In physics, we inevitably have to deal with quantities that have units. The basic dimension-full quantities in physics involve length ( L ), time ( T ), and mass ( M ). There are a lot of redundant dimension-full quantities like charge and temperature. Charge, for example, can be expressed in terms of Planck’s constant, \hbar and c the speed of light, which will be discussing momentarily. Temperature can be expressed in terms of energy through the formula, E=kT , where k is the Boltzmann constant and T is the temperature. k turns out to be convenient in thermodynamics, but it does not add a new dimension to physics. Physicists could have continued to talk about temperature in terms of joules, a unit of energy, without ever discussing k , though there’s usually nothing wrong with choosing a more expedient approach. At certain junctures, physicists thought they had found a new fundamental quantity, only to discover that it was related to the original three.
So why are there only three independent dimension-full quantities, L,T, and M ? I know of no deep explanation of this fact; it just seems to be an intrinsic feature of our universe. Note that you could choose three other independent combinations of L,T, and M to serve as basic quantities, but regardless of how you choose, there will always be three of them.
An amazing result of modern physics is that nature seems to choose her own fundamental units for L,T , and M . It turns out that these three units are related to the three fields of classical mechanics, electromagnetism/relativity, and quantum mechanics. What we mean by that is that each of these subjects introduces a fundamental unit of nature:
