time in physics

TheInfoList

Time in physics is defined by its
measurement ' Measurement is the number, numerical quantification (science), quantification of the variable and attribute (research), attributes of an object or event, which can be used to compare with other objects or events. The scope and application of meas ...
: time is what a
clock A clock or a timepiece is a device used to Measurement, measure and indicate time. The clock is one of the oldest Invention, human inventions, meeting the need to measure intervals of time shorter than the natural units: the day, the lunar ...

reads. In classical, non-relativistic physics, it is a
scalar Scalar may refer to: *Scalar (mathematics), an element of a field, which is used to define a vector space, usually the field of real numbers *Scalar (physics), a physical quantity that can be described by a single element of a number field such as ...
quantity (often denoted by the symbol $t$) and, like
length Length is a measure of distance. In the International System of Quantities The International System of Quantities (ISQ) is a set of quantities and the equation In mathematics, an equation is a statement that asserts the equality (mathema ...

,
mass Mass is the physical quantity, quantity of ''matter'' in a physical body. It is also a measure (mathematics), measure of the body's ''inertia'', the resistance to acceleration (change of velocity) when a net force is applied. An object's mass ...
, and
charge Charge or charged may refer to: Arts, entertainment, and media Films * ''Charge, Zero Emissions/Maximum Speed'', a 2011 documentary Music * Charge (David Ford album), ''Charge'' (David Ford album) * Charge (Machel Montano album), ''Charge'' (Mac ...
, is usually described as a fundamental quantity. Time can be combined mathematically with other
physical quantities A physical quantity is any phenomenon that can be measured with an instrument or be calculated for. A physical quantity can be expressed as the combination of a numerical value and a unit Unit may refer to: Arts and entertainment * UNIT, a fictiona ...
to
derive Derive may refer to: *Derive (computer algebra system), a commercial system made by Texas Instruments *Dérive (magazine), ''Dérive'' (magazine), an Austrian science magazine on urbanism *Dérive, a psychogeographical concept See also

* *Deri ...
other concepts such as
motion Image:Leaving Yongsan Station.jpg, 300px, Motion involves a change in position In physics, motion is the phenomenon in which an object changes its position (mathematics), position over time. Motion is mathematically described in terms of Displacem ...
,
kinetic energy In physics, the kinetic energy of an object is the energy that it possesses due to its motion (physics), motion. It is defined as the work (physics), work needed to accelerate a body of a given mass from rest to its stated velocity. Having gaine ...
and time-dependent
fields File:A NASA Delta IV Heavy rocket launches the Parker Solar Probe (29097299447).jpg, FIELDS heads into space in August 2018 as part of the ''Parker Solar Probe'' FIELDS is a science instrument on the ''Parker Solar Probe'' (PSP), designed to mea ...
. ''
Timekeeping Time is the indefinite continued progress of existence Existence is the ability of an entity to interact with physical or mental reality Reality is the sum or aggregate of all that is real or existent within a system, as opposed to that wh ...
'' is a complex of technological and scientific issues, and part of the foundation of ''
recordkeepingRecords management, also known as records and information management, is an organizational function devoted to the information management , management of information in an organization throughout its records life-cycle, life cycle, from the time of ...
''.

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 risingThe 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 (disambiguation)#Astronomy, mo ...
) of
Sirius Sirius () is the brightest star in the night sky The term night sky, usually associated with astronomy from Earth, refers to the nighttime appearance of astronomical object, celestial objects like stars, planets, and the Moon, ...

to mark the
flooding of the Nile The flooding of the Nile has been an important natural cycle in Egypt Egypt ( ; ar, مِصر ), officially the Arab Republic of Egypt, is a transcontinental country spanning the North Africa, northeast corner of Africa and Western Asia, so ...
each year
Otto Neugebauer Otto Eduard Neugebauer (May 26, 1899 – February 19, 1990) was an Austrian-American mathematician A mathematician is someone who uses an extensive knowledge of mathematics Mathematics (from Ancient Greek, Greek: ) includes the study of s ...
''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, night-time, or nighttime, unconventionally spelled as ''nite'') is the period of ambient Ambient or Ambiance or Ambience may refer to: Music and sound * Ambience (sound recording), also known as atmosphere ...

and
day A day is approximately the period during which the Earth completes one rotation around its axis, which takes around 24 hours. A solar day is the length of time which elapses between the Sun reaching its highest point in the sky two consecutive t ...

