A Kilogram Is No More a Kilogram: The Revision of SI units Through a Marxist Philosophical Lens

The International Bureau of Weights and Measures (BIPM) revised the International System of Units (SI) on May 20, 2019. After this revision, the definitions of kilogram, ampere (unit of current), kelvin (unit of temperature) and mole are now given in terms of fundamental constants. This completes the process of the shift of units of physical quantities away from human-made artefacts to natural constants, which was initiated in 1983 when metre was redefined in terms of the speed of light, away from the prototype metre rod kept in BIPM campus since 1889. This time the prototype 1kg mass first taken as the unit of mass in 1875, has been discarded and this unit has been defined in terms of Planck’s constant, and units of time and distance. The change would not have any immediate impact on our understanding of the physical world. It will help reduce errors in future high precision experiments. This revision is, however, more than a mere technical step. It also throws light on the dialectical aspects of the practice of science, which if not appreciated correctly may appear arbitrary and contradictory.

Why is reduction in error in future experiments by correct units of measurement important? An anecdote from an undergraduate lab the author teaches can help appreciate the issues involved. Students in mechanics lab one year were consistently getting less value of the acceleration due to gravity in a pendulum experiment than students from earlier years. The difference was about one per cent. Since the difference was always of the same size, rather than randomly positive or negative, it indicated a systematic cause. Through a process of elimination it was finally found out that the metre sticks bought that year were about two millimetres shorter than metre sticks used by students of earlier years. This was only a difference of 0.2 per cent, not too important for most activities of everyday life, but fairly significant even in a college physics lab. One can translate the students of two different years as scientists working in different labs, trying to quantify the same physical quantity, but finding different values. Which group of scientists (or students) is correct? For an occurrence like this, researchers in India would compare their metre sticks with a copy of the BIPM prototype metre kept at the National Physical Laboratory, Delhi.

However, why should scientists be worried about small differences in their experimental results anyway? Small, barely measured differences in experimental science do not amount to nit-picking. Actually, new physical effect are discovered precisely in these small differences. Kepler could not have established his laws of planetary motion, if Tycho Brahe’s measurements of the orbit of Mars were not precise enough to show deviations from a circular orbit. The General Relativity effect on the perihelion of Mercury is an extra rotation of 43 arc seconds (an arc-second is 1/3600th part of a degree) in a century. During one hundred years, the planet revolves for about 5.18x108 arc seconds around the Sun. If errors in locating Mercury were more than a few arc seconds, these would have completely masked the relativity effect. Coming back to the pendulum experiment performed in undergraduate labs, 99.9 per cent of the value of the acceleration due to gravity depends upon the mass and the average radius of the Earth. Other physical effects due to the rotation of the Earth (whose contribution depends on the latitude) and the height about sea level are very small. Which means that if the measurements are not precise enough, the very existence of these effects will not be noted.

Physical World in the Mirror of a System of Units

Systems of units are generally taken to be a matter of technical detail, essential for science students to learn, but otherwise not much of any fundamental significance. This is a gross misconception. Systems of units reflect the depth and certainty of our understanding of the physical world. For example, the SI has only seven basic units. It turns out that all diverse kinds of physical quantities we encounter – from the largest scales in the cosmos to the smallest scales in modern particle accelerators, from simple machines like levers to most complex biological systems – can all be expressed in terms of the powers and combinations of the seven basic units. The reason is the underlying unity of the physical world, which is represented for example in conservation laws. Frederick Engels was among the first philosophers of science to note this character of the physical world. He interpreted it in terms of dialectics of nature. Now, when the SI has been revised on the basis of constants of nature rather than human-made artefacts, this indicates that scientists have greater confidence in the accuracy of laws of nature, which have been discovered through a complex interplay of experimental observations and theoretical investigations. This is despite the fact that the technology to manufacture these human-made artefacts is more advanced than ever before.

Also read: Why Definition of Kilogram has been Changed?

The development of sciences is a contradictory dialectic at work. Our understanding of the microscopic quantum world is more precise than the understanding of the world of our everyday experience. Hence, the further the definition of basic units has moved away from human-made artefacts to more abstract notions of ‘facts’ and ‘laws’ of nature, more precise these definitions have become. First set of units everywhere have been human artefacts. The makers of pyramids used a unit called ‘cubit’ which was approximately equal to the length of the human forearm. A section of the Egyptian priesthood was the custodian of the knowledge of the exact length of the cubit, who guarded it as part divine, part secret knowledge. The prototype of one metre length and one kg of the BIPM are other examples of human artefacts used as units of measurements. A prime requirement for an artefact to be used as a unit is that it should be least affected by changes in the environment, and should remain same over time. Since an artefact chosen as the unit cannot be directly used in every instance of measurement, in practice, copies of the artefacts are used. Hence, accuracy in the use of any unit depends upon the technology available to make copies of the chosen artefact. Another limiting factor is the fact at all objects suffer wear and tear naturally, and with use. The metre bars adopted as standards in 1889 were discovered to be accurate only up to 0.2x10-6m in measurements done during 1921-36. The comparison of different standard kilograms kept in different countries with the international prototype kept at BIMP laboratories in 1980s showed an instability of 30x10-6kg , which was attributed to little understood surface effects.

