Measurement

# Measurement

Overview
Measurement is the process or the result of determining the ratio
Ratio
In mathematics, a ratio is a relationship between two numbers of the same kind , usually expressed as "a to b" or a:b, sometimes expressed arithmetically as a dimensionless quotient of the two which explicitly indicates how many times the first number contains the second In mathematics, a ratio is...

of a physical quantity
Physical quantity
A physical quantity is a physical property of a phenomenon, body, or substance, that can be quantified by measurement.-Definition of a physical quantity:Formally, the International Vocabulary of Metrology, 3rd edition defines quantity as:...

, such as a length, time, temperature etc., to a unit of measurement, such as the metre, second or degree Celsius. The science of measurement is called metrology
Metrology
Metrology is the science of measurement. Metrology includes all theoretical and practical aspects of measurement. The word comes from Greek μέτρον , "measure" + "λόγος" , amongst others meaning "speech, oration, discourse, quote, study, calculation, reason"...

.

The English word measurement originates from the Latin
Latin
Latin is an Italic language originally spoken in Latium and Ancient Rome. It, along with most European languages, is a descendant of the ancient Proto-Indo-European language. Although it is considered a dead language, a number of scholars and members of the Christian clergy speak it fluently, and...

and the verb through the Middle French
Middle French
Middle French is a historical division of the French language that covers the period from 1340 to 1611. It is a period of transition during which:...

.

With the exception of a few seemingly fundamental quantum
Quantum
In physics, a quantum is the minimum amount of any physical entity involved in an interaction. Behind this, one finds the fundamental notion that a physical property may be "quantized," referred to as "the hypothesis of quantization". This means that the magnitude can take on only certain discrete...

constants, units of measurement are essentially arbitrary; in other words, people make them up and then agree to use them.
Discussion

Encyclopedia
Measurement is the process or the result of determining the ratio
Ratio
In mathematics, a ratio is a relationship between two numbers of the same kind , usually expressed as "a to b" or a:b, sometimes expressed arithmetically as a dimensionless quotient of the two which explicitly indicates how many times the first number contains the second In mathematics, a ratio is...

of a physical quantity
Physical quantity
A physical quantity is a physical property of a phenomenon, body, or substance, that can be quantified by measurement.-Definition of a physical quantity:Formally, the International Vocabulary of Metrology, 3rd edition defines quantity as:...

, such as a length, time, temperature etc., to a unit of measurement, such as the metre, second or degree Celsius. The science of measurement is called metrology
Metrology
Metrology is the science of measurement. Metrology includes all theoretical and practical aspects of measurement. The word comes from Greek μέτρον , "measure" + "λόγος" , amongst others meaning "speech, oration, discourse, quote, study, calculation, reason"...

.

The English word measurement originates from the Latin
Latin
Latin is an Italic language originally spoken in Latium and Ancient Rome. It, along with most European languages, is a descendant of the ancient Proto-Indo-European language. Although it is considered a dead language, a number of scholars and members of the Christian clergy speak it fluently, and...

and the verb through the Middle French
Middle French
Middle French is a historical division of the French language that covers the period from 1340 to 1611. It is a period of transition during which:...

.

## Standards

With the exception of a few seemingly fundamental quantum
Quantum
In physics, a quantum is the minimum amount of any physical entity involved in an interaction. Behind this, one finds the fundamental notion that a physical property may be "quantized," referred to as "the hypothesis of quantization". This means that the magnitude can take on only certain discrete...

constants, units of measurement are essentially arbitrary; in other words, people make them up and then agree to use them. Nothing inherent in nature dictates that an inch
Inch
An inch is the name of a unit of length in a number of different systems, including Imperial units, and United States customary units. There are 36 inches in a yard and 12 inches in a foot...

has to be a certain length, or that a mile
Mile
A mile is a unit of length, most commonly 5,280 feet . The mile of 5,280 feet is sometimes called the statute mile or land mile to distinguish it from the nautical mile...

is a better measure of distance than a kilometre
Kilometre
The kilometre is a unit of length in the metric system, equal to one thousand metres and is therefore exactly equal to the distance travelled by light in free space in of a second...

