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It seems to me that the SI units we use today are nothing but the result of a historical 'coincidence'.

I recently began researching about natural (absolute) systems of units, which are defined in such a way that selected universal physical constants are normalized to unity. These are very convenient, since almost all equations in physics are simplified.

Planck Units

Take for example the Planck units, where five fundamental physical constants take on the numerical value of 1.

To quote from Wikipedia:

Planck units have a profound significance since they elegantly simplify several recurring algebraic expressions of physical law by nondimensionalization. They are particularly relevant in research on unified theories.

Planck units are even dubbed "God's units", since Planck units are free of anthropocentric arbitrariness.

Justification

I know that many 'everyday' quantities for a physicist in terms of Planck units would be very small numbers (for instance) but that shouldn't be a problem if we use scientific notation. In fact, it's a great thing since it can give us a better picture about those quantities being now in a unit system which is conceptually linked at a fundamental physical level. Besides, many such 'everyday' quantities are also expressed by very small / very large numbers in SI units. Think Planck's constant.

Frank Wilczek even argues that using Planck units would help us re-frame important questions in physics:

We see that the question is not, "Why is gravity so feeble?" but rather, "Why is the proton's mass so small?" For in [Planck] units, the strength of gravity simply is what it is, a primary quantity, while the proton's mass is the tiny number [1/(13 quintillion)].

AI am aware that it would be a big upheaval if we are to change our SI units but if it is to be done it better be done right now before more physicists grow up using the old unit system. The change is not likely to render old written material useless since, for instance, Newton's Principia Mathematica remains a fundamental text in mechanics even though it uses outdated notions such as "quantity of motion" and "quantity of matter".

Question

Given all that I explained, is there a reason we choose to stick with the old and weary unit system?

Why didn't we leave the kilogram, defined by an arbitrary French rod, to ladies gossiping about Kim Kardashian's weight and choose something that makes more sense scientifically?

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closed as primarily opinion-based by Kyle Kanos, John Rennie, tpg2114, Brandon Enright, jinawee May 10 at 17:00

Many good questions generate some degree of opinion based on expert experience, but answers to this question will tend to be almost entirely based on opinions, rather than facts, references, or specific expertise.If this question can be reworded to fit the rules in the help center, please edit the question.

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What sense is there to describe my mass as $3215862471.3444\,m_{Pl}$ instead of 70 kg? –  Kyle Kanos May 10 at 13:58
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While we are at it , why don't we replace the decimal system with the binary system? The digital came because we have 10 fingers. Think how you would teach a child to count; counting on fingers was natural and probably in our DNA :) –  anna v May 10 at 14:00
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Right, physicists in the different subfields have different unit systems that work for them. I use cgs b/c I am an astronomer, others might use SI, still others use Imperial units. Restricting all to one unit system seems futile because it's not practical. –  Kyle Kanos May 10 at 14:02
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@fibonatic The physical constants have perfect precision. Our ability to compare something to them (i.e. measure them) lacks precision. This is true of any unit system though. –  Chris Mueller May 10 at 15:08
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If changing units were so easy, Imperial units would have already died. –  jinawee May 10 at 21:03

3 Answers 3

up vote 3 down vote accepted

A proposal to revise the SI is already being drafted (as we speak). It appears the 'arbitrary French rod' a.k.a. the international prototype kilogram (IPK) is already on its way out. BIPM's 'On the possible future revision of the SI' gives some of the details. (BIPM is not some obscure club, it is in fact the International Bureau of Weights and Measures. They also have the IPK in their basement.)

In the "New SI" four of the SI base units, namely the kilogram, the ampere, the kelvin and the mole, will be redefined in terms of invariants of nature; the new definitions will be based on fixed numerical values of the Planck constant ($h$), the elementary charge ($e$), the Boltzmann constant ($k$), and the Avogadro constant ($N_\text{A}$), respectively. Further, the definitions of all seven base units of the SI will also be uniformly expressed using the explicit-constant formulation, and specific mises en pratique will be drawn up to explain the realization of the definitions of each of the base units in a practical way.

The kilogram will get the following treatment. (This is a 16 December 2013 draft.)