, 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
noon Noon (or midday) is 12 o'clock in the daytime On Earth, daytime is the period of the day during which a given location experiences Daylight, natural illumination from direct sunlight. Daytime occurs when the Sun appears above the local h ...

time during the day *the length of the shadow cast by a
gnomon A gnomon (, from Greek , ''gnōmōn'', literally: "one that knows or examines") 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 2 ...

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 International is an adjective (also used as a noun) meaning "between nations". International may also refer to: Music Albums * International (Kevin Michael album), ''International'' (Kevin Michael album), 2011 * International (New Order album), '' ...
(SI), the unit of time is the
second The second (symbol: s, also abbreviated: sec) is the base unit of time Time is the indefinite continued sequence, progress of existence and event (philosophy), events that occur in an apparently irreversible process, irreversible succession ...
(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 all ot ...

, and has been defined since 1967 as "the duration of yclesof the
radiation upThe international symbol for types and levels of ionizing radiation (radioactivity) that are unsafe for unshielded humans. Radiation, in general, exists throughout nature, such as in light and sound. In physics Physics (from grc ...

corresponding to the transition between the two hyperfine levels of the
ground state The ground state of a quantum mechanics, quantum-mechanical system is its lowest-energy stationary state, state; 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 ...
of the
caesium Caesium (IUPAC spelling) (American and British English spelling differences, also spelled cesium in American English) is a chemical element with the Symbol (chemistry), symbol Cs and atomic number 55. It is a soft, silvery-golden alkali ...

133 atom". This definition is based on the operation of a caesium
atomic clock An atomic clock is a clock A clock is a device used to measure, verify, keep, 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: the day, t ...

. 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. The term derives from rubber stamp Rubber sta ...

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 In particle physics Particle physics (also known as high energy physics) is a branch of physics Physics (from grc, φυσική (ἐπιστήμη), physikḗ (epistḗmē), knowledge of nature, from ''phýsis'' 'nature'), , is the ...
, 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, 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), commonly referred to as Galileo, was an astronomer, physicist and engineer, sometimes described as a polymath, from Pisa, in modern-day Italy. Galileo h ...

,
Newton Newton most commonly refers to: * Isaac Newton (1642–1726/1727), English scientist * Newton (unit), SI unit of force named after Isaac Newton Newton may also refer to: Arts and entertainment * Newton (film), ''Newton'' (film), a 2017 Indian fil ...

, 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 222px, Joseph Scaliger's ''De emendatione temporum'' (1583) began the modern science of chronology Chronology (from Latin Latin (, or , ) is a classical language belonging ...
s, where time is a
parameter A parameter (), generally, is any characteristic that can help in defining or classifying a particular system A system is a group of Interaction, interacting or interrelated elements that act according to a set of rules to form a unified whol ...

. The modern understanding of time is based on
Einstein Albert Einstein ( ; ; 14 March 1879 – 18 April 1955) was a German-born theoretical physicist, widely acknowledged to be one of the greatest physicists of all time. Einstein is known for developing the theory of relativity The theory ...