. Over the course of human history, however, first for convenience and then for necessity, standards of measurement evolved so that communities would have certain common benchmarks. Law
Law
Law is a system of rules and guidelines which are enforced through social institutions to govern behavior, wherever possible. It shapes politics, economics and society in numerous ways and serves as a social mediator of relations between people. Contract law regulates everything from buying a bus...

s regulating measurement were originally developed to prevent fraud
Fraud
In criminal law, a fraud is an intentional deception made for personal gain or to damage another individual; the related adjective is fraudulent. The specific legal definition varies by legal jurisdiction. Fraud is a crime, and also a civil law violation...

in commerce.

Today, units of measurement are generally defined on a scientific basis, overseen by governmental or supra-governmental agencies, and established in international treaties, pre-eminent of which is the General Conference on Weights and Measures
General Conference on Weights and Measures
The General Conference on Weights and Measures is the English name of the Conférence générale des poids et mesures . It is one of the three organizations established to maintain the International System of Units under the terms of the Convention du Mètre of 1875...

(CGPM), established in 1875 by the Treaty of the metre and which oversees the International System of Units
International System of Units
The International System of Units is the modern form of the metric system and is generally a system of units of measurement devised around seven base units and the convenience of the number ten. The older metric system included several groups of units...

(SI) and which has custody of the International Prototype Kilogram. The metre, for example, was redefined in 1983 by the CGPM as the distance traveled by light in free space in 1⁄299,792,458 of a second while in 1960 the international yard was defined by the governments of the United States, United Kingdom, Australia and South Africa as being exactly 0.9144 metres.

In the United States
United States
The United States of America is a federal constitutional republic comprising fifty states and a federal district...

, the National Institute of Standards and Technology (NIST), a division of the United States Department of Commerce
United States Department of Commerce
The United States Department of Commerce is the Cabinet department of the United States government concerned with promoting economic growth. It was originally created as the United States Department of Commerce and Labor on February 14, 1903...

, regulates commercial measurements. In the United Kingdom, the role is performed by the National Physical Laboratory (NPL), in Australia by the Commonwealth Scientific and Industrial Research Organisation
Commonwealth Scientific and Industrial Research Organisation
The Commonwealth Scientific and Industrial Research Organisation is the national government body for scientific research in Australia...

, in South Africa by the Council for Scientific and Industrial Research
Council for Scientific and Industrial Research
The Council for Scientific and Industrial Research is South Africa's central and premier scientific research and development organisation. It was established by an act of parliament in 1945 and is situated on its own campus in the city of Pretoria...

and in India the National Physical Laboratory of India.

## Units and systems

### Imperial system

Before SI units were widely adopted around the world, the British systems of English unit
English unit
English units are the historical units of measurement used in England up to 1824, which evolved as a combination of the Anglo-Saxon and Roman systems of units...

s and later imperial units were used in Britain, the Commonwealth
Commonwealth of Nations
The Commonwealth of Nations, normally referred to as the Commonwealth and formerly known as the British Commonwealth, is an intergovernmental organisation of fifty-four independent member states...

and the United States. The system came to be known as U.S. customary units in the United States and is still in use there and in a few Caribbean
Caribbean
The Caribbean is a crescent-shaped group of islands more than 2,000 miles long separating the Gulf of Mexico and the Caribbean Sea, to the west and south, from the Atlantic Ocean, to the east and north...

countries. These various systems of measurement have at times been called foot-pound-second systems after the Imperial units for length, weight and time even though the tons, hundredweights, gallons, and nautical miles, for example, are different for the U.S. units. Many Imperial units remain in use in Britain which has officially partially switched to the SI system. Road signs are still in miles, yards, miles per hour; milk, beer and cider are sold by the pint; people measure their height in feet and inches and their weight in stone and pounds, to give just a few examples. Imperial units are used in many other places, for example, in many Commonwealth countries that are considered metricated, land area is measured in acres and floor space in square feet, particularly for commercial transactions (rather than government statistics). Similarly, gasoline is sold by the gallon in many countries that are considered metricated.

