# Is there an official list of independent units of measurements?

When I say 'independent units', I mean those which cannot be broken down anymore, and simultaneously forms the basis for any more, complex measurements. For example, height, length, and width can all be multiplied to derive volume, which can be used with mass to define density.

I think it would be both useful and interesting as such units will basically define how you look at the universe, if every such measurement that can be known, is known, then there isn't a property out there which wouldn't be able to be defined via the manipulation of said units.

Anyway, whilst I can find lists of various units, I wonder if there is an 'official list', which contains all known units currently discovered?

• Units are not discovered.... they are defined. – Cort Ammon May 20 '16 at 2:36
• Mmmm, nope I would have to disagree very strongly on that one. No one is ask to be born, we discover things that came before us in this universe. We define how much length a metre is, but not length. But then, perhaps I have used the wrong terminology, is there a word that describes... types of units? – user108262 May 20 '16 at 2:39
• Exactly. The meter, a unit, is defined. Length, a dimensionality, is traditionally considered a fundamental concept in the universe. Even then, once you get a bit further into the philosophy behind science and mathematics, questions start to arise as to whether length is a fundamental concept in the universe, or something we invented as part of our epistomological journey to understand it. – Cort Ammon May 20 '16 at 2:41
• en.wikipedia.org/wiki/Physical_quantity may be a helpful page for clarifying ideas. It includes the 9 basic quantities recognized by the SI unit system – Cort Ammon May 20 '16 at 2:43
• Wait, is property the word to use? mmm, maybe. It's just that my logic was that measurements have to based of something, which is units, you know, 'units of measurements', which led to me to think about types of units. Though, I think property is a better fit as it's less ambiguous. – user108262 May 20 '16 at 2:43

The concept you are looking for is called "dimensionality," which was a concept first coined in 1822. The simplest way of thinking of dimensionalities is that you cannot add two values unless their dimensionalities are the same.

Thus, if we think in terms of units, 1 foot + 1 meter is a valid addition statement. This is because both foot and meter are units measuring length, a dimensionality. However, 1 foot + 1 second is invalid because the dimensionality of seconds is "time," and you cannot add length + time.

Wikipedia has a nice concise article on the concept of Physical Quantities, which covers the more exacting details.

The SI system recognizes 7 base dimensionalities, from which it derives all others (editor's note: this is in direct conflict with the sourced wikipedia page above.):

• length
• time
• mass
• temperature
• amount of substance
• electric current
• Luminous intensity

Of course, this is not the last words on this topic. Consider planar angle and solid angle (radians and sterradians respectively). Are they units? After much debate in comments below the official answer is no. However, it is extremely common to treat them as units because you get in all sorts of trouble if you treat them as non-units. For example, Iradiannce (W/sr) becomes the same units as Power (W), which is an issue because iradiance and power very often appear in the same document, or the same equation. Confusing one with the other would be a major issue. As pointed out in the comments, wikipedia is even inconsistent in their treatment of angles. Some pages on the SI system treat them as fundamental units, other pages treat them as nothing at all! Boost, in their unit framework for C++, chose to make them full fledged units. Can they get away with it? Maybe. Nobody has every actually axiomized a theory of units which has been considered sufficient by the general body of scientists and engineers. As for the SI system, they gave radians and steradians a special status as "named" derived dimensionless units, recognizing that they are too special to ignore.

On the other hand, some do not even consider luminous intensity to be a true unit. As seen in the comments, there is considerable disagreement as to whether such a human-eye based measure should be a base unit.

It gets murkier once you start entering the world of abstract units. It is not universally agreed upon whether dB is a unit or not, due to its logarithmic nature. Long story short, don't assume these things are set in stone. The real world is quite a lot murkier.

• Am surprised temperature is a base unit too, as all energy seems to boil down to kinetic energy (ahhhhhhh, get it? xD). Thanks for this, it's very useful. – user108262 May 20 '16 at 2:52
• dB is not a physical unit and one can be of divided opinion whether spatial and temporal units are independent. The relativists will tell you that they are the same up to a proportionality, I beg to differ a little, but that's a matter of opinion. Temperature is certainly not an independent unit but, as @user108262 points out a different way of measuring average energy. "Amount of substance" is meaningless in general, we need specific thermodynamic and quantum mechanical circumstances to have it well defined. – CuriousOne May 20 '16 at 2:59
• While luminous intensity is a base unit in SI, it is not to physicists. Luminous intensity is essentially the weighted radiant flux of a light source (power per unit solid angle), with the weighting function specifically targeted to how the human eye works. – David Hammen May 20 '16 at 3:31
• @CuriousOne Feel free to correct the SI community in general, if you believe you have a better understanding of units. ISO 80000:1 set their decision regarding which units are independent and which ones are not in stone. – Cort Ammon May 20 '16 at 3:45
• @CortAmmon -- The SI exists primarily for industrial standardization. It relies upon physics (where convenient) rather than defining physics. – David Hammen May 20 '16 at 4:12

Physics is not a bureaucracy, so there are no "official" documents like that. There are people called "metrologists" who think all week long about how to make physical standards more precise and they do have fairly well thought out ideas with what physical effects one should start to make precise measurements. These are not necessarily the standards that one would naively expect and they do change in time and as technology progresses. Metrological definitions are therefor not unique (and can not be) and you just have to keep up with them and understand why changes in the basic definitions of units are useful and necessary.

