Measurement
Measurement is the quantification of attributes of an object or event, which can be used to compare with other objects or events.[1][2] In other words, measurement is a process of determining how large or small a physical quantity is as compared to a basic reference quantity of the same kind.[3] The scope and application of measurement are dependent on the context and discipline. In
Measurement is a cornerstone of
Measurement is defined as the process of comparison of an unknown quantity with a known or standard quantity.
History
Methodology
The measurement of a property may be categorized by the following criteria:
- The level of measurement is a taxonomy for the methodological character of a comparison. For example, two states of a property may be compared by ratio, difference, or ordinal preference. The type is commonly not explicitly expressed, but implicit in the definition of a measurement procedure.
- The magnitude is the numerical value of the characterization, usually obtained with a suitably chosen measuring instrument.
- A unit assigns a mathematical weighting factor to the magnitude that is derived as a ratio to the property of an artifact used as standard or a natural physical quantity.
- An uncertainty represents the random and systemic errors of the measurement procedure; it indicates a confidence level in the measurement. Errors are evaluated by methodically repeating measurements and considering the accuracy and precision of the measuring instrument.
Standardization of measurement units
Measurements most commonly use the
The first proposal to tie an SI base unit to an experimental standard independent of fiat was by Charles Sanders Peirce (1839–1914),[5] who proposed to define the metre in terms of the wavelength of a spectral line.[6] This directly influenced the Michelson–Morley experiment; Michelson and Morley cite Peirce, and improve on his method.[7]
Standards
With the exception of a few fundamental quantum constants, units of measurement are derived from historical agreements. Nothing inherent in nature dictates that an inch has to be a certain length, nor that a mile is a better measure of distance than a kilometre. 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. Laws regulating measurement were originally developed to prevent fraud in commerce.
In the United States, the National Institute of Standards and Technology (
Units and systems
unit is known or standard quantity in terms of which other physical quantities are measured.
Imperial and US customary systems
Before
Metric system
The
International System of Units
The
Base quantity | Base unit | Symbol | Defining constant |
---|---|---|---|
time | Second | s | hyperfine splitting in caesium-133
|
length | Metre | m | speed of light, c |
mass | Kilogram | kg | Planck constant, h |
electric current | Ampere | A | elementary charge, e |
temperature | Kelvin | K | Boltzmann constant, k |
amount of substance | Mol | mol | Avogadro constant NA |
luminous intensity | Candela | cd | luminous efficacy of a 540 THz source Kcd |
In the SI, 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, 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 divides the number of centimetres by 100.
Length
A ruler or rule is a tool used in, for example, geometry, technical drawing, 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.
Time
Time is an abstract measurement of elemental changes over a non-spatial continuum. It is denoted by numbers and/or named periods such as hours, days, weeks, months and years. 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, (no net gravitational forces) objects lack weight but retain their mass. The Imperial units of mass include the ounce, pound, and ton. The metric units gram 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,
Survey research
In the field of survey research, measures are taken from individual attitudes, values, and behavior using
Exactness designation
The following rules generally apply for displaying the exactness of measurements:[11]
- All non-0 digits and any 0s appearing between them are significant for the exactness of any number. For example, the number 12000 has two significant digits, and has implied limits of 11500 and 12500.
- Additional 0s may be added after a decimal separator to denote a greater exactness, increasing the number of decimals. For example, 1 has implied limits of 0.5 and 1.5 whereas 1.0 has implied limits 0.95 and 1.05.
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 it takes an object to fall a distance of one metre (about 39 in). 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 that arise:
- This computation used for the acceleration of gravity 9.8 metres per second squared (32 ft/s2). But this measurement is not exact, but only precise to two significant digits.
- The Earth's gravitational field varies slightly depending on height above sea level and other factors.
- The computation of 0.45 seconds involved extracting a mathematical operationthat required rounding off to some number of significant digits, in this case two significant digits.
Additionally, other sources of
- carelessness,
- determining of the exact time at which the object is released and the exact time it hits the ground,
- measurement of the height and the measurement of the time both involve some error,
- Air resistance.
- posture of human participants[12]
Scientific experiments must be carried out with great care to eliminate as much error as possible, and to keep error estimates realistic.