### Metric system

The metric system
Metric system
The metric system is an international decimalised system of measurement. France was first to adopt a metric system, in 1799, and a metric system is now the official system of measurement, used in almost every country in the world...

is a decimal systems of measurement
Systems of measurement
A system of measurement is a set of units which can be used to specify anything which can be measured and were historically important, regulated and defined because of trade and internal commerce...

based on its units for length, the metre
Metre
The metre , symbol m, is the base unit of length in the International System of Units . Originally intended to be one ten-millionth of the distance from the Earth's equator to the North Pole , its definition has been periodically refined to reflect growing knowledge of metrology...

and for mass, the kilogram
Kilogram
The kilogram or kilogramme , also known as the kilo, is the base unit of mass in the International System of Units and is defined as being equal to the mass of the International Prototype Kilogram , which is almost exactly equal to the mass of one liter of water...

. It exists in several variations, with different choices of base units, though these do not affect its day-to-day use. Since the 1960s, the International System of Units
International System of Units
The International System of Units is the modern form of the metric system and is generally a system of units of measurement devised around seven base units and the convenience of the number ten. The older metric system included several groups of units...

(SI) is the internationally recognized metric system. Metric units of mass, length, and electricity are widely used around the world for both everyday and scientific purposes.

The metric system features a single base unit for many physical quantities. Other quantities are derived from the standard SI units. Multiples and fractions of the units are expressed as Powers of 10
Powers of 10
In mathematics, a power of ten is any of the integer powers of the number ten; in other words, ten multiplied by itself a certain number of times. By definition, the number one is a power of ten. The first few powers of ten are:...

of each unit. Unit conversions are always simple because they are in the ratio of ten, one hundred, one thousand, etc., so that convenient magnitudes for measurements are achieved by simply moving the decimal place: 1.234 metres is 1234 millimetres or 0.001234 kilometres. The use of fractions
Fraction (mathematics)
A fraction represents a part of a whole or, more generally, any number of equal parts. When spoken in everyday English, we specify how many parts of a certain size there are, for example, one-half, five-eighths and three-quarters.A common or "vulgar" fraction, such as 1/2, 5/8, 3/4, etc., consists...

, such as 2/5 of a metre, is not prohibited, but uncommon. All lengths and distances, for example, are measured in metres, or thousandths of a metre (millimetres), or thousands of metres (kilometres). There is no profusion of different units with different conversion factors as in the Imperial system which uses, for example, inch
Inch
An inch is the name of a unit of length in a number of different systems, including Imperial units, and United States customary units. There are 36 inches in a yard and 12 inches in a foot...

es, feet, yard
Yard
A yard is a unit of length in several different systems including English units, Imperial units and United States customary units. It is equal to 3 feet or 36 inches...

s, fathom
Fathom
A fathom is a unit of length in the imperial and the U.S. customary systems, used especially for measuring the depth of water.There are 2 yards in an imperial or U.S. fathom...

s, rods
Rod (unit)
The rod is a unit of length equal to 5.5 yards, 5.0292 metres, 16.5 feet, or of a statute mile. A rod is the same length as a perch or a pole. In old English, the term lug is also used.-History:...

.

### International System of Units

The International System of Units
International System of Units
The International System of Units is the modern form of the metric system and is generally a system of units of measurement devised around seven base units and the convenience of the number ten. The older metric system included several groups of units...

(abbreviated as SI from the French language
French language
French is a Romance language spoken as a first language in France, the Romandy region in Switzerland, Wallonia and Brussels in Belgium, Monaco, the regions of Quebec and Acadia in Canada, and by various communities elsewhere. Second-language speakers of French are distributed throughout many parts...

name Système International d'Unités) is the modern revision of the metric system
Metric system
The metric system is an international decimalised system of measurement. France was first to adopt a metric system, in 1799, and a metric system is now the official system of measurement, used in almost every country in the world...

. It is the world's most widely used system of units, both in everyday commerce
Commerce
While business refers to the value-creating activities of an organization for profit, commerce means the whole system of an economy that constitutes an environment for business. The system includes legal, economic, political, social, cultural, and technological systems that are in operation in any...

and in science
Science
Science is a systematic enterprise that builds and organizes knowledge in the form of testable explanations and predictions about the universe...

