Time

 Time is the continuous progression of our changing existence that occurs in an apparently irreversible succession from the past, through the present, and into the future.[1][2][3] It is a component quantity of various measurements used to sequence events, to compare the duration of events (or the intervals between them), and to quantify rates of change of quantities in material reality or in the conscious experience.[4][5][6][7] Time is often referred to as a fourth dimension, along with three spatial dimensions.[8][9] Scientists have theorized a beginning of time in our universe (the Big Bang) and an end (e.g., heat death or the Big Crunch). A cyclic model describes a cyclical nature, whereas the philosophy of eternalism views the subject from a different angle.

Time is one of the seven fundamental physical quantities in both the International System of Units (SI) and International System of Quantities. The SI base unit of time is the second, which is defined by measuring the electronic transition frequency of caesium atoms. General relativity is the primary framework for understanding how spacetime works.[10] Through advances in both theoretical and experimental investigations of spacetime, it has been shown that time can be distorted and dilated, particularly at the edges of black holes.

Throughout history, time has been an important subject of study in religion, philosophy, and science. Temporal measurement has occupied scientists and technologists and has been a prime motivation in navigation and astronomy. Time is also of significant social importance, having economic value ("time is money") as well as personal value, due to an awareness of the limited time in each day and in human life spans. Cultural attitudes towards the human use of time are apparent in the verbs used—from "kill" to "waste" to "pass"—and sayings (like carpe diem).

Definition

The concept of time can be complex. Multiple notions exist and defining time in a manner applicable to all fields without circularity has consistently eluded scholars.[7][11][12] Nevertheless, diverse fields such as business, industry, sports, the sciences, and the performing arts all incorporate some notion of time into their respective measuring systems.[13][14][15] Traditional definitions of time involved the observation of periodic motion such as the apparent motion of the sun across the sky, the phases of the moon, and the passage of a free-swinging pendulum. More modern systems include the Global Positioning System, other satellite systems, Coordinated Universal Time and mean solar time. Although these systems differ from one another, with careful measurements they can be synchronized.

In physics, time is a fundamental concept to define other quantities, such as velocity. To avoid a circular definition,[16] time in physics is operationally defined as "what a clock reads", specifically a count of repeating events such as the SI second.[6][17][18] Although this aids in practical measurements, it does not address the essence of time. Physicists developed the concept of the spacetime continuum, where events are assigned four coordinates: three for space and one for time. Events like particle collisions, supernovas, or rocket launches have coordinates that may vary for different observers, making concepts like "now" and "here" relative. In general relativity, these coordinates do not directly correspond to the causal structure of events. Instead, the spacetime interval is calculated and classified as either space-like or time-like, depending on whether an observer exists that would say the events are separated by space or by time.[19] Since the time required for light to travel a specific distance is the same for all observers—a fact first publicly demonstrated by the Michelson–Morley experiment—all observers will consistently agree on this definition of time as a causal relation.[20]

General relativity does not address the nature of time for extremely small intervals where quantum mechanics holds. In quantum mechanics, time is treated as a universal and absolute parameter, differing from general relativity's notion of independent clocks. The problem of time consists of reconciling these two theories.[21] As of 2024, there is no generally accepted theory of quantum general relativity.[22]

Measurement

A sand timer uses the flow of sand to measure the passage of time.

Generally speaking, historical methods of temporal measurement, or chronometry, have taken two distinct forms: the calendar, a mathematical tool for organising long intervals of time,[23] and the clock (e.g., watch), a physical mechanism that counts the passage of time. In day-to-day life, a clock was consulted for periods less than a day, whereas a calendar was consulted for periods longer than a day.

Increasingly, personal electronic devices display both calendars and clocks simultaneously. The number (as on a clock dial or calendar) that marks the occurrence of a specified event (as to hour or date) is obtained by counting from certain starting date (epoch), and relevant to a certain time zone (including daylight saving time). Precise measurements, as in astronomy, use a fiducial epoch – a central reference point.

History of the calendar

Main article: Calendar

Artifacts from the Paleolithic suggest that the moon was used to reckon time as early as 6,000 years ago.[24] Lunar calendars were among the first to appear, with years of either 12 or 13 lunar months (either 354 or 384 days). Without intercalation to add days or months to some years, seasons quickly drift in a calendar based solely on twelve lunar months. Lunisolar calendars have a thirteenth month added to some years to make up for the difference between a full year (now known to be about 365.24 days) and a year of just twelve lunar months. The numbers twelve and thirteen came to feature prominently in many cultures, at least partly due to this relationship of months to years. Other early forms of calendars originated in Mesoamerica, particularly in ancient Mayan civilization. These calendars were religiously and astronomically based, with 18 months in a year and 20 days in a month, plus five epagomenal days at the end of the year.[25]

The reforms of Julius Caesar in 45 BC put the Roman world on a solar calendar. This Julian calendar was faulty in that its intercalation still allowed the astronomical solstices and equinoxes to advance against it by about 11 minutes per year. Pope Gregory XIII introduced a correction in 1582; the Gregorian calendar was only slowly adopted by different nations over a period of centuries, but it is now by far the most commonly used calendar around the world.

During the French Revolution, a new clock and calendar were invented as part of the dechristianization of France and to create a more rational system in order to replace the Gregorian calendar. The French Republican Calendar's days consisted of ten hours of a hundred minutes of a hundred seconds, which marked a deviation from the base 12 (duodecimal) system used in many other devices by many cultures. The system was abolished in 1806.[26]

History of other devices

Horizontal sundial in Canberra

24-hour clock face in Florence

Main article: History of timekeeping devices

See also: Clock

A large variety of devices have been invented to measure time. The study of these devices is called horology.[27]

An Egyptian device that dates to c. 1500 BC, similar in shape to a bent T-square, measured the passage of time from the shadow cast by its crossbar on a nonlinear rule. The T was oriented eastward in the mornings. At noon, the device was turned around so that it could cast its shadow in the evening direction.[28]

A sundial uses a gnomon to cast a shadow on a set of markings calibrated to the hour. The position of the shadow marks the hour in local time. The idea to separate the day into smaller parts is credited to Egyptians because of their sundials, which operated on a duodecimal system. The importance of the number 12 is due to the number of lunar cycles in a year and the number of stars used to count the passage of night.[29]

The most precise timekeeping device of the ancient world was the water clock, or clepsydra, one of which was found in the tomb of Egyptian pharaoh Amenhotep I. They could be used to measure the hours even at night but required manual upkeep to replenish the flow of water. The ancient Greeks and the people from Chaldea (southeastern Mesopotamia) regularly maintained timekeeping records as an essential part of their astronomical observations. Arab inventors and engineers, in particular, made improvements on the use of water clocks up to the Middle Ages.[30] In the 11th century, Chinese inventors and engineers invented the first mechanical clocks driven by an escapement mechanism.

A contemporary quartz watch, 2007

The hourglass uses the flow of sand to measure the flow of time. They were used in navigation. Ferdinand Magellan used 18 glasses on each ship for his circumnavigation of the globe (1522).[31]

Incense sticks and candles were, and are, commonly used to measure time in temples and churches across the globe. Water clocks, and, later, mechanical clocks, were used to mark the events of the abbeys and monasteries of the Middle Ages. Richard of Wallingford (1292–1336), abbot of St. Alban's abbey, famously built a mechanical clock as an astronomical orrery about 1330.[32][33]

Great advances in accurate time-keeping were made by Galileo Galilei and especially Christiaan Huygens with the invention of pendulum-driven clocks along with the invention of the minute hand by Jost Burgi.[34]

The English word clock probably comes from the Middle Dutch word klocke which, in turn, derives from the medieval Latin word clocca, which ultimately derives from Celtic and is cognate with French, Latin, and German words that mean bell. The passage of the hours at sea was marked by bells and denoted the time (see ship's bell). The hours were marked by bells in abbeys as well as at sea.

Chip-scale atomic clocks, such as this one unveiled in 2004, are expected to greatly improve GPS location.[35]

Clocks can range from watches to more exotic varieties such as the Clock of the Long Now. They can be driven by a variety of means, including gravity, springs, and various forms of electrical power, and regulated by a variety of means such as a pendulum.

Alarm clocks first appeared in ancient Greece around 250 BC with a water clock that would set off a whistle. This idea was later mechanized by Levi Hutchins and Seth E. Thomas.[34]

A chronometer is a portable timekeeper that meets certain precision standards. Initially, the term was used to refer to the marine chronometer, a timepiece used to determine longitude by means of celestial navigation, a precision first achieved by John Harrison. More recently, the term has also been applied to the chronometer watch, a watch that meets precision standards set by the Swiss agency COSC.

The most accurate timekeeping devices are atomic clocks, which are accurate to seconds in many millions of years,[36] and are used to calibrate other clocks and timekeeping instruments.

Atomic clocks use the frequency of electronic transitions in certain atoms to measure the second. One of the atoms used is caesium; most modern atomic clocks probe caesium with microwaves to determine the frequency of these electron vibrations.[37] Since 1967, the International System of Measurements bases its unit of time, the second, on the properties of caesium atoms. SI defines the second as 9,192,631,770 cycles of the radiation that corresponds to the transition between two electron spin energy levels of the ground state of the 133Cs atom.

Today, the Global Positioning System in coordination with the Network Time Protocol can be used to synchronize timekeeping systems across the globe.

In medieval philosophical writings, the atom was a unit of time referred to as the smallest possible division of time. The earliest known occurrence in English is in Byrhtferth's Enchiridion (a science text) of 1010–1012,[38] where it was defined as 1/564 of a momentum (11⁄2 minutes),[39] and thus equal to 15/94 of a second. It was used in the computus, the process of calculating the date of Easter.

As of May 2010, the smallest time interval uncertainty in direct measurements is on the order of 12 attoseconds (1.2 × 10−17 seconds), about 3.7 × 1026 Planck times.[40]

Units

See also: Time (Orders of magnitude) and Unit of time § List

The second (s) is the SI base unit. A minute (min) is 60 seconds in length (or, rarely, 59 or 61 seconds when leap seconds are employed), and an hour is 60 minutes or 3600 seconds in length. A day is usually 24 hours or 86,400 seconds in length; however, the duration of a calendar day can vary due to Daylight saving time and Leap seconds.

Time standards

Main article: Time standard

A time standard is a specification for measuring time: assigning a number or calendar date to an instant (point in time), quantifying the duration of a time interval, and establishing a chronology (ordering of events). In modern times, several time specifications have been officially recognized as standards, where formerly they were matters of custom and practice. The invention in 1955 of the caesium atomic clock has led to the replacement of older and purely astronomical time standards such as sidereal time and ephemeris time, for most practical purposes, by newer time standards based wholly or partly on atomic time using the SI second.

International Atomic Time (TAI) is the primary international time standard from which other time standards are calculated. Universal Time (UT1) is mean solar time at 0° longitude, computed from astronomical observations. It varies from TAI because of the irregularities in Earth's rotation. Coordinated Universal Time (UTC) is an atomic time scale designed to approximate Universal Time. UTC differs from TAI by an integral number of seconds. UTC is kept within 0.9 second of UT1 by the introduction of one-second steps to UTC, the leap second. The Global Positioning System broadcasts a very precise time signal based on UTC time.

The surface of the Earth is split into a number of time zones. Standard time or civil time in a time zone deviates a fixed, round amount, usually a whole number of hours, from some form of Universal Time, usually UTC. Most time zones are exactly one hour apart, and by convention compute their local time as an offset from UTC. For example, time zones at sea are based on UTC. In many locations (but not at sea) these offsets vary twice yearly due to daylight saving time transitions.

Some other time standards are used mainly for scientific work. Terrestrial Time is a theoretical ideal scale realized by TAI. Geocentric Coordinate Time and Barycentric Coordinate Time are scales defined as coordinate times in the context of the general theory of relativity. Barycentric Dynamical Time is an older relativistic scale that is still in use.

Philosophy

Religion

Scale of time in Jain texts shown logarithmically

Further information: Time and fate deities

Religions which view time as cyclical

See also: Calendar and Wheel of time

Many ancient cultures, particularly in the East, had a cyclical view of time. In these traditions, time was often seen as a recurring pattern of ages or cycles, where events and phenomena repeated themselves in a predictable manner. One of the most famous examples of this concept is found in Hindu philosophy, where time is depicted as a wheel called the "Kalachakra" or "Wheel of Time." According to this belief, the universe undergoes endless cycles of creation, preservation, and destruction.[41]

Similarly, in other ancient cultures such as those of the Mayans, Aztecs, and Chinese, there were also beliefs in cyclical time, often associated with astronomical observations and calendars.[42] These cultures developed complex systems to track time, seasons, and celestial movements, reflecting their understanding of cyclical patterns in nature and the universe.