Another way to define units of measurements is in terms of properties of certain unique states of nature. For instance, a second was historically defined as 1/(24x60x60) of the rotation period of the Earth. This definition has been discarded because it is now known that the Earth’s rotation period is not constant, but is increasing slowly. It also changes randomly due to weather effects and redistribution of Earth’s matter during earthquakes, volcanic eruptions, meteorite hits, etc. At present, the SI definition of second is given in terms of the ‘unperturbed ground state hyperfine transition frequency of the caesium 133 atom’. A second is defined as 9,192,631,770 times the oscillation period of photons emitted in this transition. The caesium transition is used because it is found to be remarkably stable and its behaviour under different circumstances is fairly well understood. Another natural state used for a basic unit is the triple point of water, which is a state in which the three states of water, namely steam, water and ice, are in thermodynamic equilibrium. Till recently, this state was used to define the Kelvin unit for temperature. The naturally occurring states of nature, obviously suffer no ‘wear and tear’. These are naturally available in any lab following well defined procedures, hence, there is no need to make ‘copies’ of these states.

The third step in the use of increasingly more idealised and abstract definition of base units is to define them in terms of constants of nature. The meaning of constants of nature can be determined only within the context of laws of nature. In Physics, these laws are expressed as mathematical equations. Constants of nature are parameters of these equations. Values of these constants of nature are determined from results of experiments. All experimental results have errors due to inaccuracies of the measuring apparatuses and uncontrolled random effects. Hence, even though constants of nature are assumed to have only one specific value, experimental results fix this value within an uncertainty. The uncertainty becomes less with increasing accuracy of experimental measurements. Foucault in 1862 had determined the speed of light to be 298000±500 km/s using a rotating mirror method which involved mechanical contraptions. In 1972, it was found to be 299792.4562±0.0011 km/s from laser interferometric experiments. The General Council on Weights and Measures (CGPM) in 1983 turned the process of finding the value of constants of nature from experiments on its head. It decided to literally ‘fix’ the value of speed of light as 299 792 458 m/s, and defined a meter as the distance travelled by light in 1/299792458 seconds.

Revision of Units: The Dialectic of Science at Work

How can we humans set the value of a supposed constant of nature? Is not its value an objective fact of nature, which remains what it is whether we humans know it or not? A complex dialectic of human practice and the objectivity of nature is at play here. After centuries of experiments, and theoretical work, scientists are now fairly certain that the speed of light is indeed a constant of nature having same value in all physical contexts encountered so far. In the experiments to measure the speed of light earlier, the standard metre was taken as a precise measure and errors of experiments were interpreted as uncertainty in the value of the speed of light. Now, the errors in experimental results are going to be interpreted as uncertainty in the base unit of length. The latter interpretation is actually closer to reality. As was mentioned earlier, the defining prototypes of the standard metre and kilogram were indeed found to be of uncertain value.

As the 9th edition of the International System of Units (SI) brochure published by the BIPM comments, the most recent revision of base units is indeed ‘a new approach to articulating definitions of the units in general, and of the seven base units in particular, by fixing the numerical values of seven “defining” constants (quotes in the original).’ The revised SI is now a system of units in which the numerical values of four constants of nature (the speed of light, elementary charge, Planck constant and Boltzmann constant), values of two specific physical quantities (the frequency of caesium transition, and luminous efficacy of 540x1012 Hz radiation) and one conventional constant (Avogadro constant) is fixed. All units of measurements are now to be determined from these fixed values through well defined experimental procedures which can be performed anywhere.

The erstwhile international prototype kilogram, a platinum iridium alloy cylinder at the Paris office of BIPM, kept inside two bell jars under lock and in very special conditions, was an effort to create an object in splendid isolation. That is how things appear to a non-dialectical, metaphysical way of thinking – as self-complete objects. The dialectical perspective focuses on relations between objects, rather than objects. In his comments of Hegel’s Science of Logic, Lenin at one point identifies a recognition of ‘the entire totality of the manifold relations (emphasis in the original) of things to other’ as an essential element of dialectics. Laws of the physical world should best be seen as theoretical representations of the nodal properties of the network of relationships in which all physical objects are enmeshed. The most recent revisions of the SI towards constants of nature underscores the importance of the viewpoint which puts greater emphasis on the relationships between physical objects, rather than objects themselves.

According to the BIPM brochure mentioned above, unit definitions based on natural constants are ‘increasingly abstract or idealised.’ A constant of nature is definitely a different kind of entity than an object like a standard metre length rod. It cannot be localised in space and time. It has an objective existence, independent of whether humans are aware of it or not, but it is not an obvious fact of nature. Humans ‘discover’ it through their intellectual labour, which is embedded in the physical world via methods of experimental sciences. Discussions on Marx’s methodology in Capital often use the term ‘real abstraction’ to refer to concepts like value, capital, abstract labour, etc., which are basic to Marxist understanding of capitalism. Real abstractions need to be distinguished from ‘mental abstractions’ which exist only in our mind. Abstraction in Latin original (ab (off)+trahere(to draw, drag, move)) indicates a process of pulling away one aspect of a multidimensional entity, and registering it as complete in itself. In this sense, mental abstractions are integral to our everyday perception and thinking, when, for an example, we ‘hear’ sound of only one instrument in an orchestra. Real abstractions refer to properties of the real world. Their abstract character inheres in the fact that they refer to properties which are common to a number of objects, or are properties of a system of objects. In this sense, constants of nature should best be seen ‘real abstractions’. The fact that the system of physical units is now based on a set of constants of nature is proof of the richly dialectical nature of the practice of modern science.

Sanjay Kumar teaches Physics at St Stephen’s College, Delhi