. The SI was developed in 1960 from the metre-kilogram-second
Second
The second is a unit of measurement of time, and is the International System of Units base unit of time. It may be measured using a clock....

(MKS) system, rather than the centimetre-gram-second
Centimetre gram second system of units
The centimetre–gram–second system is a metric system of physical units based on centimetre as the unit of length, gram as a unit of mass, and second as a unit of time...

(CGS) system, which, in turn, had many variants. During its development the SI also introduced several newly named units that were previously not a part of the metric system. The original SI units for the six basic physical quantities were:
• metre (m) :SI unit of length
• second (s) :SI unit of time
• kilogram (kg) :SI unit of mass
• ampere
Ampere
The ampere , often shortened to amp, is the SI unit of electric current and is one of the seven SI base units. It is named after André-Marie Ampère , French mathematician and physicist, considered the father of electrodynamics...

(A) :SI unit of electric current
• degree kelvin
Kelvin
The kelvin is a unit of measurement for temperature. It is one of the seven base units in the International System of Units and is assigned the unit symbol K. The Kelvin scale is an absolute, thermodynamic temperature scale using as its null point absolute zero, the temperature at which all...

(K) :SI unit of thermodynamic temperature
• candela
Candela
The candela is the SI base unit of luminous intensity; that is, power emitted by a light source in a particular direction, weighted by the luminosity function . A common candle emits light with a luminous intensity of roughly one candela...

(cd) :SI unit of luminous intensity

The mole
Mole (unit)
The mole is a unit of measurement used in chemistry to express amounts of a chemical substance, defined as an amount of a substance that contains as many elementary entities as there are atoms in 12 grams of pure carbon-12 , the isotope of carbon with atomic weight 12. This corresponds to a value...

was subsequently added to this list and the degree Kelvin renamed the kelvin.

There are two types of SI units, base units and derived units. Base units are the simple measurements for time, length, mass, temperature, amount of substance, electric current and light intensity. Derived units are constructed from the base units, for example, the watt
Watt
The watt is a derived unit of power in the International System of Units , named after the Scottish engineer James Watt . The unit, defined as one joule per second, measures the rate of energy conversion.-Definition:...

, i.e. the unit for power, is defined from the base units as m2·kg·s−3. Other physical properties may be measured in compound units, such as material density, measured in kg/m3.

#### Converting prefixes

The SI allows easy multiplication when switching among units having the same base but different prefixes. To convert from metres to centimetres it is only necessary to multiply the number of metres by 100, since there are 100 centimetres in a metre. Inversely, to switch from centimetres to metres one multiplies the number of centimetres by 0.01 or divide centimetres by 100.

### Length

A ruler
Ruler
A ruler, sometimes called a rule or line gauge, is an instrument used in geometry, technical drawing, printing and engineering/building to measure distances and/or to rule straight lines...

or rule is a tool used in, for example, geometry
Geometry
Geometry arose as the field of knowledge dealing with spatial relationships. Geometry was one of the two fields of pre-modern mathematics, the other being the study of numbers ....

, technical drawing
Technical drawing
Technical drawing, also known as drafting or draughting, is the act and discipline of composing plans that visually communicate how something functions or has to be constructed.Drafting is the language of industry....

, engineering, and carpentry, to measure lengths or distances or to draw straight lines. Strictly speaking, the ruler is the instrument used to rule straight lines and the calibrated instrument used for determining length is called a measure, however common usage calls both instruments rulers and the special name straightedge is used for an unmarked rule. The use of the word measure, in the sense of a measuring instrument, only survives in the phrase tape measure, an instrument that can be used to measure but cannot be used to draw straight lines. As can be seen in the photographs on this page, a two-metre carpenter's rule can be folded down to a length of only 20 centimetres, to easily fit in a pocket, and a five-metre-long tape measure easily retracts to fit within a small housing.