The cyclical view of time contrasts with the linear concept of time more common in Western thought, where time is seen as progressing in a straight line from past to future without repetition.[43]

Time in Abrahamic religions

In general, the Islamic and Judeo-Christian world-view regards time as linear[44] and directional,[45] beginning with the act of creation by God. The traditional Christian view sees time ending, teleologically,[46] with the eschatological end of the present order of things, the "end time".

In the Old Testament book Ecclesiastes, traditionally ascribed to Solomon (970–928 BC), time (as the Hebrew word עידן, זמן iddan (age, as in "Ice age") zĕman(time) is often translated) is a medium for the passage of predestined events.[citation needed] (Another word, زمان" זמן" zamān, meant time fit for an event, and is used as the modern Arabic, Persian, and Hebrew equivalent to the English word "time".)

Time in Greek mythology

The Greek language denotes two distinct principles, Chronos and Kairos. The former refers to numeric, or chronological, time. The latter, literally "the right or opportune moment", relates specifically to metaphysical or Divine time. In theology, Kairos is qualitative, as opposed to quantitative.[47]

In Greek mythology, Chronos (ancient Greek: Χρόνος) is identified as the Personification of Time. His name in Greek means "time" and is alternatively spelled Chronus (Latin spelling) or Khronos. Chronos is usually portrayed as an old, wise man with a long, gray beard, such as "Father Time". Some English words whose etymological root is khronos/chronos include chronology, chronometer, chronic, anachronism, synchronise, and chronicle.

Time in Kabbalah & Rabbinical thought

Rabbis sometimes saw time like "an accordion that was expanded and collapsed at will." [48] According to Kabbalists, "time" is a paradox[49] and an illusion.[50]

Time in Advaita Vedanta

According to Advaita Vedanta, time is integral to the phenomenal world, which lacks independent reality. Time and the phenomenal world are products of maya, influenced by our senses, concepts, and imaginations. The phenomenal world, including time, is seen as impermanent and characterized by plurality, suffering, conflict, and division. Since phenomenal existence is dominated by temporality (kala), everything within time is subject to change and decay. Overcoming pain and death requires knowledge that transcends temporal existence and reveals its eternal foundation.[51]

In Western philosophy

Main articles: Philosophy of space and time and Temporal finitism

Time's mortal aspect is personified in this bronze statue by Charles van der Stappen.

Two contrasting viewpoints on time divide prominent philosophers. One view is that time is part of the fundamental structure of the universe – a dimension independent of events, in which events occur in sequence. Isaac Newton subscribed to this realist view, and hence it is sometimes referred to as Newtonian time.[52][53]

The opposing view is that time does not refer to any kind of "container" that events and objects "move through", nor to any entity that "flows", but that it is instead part of a fundamental intellectual structure (together with space and number) within which humans sequence and compare events. This second view, in the tradition of Gottfried Leibniz[17] and Immanuel Kant,[54][55] holds that time is neither an event nor a thing, and thus is not itself measurable nor can it be travelled.

Furthermore, it may be that there is a subjective component to time, but whether or not time itself is "felt", as a sensation, or is a judgment, is a matter of debate.[2][6][7][56][57]

In Philosophy, time was questioned throughout the centuries; what time is and if it is real or not. Ancient Greek philosophers asked if time was linear or cyclical and if time was endless or finite.[58] These philosophers had different ways of explaining time; for instance, ancient Indian philosophers had something called the Wheel of Time. It is believed that there was repeating ages over the lifespan of the universe.[59] This led to beliefs like cycles of rebirth and reincarnation.[59] The Greek philosophers believe that the universe was infinite, and was an illusion to humans.[59] Plato believed that time was made by the Creator at the same instant as the heavens.[59] He also says that time is a period of motion of the heavenly bodies.[59] Aristotle believed that time correlated to movement, that time did not exist on its own but was relative to motion of objects.[59] He also believed that time was related to the motion of celestial bodies; the reason that humans can tell time was because of orbital periods and therefore there was a duration on time.[60]

The Vedas, the earliest texts on Indian philosophy and Hindu philosophy dating to the late 2nd millennium BC, describe ancient Hindu cosmology, in which the universe goes through repeated cycles of creation, destruction and rebirth, with each cycle lasting 4,320 million years.[61] Ancient Greek philosophers, including Parmenides and Heraclitus, wrote essays on the nature of time.[62] Plato, in the Timaeus, identified time with the period of motion of the heavenly bodies. Aristotle, in Book IV of his Physica defined time as 'number of movement in respect of the before and after'.[63]

In Book 11 of his Confessions, St. Augustine of Hippo ruminates on the nature of time, asking, "What then is time? If no one asks me, I know: if I wish to explain it to one that asketh, I know not." He begins to define time by what it is not rather than what it is,[64] an approach similar to that taken in other negative definitions. However, Augustine ends up calling time a "distention" of the mind (Confessions 11.26) by which we simultaneously grasp the past in memory, the present by attention, and the future by expectation.

Isaac Newton believed in absolute space and absolute time; Leibniz believed that time and space are relational.[65] The differences between Leibniz's and Newton's interpretations came to a head in the famous Leibniz–Clarke correspondence.

Philosophers in the 17th and 18th century questioned if time was real and absolute, or if it was an intellectual concept that humans use to understand and sequence events.[58] These questions lead to realism vs anti-realism; the realists believed that time is a fundamental part of the universe, and be perceived by events happening in a sequence, in a dimension.[66] Isaac Newton said that we are merely occupying time, he also says that humans can only understand relative time.[66] Relative time is a measurement of objects in motion.[66] The anti-realists believed that time is merely a convenient intellectual concept for humans to understand events.[66] This means that time was useless unless there were objects that it could interact with, this was called relational time.[66] René Descartes, John Locke, and David Hume said that one's mind needs to acknowledge time, in order to understand what time is.[60] Immanuel Kant believed that we can not know what something is unless we experience it first hand.[67]

Time is not an empirical concept. For neither co-existence nor succession would be perceived by us, if the representation of time did not exist as a foundation a priori. Without this presupposition, we could not represent to ourselves that things exist together at one and the same time, or at different times, that is, contemporaneously, or in succession.

Immanuel Kant, Critique of Pure Reason (1781), trans. Vasilis Politis (London: Dent., 1991), p. 54.

Immanuel Kant, in the Critique of Pure Reason, described time as an a priori intuition that allows us (together with the other a priori intuition, space) to comprehend sense experience.[68] With Kant, neither space nor time are conceived as substances, but rather both are elements of a systematic mental framework that necessarily structures the experiences of any rational agent, or observing subject. Kant thought of time as a fundamental part of an abstract conceptual framework, together with space and number, within which we sequence events, quantify their duration, and compare the motions of objects. In this view, time does not refer to any kind of entity that "flows," that objects "move through," or that is a "container" for events. Spatial measurements are used to quantify the extent of and distances between objects, and temporal measurements are used to quantify the durations of and between events. Time was designated by Kant as the purest possible schema of a pure concept or category.

Henri Bergson believed that time was neither a real homogeneous medium nor a mental construct, but possesses what he referred to as Duration. Duration, in Bergson's view, was creativity and memory as an essential component of reality.[69]

According to Martin Heidegger we do not exist inside time, we are time. Hence, the relationship to the past is a present awareness of having been, which allows the past to exist in the present. The relationship to the future is the state of anticipating a potential possibility, task, or engagement. It is related to the human propensity for caring and being concerned, which causes "being ahead of oneself" when thinking of a pending occurrence. Therefore, this concern for a potential occurrence also allows the future to exist in the present. The present becomes an experience, which is qualitative instead of quantitative. Heidegger seems to think this is the way that a linear relationship with time, or temporal existence, is broken or transcended.[70] We are not stuck in sequential time. We are able to remember the past and project into the future – we have a kind of random access to our representation of temporal existence; we can, in our thoughts, step out of (ecstasis) sequential time.[71]

Modern era philosophers asked: is time real or unreal, is time happening all at once or a duration, is time tensed or tenseless, and is there a future to be?[58] There is a theory called the tenseless or B-theory; this theory says that any tensed terminology can be replaced with tenseless terminology.[72] For example, "we will win the game" can be replaced with "we do win the game", taking out the future tense. On the other hand, there is a theory called the tense or A-theory; this theory says that our language has tense verbs for a reason and that the future can not be determined.[72] There is also something called imaginary time, this was from Stephen Hawking, who said that space and imaginary time are finite but have no boundaries.[72] Imaginary time is not real or unreal, it is something that is hard to visualize.[72] Philosophers can agree that physical time exists outside of the human mind and is objective, and psychological time is mind-dependent and subjective.[60]

Unreality

In 5th century BC Greece, Antiphon the Sophist, in a fragment preserved from his chief work On Truth, held that: "Time is not a reality (hypostasis), but a concept (noêma) or a measure (metron)." Parmenides went further, maintaining that time, motion, and change were illusions, leading to the paradoxes of his follower Zeno.[73] Time as an illusion is also a common theme in Buddhist thought.[74][75]

J. M. E. McTaggart's 1908 The Unreality of Time argues that, since every event has the characteristic of being both present and not present (i.e., future or past), that time is a self-contradictory idea (see also The flow of time).[citation needed]

These arguments often center on what it means for something to be unreal. Modern physicists generally believe that time is as real as space – though others, such as Julian Barbour, argue quantum equations of the universe take their true form when expressed in the timeless realm containing every possible now or momentary configuration of the universe.[citation needed]

A modern philosophical theory called presentism views the past and the future as human-mind interpretations of movement instead of real parts of time (or "dimensions") which coexist with the present. This theory rejects the existence of all direct interaction with the past or the future, holding only the present as tangible. This is one of the philosophical arguments against time travel. This contrasts with eternalism (all time: present, past and future, is real) and the growing block theory (the present and the past are real, but the future is not).[citation needed]

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Main article: Time in physics

Until Einstein's reinterpretation of the physical concepts associated with time and space in 1907, time was considered to be the same everywhere in the universe, with all observers measuring the same time interval for any event.[76] Non-relativistic classical mechanics is based on this Newtonian idea of time.

Einstein, in his special theory of relativity,[77] postulated the constancy and finiteness of the speed of light for all observers. He showed that this postulate, together with a reasonable definition for what it means for two events to be simultaneous, requires that distances appear compressed and time intervals appear lengthened for events associated with objects in motion relative to an inertial observer.

The theory of special relativity finds a convenient formulation in Minkowski spacetime, a mathematical structure that combines three dimensions of space with a single dimension of time. In this formalism, distances in space can be measured by how long light takes to travel that distance, e.g., a light-year is a measure of distance, and a meter is now defined in terms of how far light travels in a certain amount of time. Two events in Minkowski spacetime are separated by an invariant interval, which can be either space-like, light-like, or time-like. Events that have a time-like separation cannot be simultaneous in any frame of reference, there must be a temporal component (and possibly a spatial one) to their separation. Events that have a space-like separation will be simultaneous in some frame of reference, and there is no frame of reference in which they do not have a spatial separation. Different observers may calculate different distances and different time intervals between two events, but the invariant interval between the events is independent of the observer (and his or her velocity).

Arrow of time

Main article: Arrow of time

Unlike space, where an object can travel in the opposite directions (and in 3 dimensions), time appears to have only one dimension and only one direction – the past lies behind, fixed and immutable, while the future lies ahead and is not necessarily fixed. Yet most laws of physics allow any process to proceed both forward and in reverse. There are only a few physical phenomena, that violate the reversibility of time. This time directionality is known as the arrow of time. Acknowledged examples of the arrow of time are:[78][79][80][81][82][83][84][85]

Radiative arrow of time, manifested in waves (e.g. light and sound) travelling only expanding (rather than focusing) in time (see light cone);

Entropic arrow of time: according to the second law of thermodynamics an isolated system evolves toward a larger disorder rather than orders spontaneously;

Quantum arrow time, which is related to irreversibility of measurement in quantum mechanics according to the Copenhagen interpretation of quantum mechanics;

Weak arrow of time: preference for a certain time direction of weak force in particle physics (see violation of CP symmetry);

Cosmological arrow of time, which follows the accelerated expansion of the Universe after the Big Bang.

The relationship(s) between these different Arrows of Time is a hotly debated topic in theoretical physics.[86]

Classical mechanics

In non-relativistic classical mechanics, Newton's concept of "relative, apparent, and common time" can be used in the formulation of a prescription for the synchronization of clocks. Events seen by two different observers in motion relative to each other produce a mathematical concept of time that works sufficiently well for describing the everyday phenomena of most people's experience. In the late nineteenth century, physicists encountered problems with the classical understanding of time, in connection with the behavior of electricity and magnetism. Einstein resolved these problems by invoking a method of synchronizing clocks using the constant, finite speed of light as the maximum signal velocity. This led directly to the conclusion that observers in motion relative to one another measure different elapsed times for the same event.

