Early on in our history on Earth, we humans realized the importance of measuring quantities. This happened much before scientists needed to measure things accurately to be able to develop our understanding of the world. It was important even in daily life. To get paid for the wheat a farmer produced, it needed to be weighed. How heavy is the produce? - Mass. How far is that lake? - Distance or Length. How much time would it take for the enemy army to attack us based on their current location? - Time. The answers to these questions were much more a necessity than curiosity. So, we learned to count and measure, albeit differently in different areas. But the idea everywhere was the same - the need to know quantities in numbers. After this the idea of units is easily understood. Example: if one wants to know the length of a piece of clothing, just measure it with respect to something. Call that something one ‘unit’ of length. Like measure it with the span of your hand and say it's 8 handspans long or 8 units long, with the ‘unit’ as already defined.
This idea proved to be quintessential to science. Galileo revolutionized physics by carrying out organized quantitative experiments to find physical laws of nature. After him, it was quickly realized what a blessing this was and the scientific method was born. Physics and in general, science would be nowhere near to where they stand now without this scientific method accepted throughout the world without experiments and observations to measure quantities in clearly defined units. As scientists gained experience, two things popped up:
More and more types of physical quantities, which also needed to be measured (apart from already hinted: mass, length and time) came into picture. Like speed, current, force etc.
The question of what should be the characteristics of a ‘good’ unit? - universality, accessibility, unambiguity etc. The answers contain both theoretical and practical considerations that are not mutually exclusive.
The first point led to the recognition of 7 base or fundamental quantities in nature(not units!). Rest all physical quantities (and they are quite huge in number) are derived from them. Familiar example: speed is distance per unit time.
The second point has many aspects to be understood. We take examples. The same piece of clothing could be measured 8 handspan long by a child and 6 by an adult. Ambiguity! Conclusion: Handspan is not a good choice for measuring length. Universality implies that the realization of the unit should be universally possible. It shouldn’t be localized. Let’s take the case of time itself. For the past centuries the idea of measuring time has always been to refer to a naturally established process that occurred regularly at equal intervals of time, without fail. Like movement of the sun, moon, rotation of the Earth, etc. And take 1 unit of time based on that. With improved techniques astronomers realized that these processes were not precisely regular. So, it's not correct to take 1 second as 1/86400 of Earth’s rotation period(mean solar day) as was done till 1956, since a mean solar day itself is not of fixed duration. Its duration gradually slows and worse, it fluctuates unpredictably.[1][2] So, it lacks universality and unambiguity. Another thing while looking for a good unit of time - based on practical considerations- is to look for a regular natural process that happens very frequently. Then the timekeeping devices based on counting this process can measure much smaller durations without uncertainty. This led to pendulum clocks being replaced by quartz clocks. Since vibrations in quartz were much faster than swings of a pendulum.[1] And later atomic clocks being used in GPS, UCT etc.[3]
Now we can appreciate why it was agreed to have the International System of Units or Système International d'Unités, - the SI unit system, established in 1960 by the 11th General Conference on Weights and Measures - CGPM.
The seven base physical quantities which are measured by the SI units are: Mass, Length, Time, Electric Current, Temperature, Luminous intensity and amount of substance. And the SI units that measure these are, respectively: kilogram, metre, second, Ampere, Kelvin, Candela and mole. All these 7 units were defined/revised in 1960 to be used throughout the scientific community thereafter. But only gradual developments from then until 2019, have made the SI units stand far above in terms of universality, unambiguity, precision and other significant benefits than any units we have ever used. We will restrict to exploring only the SI metre, kilogram and second but it will give us the rationale behind the constant changes in the SI.
International prototype for kilogram
The SI system of 1960 focused on improving precision and unambiguity in the definitions. 1 Kilogram was defined as equal to the mass of the ‘international prototype of kilogram’ - an artifact of platinum-iridium kept in a triple-locked vault on the outskirts of Paris! 1 second redefined by the duration of the tropical year of 1900. 1 metre redefined by the wavelength of the radiation corresponding to a particular transition in krypton 86, to be able to realise 1 metre with much more accuracy. These definitions were not really universal in nature and needed to be improved. Kilogram was still based on a material artefact - the last thing you want when trying to achieve universality. Although all other 6 were not based on material artefacts, yet they weren’t the best choices as explained later.