The kilogram, symbol $\text{kg}$, is the SI unit of mass; its magnitude is set by fixing the numerical value of the Planck constant to be exactly $6.626\text{ }069\text{ }57\times 10^{−34}$ when it is expressed in the SI unit for action $\text{J s} = \text{kg m}^2\text{ s}^{−1}$.


This is what the New SI will look like in terms of seven defining constants (again: draft).

The international system of units, the SI, is the system of units in which

the unperturbed ground state hyperfine splitting frequency of the caesium 133 atom $\Delta v(^{133}\text{Cs})_{\text{hfs}}$ is exactly $9\text{ }192\text{ }631\text{ }770$ hertz,

the speed of light in vacuum $c$ is exactly $299\text{ }792\text{ }458$ metre per second,

the Planck constant $h$ is exactly $6.626\text{ }069\text{ }57\times10^{-34}$ joule second,

the elementary charge $e$ is exactly $1.602\text{ }176\text{ }565\times10^{-19}$ coulomb,

the Boltzmann constant $k$ is exactly $1.380\text{ }648\text{ }8\times10^{-23}$ joule per kelvin,

the Avogadro constant $N_\text{A}$ is exactly $6.022\text{ }141\text{ }29\times10^{23}$ reciprocal mole,

the luminous efficacy $K_\text{cd}$ of monochromatic radiation of frequency $540\times 10^{12}$ hertz is exactly $683$ lumen per watt,

where the hertz, joule, coulomb, lumen, and watt, with unit symbols $\text{Hz}$, $\text{J}$, $\text{C}$, $\text{lm}$, and $\text{W}$, respectively, are related to the units second, metre, kilogram, ampere, kelvin, mole, and candela, with unit symbols $\text{s}$, $\text{m}$, $\text{kg}$, $\text{A}$, $\text{K}$, $\text{mol}$, and $\text{cd}$, respectively, according to the relations $\text{Hz} = \text{s}^{–1}$ (for periodic phenomena), $\text{J} = \text{kg m}^2\text{ s}^{–2}$, $\text{C} = \text{A s}$, $\text{lm} = \text{cd sr}$, and $\text{W} = \text{kg m}^2\text{ s}^{–3}$. The steradian, symbol $\text{sr}$, is the SI unit of solid angle and is a special name and symbol for the number $1$, so that $\text{sr} = \text{m}^2\text{ m}^{−2} = 1$.

Note that all are exact.


Example 1. What does that mean for a meter?

$$\text{m}=\frac{9\text{ }192\text{ }631\text{ }770}{299\text{ }792\text{ }458}\frac{c}{\Delta v(^{133}\text{Cs})_{\text{hfs}}}$$


Example 2. Kyle Kanos has a mass of $70\text{ kg}$ in the current SI. If he wants to make sure he has the "same" mass after the adoption of this New SI, he needs to make sure that his mass will be

$$70\cdot1.475\text{ }521\ldots \times10^{40}\frac{h~\Delta v(^{133}\text{Cs})_{\text{hfs}}}{c^2}=70\text{ kg}.$$

He can choose left or right. They are exactly the same in the New SI. (The $\ldots$ reflects numerical rounding of a quotient, not a measurement error or uncertainty.)


The BIPM has some FAQs about the New SI here.

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So they want to define a mass by using a quantity with 2 other units with precision errors. I think I would rather go with a defined number of mono-isotopic atoms. –  LDC3 May 10 at 15:50
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@LDC3 I think not. I think that the new SI will be such that the constants are fixed numbers without precision errors. I guess that's the whole point. The numerical value of the Planck constant will be $6.626\text{ }069\text{ }57\times 10^{−34}$, exactly. –  Glen The Udderboat May 10 at 15:54
    
A meter is defined as the distance traveled in a specific amount of time. The second is defined by the number of wavelengths of a certain frequency. Both are used in the calculation of mass from Planck's constant. These are not fixed numbers. –  LDC3 May 10 at 15:56
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@GlenTheUdderboat This at face value seems to make the best of both ideas. It uses familiar units but also defines them in better, more absolute terms. Interesting. –  hb20007 May 10 at 16:00
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@LDC3 In the New SI, they are not measured anymore. They are defined. In fact, $c$ was already defined in SI. Did it never surprise you that the speed of light was integer-valued? –  Glen The Udderboat May 10 at 16:37

The short answer is that it is simply not possible to design a "one size fits all" unit system. The staggeringly large range of mass, time and length scales that appear in the Universe prevent this. The Planck unit system you mentioned is mainly useful for people who will never touch an experimental apparatus. The vast majority of scientists and engineers do not even do physics, let alone theoretical quantum or cosmological physics, and need a standard unit system that reflects the magnitude of quantities that are most likely to be found in their everyday work.