's
theory of relativity The theory of relativity usually encompasses two interrelated theories by Albert Einstein: special relativity and general relativity. Special relativity applies to all physical phenomena in the absence of gravity. General relativity explains th ...
, in which rates of time run differently depending on relative motion, and
space Space is the boundless three-dimensional Three-dimensional space (also: 3-space or, rarely, tri-dimensional space) is a geometric setting in which three values (called parameter A parameter (from the Ancient Greek language, Ancient Gree ...

and time are merged into
spacetime In physics Physics is the natural science that studies matter, its Elementary particle, fundamental constituents, its Motion (physics), motion and behavior through Spacetime, space and time, and the related entities of energy and force. "P ...
, where we live on a
world line The world line (or worldline) of an object is the path that an object traces in 4-dimension thumb , 236px , The first four spatial dimensions, represented in a two-dimensional picture. In physics Physics (from grc, φυσι ...

rather than a timeline. In this view time is a
coordinate In geometry Geometry (from the grc, γεωμετρία; ''wikt:γῆ, geo-'' "earth", ''wikt:μέτρον, -metron'' "measurement") is, with arithmetic, one of the oldest branches of mathematics. It is concerned with properties of space t ...

. According to the prevailing
cosmological Cosmology (from Greek κόσμος, ''kosmos'' "world" and -λογία, ''-logia'' "study of") is a branch of astronomy Astronomy (from el, ἀστρονομία, literally meaning the science that studies the laws of the stars) is a ...
model In general, a model is an informative representation of an object, person or system. The term originally denoted the plans of a building in late 16th-century English, and derived via French and Italian ultimately from Latin ''modulus'', a measure. ...
of the
Big Bang The Big Bang Scientific theory, theory is the prevailing cosmological model explaining the existence of the observable universe from the Planck units#Cosmology, earliest known periods through its subsequent large-scale evolution. The model d ...

theory, time itself began as part of the entire
Universe The universe ( la, universus) is all of space and time and their contents, including planets, stars, galaxy, galaxies, and all other forms of matter and energy. The Big Bang theory is the prevailing cosmological description of the development ...

Regularities in nature

In order to measure time, one can record the number of occurrences (events) of some
phenomenon A phenomenon (; plural phenomena) is an observable In physics Physics (from grc, φυσική (ἐπιστήμη), physikḗ (epistḗmē), knowledge of nature, from ''phýsis'' 'nature'), , is the natural science that studies mat ...
. The regular recurrences of the
seasons A season is a division of the year based on changes in weather Weather is the state of the atmosphere, describing for example the degree to which it is hot or cold, wet or dry, calm or stormy, clear or cloudy. On Earth Earth is the ...

, the
motion Image:Leaving Yongsan Station.jpg, 300px, Motion involves a change in position In physics, motion is the phenomenon in which an object changes its position (mathematics), position over time. Motion is mathematically described in terms of Displacem ...
s of the
sun The Sun is the star A star is an astronomical object consisting of a luminous spheroid of plasma (physics), plasma held together by its own gravity. The List of nearest stars and brown dwarfs, nearest star to Earth is the Sun. Many othe ...

,
moon The Moon is Earth's only natural satellite. At about one-quarter the diameter of Earth (comparable to the width of Australia (continent), Australia), it is the largest natural satellite in the Solar System relative to the size of its planet ...

and
star A star is an astronomical object consisting of a luminous spheroid of plasma Plasma or plasm may refer to: Science * Plasma (physics), one of the four fundamental states of matter * Plasma (mineral) or heliotrope, a mineral aggregate * Quark ...

s were noted and tabulated for millennia, before the
laws of physics Scientific laws or laws of science are statements, based on repeated experiment An experiment is a procedure carried out to support, refute, or validate a hypothesis. Experiments provide insight into Causality, cause-and-effect by demonstrat ...
were formulated. The sun was the arbiter of the flow of time, but
time Time is the indefinite continued sequence, progress of existence and event (philosophy), events that occur in an apparently irreversible process, irreversible succession from the past, through the present, into the future. It is a component qua ...

was known only to the
hour An hour (metric symbol, symbol: h; also abbreviated hr) is a unit of measurement, unit of time conventionally reckoned as of a day and scientifically reckoned as 3,599–3,601 seconds, depending on conditions. There are 60 minutes in an hour, a ...
for
millennia A millennium (plural millennia or millenniums) is a period of one thousand year A year is the orbital period of a planetary body, for example, the Earth, moving in Earth's orbit, its orbit around the Sun. Due to the Earth's axial tilt, the ...