## Some special names

We also use some special names for some multiples of some units.
• 100 kilograms = 1 quintal; 1000 kilogram = 1 metric tonne;
• 10 years = 1 decade; 100 years = 1 century; 1000 years = 1 millennium

Metric system
The metric system is an international decimalised system of measurement. France was first to adopt a metric system, in 1799, and a metric system is now the official system of measurement, used in almost every country in the world...

in 1966 and the units used for measurement of length are metres (m) and millimetres (mm). Centimetres (cm) are avoided as they cause confusion when reading plans
PLANS
People for Legal and Non-Sectarian Schools is an organization based in California in the United States which campaigns against the public funding of Waldorf methods charter schools alleging they violate the United States Constitution's separation of church and state...

. For example, the length two and a half metres is usually recorded as 2500 mm or 2.5 m; it would be considered non-standard to record this length as 250 cm.

American surveyors use a decimal-based system of measurement devised by Edmund Gunter
Edmund Gunter
Edmund Gunter , English mathematician, of Welsh descent, was born in Hertfordshire in 1581.He was educated at Westminster School, and in 1599 was elected a student of Christ Church, Oxford. He took orders, became a preacher in 1614, and in 1615 proceeded to the degree of bachelor in divinity...

in 1620. The base unit is Gunter's chain
Gunter's chain
Gunter's chain is a measuring device used for land survey. It was designed and introduced in 1620 by English clergyman and mathematician Edmund Gunter long before the development of the theodolite and other more sophisticated equipment, enabling plots of land to be accurately surveyed and plotted,...

of 66 feet (20.1 m) which is subdivided into 4 rods, each of 16.5 ft or 100 links of 0.66 feet. A link is abbreviated "lk," and links "lks" in old deeds and Land Surveys done for the government.

### Time

Time is an abstract measurement we have invented in order to keep track of elemental changes over a non spatial continuum. It is denoted by numbers and/or named periods such as hours, days, weeks, or months. It is an apparently irreversible series of occurrences within this non spatial continuum. It is also used to denote an interval between two relative points on this continuum.

### Mass

Mass refers to the intrinsic property of all material objects to resist changes in their momentum. Weight, on the other hand, refers to the downward force produced when a mass is in a gravitational field. In free fall
Free fall
Free fall is any motion of a body where gravity is the only force acting upon it, at least initially. These conditions produce an inertial trajectory so long as gravity remains the only force. Since this definition does not specify velocity, it also applies to objects initially moving upward...

, (no net gravitational forces) objects lack weight but retain their mass. The Imperial units of mass include the ounce
Ounce
The ounce is a unit of mass with several definitions, the most commonly used of which are equal to approximately 28 grams. The ounce is used in a number of different systems, including various systems of mass that form part of the imperial and United States customary systems...

, pound
Pound (mass)
The pound or pound-mass is a unit of mass used in the Imperial, United States customary and other systems of measurement...

, and ton
Ton
The ton is a unit of measure. It has a long history and has acquired a number of meanings and uses over the years. It is used principally as a unit of weight, and as a unit of volume. It can also be used as a measure of energy, for truck classification, or as a colloquial term.It is derived from...

. The metric units gram
Gram
The gram is a metric system unit of mass....

and kilogram are units of mass.

One device for measuring weight or mass is called a weighing scale or, often, simply a scale. A spring scale measures force but not mass, a balance compares weight, both require a gravitational field to operate. Some of the most accurate instruments for measuring weight or mass are based on load cells with a digital read-out, but require a gravitational field to function and would not work in free fall.

### Economics

The measures used in economics are physical measures, nominal price value measures and fixed price value measures. These measures differ from one another by the variables they measure and by the variables excluded from measurements. The measurable variables in economics are quantity, quality and distribution. By excluding variables from measurement makes it possible to better focus the measurement on a given variable, yet, this means a narrower approach.

## Difficulties

Since accurate measurement is essential in many fields, and since all measurements are necessarily approximations, a great deal of effort must be taken to make measurements as accurate as possible. For example, consider the problem of measuring the time
History of timekeeping devices
For thousands of years, devices have been used to measure and keep track of time. The current sexagesimal system of time measurement dates to approximately 2000 BC, in Sumer. The Ancient Egyptians divided the day into two 12-hour periods, and used large obelisks to track the movement of the Sun...

it takes an object to fall a distance of one metre (about 39 in
Inch
An inch is the name of a unit of length in a number of different systems, including Imperial units, and United States customary units. There are 36 inches in a yard and 12 inches in a foot...