Two-dimensional space depicted in three-dimensional spacetime. The past and future light cones are absolute, the "present" is a relative concept different for observers in relative motion.

Spacetime

Main article: Spacetime

Time has historically been closely related with space, the two together merging into spacetime in Einstein's special relativity and general relativity. According to these theories, the concept of time depends on the spatial reference frame of the observer, and the human perception, as well as the measurement by instruments such as clocks, are different for observers in relative motion. For example, if a spaceship carrying a clock flies through space at (very nearly) the speed of light, its crew does not notice a change in the speed of time on board their vessel because everything traveling at the same speed slows down at the same rate (including the clock, the crew's thought processes, and the functions of their bodies). However, to a stationary observer watching the spaceship fly by, the spaceship appears flattened in the direction it is traveling and the clock on board the spaceship appears to move very slowly.

On the other hand, the crew on board the spaceship also perceives the observer as slowed down and flattened along the spaceship's direction of travel, because both are moving at very nearly the speed of light relative to each other. Because the outside universe appears flattened to the spaceship, the crew perceives themselves as quickly traveling between regions of space that (to the stationary observer) are many light years apart. This is reconciled by the fact that the crew's perception of time is different from the stationary observer's; what seems like seconds to the crew might be hundreds of years to the stationary observer. In either case, however, causality remains unchanged: the past is the set of events that can send light signals to an entity and the future is the set of events to which an entity can send light signals.[87][88]

Dilation

Main article: Time dilation

Relativity of simultaneity: Event B is simultaneous with A in the green reference frame, but it occurred before in the blue frame, and occurs later in the red frame.

Einstein showed in his thought experiments that people travelling at different speeds, while agreeing on cause and effect, measure different time separations between events, and can even observe different chronological orderings between non-causally related events. Though these effects are typically minute in the human experience, the effect becomes much more pronounced for objects moving at speeds approaching the speed of light. Subatomic particles exist for a well-known average fraction of a second in a lab relatively at rest, but when travelling close to the speed of light they are measured to travel farther and exist for much longer than when at rest. According to the special theory of relativity, in the high-speed particle's frame of reference, it exists, on the average, for a standard amount of time known as its mean lifetime, and the distance it travels in that time is zero, because its velocity is zero. Relative to a frame of reference at rest, time seems to "slow down" for the particle. Relative to the high-speed particle, distances seem to shorten. Einstein showed how both temporal and spatial dimensions can be altered (or "warped") by high-speed motion.

Einstein (The Meaning of Relativity): "Two events taking place at the points A and B of a system K are simultaneous if they appear at the same instant when observed from the middle point, M, of the interval AB. Time is then defined as the ensemble of the indications of similar clocks, at rest relative to K, which register the same simultaneously."

Einstein wrote in his book, Relativity, that simultaneity is also relative, i.e., two events that appear simultaneous to an observer in a particular inertial reference frame need not be judged as simultaneous by a second observer in a different inertial frame of reference.

Relativistic versus Newtonian

Views of spacetime along the world line of a rapidly accelerating observer in a relativistic universe. The events ("dots") that pass the two diagonal lines in the bottom half of the image (the past light cone of the observer in the origin) are the events visible to the observer.

The animations visualise the different treatments of time in the Newtonian and the relativistic descriptions. At the heart of these differences are the Galilean and Lorentz transformations applicable in the Newtonian and relativistic theories, respectively.

In the figures, the vertical direction indicates time. The horizontal direction indicates distance (only one spatial dimension is taken into account), and the thick dashed curve is the spacetime trajectory ("world line") of the observer. The small dots indicate specific (past and future) events in spacetime.

The slope of the world line (deviation from being vertical) gives the relative velocity to the observer. In both pictures the view of spacetime changes when the observer accelerates.

In the Newtonian description these changes are such that time is absolute:[89] the movements of the observer do not influence whether an event occurs in the 'now' (i.e., whether an event passes the horizontal line through the observer).

However, in the relativistic description the observability of events is absolute: the movements of the observer do not influence whether an event passes the "light cone" of the observer. Notice that with the change from a Newtonian to a relativistic description, the concept of absolute time is no longer applicable: events move up and down in the figure depending on the acceleration of the observer.

Quantization

See also: Chronon

Time quantization is a hypothetical concept. In the modern established physical theories (the Standard Model of Particles and Interactions and General Relativity) time is not quantized.

Planck time (~ 5.4 × 10−44 seconds) is the unit of time in the system of natural units known as Planck units. Current established physical theories are believed to fail at this time scale, and many physicists expect that the Planck time might be the smallest unit of time that could ever be measured, even in principle. Tentative physical theories that describe this time scale exist; see for instance loop quantum gravity.

Thermodynamics

The second law of thermodynamics states that entropy must increase over time (see Entropy). This can be in either direction – Brian Greene theorizes that, according to the equations, the change in entropy occurs symmetrically whether going forward or backward in time. So entropy tends to increase in either direction, and our current low-entropy universe is a statistical aberration, in a similar manner as tossing a coin often enough that eventually heads will result ten times in a row. However, this theory is not supported empirically in local experiment.[90]

Travel

Main article: Time travel

See also: Time travel in fiction, Wormhole, and Twin paradox

Time travel is the concept of moving backwards or forwards to different points in time, in a manner analogous to moving through space, and different from the normal "flow" of time to an earthbound observer. In this view, all points in time (including future times) "persist" in some way. Time travel has been a plot device in fiction since the 19th century. Travelling backwards or forwards in time has never been verified as a process, and doing so presents many theoretical problems and contradictive logic which to date have not been overcome. Any technological device, whether fictional or hypothetical, that is used to achieve time travel is known as a time machine.

A central problem with time travel to the past is the violation of causality; should an effect precede its cause, it would give rise to the possibility of a temporal paradox. Some interpretations of time travel resolve this by accepting the possibility of travel between branch points, parallel realities, or universes.

Another solution to the problem of causality-based temporal paradoxes is that such paradoxes cannot arise simply because they have not arisen. As illustrated in numerous works of fiction, free will either ceases to exist in the past or the outcomes of such decisions are predetermined. As such, it would not be possible to enact the grandfather paradox because it is a historical fact that one's grandfather was not killed before his child (one's parent) was conceived. This view does not simply hold that history is an unchangeable constant, but that any change made by a hypothetical future time traveller would already have happened in his or her past, resulting in the reality that the traveller moves from. More elaboration on this view can be found in the Novikov self-consistency principle.

Perception

Philosopher and psychologist William James

Main article: Time perception

The specious present refers to the time duration wherein one's perceptions are considered to be in the present. The experienced present is said to be 'specious' in that, unlike the objective present, it is an interval and not a durationless instant. The term specious present was first introduced by the psychologist E. R. Clay, and later developed by William James.[91]

Biopsychology

The brain's judgment of time is known to be a highly distributed system, including at least the cerebral cortex, cerebellum and basal ganglia as its components. One particular component, the suprachiasmatic nuclei, is responsible for the circadian (or daily) rhythm, while other cell clusters appear capable of shorter-range (ultradian) timekeeping.

Psychoactive drugs can impair the judgment of time. Stimulants can lead both humans and rats to overestimate time intervals,[92][93] while depressants can have the opposite effect.[94] The level of activity in the brain of neurotransmitters such as dopamine and norepinephrine may be the reason for this.[95] Such chemicals will either excite or inhibit the firing of neurons in the brain, with a greater firing rate allowing the brain to register the occurrence of more events within a given interval (speed up time) and a decreased firing rate reducing the brain's capacity to distinguish events occurring within a given interval (slow down time).[96]

Mental chronometry is the use of response time in perceptual-motor tasks to infer the content, duration, and temporal sequencing of cognitive operations.

Early childhood education

Children's expanding cognitive abilities allow them to understand time more clearly. Two- and three-year-olds' understanding of time is mainly limited to "now and not now". Five- and six-year-olds can grasp the ideas of past, present, and future. Seven- to ten-year-olds can use clocks and calendars.[97]

Alterations

In addition to psychoactive drugs, judgments of time can be altered by temporal illusions (like the kappa effect),[98] age,[99] and hypnosis.[100] The sense of time is impaired in some people with neurological diseases such as Parkinson's disease and attention deficit disorder.

Psychologists assert that time seems to go faster with age, but the literature on this age-related perception of time remains controversial.[101] Those who support this notion argue that young people, having more excitatory neurotransmitters, are able to cope with faster external events.[96]

Spatial conceptualization

Although time is regarded as an abstract concept, there is increasing evidence that time is conceptualized in the mind in terms of space.[102] That is, instead of thinking about time in a general, abstract way, humans think about time in a spatial way and mentally organize it as such. Using space to think about time allows humans to mentally organize temporal events in a specific way.

This spatial representation of time is often represented in the mind as a Mental Time Line (MTL).[103] Using space to think about time allows humans to mentally organize temporal order. These origins are shaped by many environmental factors[102]––for example, literacy appears to play a large role in the different types of MTLs, as reading/writing direction provides an everyday temporal orientation that differs from culture to culture.[103] In western cultures, the MTL may unfold rightward (with the past on the left and the future on the right) since people read and write from left to right.[103] Western calendars also continue this trend by placing the past on the left with the future progressing toward the right. Conversely, Arabic, Farsi, Urdu and Israeli-Hebrew speakers read from right to left, and their MTLs unfold leftward (past on the right with future on the left), and evidence suggests these speakers organize time events in their minds like this as well.[103]

This linguistic evidence that abstract concepts are based in spatial concepts also reveals that the way humans mentally organize time events varies across cultures––that is, a certain specific mental organization system is not universal. So, although Western cultures typically associate past events with the left and future events with the right according to a certain MTL, this kind of horizontal, egocentric MTL is not the spatial organization of all cultures. Although most developed nations use an egocentric spatial system, there is recent evidence that some cultures use an allocentric spatialization, often based on environmental features.[102]

A study of the indigenous Yupno people of Papua New Guinea focused on the directional gestures used when individuals used time-related words.[102] When speaking of the past (such as "last year" or "past times"), individuals gestured downhill, where the river of the valley flowed into the ocean. When speaking of the future, they gestured uphill, toward the source of the river. This was common regardless of which direction the person faced, revealing that the Yupno people may use an allocentric MTL, in which time flows uphill.[102]

A similar study of the Pormpuraawans, an aboriginal group in Australia, revealed a similar distinction in which when asked to organize photos of a man aging "in order," individuals consistently placed the youngest photos to the east and the oldest photos to the west, regardless of which direction they faced.[104] This directly clashed with an American group that consistently organized the photos from left to right. Therefore, this group also appears to have an allocentric MTL, but based on the cardinal directions instead of geographical features.[104]

The wide array of distinctions in the way different groups think about time leads to the broader question that different groups may also think about other abstract concepts in different ways as well, such as causality and number.[102]

Use

See also: Time management

In sociology and anthropology, time discipline is the general name given to social and economic rules, conventions, customs, and expectations governing the measurement of time, the social currency and awareness of time measurements, and people's expectations concerning the observance of these customs by others. Arlie Russell Hochschild[105][106] and Norbert Elias[107] have written on the use of time from a sociological perspective.

The use of time is an important issue in understanding human behavior, education, and travel behavior. Time-use research is a developing field of study. The question concerns how time is allocated across a number of activities (such as time spent at home, at work, shopping, etc.). Time use changes with technology, as the television or the Internet created new opportunities to use time in different ways. However, some aspects of time use are relatively stable over long periods of time, such as the amount of time spent traveling to work, which despite major changes in transport, has been observed to be about 20–30 minutes one-way for a large number of cities over a long period.

Time management is the organization of tasks or events by first estimating how much time a task requires and when it must be completed, and adjusting events that would interfere with its completion so it is done in the appropriate amount of time. Calendars and day planners are common examples of time management tools.

Sequence of events

A sequence of events, or series of events, is a sequence of items, facts, events, actions, changes, or procedural steps, arranged in time order (chronological order), often with causality relationships among the items.[108][109][110] Because of causality, cause precedes effect, or cause and effect may appear together in a single item, but effect never precedes cause. A sequence of events can be presented in text, tables, charts, or timelines. The description of the items or events may include a timestamp. A sequence of events that includes the time along with place or location information to describe a sequential path may be referred to as a world line.

Uses of a sequence of events include stories,[111] historical events (chronology), directions and steps in procedures,[112] and timetables for scheduling activities. A sequence of events may also be used to help describe processes in science, technology, and medicine. A sequence of events may be focused on past events (e.g., stories, history, chronology), on future events that must be in a predetermined order (e.g., plans, schedules, procedures, timetables), or focused on the observation of past events with the expectation that the events will occur in the future (e.g., processes, projections). The use of a sequence of events occurs in fields as diverse as machines (cam timer), documentaries (Seconds From Disaster), law (choice of law), finance (directional-change intrinsic time), computer simulation (discrete event simulation), and electric power transmission[113] (sequence of events recorder). A specific example of a sequence of events is the timeline of the Fukushima Daiichi nuclear disaster.

