When volume is consider as fundamental quantity instead of length what difficulties occur?


closed as unclear what you're asking by Aaron Stevens, Kyle Kanos, JMac, GiorgioP, rob Apr 16 at 21:30

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  • $\begingroup$ What does it mean to be a "fundamental quantity"? $\endgroup$ – probably_someone Apr 16 at 15:20
  • $\begingroup$ This definitely needs more context $\endgroup$ – Aaron Stevens Apr 16 at 15:22
  • $\begingroup$ Fundamental means based quantity $\endgroup$ – Sardar Mohsin Manzoor Apr 16 at 15:29
  • $\begingroup$ So are you asking what would happen if there was an SI base unit of volume instead of length? $\endgroup$ – probably_someone Apr 16 at 15:31
  • $\begingroup$ Assuming you know how to measure angles, you can go from volumes to lengths and vice versa. $\endgroup$ – jacob1729 Apr 16 at 16:07

Do you mean volume in the "usual" sense, of dimensions $\text{length}^3$? Sure, let's do it, let's move to the volume being the "fundamental" quantity and give it units of $[\text{SMM}]$. How do you define a length element then? the units would have to be $[\text{SMM}]^{1/3}$, and an area would have to have units of $[\text{SMM}]^{2/3}$ not very practical for everyday life...

Also, the units for the "fundamental" quantity length in , e.g. SI units, is determined by the distance light travels in $\sim \frac{1}{3\times10^8}$ seconds. You will have to come up with a way to define your "fundamental" volume in your base/using other SI units which is easier than the above...


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