). Using physics, it can be shown that, in the gravitational field of the Earth, it should take any object about 0.45 second to fall one metre. However, the following are just some of the sources of error
Measurement uncertainty
In metrology, measurement uncertainty is a non-negative parameter characterizing the dispersion of the values attributed to a measured quantity. The uncertainty has a probabilistic basis and reflects incomplete knowledge of the quantity. All measurements are subject to uncertainty and a measured...

that arise:
1. This computation used for the acceleration of gravity 9.8 m/s2. But this measurement is not exact, but only precise to two significant digits.
2. The Earth's gravitational field varies slightly depending on height above sea level and other factors.
3. The computation of .45 seconds involved extracting a square root
Square root
In mathematics, a square root of a number x is a number r such that r2 = x, or, in other words, a number r whose square is x...

, a mathematical operation that required rounding off to some number of significant digits, in this case two significant digits.

So far, we have only considered scientific sources of error. In actual practice, dropping an object from a height of a metre stick and using a stopwatch
Stopwatch
A stopwatch is a handheld timepiece designed to measure the amount of time elapsed from a particular time when activated to when the piece is deactivated. A large digital version of a stopwatch designed for viewing at a distance, as in a sports stadium, is called a stopclock.The timing functions...

to time its fall, we have other sources of error:
1. Most common, is simple carelessness.
2. Determining the exact time at which the object is released and the exact time it hits the ground. There is also the problem that the measurement of the height and the measurement of the time both involve some error.
3. Air resistance

Scientific experiments must be carried out with great care to eliminate as much error as possible, and to keep error estimates realistic.

### Classical definition

In the classical definition, which is standard throughout the physical sciences, measurement is the determination or estimation of ratios of quantities. Quantity and measurement are mutually defined: quantitative attributes are those possible to measure, at least in principle. The classical concept of quantity can be traced back to John Wallis and Isaac Newton
Isaac Newton
Sir Isaac Newton PRS was an English physicist, mathematician, astronomer, natural philosopher, alchemist, and theologian, who has been "considered by many to be the greatest and most influential scientist who ever lived."...

, and was foreshadowed in Euclid's Elements
Euclid's Elements
Euclid's Elements is a mathematical and geometric treatise consisting of 13 books written by the Greek mathematician Euclid in Alexandria c. 300 BC. It is a collection of definitions, postulates , propositions , and mathematical proofs of the propositions...

.

### Representational theory

In the representational theory, measurement is defined as "the correlation of numbers with entities that are not numbers". The most technically elaborate form of representational theory is also known as additive conjoint measurement. In this form of representational theory, numbers are assigned based on correspondences or similarities between the structure of number systems and the structure of qualitative systems. A property is quantitative if such structural similarities can be established. In weaker forms of representational theory, such as that implicit within the work of Stanley Smith Stevens
Stanley Smith Stevens
Stanley Smith Stevens was an American psychologist who founded Harvard's Psycho-Acoustic Laboratory and is credited with the introduction of Stevens' power law. Stevens authored a milestone textbook, the 1400+ page "Handbook of Experimental Psychology" . He was also one of the founding organizers...

, numbers need only be assigned according to a rule.

The concept of measurement is often misunderstood as merely the assignment of a value, but it is possible to assign a value in a way that is not a measurement in terms of the requirements of additive conjoint measurement. One may assign a value to a person's height, but unless it can be established that there is a correlation between measurements of height and empirical relations, it is not a measurement according to additive conjoint measurement theory. Likewise, computing and assigning arbitrary values, like the "book value" of an asset in accounting, is not a measurement because it does not satisfy the necessary criteria.