See also

List of UTC timing centers

Loschmidt's paradox

Time metrology

Organizations

Antiquarian Horological Society – AHS (United Kingdom)

Chronometrophilia (Switzerland)

Deutsche Gesellschaft für Chronometrie – DGC (Germany)

National Association of Watch and Clock Collectors – NAWCC (United States)

Miscellaneous arts and sciences

Date and time representation by country

List of cycles

Nonlinear narrative

Philosophy of physics

Rate (mathematics)

Miscellaneous units

Fiscal year

Half-life

Hexadecimal time

Tithi

Unix epoch

References

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"Dictionary.com Unabridged, based on Random House Dictionary". 2010. Archived from the original on 5 March 2012. Retrieved 9 April 2011. 1. the system of those sequential relations that any event has to any other, as past, present, or future; indefinite and continuous duration regarded as that in which events succeed one another.... 3. (sometimes initial capital letter) a system or method of measuring or reckoning the passage of time: mean time; apparent time; Greenwich Time. 4. a limited period or interval, as between two successive events: a long time.... 14. a particular or definite point in time, as indicated by a clock: What time is it? ... 18. an indefinite, frequently prolonged period or duration in the future: Time will tell if what we have done here today was right.

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^ "Official Baseball Rules – 8.03 and 8.04" (Free PDF download). Major League Baseball. 2011. Archived (PDF) from the original on 1 July 2017. Retrieved 18 May 2017. Rule 8.03 Such preparatory pitches shall not consume more than one minute of time...Rule 8.04 When the bases are unoccupied, the pitcher shall deliver the ball to the batter within 12 seconds...The 12-second timing starts when the pitcher is in possession of the ball and the batter is in the box, alert to the pitcher. The timing stops when the pitcher releases the ball.

^ "Guinness Book of Baseball World Records". Guinness World Records, Ltd. Archived from the original on 6 June 2012. Retrieved 7 July 2012. The record for the fastest time for circling the bases is 13.3 seconds, set by Evar Swanson at Columbus, Ohio in 1932...The greatest reliably recorded speed at which a baseball has been pitched is 100.9 mph by Lynn Nolan Ryan (California Angels) at Anaheim Stadium in California on 20 August 1974.

^ Zeigler, Kenneth (2008). Getting organized at work : 24 lessons to set goals, establish priorities, and manage your time. McGraw-Hill. ISBN 978-0-07-159138-6. Archived from the original on 18 August 2020. Retrieved 30 July 2019. 108 pages.

^ Duff, Okun, Veneziano, ibid. p. 3. "There is no well established terminology for the fundamental constants of Nature. ... The absence of accurately defined terms or the uses (i.e., actually misuses) of ill-defined terms lead to confusion and proliferation of wrong statements."

^ ঝাঁপ দিন:a b Burnham, Douglas: Staffordshire University (2006). "Gottfried Wilhelm Leibniz (1646–1716) Metaphysics – 7. Space, Time, and Indiscernibles". The Internet Encyclopedia of Philosophy. Archived from the original on 14 May 2011. Retrieved 9 April 2011. First of all, Leibniz finds the idea that space and time might be substances or substance-like absurd (see, for example, "Correspondence with Clarke," Leibniz's Fourth Paper, §8ff). In short, an empty space would be a substance with no properties; it will be a substance that even God cannot modify or destroy.... That is, space and time are internal or intrinsic features of the complete concepts of things, not extrinsic.... Leibniz's view has two major implications. First, there is no absolute location in either space or time; location is always the situation of an object or event relative to other objects and events. Second, space and time are not in themselves real (that is, not substances). Space and time are, rather, ideal. Space and time are just metaphysically illegitimate ways of perceiving certain virtual relations between substances. They are phenomena or, strictly speaking, illusions (although they are illusions that are well-founded upon the internal properties of substances).... It is sometimes convenient to think of space and time as something "out there," over and above the entities and their relations to each other, but this convenience must not be confused with reality. Space is nothing but the order of co-existent objects; time nothing but the order of successive events. This is usually called a relational theory of space and time.

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^ Macías, Alfredo; Camacho, Abel (May 2008). "On the incompatibility between quantum theory and general relativity". Physics Letters B. 663 (1–2): 99–102. Bibcode:2008PhLB..663...99M. doi:10.1016/j.physletb.2008.03.052. In our opinion, it is not possible to reconciliate and integrate into a common scheme the absolute and non-dynamical character of Newtonian time of canonical quantization and path integral approaches with the relativistic and dynamical character of time in general relativity.

^ Shavit, Joseph (18 July 2024). "Revolutionary theory finally unites quantum mechanics and Einstein's theory of general relativity". The Brighter Side of News. The prevailing consensus has been that Einstein's theory of gravity must be modified to fit within the framework of quantum theory [...] when it comes to merging these two theories into a single, comprehensive framework, the scientific community has hit a roadblock.

^ Richards, E. G. (1998). Mapping Time: The Calendar and its History. Oxford University Press. pp. 3–5. ISBN 978-0-19-850413-9.

^ Rudgley, Richard (1999). The Lost Civilizations of the Stone Age. New York: Simon & Schuster. pp. 86–105.

^ Van Stone, Mark (2011). "The Maya Long Count Calendar: An Introduction". Archaeoastronomy. 24: 8–11.

^ "French Republican Calendar | Chronology." Encyclopædia Britannica Online. Encyclopædia Britannica, n.d. Web. 21 February 2016.

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^ Barnett, Jo Ellen (1999). Time's Pendulum: From Sundials to Atomic Clocks, the Fascinating History of Timekeeping and how Our Discoveries Changed the World (reprinted ed.). Harcourt Brace. p. 28. ISBN 978-0-15-600649-1.

^ Lombardi, Michael A. "Why Is a Minute Divided into 60 Seconds, an Hour into 60 Minutes, Yet There Are Only 24 Hours in a Day?" Scientific American. Springer Nature, 5 March 2007. Web. 21 February 2016.

^ Barnett, ibid, p. 37.

^ Bergreen, Laurence. Over the Edge of the World: Magellan's Terrifying Circumnavigation of the Globe (HarperCollins Publishers, 2003), ISBN 0-06-621173-5[page needed]

^ North, J. (2004) God's Clockmaker: Richard of Wallingford and the Invention of Time. Oxbow Books. ISBN 1-85285-451-0

^ Watson, E., (1979) "The St Albans Clock of Richard of Wallingford". Antiquarian Horology, pp. 372–384.

^ ঝাঁপ দিন:a b "History of Clocks." About.com Inventors. About.com, n.d. Web. 21 February 2016.

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^ Newman, John (1991). Geshe Lhundub Sopa (ed.). The Wheel of Time: Kalachakra in Context. Shambhala. pp. 51–54, 62–77. ISBN 978-1-55939-779-7.

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^ Jennifer M. Gidley (2017). The Future: A Very Short Introduction. Oxford University Press. p. 13. ISBN 978-0-19-105424-2. Extract of page 13

^ Rust, Eric Charles (1981). Religion, Revelation and Reason. Mercer University Press. p. 60. ISBN 978-0-86554-058-3. Archived from the original on 3 April 2017. Retrieved 20 August 2015. Profane time, as Eliade points out, is linear. As man dwelt increasingly in the profane and a sense of history developed, the desire to escape into the sacred began to drop in the background. The myths, tied up with cyclic time, were not so easily operative. [...] So secular man became content with his linear time. He could not return to cyclic time and re-enter sacred space though its myths. [...] Just here, as Eliade sees it, a new religious structure became available. In the Judaeo-Christian religions – Judaism, Christianity, Islam – history is taken seriously, and linear time is accepted. The cyclic time of the primordial mythical consciousness has been transformed into the time of profane man, but the mythical consciousness remains. It has been historicized. The Christian mythos and its accompanying ritual are bound up, for example, with history and center in authentic history, especially the Christ-event. Sacred space, the Transcendent Presence, is thus opened up to secular man because it meets him where he is, in the linear flow of secular time. The Christian myth gives such time a beginning in creation, a center in the Christ-event, and an end in the final consummation.

^ Betz, Hans Dieter, ed. (2008). Religion Past & Present: Encyclopedia of Theology and Religion. Vol. 4 (4 ed.). Brill. p. 101. ISBN 978-90-04-14688-4. Archived from the original on 24 September 2015. Retrieved 20 August 2015. [...] God produces a creation with a directional time structure [...].

^ Lundin, Roger; Thiselton, Anthony C.; Walhout, Clarence (1999). The Promise of Hermeneutics. Wm. B. Eerdmans Publishing. p. 121. ISBN 978-0-8028-4635-8. Archived from the original on 19 September 2015. Retrieved 20 August 2015. We need to note the close ties between teleology, eschatology, and utopia. In Christian theology, the understanding of the teleology of particular actions is ultimately related to the teleology of history in general, which is the concern of eschatology.

^ "(Dictionary Entry)". Henry George Liddell, Robert Scott, A Greek-English Lexicon. Archived from the original on 7 May 2022. Retrieved 13 July 2015.

^ New Myths and Meanings in Jewish New Moon Rituals David M. Rosen, Victoria P. Rosen Ethnology, Vol. 39, No. 3 (Summer, 2000), pp. 263–277 (referencing Yerushalmi 1989)

^ Hus, Boʿaz; Pasi, Marco; Stuckrad, Kocku von (2011). Kabbalah and Modernity: Interpretations, Transformations, Adaptations. BRILL. ISBN 978-90-04-18284-4. Archived from the original on 13 May 2016. Retrieved 27 February 2016.

^ Wolfson, Elliot R. (2006). Alef, Mem, Tau: Kabbalistic Musings on Time, Truth, and Death. University of California Press. p. 111. ISBN 978-0-520-93231-9. Archived from the original on 19 August 2020. Retrieved 7 May 2020. Extract of page 111 Archived 11 May 2022 at the Wayback Machine

^ Puligandla, R. (1974). "Time and History in the Indian Tradition". Philosophy East and West. 24 (2): 165–170. doi:10.2307/1398019. ISSN 0031-8221. JSTOR 1398019.

^ Rynasiewicz, Robert: Johns Hopkins University (12 August 2004). "Newton's Views on Space, Time, and Motion". Stanford Encyclopedia of Philosophy. Stanford University. Archived from the original on 16 July 2012. Retrieved 5 February 2012. Newton did not regard space and time as genuine substances (as are, paradigmatically, bodies and minds), but rather as real entities with their own manner of existence as necessitated by God's existence ... To paraphrase: Absolute, true, and mathematical time, from its own nature, passes equably without relation to anything external, and thus without reference to any change or way of measuring of time (e.g., the hour, day, month, or year).

^ Markosian, Ned. "Time". In Edward N. Zalta (ed.). The Stanford Encyclopedia of Philosophy (Winter 2002 Edition). Archived from the original on 14 September 2006. Retrieved 23 September 2011. The opposing view, normally referred to either as "Platonism with Respect to Time" or as "Absolutism with Respect to Time", has been defended by Plato, Newton, and others. On this view, time is like an empty container into which events may be placed; but it is a container that exists independently of whether or not anything is placed in it.

^ Mattey, G. J. (22 January 1997). "Critique of Pure Reason, Lecture notes: Philosophy 175 UC Davis". Archived from the original on 14 March 2005. Retrieved 9 April 2011. What is correct in the Leibnizian view was its anti-metaphysical stance. Space and time do not exist in and of themselves, but in some sense are the product of the way we represent things. The[y] are ideal, though not in the sense in which Leibniz thought they are ideal (figments of the imagination). The ideality of space is its mind-dependence: it is only a condition of sensibility.... Kant concluded ... "absolute space is not an object of outer sensation; it is rather a fundamental concept which first of all makes possible all such outer sensation."...Much of the argumentation pertaining to space is applicable, mutatis mutandis, to time, so I will not rehearse the arguments. As space is the form of outer intuition, so time is the form of inner intuition.... Kant claimed that time is real, it is "the real form of inner intuition."

^ McCormick, Matt (2006). "Immanuel Kant (1724–1804) Metaphysics: 4. Kant's Transcendental Idealism". The Internet Encyclopedia of Philosophy. Archived from the original on 26 April 2011. Retrieved 9 April 2011. Time, Kant argues, is also necessary as a form or condition of our intuitions of objects. The idea of time itself cannot be gathered from experience because succession and simultaneity of objects, the phenomena that would indicate the passage of time, would be impossible to represent if we did not already possess the capacity to represent objects in time.... Another way to put the point is to say that the fact that the mind of the knower makes the a priori contribution does not mean that space and time or the categories are mere figments of the imagination. Kant is an empirical realist about the world we experience; we can know objects as they appear to us. He gives a robust defense of science and the study of the natural world from his argument about the mind's role in making nature. All discursive, rational beings must conceive of the physical world as spatially and temporally unified, he argues.

