concept positing the "one-way direction" or "asymmetry" of time. It was developed in 1927 by the British astrophysicist Arthur Eddington, and is an unsolved general physics question. This ...
. In particular, Stephen Hawking identifies three arrows of time:pp. 182–195. Stephen Hawking 1996. ''The Illustrated Brief History of Time'': updated and expanded edition *Psychological arrow of time - our perception of an inexorable flow. *Thermodynamic arrow of time - distinguished by the growth of
entropy Entropy is a scientific concept, as well as a measurable physical property, that is most commonly associated with a state of disorder, randomness, or uncertainty. The term and the concept are used in diverse fields, from classical thermodyna ...
. *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 that
life Life is a quality that distinguishes matter that has biological processes, such as signaling and self-sustaining processes, from that which does not, and is defined by the capacity for growth, reaction to stimuli, metabolism, energy ...
depends on a ''"negative entropy flow"''. 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, the Belousov–Zhabotinsky reactions were reported, which demonstrate oscillating colors in a chemical solution. These nonequilibrium thermodynamic branches reach a '' bifurcation point'', which is unstable, and another thermodynamic branch becomes stable in its stead.


Electromagnetism and the speed of light

In 1864,
James Clerk Maxwell James Clerk Maxwell (13 June 1831 – 5 November 1879) was a Scottish mathematician and scientist responsible for the classical theory of electromagnetic radiation, which was the first theory to describe electricity, magnetism and ligh ...
(1831–1879) presented a combined theory of
electricity Electricity is the set of physical phenomena associated with the presence and motion of matter that has a property of electric charge. Electricity is related to magnetism, both being part of the phenomenon of electromagnetism, as describe ...
and
magnetism Magnetism is the class of physical attributes that are mediated by a magnetic field, which refers to the capacity to induce attractive and repulsive phenomena in other entities. Electric currents and the magnetic moments of elementary particles ...
. He combined all the laws then known relating to those two phenomenon into four equations. These equations are known as
Maxwell's equations Maxwell's equations, or Maxwell–Heaviside equations, are a set of coupled partial differential equations that, together with the Lorentz force law, form the foundation of classical electromagnetism, classical optics, and electric circuits ...
for
electromagnetism In physics, electromagnetism is an interaction that occurs between particles with electric charge. It is the second-strongest of the four fundamental interactions, after the strong force, and it is the dominant force in the interactions o ...
; 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 speed ''c'' would be incompatible with Galilean relativity if Maxwell's equations were assumed to hold in any
inertial frame In classical physics and special relativity, an inertial frame of reference (also called inertial reference frame, inertial frame, inertial space, or Galilean reference frame) is a frame of reference that is not undergoing any acceleration ...
(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 the luminiferous aether, in which Maxwell's equations held unmodified in the known form. The
Michelson–Morley experiment The Michelson–Morley experiment was an attempt to detect the existence of the luminiferous aether, a supposed medium permeating space that was thought to be the carrier of light waves. The experiment was performed between April and July 188 ...
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 Hendrik Antoon Lorentz (; 18 July 1853 – 4 February 1928) was a Dutch physicist who shared the 1902 Nobel Prize in Physics with Pieter Zeeman for the discovery and theoretical explanation of the Zeeman effect. He also derived the Lorent ...
(1853–1928) discovered Lorentz transformations, which left Maxwell's equations unchanged, allowing Michelson and Morley's negative result to be explained.
Henri Poincaré Jules Henri Poincaré ( S: stress final syllable ; 29 April 1854 – 17 July 1912) was a French mathematician, theoretical physicist, engineer, and philosopher of science. He is often described as a polymath, and in mathematics as "Th ...
(1854–1912) noted the importance of Lorentz's transformation and popularized it. In particular, the railroad car description can be found in '' Science and Hypothesis'', which was published before Einstein's articles of 1905. The Lorentz transformation predicted space contraction and
time dilation In physics and relativity, time dilation is the difference in the elapsed time as measured by two clocks. It is either due to a relative velocity between them ( special relativistic "kinetic" time dilation) or to a difference in gravitational ...
; 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.