### Information theory

Information theory
Information theory
Information theory is a branch of applied mathematics and electrical engineering involving the quantification of information. Information theory was developed by Claude E. Shannon to find fundamental limits on signal processing operations such as compressing data and on reliably storing and...

recognizes that all data are inexact and statistical in nature. Thus the definition of measurement is: "A set of observations that reduce uncertainty where the result is expressed as a quantity." This definition is implied in what scientists actually do when they measure something and report both the mean
Mean
In statistics, mean has two related meanings:* the arithmetic mean .* the expected value of a random variable, which is also called the population mean....

and statistics
Statistics
Statistics is the study of the collection, organization, analysis, and interpretation of data. It deals with all aspects of this, including the planning of data collection in terms of the design of surveys and experiments....

of the measurements. In practical terms, one begins with an initial guess as to the value of a quantity, and then, using various methods and instruments, reduces the uncertainty in the value. Note that in this view, unlike the positivist representational theory, all measurements are uncertain, so instead of assigning one value, a range of values is assigned to a measurement. This also implies that there is not a clear or neat distinction between estimation
Estimation
Estimation is the calculated approximation of a result which is usable even if input data may be incomplete or uncertain.In statistics,*estimation theory and estimator, for topics involving inferences about probability distributions...

and measurement. Ascertaining the degree measurement error is also a basic facet of metrology, and sources of errors are divided into systematic and non-systematic.

### Quantum mechanics

In quantum mechanics
Quantum mechanics
Quantum mechanics, also known as quantum physics or quantum theory, is a branch of physics providing a mathematical description of much of the dual particle-like and wave-like behavior and interactions of energy and matter. It departs from classical mechanics primarily at the atomic and subatomic...

, a measurement is an action that determines the location of an object, its momentum, its polarity (if it is a photon), etc. Before a measurement is made, the wavefunction
Wavefunction
Not to be confused with the related concept of the Wave equationA wave function or wavefunction is a probability amplitude in quantum mechanics describing the quantum state of a particle and how it behaves. Typically, its values are complex numbers and, for a single particle, it is a function of...

of what is to be measured gives a range of probabilities for the outcomes of measurement, but when a measurement is accomplished that results in what is called the collapse of the wavefunction− at which time there is one definite value rather than a range of possible values. The unambiguous meaning of the measurement problem
Measurement problem
The measurement problem in quantum mechanics is the unresolved problem of how wavefunction collapse occurs. The inability to observe this process directly has given rise to different interpretations of quantum mechanics, and poses a key set of questions that each interpretation must answer...

is an unresolved fundamental problem in quantum mechanics
Quantum mechanics
Quantum mechanics, also known as quantum physics or quantum theory, is a branch of physics providing a mathematical description of much of the dual particle-like and wave-like behavior and interactions of energy and matter. It departs from classical mechanics primarily at the atomic and subatomic...

.

• Airy points
Airy Points
Airy Points are used for precision measurement to support a length standard in such a way as to minimise bending or droop. The points are symmetrically arranged around the centre of the length standard and are separated by a distance equal to...

• Conversion of units
Conversion of units
Conversion of units is the conversion between different units of measurement for the same quantity, typically through multiplicative conversion factors.- Process :...

• Detection limit
Detection limit
In analytical chemistry, the detection limit, lower limit of detection, or LOD , is the lowest quantity of a substance that can be distinguished from the absence of that substance within a stated confidence limit...

• Differential linearity
Differential linearity
In measurement systems differential linearity refers to a constant relation between the change in the output and input. For transducers if a change in the input produces a uniform step change in the output the tranducer possess differential linearity...

• Dimensional analysis
Dimensional analysis
In physics and all science, dimensional analysis is a tool to find or check relations among physical quantities by using their dimensions. The dimension of a physical quantity is the combination of the basic physical dimensions which describe it; for example, speed has the dimension length per...

• Dimensionless number
• Econometrics
Econometrics
Econometrics has been defined as "the application of mathematics and statistical methods to economic data" and described as the branch of economics "that aims to give empirical content to economic relations." More precisely, it is "the quantitative analysis of actual economic phenomena based on...

• History of measurement
History of measurement
Units of measurement were among the earliest tools invented by humans. Primitive societies needed rudimentary measures for numerous tasks such as: constructing dwellings of an appropriate size and shape, fashioning clothing, or bartering food or raw materials....

• History of science and technology
History of science and technology
The history of science and technology is a field of history which examines how humanity's understanding of the natural world and ability to manipulate it have changed over the centuries...