, hence, the use of the
gnomon A gnomon (, from Greek , ''gnōmōn'', literally: "one that knows or examines") 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 2 ...

was known across most of the world, especially
Eurasia Eurasia () is the largest continent A continent is any of several large landmasses. Generally identified by convention (norm), convention rather than any strict criteria, up to seven geographical regions are commonly regarded as contin ...

, 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 or SEA, is the geographical southeastern subregion of Asia, consisting of the regions that are south of China, south-east of the Indian sub ...

. 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 indefinite continued progress of existence Existence is the ability of an entity to interact with physical or mental reality Reality is the sum or aggregate of all that is real or existent within a system, as opposed to that wh ...
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 An equinox is traditionally defined as the time when the plane In mathematics, a plane is a flatness (mathematics), flat, two-dimensional surface (mathematics), surface that extends infinitely far. A plane is the two-dimensional space, two-di ...

es, the sandglass, and the
water clock A water clock or clepsydra (Greek Greek may refer to: Greece Anything of, from, or related to Greece Greece ( el, Ελλάδα, , ), officially the Hellenic Republic, is a country located in Southeast Europe. Its population is approximat ...
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 The first or given name Richard originates, via Old French Old French (, , ; French language, Modern French: ) was the language spoken in Northern France from the 8th century to the 14th century. Rather than a unified Dialect#Dialect or lan ...

(1292–1336), abbot of St. Alban's abbey, famously built a mechanical clock as an astronomical
orrery An orrery is a mechanical Solar system model, model of the Solar System that illustrates or predicts the relative positions and motions of the planets and natural satellite, moons, usually according to the heliocentric Scientific modelling, model ...
about 1330. By the time of Richard of Wallingford, the use of ratchets and
gear Cast iron mortise wheel with wooden cogs (powered by an external water wheel) meshing with a cast iron gear wheel, connected to a pulley A pulley is a wheel on an axle or shaft (mechanical engineering), shaft that is designed to support ...

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 A clock or a timepiece is a device used to Measurement, measure and indicate time. The clock is one of the oldest Invention, human inventions, meeting the need to measure intervals of time shorter than the nat ...
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 Tetrahedral molecular geometry, tetrahedra, with each oxygen being shared between two tetrahedra, ...

and
digital clock A digital clock is a type of clock A clock is a device used to measure, verify, keep, 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: the ...

s.
Atomic clocks An atomic clock is a clock whose timekeeping mechanism is based on the interaction of electromagnetic radiation with the Excited state, excited states of certain Atom, atoms. Specifically, either a Hyperfine structure, hyperfine transition in t ...

can theoretically keep accurate time for millions of years. They are appropriate for
standard Standard may refer to: Flags * Colours, standards and guidons * Standard (flag), a type of flag used for personal identification Norm, convention or requirement * Standard (metrology), an object that bears a defined relationship to a unit of ...
s 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 An astronomer is a scientist in the field of astronomy who focuses their studies on a specific question or field outside the ...

(1564–1642) discovered that a has a constant period, which he learned by timing the motion of a swaying lamp in at
mass Mass is the physical quantity, quantity of ''matter'' in a physical body. It is also a measure (mathematics), measure of the body's ''inertia'', the resistance to acceleration (change of velocity) when a net force is applied. An object's mass ...
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 of Pisa, ...

, with his
pulse In medicine Medicine is the science Science (from the Latin word ''scientia'', meaning "knowledge") is a systematic enterprise that Scientific method, builds and Taxonomy (general), organizes knowledge in the form of Testability, testabl ...