Einstein's physics: spacetime

Albert Einstein Albert Einstein ( ; ; 14 March 1879 – 18 April 1955) was a German-born theoretical physicist, widely acknowledged to be one of the greatest and most influential physicists of all time. Einstein is best known for developing the theor ...
's 1905
special relativity In physics, the special theory of relativity, or special relativity for short, is a scientific theory regarding the relationship between space and time. In Albert Einstein's original treatment, the theory is based on two postulates: # The law ...
challenged the notion of absolute time, and could only formulate a definition of
synchronization Synchronization is the coordination of events to operate a system in unison. For example, the conductor of an orchestra keeps the orchestra synchronized or ''in time''. Systems that operate with all parts in synchrony are said to be synchronou ...
for clocks that mark a linear flow of time: 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 is ''defined'' by space and time: :\mathbf= \text where r is position and ''t'' is time. Indeed, the Lorentz transformation (for two reference frames in relative motion, whose ''x'' axis is directed in the direction of the relative velocity) :\begin t' &= \gamma(t - vx/c^2) \text \gamma = 1/\sqrt \\ x' &= \gamma(x - vt)\\ y' &= y \\ z' &= z \end can be said to "mix" space and time in a way similar to the way a Euclidean rotation around the ''z'' axis mixes ''x'' and ''y'' coordinates. Consequences of this include
relativity of simultaneity In physics, the relativity of simultaneity is the concept that ''distant simultaneity'' – whether two spatially separated events occur at the same time – is not absolute, but depends on the observer's reference frame. This possib ...
. More specifically, the Lorentz transformation is a hyperbolic rotation \begin ct' \\ x' \end = \begin \cosh \phi & - \sinh \phi \\ - \sinh \phi & \cosh \phi \end \begin ct \\ x \end \text \phi = \operatorname\,\frac \text which is a change of coordinates in the four-dimensional
Minkowski space In mathematical physics, Minkowski space (or Minkowski spacetime) () is a combination of three-dimensional Euclidean space and time into a four-dimensional manifold where the spacetime interval between any two events is independent of the iner ...
, a dimension of which is ''ct''. (In
Euclidean space Euclidean space is the fundamental space of geometry, intended to represent physical space. Originally, that is, in Euclid's ''Elements'', it was the three-dimensional space of Euclidean geometry, but in modern mathematics there are Euclidea ...
an ordinary rotation \begin x' \\ y' \end = \begin \cos \theta & - \sin \theta \\ \sin \theta & \cos \theta \end \begin x \\ y \end is the corresponding change of coordinates.) The speed of light ''c'' can be seen as just a conversion factor needed because we measure the dimensions of spacetime in different units; since the
metre The metre ( British spelling) or meter ( American spelling; see spelling differences) (from the French unit , from the Greek noun , "measure"), symbol m, is the primary unit of length in the International System of Units (SI), though its pre ...
is currently defined in terms of the second, it has the ''exact'' value of . We would need a similar factor in Euclidean space if, for example, we measured width in nautical miles and depth in feet. In physics, sometimes units of measurement in which ''c'' = 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''′): :\Delta t= where: *∆''τ'' 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 the proper time between the two events; *∆''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 the
speed of light The speed of light in vacuum, commonly denoted , is a universal physical constant that is important in many areas of physics. The speed of light is exactly equal to ). According to the special theory of relativity, is the upper limit fo ...
. Moving objects therefore are said to ''show a slower passage of time''. This is known as
time dilation In physics and relativity, time dilation is the difference in the elapsed time as measured by two clocks. It is either due to a relative velocity between them ( special relativistic "kinetic" time dilation) or to a difference in gravitational ...
. These transformations are only valid for two frames at ''constant'' relative velocity. Naively applying them to other situations gives rise to such paradoxes as the
twin paradox In physics, the twin paradox is a thought experiment in special relativity involving identical twins, one of whom makes a journey into space in a high-speed rocket and returns home to find that the twin who remained on Earth has aged more. T ...
. That paradox can be resolved using for instance Einstein's General theory of relativity, which uses Riemannian geometry, geometry in accelerated, noninertial reference frames. Employing the