^ Carrol, Sean (2010). "Chapter One, Section Two, Plume". From Eternity to Here: The Quest for the Ultimate Theory of Time. Penguin. ISBN 978-0-452-29654-1. As human beings we 'feel' the passage of time.

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^ Bergson, Henri (1907) Creative Evolution. trans. by Arthur Mitchell. Mineola: Dover, 1998.

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^ Herman M. Schwartz, Introduction to Special Relativity, McGraw-Hill Book Company, 1968, hardcover 442 pages, see ISBN 0-88275-478-5 (1977 edition), pp. 10–13

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^ Quantum causality and the arrows of time and thermodynamics. 2020. Prog Part Nucl Phys. 115/13. J.F. Donoghue, G. Menezes. doi: 10.1016/j.ppnp.2020.103812.

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^ Time irreversibility in active matter, from micro to macro. 2022. Nat Rev Phys. 4/3, pp. 167–183.

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^ Knudsen, Jens M.; Hjorth, Poul G. (6 December 2012). Elements of Newtonian Mechanics. Springer Science & Business Media. p. 30. ISBN 978-3-642-97599-8.

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^ Wittmann, M.; Leland, D. S.; Churan, J.; Paulus, M. P. (8 October 2007). "Impaired time perception and motor timing in stimulant-dependent subjects". Drug Alcohol Depend. 90 (2–3): 183–192. doi:10.1016/j.drugalcdep.2007.03.005. PMC 1997301. PMID 17434690.

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Further reading

Barbour, Julian (1999). The End of Time: The Next Revolution in Our Understanding of the Universe. Oxford University Press. ISBN 978-0-19-514592-2.

Craig Callendar, Introducing Time, Icon Books, 2010, ISBN 978-1-84831-120-6

Das, Tushar Kanti (1990). The Time Dimension: An Interdisciplinary Guide. New York: Praeger. ISBN 978-0-275-92681-6. – Research bibliography

Davies, Paul (1996). About Time: Einstein's Unfinished Revolution. New York: Simon & Schuster Paperbacks. ISBN 978-0-684-81822-1.

Feynman, Richard (1994) [1965]. The Character of Physical Law. Cambridge (Mass): The MIT Press. pp. 108–126. ISBN 978-0-262-56003-0.

Galison, Peter (1992). Einstein's Clocks and Poincaré's Maps: Empires of Time. New York: W.W. Norton. ISBN 978-0-393-02001-4.

Benjamin Gal-Or, Cosmology, Physics and Philosophy, Springer Verlag, 1981, 1983, 1987, ISBN 0-387-90581-2, 0-387-96526-2.

Charlie Gere, (2005) Art, Time and Technology: Histories of the Disappearing Body, Berg

Highfield, Roger (1992). Arrow of Time: A Voyage through Science to Solve Time's Greatest Mystery. Random House. ISBN 978-0-449-90723-8.

Landes, David (2000). Revolution in Time. Harvard University Press. ISBN 978-0-674-00282-1.

Lebowitz, Joel L. (2008). "Time's arrow and Boltzmann's entropy". Scholarpedia. 3 (4): 3448. Bibcode:2008SchpJ...3.3448L. doi:10.4249/scholarpedia.3448.

Mermin, N. David (2005). It's About Time: Understanding Einstein's Relativity. Princeton University Press. ISBN 978-0-691-12201-4.

Morris, Richard (1985). Time's Arrows: Scientific Attitudes Toward Time. New York: Simon and Schuster. ISBN 978-0-671-61766-0.

Penrose, Roger (1999) [1989]. The Emperor's New Mind: Concerning Computers, Minds, and the Laws of Physics. New York: Oxford University Press. pp. 391–417. ISBN 978-0-19-286198-6. Archived from the original on 26 December 2010. Retrieved 9 April 2011.

Price, Huw (1996). Time's Arrow and Archimedes' Point. Oxford University Press. ISBN 978-0-19-511798-1. Retrieved 9 April 2011.

Reichenbach, Hans (1999) [1956]. The Direction of Time. New York: Dover. ISBN 978-0-486-40926-9.

Rovelli, Carlo (2006). What is time? What is space?. Rome: Di Renzo Editore. ISBN 978-88-8323-146-9. Archived from the original on 27 January 2007.

Rovelli, Carlo (2018). The Order of Time. New York: Riverhead. ISBN 978-0735216105.

Stiegler, Bernard, Technics and Time, 1: The Fault of Epimetheus

Roberto Mangabeira Unger and Lee Smolin, The Singular Universe and the Reality of Time, Cambridge University Press, 2014, ISBN 978-1-107-07406-4.

Whitrow, Gerald J. (1973). The Nature of Time. Holt, Rinehart and Wilson (New York).

Whitrow, Gerald J. (1980). The Natural Philosophy of Time. Clarendon Press (Oxford).

Whitrow, Gerald J. (1988). Time in History. The evolution of our general awareness of time and temporal perspective. Oxford University Press. ISBN 978-0-19-285211-3.

EMR

 In physics, electromagnetic radiation (EMR) is the set of waves of an electromagnetic (EM) field, which propagate through space and carry momentum and electromagnetic radiant energy.[1][2]

Classically, electromagnetic radiation consists of electromagnetic waves, which are synchronized oscillations of electric and magnetic fields. In a vacuum, electromagnetic waves travel at the speed of light, commonly denoted c. There, depending on the frequency of oscillation, different wavelengths of electromagnetic spectrum are produced. In homogeneous, isotropic media, the oscillations of the two fields are on average perpendicular to each other and perpendicular to the direction of energy and wave propagation, forming a transverse wave.

Electromagnetic radiation is commonly referred to as "light", EM, EMR, or electromagnetic waves.[2]

The position of an electromagnetic wave within the electromagnetic spectrum can be characterized by either its frequency of oscillation or its wavelength. Electromagnetic waves of different frequency are called by different names since they have different sources and effects on matter. In order of increasing frequency and decreasing wavelength, the electromagnetic spectrum includes: radio waves, microwaves, infrared, visible light, ultraviolet, X-rays, and gamma rays.[3][4]

Electromagnetic waves are emitted by electrically charged particles undergoing acceleration,[5][6] and these waves can subsequently interact with other charged particles, exerting force on them. EM waves carry energy, momentum, and angular momentum away from their source particle and can impart those quantities to matter with which they interact. Electromagnetic radiation is associated with those EM waves that are free to propagate themselves ("radiate") without the continuing influence of the moving charges that produced them, because they have achieved sufficient distance from those charges. Thus, EMR is sometimes referred to as the far field, while the near field refers to EM fields near the charges and current that directly produced them, specifically electromagnetic induction and electrostatic induction phenomena.

In quantum mechanics, an alternate way of viewing EMR is that it consists of photons, uncharged elementary particles with zero rest mass which are the quanta of the electromagnetic field, responsible for all electromagnetic interactions.[7] Quantum electrodynamics is the theory of how EMR interacts with matter on an atomic level.[8] Quantum effects provide additional sources of EMR, such as the transition of electrons to lower energy levels in an atom and black-body radiation.[9] The energy of an individual photon is quantized and proportional to frequency according to Planck's equation E = hf, where E is the energy per photon, f is the frequency of the photon, and h is the Planck constant. Thus, higher frequency photons have more energy. For example, a 1020 Hz gamma ray photon has 1019 times the energy of a 101 Hz extremely low frequency radio wave photon.

The effects of EMR upon chemical compounds and biological organisms depend both upon the radiation's power and its frequency. EMR of lower energy ultraviolet or lower frequencies (i.e., near ultraviolet, visible light, infrared, microwaves, and radio waves) is non-ionizing because its photons do not individually have enough energy to ionize atoms or molecules or to break chemical bonds. The effect of non-ionizing radiation on chemical systems and living tissue is primarily simply heating, through the combined energy transfer of many photons. In contrast, high frequency ultraviolet, X-rays and gamma rays are ionizing – individual photons of such high frequency have enough energy to ionize molecules or break chemical bonds. Ionizing radiation can cause chemical reactions and damage living cells beyond simply heating, and can be a health hazard and dangerous.

Physics[উৎস সম্পাদনা]

Theory[উৎস সম্পাদনা]

The relative wavelengths of the electromagnetic waves of three different colours of light (blue, green, and red) with a distance scale in micrometers along the x-axis

Main articles: Maxwell's equations and Near and far field

Maxwell's equations[উৎস সম্পাদনা]

James Clerk Maxwell derived a wave form of the electric and magnetic equations, thus uncovering the wave-like nature of electric and magnetic fields and their symmetry. Because the speed of EM waves predicted by the wave equation coincided with the measured speed of light, Maxwell concluded that light itself is an EM wave.[10][11] Maxwell's equations were confirmed by Heinrich Hertz through experiments with radio waves.[12]

Near and far fields[উৎস সম্পাদনা]

Main articles: Near and far field and Liénard–Wiechert potential

In electromagnetic radiation (such as microwaves from an antenna, shown here) the term radiation applies only to the parts of the electromagnetic field that radiate into infinite space and decrease in intensity by an inverse-square law of power, such that the total energy that crosses through an imaginary sphere surrounding the source is the same regardless of the size of the sphere. Electromagnetic radiation thus reaches the far part of the electromagnetic field around a transmitter. A part of the near field (close to the transmitter) includes the changing electromagnetic field, but that is not electromagnetic radiation.

Maxwell's equations established that some charges and currents (sources) produce local electromagnetic fields near them that do not radiate. Currents directly produce magnetic fields, but such fields of a magnetic-dipole–type that dies out with distance from the current. In a similar manner, moving charges pushed apart in a conductor by a changing electrical potential (such as in an antenna) produce an electric-dipole–type electrical field, but this also declines with distance. These fields make up the near field. Neither of these behaviours is responsible for EM radiation. Instead, they only efficiently transfer energy to a receiver very close to the source, such as inside a transformer. The near field has strong effects its source, with any energy withdrawn by a receiver causing increased load (decreased electrical reactance) on the source. The near field does not propagate freely into space, carrying energy away without a distance limit, but rather oscillates, returning its energy to the transmitter if it is not absorbed by a receiver.[13]

By contrast, the far field is composed of radiation that is free of the transmitter, in the sense that the transmitter requires the same power to send changes in the field out regardless of whether anything absorbs the signal, e.g. a radio station does not need to increase its power when more receivers use the signal. This far part of the electromagnetic field is electromagnetic radiation. The far fields propagate (radiate) without allowing the transmitter to affect them. This causes them to be independent in the sense that their existence and their energy, after they have left the transmitter, is completely independent of both transmitter and receiver. Due to conservation of energy, the amount of power passing through any spherical surface drawn around the source is the same. Because such a surface has an area proportional to the square of its distance from the source, the power density of EM radiation from an isotropic source decreases with the inverse square of the distance from the source; this is called the inverse-square law. This is in contrast to dipole parts of the EM field, the near field, which varies in intensity according to an inverse cube power law, and thus does not transport a conserved amount of energy over distances but instead fades with distance, with its energy (as noted) rapidly returning to the transmitter or absorbed by a nearby receiver (such as a transformer secondary coil).

In the Liénard–Wiechert potential formulation of the electric and magnetic fields due to motion of a single particle (according to Maxwell's equations), the terms associated with acceleration of the particle are those that are responsible for the part of the field that is regarded as electromagnetic radiation. By contrast, the term associated with the changing static electric field of the particle and the magnetic term that results from the particle's uniform velocity are both associated with the near field, and do not comprise electromagnetic radiation.[14]

Properties[উৎস সম্পাদনা]

Electromagnetic waves can be imagined as a self-propagating transverse oscillating wave of electric and magnetic fields. This 3D animation shows a plane linearly polarized wave propagating from left to right. The electric and magnetic fields in such a wave are in-phase with each other, reaching minima and maxima together.