. In his ''
Two New Sciences The ''Discourses and Mathematical Demonstrations Relating to Two New Sciences'' ( it, Discorsi e dimostrazioni matematiche intorno a due nuove scienze ) published in 1638 was Galileo Galilei Galileo di Vincenzo Bonaiuti de' Galilei (; ...
'' (1638),
Galileo Galileo di Vincenzo Bonaiuti de' Galilei ( , ; 15 February 1564 – 8 January 1642), commonly referred to as Galileo, was an astronomer, physicist and engineer, sometimes described as a polymath, from Pisa, in modern-day Italy. Galileo h ...

used a
water clock A water clock or clepsydra (Greek Greek may refer to: Greece Anything of, from, or related to Greece Greece ( el, Ελλάδα, , ), officially the Hellenic Republic, is a country located in Southeast Europe. Its population is approximat ...
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, 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 classical simple machines defin ...

; this clock was :"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 Galileo di Vincenzo Bonaiuti de' Galilei ( , ; 15 February 1564 – 8 January 1642), commonly referred to as Galileo, was an astronomer, physicist and engineer, sometimes described as a polymath, from Pisa, in modern-day Italy. Galileo h ...

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 The ''Discourses and Mathematical Demonstrations Relating to Two New Sciences'' ( it, Discorsi e dimostrazioni matematiche intorno a due nuove scienze ) published in 1638 was Galileo Galilei Galileo di Vincenzo Bonaiuti de' Galilei (; ...
'', 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; german: link=no, Niclas Koppernigk, modern: ''Nikolaus Kopernikus''; 19 February 1473 – 24 May 1543) was a Renaissance The Renaissance ( , ) , from , with the same meanings. was a ...

,
Kepler Johannes Kepler (; ; 27 December 1571 – 15 November 1630) was a German astronomer, mathematician, astrologer, Natural philosophy, natural philosopher and writer on music. He is a key figure in the 17th-century Scientific Revolution, best kno ...

,
Galileo Galileo di Vincenzo Bonaiuti de' Galilei ( , ; 15 February 1564 – 8 January 1642), commonly referred to as Galileo, was an astronomer, physicist and engineer, sometimes described as a polymath, from Pisa, in modern-day Italy. Galileo h ...

,
Newton Newton most commonly refers to: * Isaac Newton (1642–1726/1727), English scientist * Newton (unit), SI unit of force named after Isaac Newton Newton may also refer to: Arts and entertainment * Newton (film), ''Newton'' (film), a 2017 Indian fil ...

, and
Einstein Albert Einstein ( ; ; 14 March 1879 – 18 April 1955) was a German-born theoretical physicist, widely acknowledged to be one of the greatest physicists of all time. Einstein is known for developing the theory of relativity The theory ...

).
Stephen Hawking Stephen William Hawking (8 January 1942 – 14 March 2018) was an English theoretical physicist, cosmologist, and author who was director of research at the Centre for Theoretical Cosmology at the University of Cambridge at the time of his ...

, ed. 2002
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 Old Style and New Style dates, 1726/27) was an English mathematician, physicist, astronomer, theologian, and author (described in his time as a "natural philosophy, natural philosopher") ...

's statement in his Principia: :''I do not define
time Time is the indefinite continued sequence, progress of existence and event (philosophy), events that occur in an apparently irreversible process, irreversible succession from the past, through the present, into the future. It is a component qua ...

,
space Space is the boundless three-dimensional Three-dimensional space (also: 3-space or, rarely, tri-dimensional space) is a geometric setting in which three values (called parameter A parameter (from the Ancient Greek language, Ancient Gree ...

,
place Place may refer to: Geography * Place (United States Census Bureau)The United States Census Bureau defines a place as a concentration of population which has a name, is locally recognized, and is not part of any other place. A place typically ha ...
and
motion Image:Leaving Yongsan Station.jpg, 300px, Motion involves a change in position In physics, motion is the phenomenon in which an object changes its position (mathematics), position over time. Motion is mathematically described in terms of Displacem ...
, as being well known to all.''
Newton Newton most commonly refers to: * Isaac Newton (1642–1726/1727), English scientist * Newton (unit), SI unit of force named after Isaac Newton Newton may also refer to: Arts and entertainment * Newton (film), ''Newton'' (film), a 2017 Indian fil ...