• Instrumentation
Instrumentation
Instrumentation is defined as the art and science of measurement and control of process variables within a production, or manufacturing area....

• Integral linearity
Integral linearity
A measurement system consists of a sensor, to input the physical parameter that is of interest, and an output to a medium that is suitable for reading by the system that needs to know the value of the parameter...

• Key relevance
Key relevance
In master locksmithing, key relevance is the measurable difference between an original key and a copy made of that key, either from a wax impression or directly from the original, and how similar the two keys are in size and shape...

in locksmithing
• Least Count
Least Count
The least count of any measuring equipment is the smallest quantity that can be measured accurately using that instrument. Thus Least Count indicates the degree of accuracy of measurement that can be achieved by the measuring instrument....

• Levels of measurement
• Measurement in quantum mechanics
Measurement in quantum mechanics
The framework of quantum mechanics requires a careful definition of measurement. The issue of measurement lies at the heart of the problem of the interpretation of quantum mechanics, for which there is currently no consensus....

• Measuring instrument
Measuring instrument
In the physical sciences, quality assurance, and engineering, measurement is the activity of obtaining and comparing physical quantities of real-world objects and events. Established standard objects and events are used as units, and the process of measurement gives a number relating the item...

• NCSL International
NCSL International
NCSL International is a global, non-profit organization whose membership is open to any organization with an interest in metrology and its application in research, development, education, and commerce.-History:...

• Number sense
Number sense
In mathematics education, number sense can refer to "an intuitive understanding of numbers, their magnitude, relationships, and how they are affected by operations." Many other definitions exist, but are similar to the one given...

• Orders of magnitude
• Psychometrics
Psychometrics
Psychometrics is the field of study concerned with the theory and technique of psychological measurement, which includes the measurement of knowledge, abilities, attitudes, personality traits, and educational measurement...

• Standard (metrology)
Standard (metrology)
In the science of measurement, a standard is an object, system, or experiment that bears a defined relationship to a unit of measurement of a physical quantity. Standards are the fundamental reference for a system of weights and measures, against which all other measuring devices are compared...

• Statistics
Statistics
Statistics is the study of the collection, organization, analysis, and interpretation of data. It deals with all aspects of this, including the planning of data collection in terms of the design of surveys and experiments....

• Systems of measurement
Systems of measurement
A system of measurement is a set of units which can be used to specify anything which can be measured and were historically important, regulated and defined because of trade and internal commerce...

• Test method
Test method
A test method is a definitive procedure that produces a test result.A test can be considered as technical operation that consists of determination of one or more characteristics of a given product, process or service according to a specified procedure. Often a test is part of an experiment.The test...

• Timeline of temperature and pressure measurement technology
Timeline of temperature and pressure measurement technology
Timeline of temperature and pressure measurement technology A history of temperature measurement and pressure measurement technology.-1500s:* 1592-1593 — Galileo Galilei builds a device showing variation of hotness known as the thermoscope using the contraction of air to draw water up a...

• Timeline of time measurement technology
Timeline of time measurement technology
Timeline of time measurement technology* 270 BC - Ctesibius builds a popular water clock, called a clepsydra* 46 BC - Julius Caesar and Sosigenes develop a solar calendar with leap years...

• Units of measurement
Units of measurement
A unit of measurement is a definite magnitude of a physical quantity, defined and adopted by convention and/or by law, that is used as a standard for measurement of the same physical quantity. Any other value of the physical quantity can be expressed as a simple multiple of the unit of...

• Uncertainty principle
Uncertainty principle
In quantum mechanics, the Heisenberg uncertainty principle states a fundamental limit on the accuracy with which certain pairs of physical properties of a particle, such as position and momentum, can be simultaneously known...

• Uncertainty
Uncertainty
Uncertainty is a term used in subtly different ways in a number of fields, including physics, philosophy, statistics, economics, finance, insurance, psychology, sociology, engineering, and information science...

in measurement
• Virtual instrumentation
Virtual instrumentation
Virtual instrumentation is the use of customizable software and modular measurement hardware to create user-defined measurement systems, called virtual instruments....

• Weights and measures