Electric and magnetic fields obey the properties of superposition. Thus, a field due to any particular particle or time-varying electric or magnetic field contributes to the fields present in the same space due to other causes. Further, as they are vector fields, all magnetic and electric field vectors add together according to vector addition.[15] For example, in optics two or more coherent light waves may interact and by constructive or destructive interference yield a resultant irradiance deviating from the sum of the component irradiances of the individual light waves.[16]

The electromagnetic fields of light are not affected by traveling through static electric or magnetic fields in a linear medium such as a vacuum. However, in nonlinear media, such as some crystals, interactions can occur between light and static electric and magnetic fields—these interactions include the Faraday effect and the Kerr effect.[17][18]

In refraction, a wave crossing from one medium to another of different density alters its speed and direction upon entering the new medium. The ratio of the refractive indices of the media determines the degree of refraction, and is summarized by Snell's law. Light of composite wavelengths (natural sunlight) disperses into a visible spectrum passing through a prism, because of the wavelength-dependent refractive index of the prism material (dispersion); that is, each component wave within the composite light is bent a different amount.[19]

EM radiation exhibits both wave properties and particle properties at the same time (see wave-particle duality). Both wave and particle characteristics have been confirmed in many experiments. Wave characteristics are more apparent when EM radiation is measured over relatively large timescales and over large distances while particle characteristics are more evident when measuring small timescales and distances. For example, when electromagnetic radiation is absorbed by matter, particle-like properties will be more obvious when the average number of photons in the cube of the relevant wavelength is much smaller than 1. It is not so difficult to experimentally observe non-uniform deposition of energy when light is absorbed, however this alone is not evidence of "particulate" behavior. Rather, it reflects the quantum nature of matter.[20] Demonstrating that the light itself is quantized, not merely its interaction with matter, is a more subtle affair.

Some experiments display both the wave and particle natures of electromagnetic waves, such as the self-interference of a single photon.[21] When a single photon is sent through an interferometer, it passes through both paths, interfering with itself, as waves do, yet is detected by a photomultiplier or other sensitive detector only once.

A quantum theory of the interaction between electromagnetic radiation and matter such as electrons is described by the theory of quantum electrodynamics.

Electromagnetic waves can be polarized, reflected, refracted, or diffracted, and can interfere with each other.[22][23][24]

Wave model[উৎস সম্পাদনা]

Representation of the electric field vector of a wave of circularly polarized electromagnetic radiation

In homogeneous, isotropic media, electromagnetic radiation is a transverse wave,[25] meaning that its oscillations are perpendicular to the direction of energy transfer and travel. It comes from the following equations:{\displaystyle {\begin{aligned}\nabla \cdot \mathbf {E} &=0\\\nabla \cdot \mathbf {B} &=0\end{aligned}}}These equations predicate that any electromagnetic wave must be a transverse wave, where the electric field E and the magnetic field B are both perpendicular to the direction of wave propagation.

The electric and magnetic parts of the field in an electromagnetic wave stand in a fixed ratio of strengths to satisfy the two Maxwell equations that specify how one is produced from the other. In dissipation-less (lossless) media, these E and B fields are also in phase, with both reaching maxima and minima at the same points in space (see illustrations). In the far-field EM radiation which is described by the two source-free Maxwell curl operator equations, a time-change in one type of field is proportional to the curl of the other. These derivatives require that the E and B fields in EMR are in-phase (see mathematics section below).[citation needed] An important aspect of light's nature is its frequency. The frequency of a wave is its rate of oscillation and is measured in hertz, the SI unit of frequency, where one hertz is equal to one oscillation per second. Light usually has multiple frequencies that sum to form the resultant wave. Different frequencies undergo different angles of refraction, a phenomenon known as dispersion.

A monochromatic wave (a wave of a single frequency) consists of successive troughs and crests, and the distance between two adjacent crests or troughs is called the wavelength. Waves of the electromagnetic spectrum vary in size, from very long radio waves longer than a continent to very short gamma rays smaller than atom nuclei. Frequency is inversely proportional to wavelength, according to the equation:[26]

{\displaystyle \displaystyle v=f\lambda }

where v is the speed of the wave (c in a vacuum or less in other media), f is the frequency and λ is the wavelength. As waves cross boundaries between different media, their speeds change but their frequencies remain constant.

Electromagnetic waves in free space must be solutions of Maxwell's electromagnetic wave equation. Two main classes of solutions are known, namely plane waves and spherical waves. The plane waves may be viewed as the limiting case of spherical waves at a very large (ideally infinite) distance from the source. Both types of waves can have a waveform which is an arbitrary time function (so long as it is sufficiently differentiable to conform to the wave equation). As with any time function, this can be decomposed by means of Fourier analysis into its frequency spectrum, or individual sinusoidal components, each of which contains a single frequency, amplitude and phase. Such a component wave is said to be monochromatic. A monochromatic electromagnetic wave can be characterized by its frequency or wavelength, its peak amplitude, its phase relative to some reference phase, its direction of propagation, and its polarization.

Interference is the superposition of two or more waves resulting in a new wave pattern. If the fields have components in the same direction, they constructively interfere, while opposite directions cause destructive interference. Additionally, multiple polarization signals can be combined (i.e. interfered) to form new states of polarization, which is known as parallel polarization state generation.[27]

The energy in electromagnetic waves is sometimes called radiant energy.[28][29][30]

Particle model and quantum theory[উৎস সম্পাদনা]

See also: Quantization (physics) and Quantum optics

An anomaly arose in the late 19th century involving a contradiction between the wave theory of light and measurements of the electromagnetic spectra that were being emitted by thermal radiators known as black bodies. Physicists struggled with this problem unsuccessfully for many years, and it later became known as the ultraviolet catastrophe. In 1900, Max Planck developed a new theory of black-body radiation that explained the observed spectrum. Planck's theory was based on the idea that black bodies emit light (and other electromagnetic radiation) only as discrete bundles or packets of energy. These packets were called quanta. In 1905, Albert Einstein proposed that light quanta be regarded as real particles. Later the particle of light was given the name photon, to correspond with other particles being described around this time, such as the electron and proton. A photon has an energy, E, proportional to its frequency, f, by

{\displaystyle E=hf={\frac {hc}{\lambda }}\,\!}

where h is the Planck constant, {\displaystyle \lambda } is the wavelength and c is the speed of light. This is sometimes known as the Planck–Einstein equation.[31] In quantum theory (see first quantization) the energy of the photons is thus directly proportional to the frequency of the EMR wave.[32]

Likewise, the momentum p of a photon is also proportional to its frequency and inversely proportional to its wavelength:

{\displaystyle p={E \over c}={hf \over c}={h \over \lambda }.}

The source of Einstein's proposal that light was composed of particles (or could act as particles in some circumstances) was an experimental anomaly not explained by the wave theory: the photoelectric effect, in which light striking a metal surface ejected electrons from the surface, causing an electric current to flow across an applied voltage. Experimental measurements demonstrated that the energy of individual ejected electrons was proportional to the frequency, rather than the intensity, of the light. Furthermore, below a certain minimum frequency, which depended on the particular metal, no current would flow regardless of the intensity. These observations appeared to contradict the wave theory, and for years physicists tried in vain to find an explanation. In 1905, Einstein explained this puzzle by resurrecting the particle theory of light to explain the observed effect. Because of the preponderance of evidence in favor of the wave theory, however, Einstein's ideas were met initially with great skepticism among established physicists. Eventually Einstein's explanation was accepted as new particle-like behavior of light was observed, such as the Compton effect.[33][34]

As a photon is absorbed by an atom, it excites the atom, elevating an electron to a higher energy level (one that is on average farther from the nucleus). When an electron in an excited molecule or atom descends to a lower energy level, it emits a photon of light at a frequency corresponding to the energy difference. Since the energy levels of electrons in atoms are discrete, each element and each molecule emits and absorbs its own characteristic frequencies. Immediate photon emission is called fluorescence, a type of photoluminescence. An example is visible light emitted from fluorescent paints, in response to ultraviolet (blacklight). Many other fluorescent emissions are known in spectral bands other than visible light. Delayed emission is called phosphorescence.[35][36]

Wave–particle duality[উৎস সম্পাদনা]

Main article: Wave–particle duality

The modern theory that explains the nature of light includes the notion of wave–particle duality.

Wave and particle effects of electromagnetic radiation[উৎস সম্পাদনা]

Together, wave and particle effects fully explain the emission and absorption spectra of EM radiation. The matter-composition of the medium through which the light travels determines the nature of the absorption and emission spectrum. These bands correspond to the allowed energy levels in the atoms. Dark bands in the absorption spectrum are due to the atoms in an intervening medium between source and observer. The atoms absorb certain frequencies of the light between emitter and detector/eye, then emit them in all directions. A dark band appears to the detector, due to the radiation scattered out of the light beam. For instance, dark bands in the light emitted by a distant star are due to the atoms in the star's atmosphere. A similar phenomenon occurs for emission, which is seen when an emitting gas glows due to excitation of the atoms from any mechanism, including heat. As electrons descend to lower energy levels, a spectrum is emitted that represents the jumps between the energy levels of the electrons, but lines are seen because again emission happens only at particular energies after excitation.[37] An example is the emission spectrum of nebulae.[38] Rapidly moving electrons are most sharply accelerated when they encounter a region of force, so they are responsible for producing much of the highest frequency electromagnetic radiation observed in nature.

These phenomena can aid various chemical determinations for the composition of gases lit from behind (absorption spectra) and for glowing gases (emission spectra). Spectroscopy (for example) determines what chemical elements comprise a particular star. Spectroscopy is also used in the determination of the distance of a star, using the red shift.[39]

Propagation speed[উৎস সম্পাদনা]

Main article: Speed of light

When any wire (or other conducting object such as an antenna) conducts alternating current, electromagnetic radiation is propagated at the same frequency as the current.

As a wave, light is characterized by a velocity (the speed of light), wavelength, and frequency. As particles, light is a stream of photons. Each has an energy related to the frequency of the wave given by Planck's relation E = hf, where E is the energy of the photon, h is the Planck constant, 6.626 × 10−34 J·s, and f is the frequency of the wave.[40]

In a medium (other than vacuum), velocity factor or refractive index are considered, depending on frequency and application. Both of these are ratios of the speed in a medium to speed in a vacuum.

History of discovery[উৎস সম্পাদনা]

See also: History of electromagnetic theory, Timeline of electromagnetism and classical optics, and Radiation § Discovery

Electromagnetic radiation of wavelengths other than those of visible light were discovered in the early 19th century. The discovery of infrared radiation is ascribed to astronomer William Herschel, who published his results in 1800 before the Royal Society of London.[41] Herschel used a glass prism to refract light from the Sun and detected invisible rays that caused heating beyond the red part of the spectrum, through an increase in the temperature recorded with a thermometer. These "calorific rays" were later termed infrared.[42]

In 1801, German physicist Johann Wilhelm Ritter discovered ultraviolet in an experiment similar to Herschel's, using sunlight and a glass prism. Ritter noted that invisible rays near the violet edge of a solar spectrum dispersed by a triangular prism darkened silver chloride preparations more quickly than did the nearby violet light. Ritter's experiments were an early precursor to what would become photography. Ritter noted that the ultraviolet rays (which at first were called "chemical rays") were capable of causing chemical reactions.[43][44]

James Clerk Maxwell

(1831–1879)

In 1862–64 James Clerk Maxwell developed equations for the electromagnetic field which suggested that waves in the field would travel with a speed that was very close to the known speed of light. Maxwell therefore suggested that visible light (as well as invisible infrared and ultraviolet rays by inference) all consisted of propagating disturbances (or radiation) in the electromagnetic field. Radio waves were first produced deliberately by Heinrich Hertz in 1887, using electrical circuits calculated to produce oscillations at a much lower frequency than that of visible light, following recipes for producing oscillating charges and currents suggested by Maxwell's equations. Hertz also developed ways to detect these waves, and produced and characterized what were later termed radio waves and microwaves.[45]: 286, 7 

Wilhelm Röntgen discovered and named X-rays. After experimenting with high voltages applied to an evacuated tube on 8 November 1895, he noticed a fluorescence on a nearby plate of coated glass. In one month, he discovered X-rays' main properties.[45]: 307 

The last portion of the EM spectrum to be discovered was associated with radioactivity. Henri Becquerel found that uranium salts caused fogging of an unexposed photographic plate through a covering paper in a manner similar to X-rays, and Marie Curie discovered that only certain elements gave off these rays of energy, soon discovering the intense radiation of radium. The radiation from pitchblende was differentiated into alpha rays (alpha particles) and beta rays (beta particles) by Ernest Rutherford through simple experimentation in 1899, but these proved to be charged particulate types of radiation. However, in 1900 the French scientist Paul Villard discovered a third neutrally charged and especially penetrating type of radiation from radium, and after he described it, Rutherford realized it must be yet a third type of radiation, which in 1903 Rutherford named gamma rays. In 1910 British physicist William Henry Bragg demonstrated that gamma rays are electromagnetic radiation, not particles, and in 1914 Rutherford and Edward Andrade measured their wavelengths, finding that they were similar to X-rays but with shorter wavelengths and higher frequency, although a 'cross-over' between X and gamma rays makes it possible to have X-rays with a higher energy (and hence shorter wavelength) than gamma rays and vice versa. The origin of the ray differentiates them, gamma rays tend to be natural phenomena originating from the unstable nucleus of an atom and X-rays are electrically generated (and hence man-made) unless they are as a result of bremsstrahlung X-radiation caused by the interaction of fast moving particles (such as beta particles) colliding with certain materials, usually of higher atomic numbers.[45]: 308, 9 

Electromagnetic spectrum[উৎস সম্পাদনা]

Main article: Electromagnetic spectrum

Electromagnetic spectrum with visible light highlighted. The bottom graph (visible spectrum) shows wavelength in units of nanometres (nm).