Definitions and theories
Classical definition
In the classical definition, which is standard throughout the physical sciences, measurement is the determination or estimation of ratios of quantities.[13] 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, and was foreshadowed in Euclid's Elements.[13]
Representational theory
In the representational theory, measurement is defined as "the correlation of numbers with entities that are not numbers".
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.
Three type of Representational theory
1) Empirical relation
In science, an empirical relationship is a relationship or correlation based solely on observation rather than theory. An empirical relationship requires only confirmatory data irrespective of theoretical basis
2) The rule of mapping
The real world is the Domain of mapping, and the mathematical world is the range. when we map the attribute to mathematical system, we have many choice for mapping and the range
3) The representation condition of measurement
Information theory
Quantum mechanics
In
Biology
In biology, there is generally no well established theory of measurement. However, the importance of the theoretical context is emphasized.[19] Moreover, the theoretical context stemming from the theory of evolution leads to articulate the theory of measurement and historicity as a fundamental notion.[20] Among the most developed fields of measurement in biology are the measurement of genetic diversity and species diversity.[21]
See also
- Conversion of units
- Electrical measurements
- History of measurement
- ISO 10012, Measurement management systems
- Levels of measurement
- List of humorous units of measurement
- List of unusual units of measurement
- Measurement in quantum mechanics
- Measurement uncertainty
- NCSL International
- Observable quantity
- Orders of magnitude
- Quantification (science)
- Standard (metrology)
- Timeline of temperature and pressure measurement technology
- Timeline of time measurement technology
- Weights and measures
References
- ^ ISBN 978-0-8058-1063-9.
- ^ a b International Vocabulary of Metrology – Basic and General Concepts and Associated Terms (VIM) (PDF) (3rd ed.). International Bureau of Weights and Measures. 2008. p. 16.
- ISBN 978-0-321-69686-1.
- ISBN 978-0-321-02106-9.
- ^ Crease 2011, pp. 182–4
- ^ C.S. Peirce (July 1879) "Note on the Progress of Experiments for Comparing a Wave-length with a Metre" American Journal of Science, as referenced by Crease 2011, p. 203
- ISBN 978-0-393-34354-0.
- ^ "About Us". National Measurement Institute of Australia. 3 December 2020.
- ISBN 978-92-822-2272-0
- ISBN 9780471483489. "By measurement error we mean a departure from the value of the measurement as applied to a sample unit and the value provided. " pp. 51–52 .
- OCLC 811317577.
- S2CID 23758581.
- ^ a b Michell, J. (1999). Measurement in psychology: a critical history of a methodological concept. New York: Cambridge University Press.
- Springer, the Netherlands
- ^ Stevens, S.S. On the theory of scales and measurement 1946. Science. 103, 677–80.
- ^ Douglas Hubbard: "How to Measure Anything", Wiley (2007), p. 21
- ^ ISBN 0486409244.
- ISBN 978-0-679-77631-4. "The jumping of the quantum state to one of the eigenstates of Q is the process referred to as state-vector reduction or collapse of the wavefunction. It is one of quantum theory's most puzzling features ..." "[T]he way in which quantum mechanics is used in practice is to take the state indeed to jump in this curious way whenever a measurement is deemed to take place." p 528 Later Chapter 29 is entitled the Measurement paradox.
- S2CID 570080. Archived from the original(PDF) on 2019-05-29.
- S2CID 96447209.
- ^ Magurran, A.E. & McGill, B.J. (Hg.) 2011: Biological Diversity: Frontiers in Measurement and Assessment Oxford University Press.
External links
- Media related to Measurement at Wikimedia Commons
- Schlaudt, Oliver 2020: "measurement". In: Kirchhoff, Thomas (ed.): Online Encyclopedia Philosophy of Nature. Heidelberg: Universitätsbibliothek Heidelberg, measurement.
- Tal, Era 2020: "Measurement in Science". In: Zalta, Edward N. (ed.): The Stanford Encyclopedia of Philosophy (Fall 2020 Edition), URL = <Measurement in Science>.
- Ball, Robert Stawell (1883). . Encyclopædia Britannica. Vol. XV (9th ed.). pp. 659–668.
- A Dictionary of Units of Measurement Archived 2018-10-06 at the Wayback Machine
- 'Metrology – in short' 3rd edition, July 2008 ISBN 978-87-988154-5-7