# Sambuddha Sanyal‘s essay: Defining One Kilogram In Modern Times

How much is one kilogram ? It is not a question that we ask often to ourselves but we accept a standard answer in the form of a piece of metal that we see everyday in the grocery shops. However in this article I will try to link this question to some of the latest developments of Physics. The international prototype of Kilogram(or known as IPK), a cylinder made of 90% platinum and 10% Iridium was introduced in 1889 as a standard of weight measurement. Recently in 2019, IPK and its six prototypes were sent to retirement, a new standard of kilogram appeared as following :“The kilogram, symbol kg, is the SI unit of mass. It is defined by taking the fixed numerical value of the Planck constant ℏ to be  6.62607015 × 10-34 when expressed in the unit Js, which is equal to  kgm2s-1, where the metre and the second are defined in terms of c and ∆νCs.” This might appear to be strange to a non-expert as one might ask why do we need metre and second, units of length and time in order to define what is one kg of mass? And why do we need to bring this change while the old standards were good enough for all these years?

In 2019, actually all the seven standard units of measurements, namely length, time, mass, current, luminous intensity, amount of matter were updated. This update is a consequence of the several breakthroughs in Physics that happened over the period of last century. In this article we started with the re-standardisation of kilogram that is connected to two revolutionary ideas in Physics i.e. quantum mechanics and relativity, these ideas were developed in the early part of last century and concertised over the rest. Almost all conceptual advancement in Physics leads to unification of ideas or quantitates that were believed to be different beforehand. For example Newton’s work on gravity and mechanics unified the laws of celestial and terrestrial bodies, development of electromagnetism in early 19th century unified electricity, magnetism and light, development of statistical physics around the same time unified microscopic and macroscopic worlds. Similarly special theory of relativity, developed by Einstein in 1905, tells us space and time can be treated as equivalent and thus one can be measured in terms of the other. Quantum Mechanics, developed in the first quarter of 20th century tells us particles can behave like waves and waves can behave like particles, thus particle attributes like momentum and energy can be measured in terms of wave attributes like frequency and wavelength. These unifications brings into another important player into the game, known as natural constants. Natural constants are quantities that can be measured and never changes with time, there is no satisfactory answer to the question that why do they exist and why do they take a particular value or magnitude. However, it turns out that these natural constants play two important roles in a physical theory; first they set the scale of the problem and second they act as the conversion factor that allows one to measure one of the two unified quantity in terms of the other. For example consider speed of light c in vacuum, the natural constant that emerges from the unification of space and time in special theory of relativity. We know by convention that speed of light is 299792458 meters per second, setting it to any other number will change nothing about the interrelation of physical quantities, speed of electronic communication or any other aspect of our live. But setting it fixed to a number allows us to measure distance in terms of time and sets the scale of measurement. So all we need to do is fix an unit of time i.e. 1 second, purely by convention and convenience is chosen to be “the time interval equal to 9192631770 periods of the radiation corresponding to the transition between the two hyper-fine levels of the ground state of the caesium-133 atom” (the frequency is dubbed as ∆νCs). Once you choose the unit of time you can set the unit of length as “The length of the path travelled by light in a vacuum within 1⁄299792458 seconds”, that is going to be constant due to the physical constant speed of light. Furthermore, the wave-particle unification in Quantum Mechanics tells us momentum can be measured in terms of wavelength and energy in terms of frequency. That leads to a universal constant knows as Planck constant described earlier in this article, by convention   is set to be 6.62607015 × 10-34 kgm2s-1. Notice the presence of units of mass, time and length in ℏ.

which is there because it connects between momentum (mass time velocity) of particle and wave-length(inverse length) of wave. Now that we have fixed the standard measurement of one unit of length and time as meter and second respectively using the physical constant speed of light, we can standardise one unit of mass(one kg) using the Planck constant and the units of length and time.

If we take a step back and try to think about what does it all means it appears to be quite remarkable that we are able to define three different units of mass, length and time just by defining an unit of time and using two natural constants that appear from two revolutionary ideas in modern physics, i.e. relativity and quantum mechanics. Standards units of measurements are extremely important in our daily lives and business, one the other side quantum mechanics and special theory of relativity are generally perceived as abstract ideas that may not be very important in the daily life of a commoner, however as one looks into the deeper reasons of how these two things are related one discovered that these two things are much more strongly connected than what we imagined and the centrepiece of that connection is an object that we don’t understand very well, namely the natural constants. The magnitude of the natural constants (not the numbers we assign to them) and their existence is a mystery and leads to many rich speculative ideas such as multiverse with different natural constants, anthropic principle etc, that could be subject matter of a different article.