1687 ''
Philosophiae Naturalis Principia Mathematica Philosophy (from , ) is the study of general and fundamental questions, such as those about reason Reason is the capacity of consciously making sense of things, applying logic Logic (from Ancient Greek, Greek: grc, wikt:λογι ...
'', Londini, Jussu Societatis Regiae ac Typis J. Streater, or '' The Mathematical Principles of Natural Philosophy'', London, 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; german: link=no, Niclas Koppernigk, modern: ''Nikolaus Kopernikus''; 19 February 1473 – 24 May 1543) was a Renaissance The Renaissance ( , ) , from , with the same meanings. was a ...

,
Kepler Johannes Kepler (; ; 27 December 1571 – 15 November 1630) was a German astronomer, mathematician, astrologer, Natural philosophy, natural philosopher and writer on music. He is a key figure in the 17th-century Scientific Revolution, best kno ...

,
Galileo Galileo di Vincenzo Bonaiuti de' Galilei ( , ; 15 February 1564 – 8 January 1642), commonly referred to as Galileo, was an astronomer, physicist and engineer, sometimes described as a polymath, from Pisa, in modern-day Italy. Galileo h ...

,
Newton Newton most commonly refers to: * Isaac Newton (1642–1726/1727), English scientist * Newton (unit), SI unit of force named after Isaac Newton Newton may also refer to: Arts and entertainment * Newton (film), ''Newton'' (film), a 2017 Indian fil ...

, and
Einstein Albert Einstein ( ; ; 14 March 1879 – 18 April 1955) was a German-born theoretical physicist, widely acknowledged to be one of the greatest physicists of all time. Einstein is known for developing the theory of relativity The theory ...

).
Stephen Hawking Stephen William Hawking (8 January 1942 – 14 March 2018) was an English theoretical physicist, cosmologist, and author who was director of research at the Centre for Theoretical Cosmology at the University of Cambridge at the time of his ...

, ed. 2002
The Galilean transformations assume that time is the same for all Frame of reference, reference frames.

Newton's physics: linear time

In or around 1665, when
Isaac Newton Sir Isaac Newton (25 December 1642 – 20 March Old Style and New Style dates, 1726/27) was an English mathematician, physicist, astronomer, theologian, and author (described in his time as a "natural philosophy, natural philosopher") ...

(1643–1727) derived the motion of objects falling under gravity, the first clear formulation for mathematical physics 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 Newton most commonly refers to: * Isaac Newton (1642–1726/1727), English scientist * Newton (unit), SI unit of force named after Isaac Newton Newton may also refer to: Arts and entertainment * Newton (film), ''Newton'' (film), a 2017 Indian fil ...

1687 page 738.
The
water clock A water clock or clepsydra (Greek Greek may refer to: Greece Anything of, from, or related to Greece Greece ( el, Ελλάδα, , ), officially the Hellenic Republic, is a country located in Southeast Europe. Its population is approximat ...
mechanism described by Galileo was engineered to provide laminar flow 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 fluent (mathematics), 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 (1753–1814) had discovered that work could be transformed to heat without limit - a precursor of the conservation of energy or *Conservation of energy, 1st law of thermodynamics In 1824 Nicolas Léonard Sadi Carnot, Sadi Carnot (1796–1832) scientifically analyzed the steam engine with his Carnot cycle, an abstract engine. Rudolf Clausius (1822–1888) noted a measure of disorder, or entropy, which affects the continually decreasing amount of free energy which is available to a Carnot engine in the: *Entropy, 2nd law of thermodynamics Thus the continual march of a thermodynamic system, from lesser to greater entropy, at any given temperature, defines an arrow of time. In particular,
Stephen Hawking Stephen William Hawking (8 January 1942 – 14 March 2018) was an English theoretical physicist, cosmologist, and author who was director of research at the Centre for Theoretical Cosmology at the University of Cambridge at the time of his ...

identifies three arrows of time:pp. 182–195.
Stephen Hawking Stephen William Hawking (8 January 1942 – 14 March 2018) was an English theoretical physicist, cosmologist, and author who was director of research at the Centre for Theoretical Cosmology at the University of Cambridge at the time of his ...