Thus, professional physicists use whatever unit system is most convenient for the problem at hand. There is no danger that "more physicists grow up using the old unit system", as if that would somehow obscure people's understanding. Actually the more redundant and bizarre unit systems that trainee physicists are exposed to, the better. This teaches you fluency in converting between these systems, and helps you to communicate with people from different subfields.

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Well thought-out answer. Indeed, there is no one-size-fits-all unit and scientists who don't like using certain units shouldn't be forced to do so. But I'm talking about the idea of "SI units". Don't you think our SI units should be defined in terms of natural phenomena instead of for example a platinum-iridium rod that could be destroyed one day and we would no longer have a "kilogram"? –  hb20007 May 10 at 14:55
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@hb20007 I do indeed. I believe that the kilogram is the only remaining SI unit that is defined so arbitrarily. For example, the second is defined in terms of the natural frequency of an atomic transition, and the metre is defined in terms of the distance light travels in a certain time. A number of scientists, such as Peter Knight, are campaigning quite forcefully that the definition of mass should also be changed; I expect they will ultimately be successful. –  Mark Mitchison May 10 at 14:58
    
This makes me think of 2 closely related units that are used frequently in chemistry, the joule and the calorie (1 cal = 4.184 J). A lot of physicists probably don't use a calorie, but it is very easily defined. It is the amount of energy needed to raise the temperature of 1 g of water 1 degree (centigrade). Chemist use it since they want to know the energy released (or needed) in a reaction and the change in water temperature was convenient. A Joule is defined as the work done by moving a mass. Really not the same thing. –  LDC3 May 10 at 15:20
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@LDC3 Yeah, actually I had in mind a different example but in the same spirit. In atomic physics people often use Hz to measure energy, because it tells you immediately about the typical timescales of the (often strongly non-equilibrium) phenomena, and the frequencies of light that could be used to probe them. But particle physicists seem to find mass units much more useful for energy, presumably since they indicate what kinds of particles you can expect to participate in the process. One physical quantity for both situations, but with different significance and therefore different units. –  Mark Mitchison May 10 at 15:31
    
@MarkMitchison The redefinition of the $\text{kg}$ is already in the draft stage (by the relevant authority). See my answer. –  Glen The Udderboat May 10 at 19:15

Because it's a good thing that in physics we use the same units as in everyday life (at least, outside of a handful of countries which shall remain nameless). It makes things easier to explain, easier to measure. It makes it easier to check in your head whether the result of an experiment makes sense.

You're never going to get the whole world to change to Planck units, because the SI units are designed to be related to sizes we encounter every day. A meter is about half the height of a person; a kilogram can be easily lifted and is a good unit of measure for things like food; seconds, minutes, and hours subdivide the day into manageable chunks.

Suppose you use the Planck length instead of the meter. If you have kids, they will probably want to measure themselves every now and then. Are you going to tell them that they are $10^{35}$ Plancks tall? Or would you rather say that they were half a meter tall a few years ago and they are one meter tall now? This is just an example off the top of my head, of course.

The moral here is that SI units allow for easy numbers. You only have to memorize the prefixes milli- and kilo-, for example, to talk about distances as small as something you can barely see or as large as the size of the Earth, using no more than about four digits. This is simply not possible with Planck/natural/whatever units.

There's one caveat, of course: theoretical physics. This is the only place, among all the things everybody does in the world, the vast majority of which are not physics, where elegance of equations is important, as your quote about gravity says. But outside of that, in all the other subfields of physics, as well as for everyday life, your proposed units are useless at best.

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Indeed, even within most subfields of theoretical physics Planck units aren't very useful! –  Mark Mitchison May 10 at 15:03
    
@JavierBadia Good answer which shows you read the whole question. Even though I don't advocate using absolute units for non-scientific purposes such as measuring your children's height, I do agree with the idea that having units that are easy to comprehend at an intuitive level is a good thing. –  hb20007 May 10 at 15:08

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