metric tensor In the mathematical field of differential geometry, a metric tensor (or simply metric) is an additional structure on a manifold (such as a surface) that allows defining distances and angles, just as the inner product on a Euclidean space allow ...
which describes
Minkowski space In mathematical physics, Minkowski space (or Minkowski spacetime) () is a combination of three-dimensional Euclidean space and time into a four-dimensional manifold where the spacetime interval between any two events is independent of the iner ...
: :\left dx^1)^2+(dx^2)^2+(dx^3)^2-c(dt)^2)\right Einstein developed a geometric solution to Lorentz's transformation that preserves
Maxwell's equations Maxwell's equations, or Maxwell–Heaviside equations, are a set of coupled partial differential equations that, together with the Lorentz force law, form the foundation of classical electromagnetism, classical optics, and electric circuits ...
. His field equations give an exact relationship between the measurements of space and time in a given region of
spacetime In physics, spacetime is a mathematical model that combines the three dimensions of space and one dimension of time into a single four-dimensional manifold. Spacetime diagrams can be used to visualize relativistic effects, such as why differ ...
and the energy density of that region. Einstein's equations predict that time should be altered by the presence of gravitational fields (see the
Schwarzschild metric In Einstein's theory of general relativity, the Schwarzschild metric (also known as the Schwarzschild solution) is an exact solution to the Einstein field equations that describes the gravitational field outside a spherical mass, on the assump ...
): :T=\frac Where: :T is the gravitational time dilation of an object at a distance of r. :dt is the change in coordinate time, or the interval of coordinate time. :G is the
gravitational constant The gravitational constant (also known as the universal gravitational constant, the Newtonian constant of gravitation, or the Cavendish gravitational constant), denoted by the capital letter , is an empirical physical constant involved in ...
:M is the
mass Mass is an intrinsic property of a body. It was traditionally believed to be related to the quantity of matter in a physical body, until the discovery of the atom and particle physics. It was found that different atoms and different ele ...
generating the field :\sqrt is the change in proper time d\tau, or the interval of proper time. Or one could use the following simpler approximation: :\frac = \frac. That is, the stronger the gravitational field (and, thus, the larger the
acceleration In mechanics, acceleration is the rate of change of the velocity of an object with respect to time. Accelerations are vector quantities (in that they have magnitude and direction). The orientation of an object's acceleration is given by ...
), the more slowly time runs. The predictions of time dilation are confirmed by particle acceleration experiments and
cosmic ray Cosmic rays are high-energy particles or clusters of particles (primarily represented by protons or atomic nuclei) that move through space at nearly the speed of light. They originate from the Sun, from outside of the Solar System in our own ...
evidence, where moving particles decay more slowly than their less energetic counterparts. Gravitational time dilation gives rise to the phenomenon of
gravitational redshift In physics and general relativity, gravitational redshift (known as Einstein shift in older literature) is the phenomenon that electromagnetic waves or photons travelling out of a gravitational well (seem to) lose energy. This loss of energy ...
and Shapiro signal travel time delays near massive objects such as the sun. The
Global Positioning System The Global Positioning System (GPS), originally Navstar GPS, is a satellite-based radionavigation system owned by the United States government and operated by the United States Space Force. It is one of the global navigation satellite ...
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 by Taylor and
Wheeler Wheeler may refer to: Places United States * Wheeler, Alabama, an unincorporated community * Wheeler, Arkansas, an unincorporated community * Wheeler, California, an unincorporated community * Wheeler, Illinois, a village * Wheeler, Indiana, a ...
as: ::''"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 an
inertial frame In classical physics and special relativity, an inertial frame of reference (also called inertial reference frame, inertial frame, inertial space, or Galilean reference frame) is a frame of reference that is not undergoing any acceleration ...
. In an inertial frame, Newton's first law holds; it has its own local geometry, and therefore its ''own'' measurements of space and time; ''there is no 'universal clock. An act of synchronization must be performed between two systems, at the least.