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. *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 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 theory, 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 (1831–1879) presented a combined theory of electricity and magnetism. He combined all the laws then known relating to those two phenomenon into four equations. These vector calculus equations which use the del, del operator ($\nabla$) are known as Maxwell's equations for electromagnetism. In free space (that is, space not containing electric charges), the equations take the form (using International System of Units, SI units): :$\nabla \times \mathbf = -\frac$ :$\nabla \times \mathbf = \mu_0 \varepsilon_0 \frac = \frac \frac$ :$\nabla \cdot \mathbf = 0$ :$\nabla \cdot \mathbf = 0$ where :''ε''0 and ''μ''0 are the vacuum permittivity, electric permittivity and the vacuum permeability, magnetic permeability of free space; :''c'' = $1/\sqrt$ is the speed of light in free space, 299 792 458 metre, m/second, s; :E is the electric field; :B is the magnetic field. These equations allow for solutions in the form of electromagnetic waves. The wave is formed by an electric field and a magnetic field oscillating together, perpendicular to each other and to the direction of propagation. These waves always propagate at the speed of light ''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 (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 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) discovered Lorentz 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 in ''Science and Hypothesis'', which was published before Einstein's articles of 1905. The Lorentz transformation predicted space contraction and time 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.

Einstein's physics: spacetime

Albert Einstein's 1905 special relativity challenged the notion of absolute time, and could only formulate a definition of synchronization 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) :$\begin t\text{'} &= \gamma\left(t - vx/c^2\right) \text \gamma = 1/\sqrt \\ x\text{'} &= \gamma\left(x - vt\right)\\ y\text{'} &= y \\ z\text{'} &= z \end$ 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. More specifically, the Lorentz transformation is a hyperbolic rotation $\begin ct\text{'} \\ x\text{'} \end = \begin \cosh \phi & - \sinh \phi \\ - \sinh \phi & \cosh \phi \end \begin ct \\ x \end \text \phi = \operatorname\,\frac \text$ which is a change of coordinates in the four-dimensional Minkowski space, a dimension of which is ''ct''. (In Euclidean space an ordinary rotation $\begin x\text{'} \\ y\text{'} \end = \begin \cos \theta & - \sin \theta \\ \sin \theta & \cos \theta \end \begin x \\ y \end$ 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 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 natural units, 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. Moving objects therefore are said to ''show a slower passage of time''. This is known as time dilation. 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. 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 which describes Minkowski space: :$\left\left[\left(dx^1\right)^2+\left(dx^2\right)^2+\left(dx^3\right)^2-c\left(dt\right)^2\right)\right\right],$ Einstein developed a geometric solution to Lorentz's transformation that preserves Maxwell's equations. His Einstein's field equations, field equations give an exact relationship between the measurements of space and time in a given region of
spacetime In physics Physics is the natural science that studies matter, its Elementary particle, fundamental constituents, its Motion (physics), motion and behavior through Spacetime, space and time, and the related entities of energy and force. "P ...
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): :$T=\frac$ 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 :$M$ is the
mass Mass is the physical quantity, quantity of ''matter'' in a physical body. It is also a measure (mathematics), measure of the body's ''inertia'', the resistance to acceleration (change of velocity) when a net force is applied. An object's mass ...
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), the more slowly time runs. The predictions of time dilation are confirmed by particle accelerator, particle acceleration experiments and cosmic ray evidence, where moving particles particle decay, decay more slowly than their less energetic counterparts. Gravitational time dilation gives rise to the phenomenon of gravitational redshift and Shapiro delay, Shapiro signal travel time delays near massive objects such as the sun. The Global 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 by Edwin F. Taylor, Taylor and John Archibald Wheeler, Wheeler 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 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. The Schrödinger equation is :$H\left(t\right) \left, \psi \left(t\right) \right\rangle = i \hbar \left, \psi \left(t\right) \right\rangle$ One solution can be :$, \psi_e\left(t\right) \rangle = e^ , \psi_e\left(0\right) \rangle$. where $e^$ is called the time evolution operator, and ''H'' is the Hamiltonian (quantum mechanics), Hamiltonian. But the Schrödinger picture shown above is equivalent to the Heisenberg picture, which enjoys a similarity to the Poisson brackets of classical mechanics. The Poisson brackets are superseded by a nonzero commutator, say [H,A] for observable A, and Hamiltonian H: :$\fracA=\left(i\hbar\right)^\left[A,H\right]+\left\left(\frac\right\right)_\mathrm.$ This equation denotes an uncertainty principle, 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 Accuracy and precision, precisely one measures the duration of a Phenomenon, 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 (physics), operator in quantum mechanics. Corresponding commutator relations also hold for momentum ''p'' and position ''q'', which are conjugate 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 the periodic table of the chemical element, elements. Starting with Otto Stern's and Walter Gerlach's experiment with molecular beams in a magnetic field, Isidor Rabi (1898–1988), was able to modulation, 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 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 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 theory, chaos'' (i.e. nonlinearity/irreversibility): the characteristic time, or rate of information entropy production, of a system. Benoît Mandelbrot, 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
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Signalling

