# Why are there just 3 main units ($L$,$T$,$M$) in physics?

Most physics books define physical units in terms of length, time and mass. Some books add temperature. And yes, the SI unit system has 7 base units, but some are clearly redundant.

Why are exactly three basic units sufficient?

Or to make the point even more direct: is the number of units somehow due to the number of dimensions of space? Did anybody speculate about this in the past?

And yes, one can get rid of all units altogether, if desired, by setting $$c=\hbar=G=1$$. Still, the question wants an answer...

This answer is inspired by arXiv: 0711.4276 [physics.class-ph].

The paper I referred to argues that, in fact, there are only two fundamental units: length, and time. Mass is not necessary. The reasons is because everything we measure are actually space and time intervals, and never really make any other direct measurements. For example, when you are measuring a mass on a scale made with a spring, you are actually measuring a space interval and using Hooke's law and Newton's law for gravity to convert this space interval to a mass. You never really measured the mass. The paper further elaborates on this and describes another aspects of how you can measure masses with rulers and clocks.

As a consequence, notice that the number of fundamental constants does not coincide with the number of spatial dimensions, and hence I'd say there isn't really much to speculate about.

• I think most texts treat charge as a fundamental quantity. I wold prefer taking force as fundamental. Then mass, charge, and entities in the nucleus could be defined in terms of force. Commented Dec 31, 2021 at 16:36
• @R.W.Bird Many modern books do treat charge as fundamental, but that is merely due to the choice of using SI units. On Gaussian units, for example, charge is derived from length, mass, and time. Taking force as a fundamental unit works as well, but the main point of the answer remains: if all we can measure are space and time intervals, then we only have two fundamental units, regardless of which we choose. Commented Dec 31, 2021 at 17:43
• Note: Measuring the stretch of a spring scale does not tell you anything unless it has been calibrated with a known force. Commented Jan 1, 2022 at 15:08
• @NíckolasAlves Thank you for the reference. But I find it only partially convincing. Some how, c, h-bar and G are the three fundamental constants - even though each of them can be defined away. Relativity, quantum theory, gravity. They are the three basic theories. They remain three, even if the units are changed. So your answer means that the question should have been about the origin of the number of basic theories...
– user85598
Commented Jan 1, 2022 at 21:36
• I disagree. Firstly, because I find it difficult to characterize what would be a fundamental theory. For example, shouldn't Electrodynamics be a fundamental theory as well? After all, the only reason you can speak only in terms of $\hbar$, $c$, and $G$ is because you have already fixed the value of $\epsilon_0$ implicitly. Similarly for $k_B$ and StatMech. Furthermore, even if we kept only Relativity, QM, and gravity, there are still many complications. For instance, $G$ is a coupling constant, and hence it is subject to an RG flow Commented Jan 1, 2022 at 21:46