Free to follow every thread. No paywall, no dead ends.
Measurement: the story on HearLore | HearLore
Measurement
The metre was once a physical bar of platinum-iridium stored in a vault in France, but today it is defined by the speed of light, a constant that has never changed since the beginning of the universe. This shift from a tangible object to an abstract physical constant represents the most profound evolution in human history regarding how we quantify reality. For centuries, humanity relied on local agreements and arbitrary standards to measure the world, often leading to confusion and fraud in trade. The first proposal to tie a unit to an experimental standard independent of a physical artefact came from Charles Sanders Peirce in the late 19th century, who suggested defining the metre using the wavelength of a spectral line. This idea directly influenced the Michelson, Morley experiment, which improved upon Peirce's method to establish a more reliable standard. The International System of Units, or SI, now defines seven fundamental units without reference to any physical object, ensuring that measurements remain exact and unchanging regardless of the deterioration or destruction of any single artefact.
The Seven Pillars of Reality
Every physical quantity in the universe can be reduced to a mathematical combination of seven base units, forming the backbone of modern science and engineering. These units are the second for time, the metre for length, the kilogram for mass, the ampere for electric current, the kelvin for temperature, the mole for amount of substance, and the candela for luminous intensity. The kilogram, once defined by a physical cylinder kept in a vault, was redefined in 2019 in terms of the Planck constant, a fundamental quantum constant. Similarly, the second is now defined by the hyperfine splitting in caesium-133, and the metre is defined by the speed of light. This system allows for easy conversion between units through prefixes, such as multiplying metres by 100 to get centimetres. The SI system, developed in 1960 from the metre, kilogram, second system, is the world's most widely used system of units, used in both everyday commerce and advanced scientific research. Derived units, such as the watt for power, are constructed from these base units, creating a universal language for describing the physical world.
The Ghost in the Machine
No measurement is ever perfectly exact, and every attempt to quantify reality introduces a layer of uncertainty that must be carefully managed. When measuring the time it takes for an object to fall one metre, the calculation involves approximations of gravity, rounding of square roots, and the influence of air resistance and human error. These sources of error, from carelessness to the posture of human participants, mean that all measurements are necessarily approximations. Scientific experiments must be carried out with great care to eliminate as much error as possible, and to keep error estimates realistic. The concept of uncertainty represents the random and systemic errors of the measurement procedure, indicating a confidence level in the measurement. Errors are evaluated by methodically repeating measurements and considering the accuracy and precision of the measuring instrument. This inherent uncertainty is not a flaw but a fundamental characteristic of measurement, requiring scientists to assign a range of values rather than a single number.
Common questions
What is the current definition of the metre?
The metre is defined by the speed of light, a constant that has never changed since the beginning of the universe. This definition replaced the physical bar of platinum-iridium that was once stored in a vault in France. The International System of Units now defines the metre without reference to any physical object to ensure measurements remain exact and unchanging.
When was the kilogram redefined in terms of the Planck constant?
The kilogram was redefined in 2019 in terms of the Planck constant, a fundamental quantum constant. This change ended the era where the kilogram was defined by a physical cylinder kept in a vault. The redefinition ensures the unit remains stable regardless of the deterioration or destruction of any single artefact.
Who proposed defining the metre using the wavelength of a spectral line?
Charles Sanders Peirce proposed defining the metre using the wavelength of a spectral line in the late 19th century. This proposal to tie a unit to an experimental standard independent of a physical artefact directly influenced the Michelson, Morley experiment. The idea helped establish a more reliable standard for measurement.
Which countries still use the British systems of English units and imperial units?
The British systems of English units and later imperial units are still used in the United States and a few Caribbean countries. In Britain, road signs still show distances in miles and speed limits are in miles per hour. The international yard was defined in 1960 by the governments of the United States, United Kingdom, Australia, and South Africa as being exactly 0.9144 metres.
What is the representational theory of measurement?
The representational theory defines measurement as the correlation of numbers with entities that are not numbers. Stanley Smith Stevens elaborated this theory, suggesting that numbers need only be assigned according to a rule. True measurement requires a structural similarity between the mathematical system and the qualitative system.
What happens to a quantum system when it is measured?
Quantum measurements alter the state of the system itself, changing the quantum state into one with the single measured quantum value. This process is referred to as state-vector reduction or collapse of the wavefunction. The measurement appears to act as a filter, creating a paradox that challenges our understanding of reality.
Before the International System of Units became the global standard, the world was a patchwork of conflicting measurement systems that often hindered trade and scientific collaboration. The British systems of English units and later imperial units were used in Britain, the Commonwealth, and the United States, creating a complex landscape of foot-pound-second systems. These systems, known as U.S. customary units in the United States, are still in use there and in a few Caribbean countries, despite the official switch to SI in many other places. In Britain, road signs still show distances in miles, and speed limits are in miles per hour, while draught beer and cider must be sold by the imperial pint. The international yard was defined in 1960 by the governments of the United States, United Kingdom, Australia, and South Africa as being exactly 0.9144 metres, a compromise that bridged the gap between different systems. This historical fragmentation highlights the necessity of standardisation, which was originally developed to prevent fraud in commerce and to ensure that communities had certain common benchmarks.
The Mind's Ruler
Measurement extends far beyond the physical world, entering the abstract realms of psychology, economics, and survey research where numbers are assigned to attitudes, values, and behaviors. In survey research, measures are taken from individual attitudes using questionnaires as a measurement instrument, but these are vulnerable to measurement error, which can lead to biased conclusions and wrongly estimated effects. The classical definition of measurement, standard throughout the physical sciences, is the determination or estimation of ratios of quantities, but in the social sciences, measurements can have multiple levels, including nominal, ordinal, interval, and ratio scales. The representational theory defines measurement as the correlation of numbers with entities that are not numbers, requiring a structural similarity between the mathematical system and the qualitative system. This theory, elaborated by Stanley Smith Stevens, suggests that numbers need only be assigned according to a rule, but unless there is a correlation between measurements and empirical relations, it is not a true measurement.
The Quantum Paradox
In the realm of quantum mechanics, measurement becomes an action that determines a particular property of a quantum system, such as position, momentum, or energy, but it also alters the state of the system itself. Quantum measurements are always statistical samples from a probability distribution, and the distribution for many quantum phenomena is discrete, not continuous. The measurement appears to act as a filter, changing the quantum state into one with the single measured quantum value, a process referred to as state-vector reduction or collapse of the wavefunction. This is one of quantum theory's most puzzling features, as the unambiguous meaning of the quantum measurement remains an unresolved fundamental problem. The 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, creating a paradox that challenges our understanding of reality.
The Evolution of Measurement
The history of measurement is a story of human ingenuity, evolving from local agreements to a unified global system that underpins modern civilization. Historically, many measurement systems existed for the varied fields of human existence to facilitate comparisons, often achieved by local agreements between trading partners or collaborators. Since the 18th century, developments progressed towards unifying, widely accepted standards that resulted in the modern International System of Units. The General Conference on Weights and Measures, established in 1875 by the Metre Convention, oversees the SI system, ensuring that units are defined on a scientific basis and established in international treaties. In the United States, the National Institute of Standards and Technology regulates commercial measurements, while in the United Kingdom, the role is performed by the National Physical Laboratory. This evolution from arbitrary standards to precise, artefact-free definitions has enabled the advancement of science, technology, and quantitative research in many disciplines.