Time in quantum mechanics

There is a time parameter in the equations of
quantum mechanics Quantum mechanics is a fundamental theory in physics that provides a description of the physical properties of nature at the scale of atoms and subatomic particles. It is the foundation of all quantum physics including quantum chemistry, ...
. The
Schrödinger equation The Schrödinger equation is a linear partial differential equation that governs the wave function of a quantum-mechanical system. It is a key result in quantum mechanics, and its discovery was a significant landmark in the development of th ...
is : H(t) \left, \psi (t) \right\rangle = i \hbar \left, \psi (t) \right\rangle One solution can be : , \psi_e(t) \rangle = e^ , \psi_e(0) \rangle . where e^ is called the time evolution operator, and ''H'' is the Hamiltonian. But the
Schrödinger picture In physics, the Schrödinger picture is a formulation of quantum mechanics in which the state vectors evolve in time, but the operators (observables and others) are mostly constant with respect to time (an exception is the Hamiltonian which ma ...
shown above is equivalent to the Heisenberg picture, which enjoys a similarity to the Poisson brackets of classical mechanics. The
Poisson bracket In mathematics and classical mechanics, the Poisson bracket is an important binary operation in Hamiltonian mechanics, playing a central role in Hamilton's equations of motion, which govern the time evolution of a Hamiltonian dynamical system. T ...
s are superseded by a nonzero
commutator In mathematics, the commutator gives an indication of the extent to which a certain binary operation fails to be commutative. There are different definitions used in group theory and ring theory. Group theory The commutator of two elements, ...
, say ,Afor observable A, and Hamiltonian H: :\fracA=(i\hbar)^ ,H\left(\frac\right)_\mathrm. This equation denotes an uncertainty relation in quantum physics. For example, with ''time'' (the observable A), the ''energy'' E (from the Hamiltonian H) gives: :\Delta E \Delta T \ge \frac :where :\Delta E is the uncertainty in energy :\Delta T is the uncertainty in time :\hbar is Planck's constant The more precisely one measures the duration of a sequence 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 an operator in quantum mechanics. Corresponding
commutator In mathematics, the commutator gives an indication of the extent to which a certain binary operation fails to be commutative. There are different definitions used in group theory and ring theory. Group theory The commutator of two elements, ...
relations also hold for momentum ''p'' and position ''q'', which are
conjugate variables Conjugate variables are pairs of variables mathematically defined in such a way that they become Fourier transform duals, or more generally are related through Pontryagin duality. The duality relations lead naturally to an uncertainty relation� ...
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 the
periodic table The periodic table, also known as the periodic table of the (chemical) elements, is a rows and columns arrangement of the chemical elements. It is widely used in chemistry, physics, and other sciences, and is generally seen as an icon of ch ...
of the elements. Starting with
Otto Stern :''Otto Stern was also the pen name of German women's rights activist Louise Otto-Peters (1819–1895)''. Otto Stern (; 17 February 1888 – 17 August 1969) was a German-American physicist and Nobel laureate in physics. He was the second most ...
's and Walter Gerlach's experiment with
molecular beam A molecular beam is produced by allowing a gas at higher pressure to expand through a small orifice into a chamber at lower pressure to form a beam of particles (atoms, free radicals, molecules or ions) moving at approximately equal velocities, ...
s in a magnetic field, Isidor Rabi (1898–1988), was able to modulate the magnetic resonance of the beam. In 1945 Rabi then suggested that this technique be the basis of a clock A Brief History of Atomic Clocks at NIST
using the
resonant frequency Resonance describes the phenomenon of increased amplitude that occurs when the frequency of an applied periodic force (or a Fourier component of it) is equal or close to a natural frequency of the system on which it acts. When an oscilla ...
of an atomic beam. In 2021 Jun Ye of JILA in Boulder Colorado observed time 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.Slashdot (25 Oct 2021) An Ultra-Precise Clock Shows How To Link the Quantum World With Gravity
Jun Ye's work at JILA


Dynamical systems

See dynamical systems and chaos theory, dissipative structures One could say that time is a parameterization of a
dynamical system In mathematics, a dynamical system is a system in which a function describes the time dependence of a point in an ambient space. Examples include the mathematical models that describe the swinging of a clock pendulum, the flow of water i ...
that allows the geometry of the system to be manifested and operated on. It has been asserted that ''time is an implicit consequence of chaos'' (i.e. nonlinearity/ irreversibility): the
characteristic time In the physical sciences, relaxation usually means the return of a perturbed system into equilibrium. Each relaxation process can be categorized by a relaxation time τ. The simplest theoretical description of relaxation as function of time ' ...
, or rate of information entropy production, of a
system A system is a group of interacting or interrelated elements that act according to a set of rules to form a unified whole. A system, surrounded and influenced by its environment, is described by its boundaries, structure and purpose and express ...
. Mandelbrot introduces intrinsic time in his book ''Multifractals and 1/f noise''.