Legend:

γ = Gamma rays

HX = Hard X-rays

SX = Soft X-Rays

EUV = Extreme-ultraviolet

NUV = Near-ultraviolet

Visible light (colored bands)

NIR = Near-infrared

MIR = Mid-infrared

FIR = Far-infrared

EHF = Extremely high frequency (microwaves)

SHF = Super-high frequency (microwaves)

UHF = Ultrahigh frequency (radio waves)

VHF = Very high frequency (radio)

HF = High frequency (radio)

MF = Medium frequency (radio)

LF = Low frequency (radio)

VLF = Very low frequency (radio)

VF = Voice frequency

ULF = Ultra-low frequency (radio)

SLF = Super-low frequency (radio)

ELF = Extremely low frequency (radio)

EM radiation (the designation 'radiation' excludes static electric and magnetic and near fields) is classified by wavelength into radio, microwave, infrared, visible, ultraviolet, X-rays and gamma rays. Arbitrary electromagnetic waves can be expressed by Fourier analysis in terms of sinusoidal waves (monochromatic radiation), which in turn can each be classified into these regions of the EMR spectrum.

For certain classes of EM waves, the waveform is most usefully treated as random, and then spectral analysis must be done by slightly different mathematical techniques appropriate to random or stochastic processes. In such cases, the individual frequency components are represented in terms of their power content, and the phase information is not preserved. Such a representation is called the power spectral density of the random process. Random electromagnetic radiation requiring this kind of analysis is, for example, encountered in the interior of stars, and in certain other very wideband forms of radiation such as the Zero point wave field of the electromagnetic vacuum.

The behavior of EM radiation and its interaction with matter depends on its frequency, and changes qualitatively as the frequency changes. Lower frequencies have longer wavelengths, and higher frequencies have shorter wavelengths, and are associated with photons of higher energy. There is no fundamental limit known to these wavelengths or energies, at either end of the spectrum, although photons with energies near the Planck energy or exceeding it (far too high to have ever been observed) will require new physical theories to describe.

Radio and microwave[উৎস সম্পাদনা]

Main articles: Radio wave and Microwave

When radio waves impinge upon a conductor, they couple to the conductor, travel along it and induce an electric current on the conductor surface by moving the electrons of the conducting material in correlated bunches of charge.

Electromagnetic radiation phenomena with wavelengths ranging from as long as one meter to as short as one millimeter are called microwaves; with frequencies between 300 MHz (0.3 GHz) and 300 GHz.

At radio and microwave frequencies, EMR interacts with matter largely as a bulk collection of charges which are spread out over large numbers of affected atoms. In electrical conductors, such induced bulk movement of charges (electric currents) results in absorption of the EMR, or else separations of charges that cause generation of new EMR (effective reflection of the EMR). An example is absorption or emission of radio waves by antennas, or absorption of microwaves by water or other molecules with an electric dipole moment, as for example inside a microwave oven. These interactions produce either electric currents or heat, or both.

Infrared[উৎস সম্পাদনা]

Main article: Infrared

Like radio and microwave, infrared (IR) also is reflected by metals (and also most EMR, well into the ultraviolet range). However, unlike lower-frequency radio and microwave radiation, Infrared EMR commonly interacts with dipoles present in single molecules, which change as atoms vibrate at the ends of a single chemical bond. It is consequently absorbed by a wide range of substances, causing them to increase in temperature as the vibrations dissipate as heat. The same process, run in reverse, causes bulk substances to radiate in the infrared spontaneously (see thermal radiation section below).

Infrared radiation is divided into spectral subregions. While different subdivision schemes exist,[46][47] the spectrum is commonly divided as near-infrared (0.75–1.4 μm), short-wavelength infrared (1.4–3 μm), mid-wavelength infrared (3–8 μm), long-wavelength infrared (8–15 μm) and far infrared (15–1000 μm).[48]

Visible light[উৎস সম্পাদনা]

Main article: Light

Natural sources produce EM radiation across the spectrum. EM radiation with a wavelength between approximately 400 nm and 700 nm is directly detected by the human eye and perceived as visible light. Other wavelengths, especially nearby infrared (longer than 700 nm) and ultraviolet (shorter than 400 nm) are also sometimes referred to as light.

As frequency increases into the visible range, photons have enough energy to change the bond structure of some individual molecules. It is not a coincidence that this happens in the visible range, as the mechanism of vision involves the change in bonding of a single molecule, retinal, which absorbs a single photon. The change in retinal causes a change in the shape of the rhodopsin protein it is contained in, which starts the biochemical process that causes the retina of the human eye to sense the light.

Photosynthesis becomes possible in this range as well, for the same reason. A single molecule of chlorophyll is excited by a single photon. In plant tissues that conduct photosynthesis, carotenoids act to quench electronically excited chlorophyll produced by visible light in a process called non-photochemical quenching, to prevent reactions that would otherwise interfere with photosynthesis at high light levels.

Animals that detect infrared make use of small packets of water that change temperature, in an essentially thermal process that involves many photons.

Infrared, microwaves and radio waves are known to damage molecules and biological tissue only by bulk heating, not excitation from single photons of the radiation.

Visible light is able to affect only a tiny percentage of all molecules. Usually not in a permanent or damaging way, rather the photon excites an electron which then emits another photon when returning to its original position. This is the source of color produced by most dyes. Retinal is an exception. When a photon is absorbed, the retinal permanently changes structure from cis to trans, and requires a protein to convert it back, i.e. reset it to be able to function as a light detector again.

Limited evidence indicate that some reactive oxygen species are created by visible light in skin, and that these may have some role in photoaging, in the same manner as ultraviolet A.[49]

Ultraviolet[উৎস সম্পাদনা]

Main article: Ultraviolet

As frequency increases into the ultraviolet, photons now carry enough energy (about three electron volts or more) to excite certain doubly bonded molecules into permanent chemical rearrangement. In DNA, this causes lasting damage. DNA is also indirectly damaged by reactive oxygen species produced by ultraviolet A (UVA), which has energy too low to damage DNA directly. This is why ultraviolet at all wavelengths can damage DNA, and is capable of causing cancer, and (for UVB) skin burns (sunburn) that are far worse than would be produced by simple heating (temperature increase) effects.

At the higher end of the ultraviolet range, the energy of photons becomes large enough to impart enough energy to electrons to cause them to be liberated from the atom, in a process called photoionisation. The energy required for this is always larger than about 10 electron volt (eV) corresponding with wavelengths smaller than 124 nm (some sources suggest a more realistic cutoff of 33 eV, which is the energy required to ionize water). This high end of the ultraviolet spectrum with energies in the approximate ionization range, is sometimes called "extreme UV". Ionizing UV is strongly filtered by the Earth's atmosphere.[citation needed]

X-rays and gamma rays[উৎস সম্পাদনা]

Main articles: X-rays and Gamma rays

Electromagnetic radiation composed of photons that carry minimum-ionization energy, or more, (which includes the entire spectrum with shorter wavelengths), is therefore termed ionizing radiation. (Many other kinds of ionizing radiation are made of non-EM particles). Electromagnetic-type ionizing radiation extends from the extreme ultraviolet to all higher frequencies and shorter wavelengths, which means that all X-rays and gamma rays qualify. These are capable of the most severe types of molecular damage, which can happen in biology to any type of biomolecule, including mutation and cancer, and often at great depths below the skin, since the higher end of the X-ray spectrum, and all of the gamma ray spectrum, penetrate matter.[citation needed]

Atmosphere and magnetosphere[উৎস সম্পাদনা]

Main articles: ozone layer, shortwave radio, skywave, ionosphere, atmospheric window, and optical window

Rough plot of Earth's atmospheric absorption and scattering (or opacity) of various wavelengths of electromagnetic radiation

Most UV and X-rays are blocked by absorption first from molecular nitrogen, and then (for wavelengths in the upper UV) from the electronic excitation of dioxygen and finally ozone at the mid-range of UV. Only 30% of the Sun's ultraviolet light reaches the ground, and almost all of this is well transmitted.

Visible light is well transmitted in air, a property known as an atmospheric window, as it is not energetic enough to excite nitrogen, oxygen, or ozone, but too energetic to excite molecular vibrational frequencies of water vapor and CO2.[50]

Absorption bands in the infrared are due to modes of vibrational excitation in water vapor. However, at energies too low to excite water vapor, the atmosphere becomes transparent again, allowing free transmission of most microwave and radio waves.[51]

Finally, at radio wavelengths longer than 10 m or so (about 30 MHz), the air in the lower atmosphere remains transparent to radio, but plasma in certain layers of the ionosphere begins to interact with radio waves (see skywave). This property allows some longer wavelengths (100 m or 3 MHz) to be reflected and results in shortwave radio beyond line-of-sight. However, certain ionospheric effects begin to block incoming radiowaves from space, when their frequency is less than about 10 MHz (wavelength longer than about 30 m).[52]

Thermal and electromagnetic radiation as a form of heat[উৎস সম্পাদনা]

Main articles: Thermal radiation and Planck's law

The basic structure of matter involves charged particles bound together. When electromagnetic radiation impinges on matter, it causes the charged particles to oscillate and gain energy. The ultimate fate of this energy depends on the context. It could be immediately re-radiated and appear as scattered, reflected, or transmitted radiation. It may get dissipated into other microscopic motions within the matter, coming to thermal equilibrium and manifesting itself as thermal energy, or even kinetic energy, in the material. With a few exceptions related to high-energy photons (such as fluorescence, harmonic generation, photochemical reactions, the photovoltaic effect for ionizing radiations at far ultraviolet, X-ray and gamma radiation), absorbed electromagnetic radiation simply deposits its energy by heating the material. This happens for infrared, microwave and radio wave radiation. Intense radio waves can thermally burn living tissue and can cook food. In addition to infrared lasers, sufficiently intense visible and ultraviolet lasers can easily set paper afire.[53]

Ionizing radiation creates high-speed electrons in a material and breaks chemical bonds, but after these electrons collide many times with other atoms eventually most of the energy becomes thermal energy all in a tiny fraction of a second. This process makes ionizing radiation far more dangerous per unit of energy than non-ionizing radiation. This caveat also applies to UV, even though almost all of it is not ionizing, because UV can damage molecules due to electronic excitation, which is far greater per unit energy than heating effects.[53][citation needed]

Infrared radiation in the spectral distribution of a black body is usually considered a form of heat, since it has an equivalent temperature and is associated with an entropy change per unit of thermal energy. However, "heat" is a technical term in physics and thermodynamics and is often confused with thermal energy. Any type of electromagnetic energy can be transformed into thermal energy in interaction with matter. Thus, any electromagnetic radiation can "heat" (in the sense of increase the thermal energy temperature of) a material, when it is absorbed.[54]

The inverse or time-reversed process of absorption is thermal radiation. Much of the thermal energy in matter consists of random motion of charged particles, and this energy can be radiated away from the matter. The resulting radiation may subsequently be absorbed by another piece of matter, with the deposited energy heating the material.[55]

The electromagnetic radiation in an opaque cavity at thermal equilibrium is effectively a form of thermal energy, having maximum radiation entropy.[56]

Biological effects[উৎস সম্পাদনা]

Main articles: Electromagnetic radiation and health and Wireless device radiation and health

Bioelectromagnetics is the study of the interactions and effects of EM radiation on living organisms. The effects of electromagnetic radiation upon living cells, including those in humans, depends upon the radiation's power and frequency. For low-frequency radiation (radio waves to near ultraviolet) the best-understood effects are those due to radiation power alone, acting through heating when radiation is absorbed. For these thermal effects, frequency is important as it affects the intensity of the radiation and penetration into the organism (for example, microwaves penetrate better than infrared). It is widely accepted that low frequency fields that are too weak to cause significant heating could not possibly have any biological effect.[57]

Some research suggests that weaker non-thermal electromagnetic fields (including weak ELF magnetic fields, although the latter does not strictly qualify as EM radiation[57][58][59]) and modulated RF and microwave fields can have biological effects, though the significance of this is unclear.[60][61]

The World Health Organization has classified radio frequency electromagnetic radiation as Group 2B – possibly carcinogenic.[62][63] This group contains possible carcinogens such as lead, DDT, and styrene.

