Time, number, distance measurement concepts

Time, number, distance measurement concepts

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Time is the continued sequence of existence and events that occurs in an apparently irreversible succession from the past, through the present, into the future. It is a component quantity of various measurements used to sequence events, to 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. Time is often referred to as a fourth dimension, along with three spatial dimensions.

Time has long been an important subject of study in religion, philosophy, and science, but defining it in a manner applicable to all fields without circularity has consistently eluded scholars. 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.
Time in physics is operationally defined as "what a clock reads
The physical nature of time is addressed by general relativity with respect to events in spacetime. Examples of events are the collision of two particles, the explosion of a supernova, or the arrival of a rocket ship. Every event can be assigned four numbers representing its time and position (the event's coordinates). However, the numerical values are different for different observers. In general relativity, the question of what time it is now only has meaning relative to a particular observer. Distance and time are intimately related, and the time required for light to travel a specific distance is the same for all observers, as first publicly demonstrated by Michelson and Morley. General relativity does not address the nature of time for extremely small intervals where quantum mechanics holds. At this time, there is no generally accepted theory of quantum general relativity.
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. Time is used to define other quantities, such as velocity, so defining time in terms of such quantities would result in circularity of definition.[16] An operational definition of time, wherein one says that observing a certain number of repetitions of one or another standard cyclical event (such as the passage of a free-swinging pendulum) constitutes one standard unit such as the second, is highly useful in the conduct of both advanced experiments and everyday affairs of life. To describe observations of an event, a location (position in space) and time are typically noted.
The operational definition of time does not address what the fundamental nature of time is. It does not address why events can happen forward and backward in space, whereas events only happen in the forward progress of time. Investigations into the relationship between space and time led physicists to define the spacetime continuum. General relativity is the primary framework for understanding how spacetime works.[17] 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.
Temporal measurement has occupied scientists and technologists and was a prime motivation in navigation and astronomy. Periodic events and periodic motion have long served as standards for units of time. Examples include the apparent motion of the sun across the sky, the phases of the moon, and the swing of a pendulum. 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.
There are many systems for determining what time it is, including the Global Positioning System, other satellite systems, Coordinated Universal Time and mean solar time. In general, the numbers obtained from different time systems differ from one another.
Measurement
The flow of sand in an hourglass can be used to measure the passage of time. It also concretely represents the present as being between the past and the future.
Generally speaking, methods of temporal measurement, or chronometry, take two distinct forms: the calendar, a mathematical tool for organising intervals of time,[18] and the clock, a physical mechanism that counts the passage of time. In day-to-day life, the clock is consulted for periods less than a day, whereas the calendar is 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 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.[19] 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.[20]
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 in an attempt to de-Christianize time and 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.
History of other devices
Horizontal sundial in Taganrog
An old kitchen clock
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.
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.[23]
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.
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.[25] 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).
Incense sticks and candles were, and are, commonly used to measure time in temples and churches across the globe. Waterclocks, 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.
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
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.
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.[29]
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 firstly 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,[31] 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.[32] 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,[33] where it was defined as 1/564 of a momentum (11⁄2 minutes),[34] 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.
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, 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.
efinitions and 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 up 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. number is a mathematical object used to count, measure, and label. The original examples are the natural numbers 1, 2, 3, 4, and so forth.[1] Numbers can be represented in language with number words. More universally, individual numbers can be represented by symbols, called numerals; for example, "5" is a numeral that represents the number five. As only a relatively small number of symbols can be memorized, basic numerals are commonly organized in a numeral system, which is an organized way to represent any number. The most common numeral system is the Hindu–Arabic numeral system, which allows for the representation of any number using a combination of ten fundamental numeric symbols, called digits.[2][a] In addition to their use in counting and measuring, numerals are often used for labels (as with telephone numbers), for ordering (as with serial numbers), and for codes (as with ISBNs). In common usage, a numeral is not clearly distinguished from the number that it represents.
In mathematics, the notion of a number has been extended over the centuries to include zero (0),[3] negative numbers,[4] rational numbers such as one half {\displaystyle \left({\tfrac {1}{2}}\right)}, real numbers such as the square root of displaystyle \left({\sqrt {2}}\right)} and π,[5] and complex numbers[6] which extend the real numbers with a square root of −1 (and its combinations with real numbers by adding or subtracting its multiples).[4] Calculations with numbers are done with arithmetical operations, the most familiar being addition, subtraction, multiplication, division, and exponentiation. Their study or usage is called arithmetic, a term which may also refer to number theory, the study of the properties of numbers.
Besides their practical uses, numbers have cultural significance throughout the world.[7][8] For example, in Western society, the number 13 is often regarded as unlucky, and "a million" may signify "a lot" rather than an exact quantity.[7] Though it is now regarded as pseudoscience, belief in a mystical significance of numbers, known as numerology, permeated ancient and medieval thought.[9] Numerology heavily influenced the development of Greek mathematics, stimulating the investigation of many problems in number theory which are still of interest today.[9]
During the 19th century, mathematicians began to develop many different abstractions which share certain properties of numbers, and may be seen as extending the concept. Among the first were the hypercomplex numbers, which consist of various extensions or modifications of the complex number system. In modern mathematics, number systems are considered important special examples of more general algebraic structures such as rings and fields, and the application of the term "number" is a matter of convention, without fundamental significance