Time crystals

Khemani, Moessner, and Sondhi define a time crystal as a "stable, conservative, macroscopic clock".Vedika Khemani, Roderich Moessner, and S. L. Sondh
(23 Oct 2019) A Brief History of Time Crystals
/ref>


Signalling

Signalling is one application of the
electromagnetic wave In physics, electromagnetic radiation (EMR) consists of waves of the electromagnetic (EM) field, which propagate through space and carry momentum and electromagnetic radiant energy. It includes radio waves, microwaves, infrared, (visible) ...
s described above. In general, a signal is part of
communication Communication (from la, communicare, meaning "to share" or "to be in relation with") is usually defined as the transmission of information. The term may also refer to the message communicated through such transmissions or the field of inqui ...
between parties and places. One example might be a yellow ribbon tied to a tree, or the ringing of a
church bell A church bell in Christian architecture is a bell which is rung in a church for a variety of religious purposes, and can be heard outside the building. Traditionally they are used to call worshippers to the church for a communal service, and to ...
. A signal can be part of a
conversation Conversation is interactive communication between two or more people. The development of conversational skills and etiquette is an important part of socialization. The development of conversational skills in a new language is a frequent focus ...
, which involves a
protocol Protocol may refer to: Sociology and politics * Protocol (politics), a formal agreement between nation states * Protocol (diplomacy), the etiquette of diplomacy and affairs of state * Etiquette, a code of personal behavior Science and technology ...
. 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 of
Time signal A time signal is a visible, audible, mechanical, or electronic signal used as a reference to determine the time of day. Church bells or voices announcing hours of prayer gave way to automatically operated chimes on public clocks; however, a ...
. We as observers can still signal different parties and places as long as we live within their ''past'' light cone. But we cannot receive signals from those parties and places outside our ''past'' light cone. Along with the formulation of the equations for the electromagnetic wave, the field of
telecommunication Telecommunication is the transmission of information by various types of technologies over wire, radio, optical, or other electromagnetic systems. It has its origin in the desire of humans for communication over a distance greater than that ...
could be founded. In 19th century
telegraphy Telegraphy is the long-distance transmission of messages where the sender uses symbolic codes, known to the recipient, rather than a physical exchange of an object bearing the message. Thus flag semaphore is a method of telegraphy, whereas ...
,
electrical circuit An electrical network is an interconnection of electrical components (e.g., batteries, resistors, inductors, capacitors, switches, transistors) or a model of such an interconnection, consisting of electrical elements (e.g., voltage source ...
s, some spanning
continent A continent is any of several large landmasses. Generally identified by convention rather than any strict criteria, up to seven geographical regions are commonly regarded as continents. Ordered from largest in area to smallest, these seven ...
s and
ocean The ocean (also the sea or the world ocean) is the body of salt water that covers approximately 70.8% of the surface of Earth and contains 97% of Earth's water. An ocean can also refer to any of the large bodies of water into which the wor ...
s, could transmit
code In communications and information processing, code is a system of rules to convert information—such as a letter, word, sound, image, or gesture—into another form, sometimes shortened or secret, for communication through a communicati ...
s - simple dots, dashes and spaces. From this, a series of technical issues have emerged; see :Synchronization. But it is safe to say that our signalling systems can be only approximately synchronized, a plesiochronous condition, from which
jitter In electronics and telecommunications, jitter is the deviation from true periodicity of a presumably periodic signal, often in relation to a reference clock signal. In clock recovery applications it is called timing jitter. Jitter is a signific ...
need be eliminated. That said,
system A system is a group of interacting or interrelated elements that act according to a set of rules to form a unified whole. A system, surrounded and influenced by its environment, is described by its boundaries, structure and purpose and express ...
s ''can'' be synchronized (at an engineering approximation), using technologies like GPS. The GPS satellites must account for the effects of gravitation and other relativistic factors in their circuitry. See: Self-clocking signal.


