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