Signalling is one application of the electromagnetic waves described above. In general, a signal is part of communication between parties and places. One example might be a yellow ribbon tied to a tree, or the ringing of a church bell. A signal can be part of a conversation, which involves a Communications protocol, protocol. 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. 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 could be founded. In 19th century telegraphy, electrical circuits, some spanning continents and oceans, could transmit codes - 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 Synchronization, synchronized, a plesiochronous condition, from which jitter need be eliminated. That said, systems ''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-cooled Caesium, Cs fountain, the latest in a series of time and frequency standards, from the ammonia-based atomic clock (1949) to the
caesium Caesium (IUPAC spelling) (American and British English spelling differences, also spelled cesium in American English) is a chemical element with the Symbol (chemistry), symbol Cs and atomic number 55. It is a soft, silvery-golden alkali ...

-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. 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. Additionally, a reference Maser#Hydrogen maser, hydrogen maser is also reported to BIPM as a frequency standard for International Atomic Time, TAI (International Atomic Time, international atomic time). The measurement of time is overseen by BIPM (''Bureau International des Poids et Mesures''), located in Sèvres, France, which ensures uniformity of measurements and their traceability to the
International System of Units International is an adjective (also used as a noun) meaning "between nations". International may also refer to: Music Albums * International (Kevin Michael album), ''International'' (Kevin Michael album), 2011 * International (New Order album), '' ...
(SI) worldwide. BIPM operates under authority of the Metre 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 national metrology 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 (1894–1966) argued, on the basis of general relativity, that the universe originated in a primordial explosion. At the fifth Solvay conference, that year, Einstein brushed him off with "" (“Your math is correct, but your physics is abominable”). In 1929, Edwin Hubble (1889–1953) announced his discovery of the expanding universe. The current generally accepted cosmological model, the Lambda-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 by Fred Hoyle (1915–2001), who invented the term '
Big Bang The Big Bang Scientific theory, theory is the prevailing cosmological model explaining the existence of the observable universe from the Planck units#Cosmology, earliest known periods through its subsequent large-scale evolution. The model d ...

' to disparage it. Enrico Fermi, 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-kelvin black-body radiation temperature for the universe, after it cooled during the expansion. This was corroborated by Discovery of cosmic microwave background radiation, 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 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 age of the universe, epoch, 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 Scientific theory, theory is the prevailing cosmological model explaining the existence of the observable universe from the Planck units#Cosmology, earliest known periods through its subsequent large-scale evolution. The model d ...

, during which starlight would not have been visible over large distances.)

Reprise

Ilya Prigogine's reprise is ''"Time precedes existence"''. 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 process, 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 and the
Big Bang The Big Bang Scientific theory, theory is the prevailing cosmological model explaining the existence of the observable universe from the Planck units#Cosmology, earliest known periods through its subsequent large-scale evolution. The model d ...

.