Technology for timekeeping standards

The primary time standard in the U.S. is currently NIST-F1, a
laser A laser is a device that emits light through a process of optical amplification based on the stimulated emission of electromagnetic radiation. The word "laser" is an acronym for "light amplification by stimulated emission of radiation". The ...
-cooled Cs fountain, the latest in a series of time and frequency standards, from the
ammonia Ammonia is an inorganic compound of nitrogen and hydrogen with the formula . A stable binary hydride, and the simplest pnictogen hydride, ammonia is a colourless gas with a distinct pungent smell. Biologically, it is a common nitrogenous ...
-based atomic clock (1949) to the
caesium Caesium (IUPAC spelling) (or cesium in American English) is a chemical element with the symbol Cs and atomic number 55. It is a soft, silvery-golden alkali metal with a melting point of , which makes it one of only five elemental metals that a ...
-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. 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 one
microkelvin List of orders of magnitude for temperature Detailed list for 100 K to 1000 K Most ordinary human activity takes place at temperatures of this order of magnitude. Circumstances where water naturally occurs in liquid form are shown in light g ...
. 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 of ''second'' 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 to
BIPM The International Bureau of Weights and Measures (french: Bureau international des poids et mesures, BIPM) is an intergovernmental organisation, through which its 59 member-states act together on measurement standards in four areas: chemistr ...
. Additionally, a reference hydrogen maser is also reported to BIPM as a frequency standard for TAI (
international atomic time International Atomic Time (abbreviated TAI, from its French name ) is a high-precision atomic coordinate time standard based on the notional passage of proper time on Earth's geoid. TAI is a weighted average of the time kept by over 450 ato ...
). The measurement of time is overseen by
BIPM The International Bureau of Weights and Measures (french: Bureau international des poids et mesures, BIPM) is an intergovernmental organisation, through which its 59 member-states act together on measurement standards in four areas: chemistr ...
(''Bureau International des Poids et Mesures''), located in
Sèvres Sèvres (, ) is a commune in the southwestern suburbs of Paris, France. It is located from the centre of Paris, in the Hauts-de-Seine department, Île-de-France region. The commune, which had a population of 23,251 as of 2018, is known for ...
, France, which ensures uniformity of measurements and their traceability to the
International System of Units The International System of Units, known by the international abbreviation SI in all languages and sometimes pleonastically as the SI system, is the modern form of the metric system and the world's most widely used system of measurement. ...
( SI) worldwide. BIPM operates under authority of the
Metre Convention The Metre Convention (french: link=no, Convention du Mètre), also known as the Treaty of the Metre, is an international treaty that was signed in Paris on 20 May 1875 by representatives of 17 nations (Argentina, Austria-Hungary, Belgium, Braz ...
, a diplomatic treaty between fifty-one nations, the Member States of the Convention, through a series of Consultative Committees, whose members are the respective national
metrology Metrology is the scientific study of measurement. It establishes a common understanding of units, crucial in linking human activities. Modern metrology has its roots in the French Revolution's political motivation to standardise units in Fran ...
laboratories.


