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The reasons for choosing length, mass, time, temperature, and amount as base quantities look (at least to me) obvious. What I'm puzzling about is why current (as opposed to resistance, electromotive force, etc.) and luminous intensity (as opposed to illuminance, emittance, etc.) were chosen to be base quantities. Does it have something to do with them being the easiest to measure?

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The one that always bugs me is mass: it's still defined in terms of the International Prototype Kilogram: a chunk of metal in Paris. One, that's crazy! Two, I find it unsatisfactory that the SI unit has an SI prefix. Surely, the SI unit of mass should be the gramme... –  Seamus Nov 8 '10 at 13:41
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@Seamus: I agree, and I like one of the proposals for redefining the kilogram, but the way it looks, it's a bit impractical with our current technology to make a perfect sphere of silicon. –  user172 Nov 8 '10 at 13:47
    
    
I'm late to the party here, but this video shows we're actually getting reasonably close to an independent, reproducible standard for weight, based on the aforementioned silicon sphere. –  Patrick M Jul 2 at 21:27

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Historical issues I suppose; indeed current definition of ampere is rather stupid (force between two cables in vacuum) in light of the fact it could be done with number of elementary charges per second.
Candela is even worse, because it involves properties of average human eye (so called "luminosity function") -- so in principle it changes instantaneously as people get birth, die and their eyes age (not to mention various eye/brain fractures and treatments).

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I've never understood the Candela at all - why is it a base unit? Surely this psychology and physiology: grounded on a large sample and in some sense meaningful to humans, yes, but hardly a physical base unit! –  WetSavannaAnimal aka Rod Vance Aug 26 '13 at 1:27

Of course, history has its own way of determining things, but I suspect that the greatest reason for the choices of the base SI units was that they were easily measurable at the time. Other quantities such as resistance, magnetic, density, power, are (or certainly were at the time) much more difficult to measure precisely. In this sense, the choices were fairly reasonable.

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SI units are pragmatic so their definition must be easily realized. That is why ampere is the basic unit, since it is easier to measure. Theoretically, the elementary charge is much more fundamental than an arbitrarily chosen amount of current, but that cannot be reproduced with equal or higher precision, at least not now.

I think the candela is chosen more arbitrarily, since its definition doesn't give a specific instruction to measure it. One can also choose lux as the fundamental unit and define it as "The lux is the illuminance of monochromatic radiation of frequency $540\times 10^{12}\,\text{Hz}$ and that has a radiant intensity in that direction of 1683 watt per steradian." I guess this has more to do with historic reasons.

And by the way, if you don't need to take into account the human vision, you don't need candela; watt is better.

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We see that candela is very well-defined, without using properties of, for example, a human eye. Let me remind the definition.

The candela is the luminous intensity, in a given direction, of a source that emits monochromatic radiation of frequency $540 \cdot 10^{12}$ hertz and that has a radiant intensity in that direction of $\frac{1}{683}$ watt per steradian.

Ampere of course cannot be defined as a number of elementary charges per second, because without definition of ampere we cannot define a value of an elementary charge! The definitions is below.

The ampere is that constant current which, if maintained in two straight parallel conductors of infinite length, of negligible circular cross-section, and placed 1 metre apart in vacuum, would produce between these conductors a force equal to $2 \cdot 10^{−7}$ newton per metre of length.

What is important, both definitions don't use any prototypes and define clear ways how to reproduce these units inside a lab. Such experiments should always give the same results anywhere in the world - and they do. The definitions are simple and unambiguous. In SI, only the definition of a kilogram uses a prototype, because the definition of mass still causes problems to physicists.

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You didn't answer the question. You're saying that those SI units are well-defined, and I agree. What I'm asking is why of all possible quantities, those two (current and luminous intensity) were chosen. –  user172 Nov 11 '10 at 1:00
    
My answer is that these two were chosen because they can be easily and unambiguously defined, with the definitions constructed so that these quantities may be reproduced in a lab and always give the same results. –  Piotr Suwara Nov 11 '10 at 12:04
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About the elementary charge: Why would we need to define it? It exists. "One Ampere is the current caused by a flux of <large number> of electrons per second"? –  Thomas Themel Nov 15 '10 at 8:55
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Due to ampere: We define base unit coulomb by electron charge and so we have ampere as a derived one. –  mbq Nov 19 '10 at 13:42
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@piotr - that was the important goal of SI. Before that when units were based on standards owned by another country any diplomatic incident caused havoc - which is why the US inch was different to the British. The french were trying to get away from traditionla units based on king's bodies but also make science and industry work better. –  Martin Beckett Mar 25 '11 at 2:53

The short answer is that all other physical units can be derived from these seven.

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@J.M., Your comment regarding the mass unit,or kilogram, is not due to the ability to perfect silicon spheres. The problems are measuring the isotopic ratio and crystal defect sites within the sphere. –  wcrupe Jun 14 '11 at 1:15
    
Alas, the same can be said for a variety of other choices. For instance (as the question suggests) why Amperes and not Coulombs? So this answer is very incomplete. –  dmckee Jun 14 '11 at 2:00

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