The definition that opened the way to real universality was that of the metre in 1983. “The metre is the length of the path travelled by light in vacuum during a time interval of 1/299792458 of a second”[4]. The reason it is universal is because the speed of light in vacuum - c is a fundamental constant that is the same throughout the universe and invariant with time. So, anywhere, anytime provided the resources, 1 metre can be determined through experiment, by a human or alien! On similar grounds stands the other redefinitions: “The second is the duration of 9,192,631,770 periods of the radiation corresponding to the transition between the two hyperfine levels of the ground state of the caesium 133 atom” in 13th CGPM. Infact, the definition of a metre actually depends on the definition of second. With such redefinitions for other SI units too(except kilogram), they became more universal and accessible. Yet they nevertheless limited practical realizations to experiments that are directly or indirectly linked to the particular conditions/states specified in each definition. In consequence, the accuracy of realization of such definitions can never be better than the accuracy of realization of the particular conditions/states specified in the definitions.[5] Like the definition of Kelvin ultimately requires to measure the triple point of water - the temperature at which all three states of water(gas-liquid-solid) exists in equilibrium .
Early prototype of 1m, still existing.
Here comes the latest redefinition of all SI units, agreed at the 26th CGPM(2018) and effected from 20 May 2019. They are redefined now by taking fixed numerical values of 7 constants of nature. All these constants are postulated to be invariant with time. The idea is that the use of a constant to define a unit disconnects definition from realization. This offers the possibility that completely different or new and superior practical realizations can be developed, as technologies evolve, without the need to change the definition[4]. Any equation known or unknown, containing the constant and which can offer a better measurement of the unit can be used without changing the definition.
CGPM meeting, November 2018
The Metre:
Fixing the numerical value of the speed of light in vacuum, c as 299 752 458 m s-1 and rearranging this equation gives:
1 metre = (c/299 752 458)s
Which essentially means that 1 metre is the length that light travels in vacuum in 1/299752458 of a second, since c is the speed of light. What we mean by defining a unit by fixing a constant is this. We fixed c = 299 752 458 metres per second. Here we are actually defining the metre(given the second is already defined). We are saying that a ‘metre’ will be that distance such that light travels 299 752 458 ‘metres’ in 1 second. There is no uncertainty. So, whatever distance light travels in 1/299752458 of a second that will be a ‘metre’. The definition is universal, unambiguous and can be realised using any equation involving c with some other considerations.
The second:
It is defined by taking the fixed numerical value of the unperturbed ground-state hyperfine transition frequency of the caesium 133 atom to be 9,192,631,770 s-1.
It just means the frequency of radiation of a particular atom in a particular case. So, as it is fixed in terms of second, by rearranging, it's clear that 1 second is that duration of time in which 9192631770 cycles of this emitted radiation takes place. It is quite amazing if you stop to think about it.
The Kilogram:
Similarly, Kilogram is now defined by fixing planck’s constant h = 6.626 070 15 × 10-34 kg m2 s-1 . Then simple rearranging of the equation gives the definition of 1 kg since metre and second are already defined. This redefinition of Kilogram was the latest, only possible after the extraordinarily precise measurements of h.[6] Again it is to be noted that this fixed value actually attempts to define a Kilogram and not the value of Planck’s constant. We are ‘forcing’ the kilogram to be so heavy that h turns out to be as given above.
A little about Ampere:
The redefinition of Ampere in terms of fixing the value of electric charge on an electron had the effect that now the value of μ0 - the permeability of vacuum is not fixed = 4π×10-7 but needs to be determined experimentally.[7]
In conclusion, the efforts to have a standard system of units, and it being constantly improved and updated led to the recent redefinitions of the SI unit system which is a profound achievement due to their numerous benefits, both theoretical and practical. Now, only the definition of second explicitly involves the microwave transition of a caesium atom, i.e. refers to a process. All other units can be reproduced/realized with a method involving any equation of physics that contains their defining constants. And it would be interesting to see how things turn out from the viewpoint of units in the continuing progress of science.
Deepanshu Bisht
2nd Physics
REFERENCES:
The following references are also amazing resources to learn and gain more in-depth understanding of the topics discussed in the article:
amazing stuffs
ReplyDeleteI wanna see more of your articles.
ReplyDelete