Time in cosmology

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 the cosmological constant, which he later described as the biggest mistake of his life. But in 1927,
Georges Lemaître Georges Henri Joseph Édouard Lemaître ( ; ; 17 July 1894 – 20 June 1966) was a Belgian Catholic priest, theoretical physicist, mathematician, astronomer, and professor of physics at the Catholic University of Louvain. He was the first to t ...
(1894–1966) argued, on the basis of
general relativity General relativity, also known as the general theory of relativity and Einstein's theory of gravity, is the geometric theory of gravitation published by Albert Einstein in 1915 and is the current description of gravitation in modern physics ...
, that the universe originated in a primordial explosion. At the fifth
Solvay conference The Solvay Conferences (french: Conseils Solvay) have been devoted to outstanding preeminent open problems in both physics and chemistry. They began with the historic invitation-only 1911 Solvay Conference on Physics, considered a turning point i ...
, that year, Einstein brushed him off with "" (“Your math is correct, but your physics is abominable”). In 1929,
Edwin Hubble Edwin Powell Hubble (November 20, 1889 – September 28, 1953) was an American astronomer. He played a crucial role in establishing the fields of extragalactic astronomy and observational cosmology. Hubble proved that many objects previousl ...
(1889–1953) announced his discovery of the expanding universe. The current generally accepted cosmological model, the
Lambda-CDM model The ΛCDM (Lambda cold dark matter) or Lambda-CDM model is a parameterization of the Big Bang cosmological model in which the universe contains three major components: first, a cosmological constant denoted by Lambda ( Greek Λ) associated ...
, 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 George Gamow (March 4, 1904 – August 19, 1968), born Georgiy Antonovich Gamov ( uk, Георгій Антонович Гамов, russian: Георгий Антонович Гамов), was a Russian-born Soviet and American polymath, theoret ...
(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 by
Fred Hoyle Sir Fred Hoyle FRS (24 June 1915 – 20 August 2001) was an English astronomer who formulated the theory of stellar nucleosynthesis and was one of the authors of the influential B2FH paper. He also held controversial stances on other sci ...
(1915–2001), who invented the term '
Big Bang The Big Bang event is a physical theory that describes how the universe expanded from an initial state of high density and temperature. Various cosmological models of the Big Bang explain the evolution of the observable universe from the ...
' to disparage it.
Fermi Enrico Fermi (; 29 September 1901 – 28 November 1954) was an Italian (later naturalized American) physicist and the creator of the world's first nuclear reactor, the Chicago Pile-1. He has been called the "architect of the nuclear age" and t ...
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-
kelvin The kelvin, symbol K, is the primary unit of temperature in the International System of Units (SI), used alongside its prefixed forms and the degree Celsius. It is named after the Belfast-born and University of Glasgow-based engineer and ...
black-body radiation Black-body radiation is the thermal electromagnetic radiation within, or surrounding, a body in thermodynamic equilibrium with its environment, emitted by a black body (an idealized opaque, non-reflective body). It has a specific, continuous spe ...
temperature for the universe, after it cooled during the expansion. This was corroborated by Penzias and Wilson in 1965. Subsequent experiments arrived at a 2.7 kelvins temperature, corresponding to an age 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 the spacetime foam; there are only hints based on broken symmetries (see Spontaneous symmetry breaking, Timeline of the Big Bang, and the articles in :Physical cosmology).
General relativity General relativity, also known as the general theory of relativity and Einstein's theory of gravity, is the geometric theory of gravitation published by Albert Einstein in 1915 and is the current description of gravitation in modern physics ...
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 our
epoch In chronology and periodization, an epoch or reference epoch is an instant in time chosen as the origin of a particular calendar era. The "epoch" serves as a reference point from which time is measured. The moment of epoch is usually decided ...
, 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 the
Big Bang The Big Bang event is a physical theory that describes how the universe expanded from an initial state of high density and temperature. Various cosmological models of the Big Bang explain the evolution of the observable universe from the ...
, during which starlight would not have been visible over large distances.)


Reprise

Ilya Prigogine's reprise is ''"
Time Time is the continued sequence of existence and event (philosophy), events that occurs in an apparently irreversible process, irreversible succession from the past, through the present, into the future. It is a component quantity of various me ...
precedes
existence Existence is the ability of an entity to interact with reality. In philosophy, it refers to the ontological property of being. Etymology The term ''existence'' comes from Old French ''existence'', from Medieval Latin ''existentia/exsistentia' ...
"''. 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 explain irreversible phenomena,Prigogine, Ilya (1996), ''The End of Certainty: Time, Chaos and the New Laws of Nature''. On pages 163 and 182. as well as the
arrow of time The arrow of time, also called time's arrow, is the concept positing the "one-way direction" or "asymmetry" of time. It was developed in 1927 by the British astrophysicist Arthur Eddington, and is an unsolved general physics question. This ...
and the
Big Bang The Big Bang event is a physical theory that describes how the universe expanded from an initial state of high density and temperature. Various cosmological models of the Big Bang explain the evolution of the observable universe from the ...
.


See also

*
Relativistic dynamics ''For classical dynamics at relativistic speeds, see relativistic mechanics.'' Relativistic dynamics refers to a combination of relativistic and quantum concepts to describe the relationships between the motion and properties of a relativistic sys ...
* :systems of units * Time in astronomy


References


Further reading

* Boorstein, Daniel J., ''The Discoverers''. Vintage. February 12, 1985. * Dieter Zeh, H., ''The physical basis of the direction of time''. Springer. * Kuhn, Thomas S., ''The Structure of Scientific Revolutions''. * Mandelbrot, Benoît, ''Multifractals and 1/f noise''. Springer Verlag. February 1999. * Prigogine, Ilya (1984), ''Order out of Chaos''. * Serres, Michel, et al., "''Conversations on Science, Culture, and Time (Studies in Literature and Science)''". March, 1995. * Stengers, Isabelle, and Ilya Prigogine, ''Theory Out of Bounds''. University of Minnesota Press. November 1997.


External links

* {{Time measurement and standards Philosophy of physics Time Timekeeping