At higher frequencies (some of visible and beyond), the effects of individual photons begin to become important, as these now have enough energy individually to directly or indirectly damage biological molecules.[64] All UV frequencies have been classed as Group 1 carcinogens by the World Health Organization. Ultraviolet radiation from sun exposure is the primary cause of skin cancer.[65][66]

Thus, at UV frequencies and higher, electromagnetic radiation does more damage to biological systems than simple heating predicts. This is most obvious in the "far" (or "extreme") ultraviolet. UV, with X-ray and gamma radiation, are referred to as ionizing radiation due to the ability of photons of this radiation to produce ions and free radicals in materials (including living tissue). Since such radiation can severely damage life at energy levels that produce little heating, it is considered far more dangerous (in terms of damage-produced per unit of energy, or power) than the rest of the electromagnetic spectrum.

Use as a weapon[উৎস সম্পাদনা]

See also: Directed energy weapons § Microwave weapons

The heat ray is an application of EMR that makes use of microwave frequencies to create an unpleasant heating effect in the upper layer of the skin. A publicly known heat ray weapon called the Active Denial System was developed by the US military as an experimental weapon to deny the enemy access to an area.[67] A death ray is a theoretical weapon that delivers heat ray based on electromagnetic energy at levels that are capable of injuring human tissue. An inventor of a death ray, Harry Grindell Matthews, claimed to have lost sight in his left eye while working on his death ray weapon based on a microwave magnetron from the 1920s (a normal microwave oven creates a tissue damaging cooking effect inside the oven at around 2 kV/m).[68]

Derivation from electromagnetic theory[উৎস সম্পাদনা]

Main article: Electromagnetic wave equation

Electromagnetic waves are predicted by the classical laws of electricity and magnetism, known as Maxwell's equations. There are nontrivial solutions of the homogeneous Maxwell's equations (without charges or currents), describing waves of changing electric and magnetic fields. Beginning with Maxwell's equations in free space:

{\displaystyle \nabla \cdot \mathbf {E} =0} 1

{\displaystyle \nabla \times \mathbf {E} =-{\frac {\partial \mathbf {B} }{\partial t}}} 2

{\displaystyle \nabla \cdot \mathbf {B} =0} 3

{\displaystyle \nabla \times \mathbf {B} =\mu _{0}\varepsilon _{0}{\frac {\partial \mathbf {E} }{\partial t}}} 4

where

{\displaystyle \mathbf {E} } and {\displaystyle \mathbf {B} } are the electric field (measured in V/m or N/C) and the magnetic field (measured in T or Wb/m2), respectively;

{\displaystyle \nabla \cdot \mathbf {X} } yields the divergence and {\displaystyle \nabla \times \mathbf {X} } the curl of a vector field {\displaystyle \mathbf {X} ;}

{\displaystyle {\frac {\partial \mathbf {B} }{\partial t}}} and {\displaystyle {\frac {\partial \mathbf {E} }{\partial t}}} are partial derivatives (rate of change in time, with location fixed) of the magnetic and electric field;

{\displaystyle \mu _{0}} is the permeability of a vacuum (4π × 10−7 H/m), and {\displaystyle \varepsilon _{0}} is the permittivity of a vacuum (8.85 × 10−12 F/m);

Besides the trivial solution{\displaystyle \mathbf {E} =\mathbf {B} =\mathbf {0} ,}useful solutions can be derived with the following vector identity, valid for all vectors {\displaystyle \mathbf {A} } in some vector field:{\displaystyle \nabla \times \left(\nabla \times \mathbf {A} \right)=\nabla \left(\nabla \cdot \mathbf {A} \right)-\nabla ^{2}\mathbf {A} .}

Taking the curl of the second Maxwell equation (2) yields:

{\displaystyle \nabla \times \left(\nabla \times \mathbf {E} \right)=\nabla \times \left(-{\frac {\partial \mathbf {B} }{\partial t}}\right)} 5

Evaluating the left hand side of (5) with the above identity and simplifying using (1), yields:

{\displaystyle \nabla \times \left(\nabla \times \mathbf {E} \right)=\nabla \left(\nabla \cdot \mathbf {E} \right)-\nabla ^{2}\mathbf {E} =-\nabla ^{2}\mathbf {E} .} 6

Evaluating the right hand side of (5) by exchanging the sequence of derivatives and inserting the fourth Maxwell equation (4), yields:

{\displaystyle \nabla \times \left(-{\frac {\partial \mathbf {B} }{\partial t}}\right)=-{\frac {\partial }{\partial t}}\left(\nabla \times \mathbf {B} \right)=-\mu _{0}\varepsilon _{0}{\frac {\partial ^{2}\mathbf {E} }{\partial t^{2}}}} 7

Combining (6) and (7) again, gives a vector-valued differential equation for the electric field, solving the homogeneous Maxwell equations:

{\displaystyle \nabla ^{2}\mathbf {E} =\mu _{0}\varepsilon _{0}{\frac {\partial ^{2}\mathbf {E} }{\partial t^{2}}}}

Taking the curl of the fourth Maxwell equation (4) results in a similar differential equation for a magnetic field solving the homogeneous Maxwell equations:

{\displaystyle \nabla ^{2}\mathbf {B} =\mu _{0}\varepsilon _{0}{\frac {\partial ^{2}\mathbf {B} }{\partial t^{2}}}.}

Both differential equations have the form of the general wave equation for waves propagating with speed {\displaystyle c_{0},} where {\displaystyle f} is a function of time and location, which gives the amplitude of the wave at some time at a certain location:{\displaystyle \nabla ^{2}f={\frac {1}{{c_{0}}^{2}}}{\frac {\partial ^{2}f}{\partial t^{2}}}}This is also written as:{\displaystyle \Box f=0}where {\displaystyle \Box } denotes the so-called d'Alembert operator, which in Cartesian coordinates is given as:{\displaystyle \Box =\nabla ^{2}-{\frac {1}{{c_{0}}^{2}}}{\frac {\partial ^{2}}{\partial t^{2}}}={\frac {\partial ^{2}}{\partial x^{2}}}+{\frac {\partial ^{2}}{\partial y^{2}}}+{\frac {\partial ^{2}}{\partial z^{2}}}-{\frac {1}{{c_{0}}^{2}}}{\frac {\partial ^{2}}{\partial t^{2}}}\ }

Comparing the terms for the speed of propagation, yields in the case of the electric and magnetic fields:{\displaystyle c_{0}={\frac {1}{\sqrt {\mu _{0}\varepsilon _{0}}}}.}

This is the speed of light in vacuum. Thus Maxwell's equations connect the vacuum permittivity {\displaystyle \varepsilon _{0}}, the vacuum permeability {\displaystyle \mu _{0}}, and the speed of light, c0, via the above equation. This relationship had been discovered by Wilhelm Eduard Weber and Rudolf Kohlrausch prior to the development of Maxwell's electrodynamics, however Maxwell was the first to produce a field theory consistent with waves traveling at the speed of light.

These are only two equations versus the original four, so more information pertains to these waves hidden within Maxwell's equations. A generic vector wave for the electric field has the form{\displaystyle \mathbf {E} =\mathbf {E} _{0}f{\left({\hat {\mathbf {k} }}\cdot \mathbf {x} -c_{0}t\right)}}

Here, {\displaystyle \mathbf {E} _{0}} is a constant vector, {\displaystyle f} is any second differentiable function, {\displaystyle {\hat {\mathbf {k} }}} is a unit vector in the direction of propagation, and {\displaystyle {\mathbf {x} }} is a position vector. {\displaystyle f{\left({\hat {\mathbf {k} }}\cdot \mathbf {x} -c_{0}t\right)}} is a generic solution to the wave equation. In other words,{\displaystyle \nabla ^{2}f{\left({\hat {\mathbf {k} }}\cdot \mathbf {x} -c_{0}t\right)}={\frac {1}{{c_{0}}^{2}}}{\frac {\partial ^{2}}{\partial t^{2}}}f{\left({\hat {\mathbf {k} }}\cdot \mathbf {x} -c_{0}t\right)},}for a generic wave traveling in the {\displaystyle {\hat {\mathbf {k} }}} direction.

From the first of Maxwell's equations, we get{\displaystyle \nabla \cdot \mathbf {E} ={\hat {\mathbf {k} }}\cdot \mathbf {E} _{0}f'{\left({\hat {\mathbf {k} }}\cdot \mathbf {x} -c_{0}t\right)}=0}

Thus,{\displaystyle \mathbf {E} \cdot {\hat {\mathbf {k} }}=0}which implies that the electric field is orthogonal to the direction the wave propagates. The second of Maxwell's equations yields the magnetic field, namely,{\displaystyle \nabla \times \mathbf {E} ={\hat {\mathbf {k} }}\times \mathbf {E} _{0}f'{\left({\hat {\mathbf {k} }}\cdot \mathbf {x} -c_{0}t\right)}=-{\frac {\partial \mathbf {B} }{\partial t}}}

Thus,{\displaystyle \mathbf {B} ={\frac {1}{c_{0}}}{\hat {\mathbf {k} }}\times \mathbf {E} }

The remaining equations will be satisfied by this choice of {\displaystyle \mathbf {E} ,\mathbf {B} }.

The electric and magnetic field waves in the far-field travel at the speed of light. They have a special restricted orientation and proportional magnitudes, {\displaystyle E_{0}=c_{0}B_{0}}, which can be seen immediately from the Poynting vector. The electric field, magnetic field, and direction of wave propagation are all orthogonal, and the wave propagates in the same direction as {\displaystyle \mathbf {E} \times \mathbf {B} }. Also, E and B far-fields in free space, which as wave solutions depend primarily on these two Maxwell equations, are in-phase with each other. This is guaranteed since the generic wave solution is first order in both space and time, and the curl operator on one side of these equations results in first-order spatial derivatives of the wave solution, while the time-derivative on the other side of the equations, which gives the other field, is first-order in time, resulting in the same phase shift for both fields in each mathematical operation.

From the viewpoint of an electromagnetic wave traveling forward, the electric field might be oscillating up and down, while the magnetic field oscillates right and left. This picture can be rotated with the electric field oscillating right and left and the magnetic field oscillating down and up. This is a different solution that is traveling in the same direction. This arbitrariness in the orientation with respect to propagation direction is known as polarization. On a quantum level, it is described as photon polarization. The direction of the polarization is defined as the direction of the electric field.

More general forms of the second-order wave equations given above are available, allowing for both non-vacuum propagation media and sources. Many competing derivations exist, all with varying levels of approximation and intended applications. One very general example is a form of the electric field equation,[69] which was factorized into a pair of explicitly directional wave equations, and then efficiently reduced into a single uni-directional wave equation by means of a simple slow-evolution approximation.

See also[উৎস সম্পাদনা]

Antenna measurement

Bioelectromagnetics

Bolometer

CONELRAD

Electromagnetic pulse

Electromagnetic radiation and health

Evanescent wave coupling

Finite-difference time-domain method

Gravitational wave

Helicon

Impedance of free space

Radiation reaction

Health effects of sunlight exposure

Sinusoidal plane-wave solutions of the electromagnetic wave equation

References[উৎস সম্পাদনা]

^ *Purcell and Morin, Harvard University. (2013). Electricity and Magnetism, 820p (3rd ed.). Cambridge University Press, New York. ISBN 978-1-107-01402-2. p 430: "These waves... require no medium to support their propagation. Traveling electromagnetic waves carry energy, and... the Poynting vector describes the energy flow...;" p 440: ... the electromagnetic wave must have the following properties: 1) The field pattern travels with speed c (speed of light); 2) At every point within the wave... the electric field strength E equals "c" times the magnetic field strength B; 3) The electric field and the magnetic field are perpendicular to one another and to the direction of travel, or propagation."

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Further reading[উৎস সম্পাদনা]

Hecht, Eugene (2001). Optics (4th ed.). Pearson Education. ISBN 978-0-8053-8566-3.

Serway, Raymond A.; Jewett, John W. (2004). Physics for Scientists and Engineers (6th ed.). Brooks Cole. ISBN 978-0-534-40842-8.

Tipler, Paul (2004). Physics for Scientists and Engineers: Electricity, Magnetism, Light, and Elementary Modern Physics (5th ed.). W. H. Freeman. ISBN 978-0-7167-0810-0.

Reitz, John; Milford, Frederick; Christy, Robert (1992). Foundations of Electromagnetic Theory (4th ed.). Addison Wesley. ISBN 978-0-201-52624-0.

Jackson, John David (1999). Classical Electrodynamics (3rd ed.). John Wiley & Sons. ISBN 978-0-471-30932-1.

Allen Taflove and Susan C. Hagness (2005). Computational Electrodynamics: The Finite-Difference Time-Domain Method, 3rd ed. Artech House Publishers. ISBN 978-1-58053-832-9.

External links[উৎস সম্পাদনা]

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The Feynman Lectures on Physics Vol. I Ch. 28: Electromagnetic Radiation

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Electromagnetic Waves from Maxwell's Equations on Project PHYSNET.