Arguably the most well-known and used system of units is the SI-system. It assigns seven units to seven ‘fundamental’ quantities (or dimensions). However, there are other possible options, such as Gaussian units or Planck units. Until recently, I thought that these different systems differed only in scale, e.g. inches and metres are different units, but they both measure length. Recently though, I discovered that it is not simply a matter of scale. In the Gaussian system for example, charge has dimensions of $[mass]^{1/2} [length]^{3/2} [time]^{−1}$, whereas in the SI-system it has dimensions of $[current] [time]$. Also, I have always found it a bit strange that mass and energy have different units even though they are equivalent, but I find it hard to grasp that a quantity can be ‘fundamental’ in one system, and not in an other system.
Does this mean that all ‘fundamental’ quantities are in fact arbitrary? Would it be possible to declare a derived SI-unit fundamental, and build a consistent system with more base units? What is the physical meaning of this?
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