In general I would warn you to adopt the idea that science is a neat top down organized tree of cause and effect. Physics, in particular, has to deal with so many different scales and so many different leading order effects on each scale, that a consistent description of the world from first principles becomes hopeless. Instead we are opting to describe the world in a variety of parallel and nested models, each of which has advantages in its domain and limits beyond which it doesn't work and should not be applied. If you want to understand physics, then you will have to learn to think in these hierarchies of explanatory models and you will have to develop a solid intuition which model might possibly be useful for a description of observations.

Once this is established, one will chose the most practical (that's one of the most important words in physics!) way to quantify that scale and its effects. For that one may even introduce a new set of units that may depend on more widely used sets of units by means of a proportionality constant.

Take the most simple examples like mass and energy. Thanks to relativity, mass and energy are proportional, but in everyday life we will prefer to use the $[\mathrm{kg}]$ over the $[\mathrm{eV}/c^2]$. Which is more fundamental unit in your mind? Is it the $[\mathrm{eV}/c^2]$, which acknowledges the equivalence between mass and energy? Would you use that to go shopping for groceries in units that live on the scale of $10^{-36}\:\mathrm{kg}$?

Or how about velocity units? Would street signs for the max. allowed traffic velocity expressed in fractions of $c$ be very useful?

• I don't really know where you're argument is going towards the end... I think you started to get less objective towards that point, no offense. But look, no one can deny the universality of the three dimensions, of time, of energy, and no matter which model you use, regardless, these units persist and are the basic starting points when conducting science. Being able to describe what an object is, where and when it exists, then allows us allows us to build such models in the first place. So, I just thought it may be useful if there was an official listings of such units. – user108262 May 20 '16 at 2:31
• By the way, it wouldn't be at all bureaucratic, as such units are discovered, not made nor regulated. Note too that am asking about the types of units, so for instance am not asking how one decides what a metre or a second is, it's merely that they exist. – user108262 May 20 '16 at 2:32
• @user108262: No offense taken, I was merely giving you two examples of "everyday" units in physics. One would not use the same units in different sub-fields of physics because the ones that are useful for one set of folks are impractical for another. Unlike effects and laws units are not "discovered", but they are defined. That is one of the things the top metrologists are doing for a living: they define good units. $F=ma$ is only an equivalence if we define units. The law itself is merely $F\propto ma$, at least that's one of the multiple ways to look at it. – CuriousOne May 20 '16 at 2:33
• Oh yeah sure, I agree, no one's going to use all the units (at the same time), it's just that it would be nice to know of them. – user108262 May 20 '16 at 2:35
• @user108262 Actually, many models currently use 4 dimensions, and energy is typically considered a derived unit. Some models actually eschew units completely, focusing on unitless quantities. I recommend en.wikipedia.org/wiki/Units_of_measurement. At the bottom there is a set of links to about 40 different unit systems you can explore. – Cort Ammon May 20 '16 at 2:35

Is there an official list of independent units of measurements? – When I say 'independent units', I mean those which cannot be broken down anymore, and simultaneously forms the basis for any more, complex measurements.

It depends a bit on what you mean by broken down:

• You could theoretically define all units on the basis of counting elementary particles, which does not require any units at all. For example, you could choose a unit of weight that is based on the mass of 10000 deuterium atoms. It is only for practical considerations that we do not do this.

• In any unit space, there is a fixed number of base units, from which all other units can be derived. For example, in the SI system, this number is seven (if you exclude the angular measures).

However, there are multiple valid choices of base units. The only important thing is that your base units are algebraically independent. (This is the same as the bases of vector spaces: If $d$ is the dimension of your vector space, any number of $d$ linearly independent vectors forms a base.) For example, if we chose to use the Coulomb ($\text{A}·\text{s}$) instead of the the Ampère ($\text{A}$) as a base unit of the SI system, we could do the same things with it.

I think it would be both useful and interesting as such units will basically define how you look at the universe, if every such measurement that can be known, is known, then there isn't a property out there which wouldn't be able to be defined via the manipulation of said units.

It’s not that easy. As already mentioned in the other answers, the number of base units of the SI system is somewhat arbitrary and based on historical and practical considerations.

For example, the SI system has (bluntly speaking) distinct units for the numbers of atoms (the mole), photons (the Talbot) and electrons (the Coulomb). That these are not broken down to one unit is only due to the fact that they impact our everyday lives in considerably different ways (in fact, photometric units are defined and only make sense with respect to the human vision). That there is no distinct unit for a number of Higgs bosons is only due to the fact that they are much less important in every-day life (in fact, the SI system predates the postulation of the Higgs boson). We cannot deduce any physical insights from the shape of current unit systems.

The concept of 'independence' of units is difficult to maintain. For large distances for example, we tend to use light-hours or light-years, effectively merging length and time. As Wrzlprmft already pointed out, you could reduce all units to numbers introducing similar concepts.

I tend to treat units as a concept to make things easier – both in everyday life as well as when formulating problems. The units I use usually depend on the problem to solve. For everyday life, the SI system is a good starting point. However, the more exotic your problems become, the more exotic can be the appropriate unit system. Famous examples are the Gaussian units and the Planck units, to name just two.

One (somehow inversed) example for adapted units in everyday life are the two ICAO units for length. The ICAO measures distance and altitude in different units: nautical miles and feet. This is because the significance of the two are different for airplanes; any pilot will confirm that distance and altitute are not the same when flying. For a box, however, it usually does not make sense to measure width using a different unit than height.

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